Answer:there are 42 students in the club.
Step-by-step explanation:
Let s represent the number of students in the club.
Tickets to the museum cost $8. Five students already have a membership to the museum, so they will get in for free. The club raised the $296 needed to take all students in the club to the museum. This means that
8(s - 5) = 296
8s - 40 = 296
8s = 296 + 40 = 336
s = 336/8
s = 42
Write an equation for Greg ordered some books online for $6 each. He paid a total of $3 for shipping. The total cost of the purchase was $75.00. How many books did he buy?
Final answer:
Greg bought 12 books online. To find the number of books, set up the equation 6n + 3 = 75, subtract the shipping fee, and divide by the price per book.
Explanation:
Greg ordered books online for $6 each and paid a total of $75, which includes a $3 shipping fee. To determine the number of books Greg bought, you need to set up an equation that represents the total cost.
The cost of the books alone can be represented by 6 times the number of books (6n), and when you add the shipping cost of $3, it equals the total cost of $75. So the equation would be:
6n + 3 = 75
To solve for n, which is the number of books Greg purchased, follow these steps:
Subtract the shipping fee from the total cost: 75 - 3 = 72.
Divide the result by the cost per book: 72 ÷ 6 = 12.
Therefore, Greg bought 12 books.
When one-fourth of a number is added to one-fifth of the number, the sum is 18. What is the number?
Step-by-step explanation:
Let the number be n.
When one-fourth of a number is added to one-fifth of the number, the sum is 18
[tex]\frac{n}{4}+\frac{n}{5}=18\\\\\frac{5n+4n}{4\times 5}=18\\\\9n=4\times 5\times 18\\\\n=20\times 2\\\\n=40[/tex]
The number is 40.
Answer:
unknown number is 40
Step-by-step explanation:
Let x be the unknown number
one-fourth of a number is added to one-fifth of the number
[tex]\frac{1}{4}x+\frac{1}{5} x[/tex]
sum is 18
[tex]\frac{1}{4}x+\frac{1}{5} x=18[/tex]
To solve for x take LCD 20
[tex]\frac{5}{20}x+\frac{4}{20} x=18\\ \frac{9}{20} x=18\\[/tex]
multiply both sides by 20
[tex]9x= 360[/tex]
divide both sides by 9
x=40
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Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "d" of Mrs. Washington's commute.
2. What does it mean that the slope is negative in context of the problem?
3. Why are the slopes different over different intervals?
4. How long does it take Mrs. Washington to get home? How did you know this?
Step-by-step explanation:
[tex]slope \: of \: section \: d \: = gradient = \frac{y2 - y1}{x2 - x1} \\slope = \frac{6 - 0}{32 - 20} = \frac{6}{12} = \frac{1}{2} = 0.5 [/tex]The slope is negative because it moves downward from the left.If it were to move upwards from the left it would be a positive slope.The slope intervals are different because;the factors responsible for slope are not constant during the journey. i.e the time taken and the distance covered for each part of the journey are differentThe speed for each part of the journey is different.For a : Speed = distance / time
Distance covered = y2 - y1 = 20 - 15 = 5
Time taken = x2 - x1 = 8 - 0 = 8
Speed in part a : 5/8 = 0.625
4. It takes her 32 minutes to get home. We can see from the graph that it is the total time taken throughout the whole journey.
The desert temperature, H, oscillates daily between 40◦F at 5 am and 80◦F at 5 pm. Write a possible for- mula for H in terms of ????, measured in hours from 5 am.
Answer:
[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]
Step-by-step explanation:
We have been given that the desert temperature, H, oscillates daily between 40◦F at 5 am and 80◦F at 5 pm. We are asked to write a formula H in terms of t, measured in hours from 5 am.
We will use cosine function to write our required formula.
[tex]y=A\text{cos}[B(x-C)]+D[/tex], where,
A = Amplitude,
[tex]\text{Period}=\frac{2\pi}{|B|}[/tex]
C = Phase shift,
D = Vertical shift.
First of all, we will find amplitude using maximum and minimum values as:
[tex]A=\frac{\text{Maximum value}-\text{Minimum value}}{2}[/tex]
[tex]A=\frac{80-40}{2}[/tex]
[tex]A=\frac{40}{2}[/tex]
[tex]A=20[/tex]
Since period is 24 hours (5 am to 5 pm), so let us find B as:
[tex]24=\frac{2\pi}{|B|}[/tex]
[tex]B=\frac{2\pi}{24}[/tex]
[tex]B=\frac{\pi}{12}[/tex]
[tex]\text{Vertical shift}=\frac{\text{Maximum value}+\text{Minimum value}}{2}[/tex]
[tex]D=\frac{80+40}{2}=\frac{120}{2}=60[/tex]
There is no phase shift.
Since temperature is minimum when [tex]t=0[/tex], so we will use negative cosine as:
[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]
Therefore, our required function would be [tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex].
To model the desert temperature, use the sinusoidal function H(t) = 20 * cos(π/12 * t) + 60, which captures daily temperature changes between 40°F and 80°F, with parameters tuned to fit the given data.
To write a formula for the desert temperature H in terms of t, measured in hours from 5 am, we can use a sinusoidal function that models the daily temperature oscillation.
We know:
The minimum temperature is 40°F at 5 amThe maximum temperature is 80°F at 5 pmThe period of the oscillation is 24 hoursThe general form for the sinusoidal function is:
H(t) = A * sin(B*(t - C)) + D
Where:
A is the amplitudeB is related to the periodC is the phase shiftD is the vertical shiftFrom the given data:
A (amplitude) = (80 - 40) / 2 = 20°FVertical shift D = (80 + 40) / 2 = 60°FThe period is 24 hours, so B = 2π / 24 = π / 12The temperature is minimum at 5 am (t = 0), we use a cosine function (which reaches the minimum at 0) shifted by 5 hours. Hence, C = 0Thus, the sinusoidal function becomes:
H(t) = 20 * cos(π/12 * t) + 60.
Which graph represents g(x)=−(x−3)2−5 ?
Answer:
see below
Step-by-step explanation:
The leading minus sign tells you the graph opens downward. (x-3) in the squared term tells you the x-coordinate of the vertex is x=3. The graph that matches these characteristics is shown below.
Joanne's age is two times Devin's age and Devin is eight years older than Christina. If the sum of their ages is 76, what is Christina's age? Joanne's age? Devin's age?
Answer: Christina's age is 13, Joanne's age is 42 and Devin's age is 21.
Step-by-step explanation: If Devin's age is represented by d, then Joanne's age will be 2d because Joanne is two times Devin's age. Also, if Devin is 8 years older than Christina, then Christina's age would be d - 8. If the sum of their ages is equal to 76, then;
2d + d + (d - 8) = 76
2d + d + d - 8 = 76
4d - 8 = 76
Add 8 to both sides of the equation
4d = 84
Divide both sides of the equation by 4
d = 21
Therefore, Devin is 21 years old
Joanne is 42 years old and
Christina is 13 years old.
Christina is 13 years old, Devin is 21 years old, and Joanne is 42 years old. This is found by defining Christina's age as x, then setting up and solving an equation based on the problem's provided relationships.
Explanation:In this math problem, we have three individuals: Joanne, Devin, and Christina, and we know their ages in relation to each other's.
We know that Joanne's age is two times Devin's. We also know Devin is eight years older than Christina. Finally, we know the sum of all three ages is 76.
Let's denote Christina's age as x. Consequently, Devin's age would be x + 8 because he is 8 years older than Christina. As Joanne's age is two times Devin's age, Joanne's age would be 2*(x + 8).
The sum of their ages is 76, which gives us the following equation:
x (Christina's age) + x + 8 (Devin's age) + 2*(x + 8) (Joanne's age) = 76.
Solving this equation, we get:
4x + 24 = 76
Subtract 24 from both sides gives us 4x = 52, and dividing both sides by 4 gives x = 13.
So, Christina's age is 13, Devin's age is 13 + 8 = 21, and Joanne's age is 2*21 = 42.
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Seventy five percent of the students in sixth grade voted to to the planiterium on their field trip if 24 voted to go to the planiterium, how many students are there in the sixth grade?
Need help on geometry
Answer:
[tex]2\sqrt {10}[/tex]
Step-by-step explanation:
Given:
[tex]x=3\sqrt 5[/tex]
[tex]y=\sqrt 5[/tex]
As seen from the triangle, the triangle is a right angled triangle. Two sides of the triangle are given and we are asked to find the third side.
'x' is the hypotenuse as this side is opposite side to the right angled.
'y' and 'z' are the two legs of the triangle.
Now, using pythagoras theorem,
[tex]x^2=y^2+z^2\\\\(3\sqrt 5)^2=(\sqrt 5)^2+z^2\\\\9\times 5=5+z^2\\\\45-5=z^2\\\\40=z^2\\\\z=\sqrt {40}\\\\z=2\sqrt {10}[/tex]
Therefore, the measure of the side 'z' is [tex]2\sqrt {10}[/tex].
Hence, the third option is correct.
Tickets for a minor league baseball game for an adult and two children cost a total of $21 the adult ticket is three dollars more than a child's ticket. Find the cost of the child's ticket and an adult ticket.
Answer:the cost of one child's ticket is $6
the cost of one adult ticket is $9
Step-by-step explanation:
Let x represent the cost of one child's ticket
Let y represent the cost of one adult ticket.
Tickets for a minor league baseball game for an adult and two children cost a total of $21. This means that
2x + y = 21 - - - - - - - - - - 1
The adult ticket is three dollars more than a child's ticket. This means that
y = x + 3
Substituting y = x + 3 into equation 1, it becomes
2x + x + 3 = 21
3x + 3 = 21
3x = 21 - 3 = 18
x = 18/3 = 6
y = x + 3 = 6 + 3
y = 9
Each peanut butter snack costs $2 each chocolate snack costs $3 how much does it cost to buy 6 peanut butter snacks and 8 chocolate snacks write an equation
in a group of 40 student students, the probability that at most 15 of them like to hike? A 44% B 64% C 55% D 38%e to hike is 36%. What is the probability that at least 16 of them like to hike
Answer:
64%
Step-by-step explanation:
pain
The answer is B) 64%.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Let X be the number of students out of 40 who like to hike. We know that P(X ≤ 15) = 0.36 and we want to find P(X ≥ 16).
Note that P(X ≥ 16) is the complement of P(X ≤ 15). That is,
P(X ≥ 16) = 1 - P(X ≤ 15) = 1 - 0.36 = 0.64
Therefore, the answer is B) 64%.
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A line in the xy-plane passes through the origin and has a slope of 1/7 Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
E) (7, 14)
====================================================
m = 1/7 is the slope
(x,y) = (0,0) is the origin the line goes through
y = mx+b
0 = (1/7)*0 + b
0 = 0+b
b = 0 is the y intercept
y = mx+b
y = (1/7)x+0
y = (1/7)x is the equation of the line
----------------------
To plot the equation of this line, mark the point (0,0) first.
Then move up 1 unit and to the right 7 units to arrive at (7,1) as the second point.
Draw a straight line through (0,0) and (7,1) as shown in the diagram below.
Point P is (0,0) and point Q is (7,1)
Points A through E in the same diagram represent the answer choices A through E.
Of the answer choices, only point D is on this line, so point D is the answer.
---------------
A non-visual way to find the answer is to plug each (x,y) coordinate from each answer choice into the equation we found above.
So for choice A we plug in x = 0 and y = 7
y = (1/7)*x
7 = (1/7)*0
7 = 0
we end up with a false equation, so choice A is ruled out. Similar stories happen with B, C, and E as well.
With choice D however, we plug in x = 14 and y = 2, and we get...
y = (1/7)*x
2 = (1/7)*14
2 = 14/7
2 = 2
Since we get a true equation, this confirms that (14,2) is on the graph of y = (1/7)x.
Defining the wrong choice:
For choice "A" when [tex]\bold{x=0, y=7 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{7=0}[/tex], which is wrong.For choice "B" when [tex]\bold{x=1, y=7 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{7=\frac{1}{7}}[/tex], which is wrong.For choice "C" when [tex]\bold{x=7, y=7 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{7=1}[/tex], which is wrong.For choice "E" when [tex]\bold{x=7, y=14 \ and\ m =\frac{1}{7}}[/tex], and put the value in [tex]\bold{y=mx}[/tex] it will give [tex]\bold{14=2}[/tex], which is wrong.Therefore, "Choice D" is the correct choice.
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Find all numbers such that the square of the number is 48 more than double the number. If you find more than one, then list all the numbers you find in increasing order, separated by commas.?
Answer:
-6, 8
Step-by-step explanation:
Let the numbers be represented by y
Square of y = y^2
Double y = 2 × y = 2y
Square of the number is 48 more than double the number is written mathematically as
y^2 = 2y +48
y^2 - 2y - 48 = 0
This is a quadratic equation and can be solved by method of factorisation
y^2 -2y - 48 = 0
y^2 + 6y - 8y - 48 = 0
(y^2 + 6y) - (8y - 48) = 0
y(y + 6) - 8(y + 6) = 0
(y + 6)(y - 8) = 0
y = -6, 8
The numbers are -6, 8
Answer:
8, -6
Step-by-step explanation:
Let the number be $n$, so we have $n^2 =48 + 2n$. Rearranging this equation gives $n^2 -2n-48=0$ and factoring gives $(n-8)(n+6)=0$. So, the numbers that fit the problem are $\boxed{n = -6~\text{and}~n = 8}$.
If Company M ordered a total of 50 computers and printers and Company N ordered a total of 60 computers and printers, how many computers did Company M order?
(1) Company M and Company N ordered the same number of computers.
(2) Company N ordered 10 more printers than Company M.
Answer:
Available information is not sufficient to solve the questions
Step-by-step explanation:
Let Cm = Computers Ordered by Company M
Let Cn = Computers Ordered by Company N
Let Pm = Printers Ordered by Company M
Let Pn = Printers Ordered by Company N
Cm + Pm = 50 --- Equation 1
Cn + Pn = 60 ----- Equation 2
1. Company M and N ordered the same number of computers
Here,
Cm = Cn
Substitute Cm for Cn in equation 2
Cm + Pm = 50
Cm + Pn = 60
Subtract Equation 2 from 1
Pm - Pn = 50 - 60
Pm - Pn = -10
Pm = Pn - 10
Substitute Pn-10 for Pm in equation 1
Cm + Pn - 10 = 50
Make Pn the subject of formula
Cm = 50+10-Pn
Cm = 60 - Pn
Hence, the number of computers ordered by Company M is 60 minus the number of printers ordered by Company n
2. Company N ordered 10 more printers than Company M.
Here,
Pn = 10 + Pm
Make Pm the subject of formula
Pm = Pn - 10
Substitute Pn-10 for Pm in equation 1
Cm + Pn - 10 = 50
Make Cm the Subject of formula
Cm = 50 + 10 - Pn
Cm = 60 - Pn
Hence, the number of computers ordered by Company M is 60 minus the number of printers ordered by Company n
Condition 1 and 2 points to the same result
Mrs.Jackson earned a $500 bonus for signing a 1 year contract to work as a nurse. Her salary is $22 per hour. If her first weeks check including the bonus is $1204 how many hours did mrs. Jackson work?
Answer:
Mrs. Jackson worked 32 hours.
Step-by-step explanation:
Given:
Mrs.Jackson earned a $500 bonus for signing a 1 year contract to work as a nurse.
Her salary is $22 per hour.
If her first weeks check including the bonus is $1204.
Now, to find the hours Mrs. Jackson work.
Amount of bonus = $500.
Total salary = $1204.
So, we deduct the amount of bonus from the total salary:
[tex]1204-500=\$704.[/tex]
The remaining salary = $704.
As, given her salary is $22 per hour.
Now, to get the hours she work we divide the remaining salary $704 by $22:
[tex]704\div 22[/tex]
[tex]=32\ hours.[/tex]
Therefore, Mrs. Jackson worked 32 hours.
The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?a. 47.72%
b. 97.72%
c. 37.45%
d. 2.28%
e. 4.56%
Return the bottles: Shawna Return some bottles to the store. She received 1.85 in quarters, dimes, nickels. Use these clues to determine the number of each kind of coin. She received at least one of each coin. There are more dimes and nickels. There is an even number of quarters. There are as many quarters and nickels together as there are dimes.
Answer:
There are 7 dimes, 3 nickels, and 4 quarters.
Luis made some trail mix. He mixed 4 2/3 cups popcorn, 1 1/4 cups of peanuts, 1 1/3 cups of raisins, and 3/4 cup of sunflower seeds. He gave 5 of his friends an equal amount of trail mix each. How much did each friend get?
Answer:
1 2/3
Step-by-step explanation:
Luis mixed all the trails thus:
4 2/3 + 1 1/4 + 1 1/3 + 3/4
= 15/3 + 5/4 + 4/3 + 3/4
= 60+15+16+9/12
Total trail mixed by Luis equals 100/12
He then divided 100/12 among his 5 friends thus:
100/12 ÷ 5
= 20/12
= 1 2/3 per friend.
Answer:
1 3/5
Step-by-step explanation:
the answer is 1.6 but you have to convert is to a fraction because there are no decimal numbers theres. if you convert it , it will be 1 3/5
Which sampling method is MOST appropriate in estimating the average number of votes for each candidate in an election across a county of three towns if town A has one million retirees, town B has two million business owners, and town C has three million office workers?
A. Simple random sampling, because the people in the sample are accessible and available.
B. Stratified sampling, because there are specific subgroups to investigate.
C. Systematic sampling, because it is difficult to identify items using a simple random sampling method.
D. Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement
E. All the above sampling methods
Answer:
B. Stratified sampling, because there are specific subgroups to investigate.
Step-by-step explanation:
Stratified Sampling is a sampling method and is used when the population has subgroups with different characteristics. Random sampling is applied in each of the sub-groups proportional to their size and then these samples combined together to create sample of the study.
Since there are three towns with people from different occupations ( retirees,business owners, office workers), it is better to use stratified sampling method.
The correct answer is option B). Stratified sampling, because there are specific subgroups to investigate.
To determine the most appropriate sampling method, one must consider the composition of the population and the goal of the study. In this scenario, the population consists of three distinct groups: retirees in town A, business owners in town B, and office workers in town C. Each group represents a different stratum within the overall population of the county.
Stratified sampling is a method that divides the population into subgroups, or strata, based on certain characteristics, such as age, occupation, or town of residence in this case. This method ensures that each subgroup is represented in the sample in proportion to its size in the overall population. Here's why stratified sampling is the most appropriate method for this situation:
1. Representation: Stratified sampling ensures that each town's unique demographic is represented in the sample. This is important because each group may have different voting patterns.
2. Precision: By sampling each stratum separately, the estimates of the average number of votes for each candidate can be more precise because the variance within each subgroup is likely to be lower than the variance across the entire population.
3. Comparability: Stratified sampling allows for direct comparison between the different strata, which in this case are the three towns.
4. Efficiency: If the strata are chosen such that the variance within each stratum is minimized, the overall variance of the estimate can be reduced, leading to a more efficient estimate.
Now, let's consider the other options:
A. Simple random sampling: While this method is unbiased, it may not provide representation from each of the three towns in proportion to their population sizes. This could lead to an inaccurate estimate if one group's voting behavior is significantly different from the others.
C. Systematic sampling: This method involves selecting elements from the population at regular intervals. It can be difficult to implement if there is no clear ordering of the population, and it may not ensure representation from each town.
D. Cluster sampling: This method would be appropriate if the population were spread across a wide area and could be divided into clusters that are more convenient to sample. However, since the population is already divided into distinct groups within specific towns, stratified sampling is a better choice.
E. All the above sampling methods: While each method has its own merits, not all are equally suitable for this particular scenario. Stratified sampling is the most appropriate because it specifically addresses the heterogeneity of the population across the three towns.
Angle 1, angle 2, and angle 3 are adjacent angles, with angle 1 supplementary to angle 2 and angle 2 complementary to angle 3. If angle 1 measures (8x + 3) and angle 2 measures (5x - 18), find the measure of angle 3
Answer:
Step-by-step explanation:
If angle 1 and angle 2 are supplementary, then
∠1 + ∠2 = 180°
If angle 2 and angle 3 are complementary, then
∠2 + ∠3 = 90°
We are given the values for angles 1 and 2, so:
(8x + 3) + ( 5x - 18) = 180 so
13x - 15 = 180 and
13x = 195 so
x = 15
Sub 15 in for x in angle 2 to find the measure of angle 2:
∠2 = 5(15) - 18 so
∠2 = 57°
That means that to find angle 3,
57° + ∠3 = 90 so
∠3 = 33°
The measure of angle 3 is found to be 33 degrees, using the relationships that angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3, along with their given expressions in terms of x.
Explanation:To find the measure of angle 3, we must use the relationships between the angles given: angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3.
Since angle 1 and angle 2 are supplementary, their sum is 180 degrees. The equation is therefore:
(8x + 3) + (5x - 18) = 180
Solving for x gives:
13x - 15 = 180
x = 195 / 13
x = 15
Substitute x back into the expression for angle 2:
(5x - 18) = (5(15) - 18) = 57 degrees
Since angle 2 and angle 3 are complementary, they add up to 90 degrees:
angle 2 + angle 3 = 90
57 + angle 3 = 90
Subtract 57 from both sides to find angle 3:
angle 3 = 90 - 57
angle 3 = 33 degrees
Therefore, the measure of angle 3 is 33 degrees.
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A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game. Find the probability that (a) the one who tosses first wins the game
Answer: the probability that the first toss wins is:
P = 1/6 or 0.1667
Step-by-step explanation:
A die has six sides (that is 6 outcome per die)
For a pair of dice:
The Total number of possible outcomes = 6 × 6 = 36
The possible outcomes of 7 is:
(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)
= 6
The probability P of getting 7 is:
P = number of possible outcomes of 7/total number of possible outcomes
P = 6/36 = 1/6
The probability that the first toss wins
P = 1/6 or 0.1667
NOTE -- THIS QUESTION HAS BEEN ANSWERED ALREADY!!!
Please click on the image below to find my question. Thank you!
Answer:
The cubic polynomial is: x³ - x² - 6x.
Step-by-step explanation:
Given the degree and the roots of the polynomial we can find it.
An n - degree polynomial has n roots.
Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.
Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.
(x + 2)(x - 0)(x - 3) = 0
Multiplying them we get:
⇒ [tex]$ (x^2 + 2x)(x - 3) $[/tex]
[tex]$ = x^3 - 3x^2 + 2x^2 - 6x $[/tex]
[tex]$ = x^3 - x^2 - 6x $[/tex] which is the required cubic polynomial.
Hence, the answer.
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Consider the following piece-wise function. Which of the below correctly describes the graph shown?
Answer:
The 3th answer is correct.
for x<2, form graph we know that if x=0 than y=-3.
For x<2 in 3th we have y=1/2x-3, so for x=0, y=(1/2)*0-3=0-3=-3. It fits.
For x=2, from graph we have that y=-2.
For x>=2 in 3th we have y=3x-8, so for x=2, y=3*2-8=-2. It fits.
These answer fit also i for first, but breakpoint for y from graph is point 2 not point -2, so the answer is 3th.
What is the solution of the system? y= 10x - 3 y= 7x + 2
Answer:
(5/3, 41/3)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define Systems
y = 10x - 3
y = 7x + 2
Step 2: Solve for x
Substitution
Substitute in y: 10x - 3 = 7x + 2[Subtraction Property of Equality] Subtract 7x on both sides: 3x - 3 = 2[Addition Property of Equality] Add 3 on both sides: 3x = 5[Division Property of Equality] Divide 3 on both sides: x = 5/3Step 3: Solve for y
Define original equation: y = 7x + 2Substitute in x: y = 7(5/3) + 2Multiply: y = 35/3 + 2Add: y = 41/3Step 4: Check
Verify the solution set to the systems of equations by graphing the systems.
Where the 2 lines intersect is the solution set to the systems of equations.
We see graphically that point (1.666667, 13.66667), equivalent to (5/3, 41/3).
∴ (5/3, 41/3) or x = 5/3 and y = 41/3 is the solution to the systems of equations.
Final answer:
The solution to the system of equations y = 10x - 3 and y = 7x + 2 is x = 5/3 and y = 19/3.
Explanation:
The solution of the system of equations given by y = 10x - 3 and y = 7x + 2 can be found by setting the two expressions for y equal to each other since they both equal y. This yields the equation 10x - 3 = 7x + 2. Solving for x, we first subtract 7x from both sides to get 3x - 3 = 2. Then we add 3 to both sides to get 3x = 5. Finally, dividing both sides by 3 gives us x = 5/3. Substituting x back into either original equation, we get y = 10(5/3) - 3 or y = 7(5/3) + 2, both of which simplify to y = 19/3. Therefore, the solution to the system is x = 5/3 and y = 19/3.
The campsite shop sells boxes of funshine cereal. The base of each box is a 180mm x 60 mm rectangle. The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle
the maximum number of boxes that will fit on the shelf is 21.
To find out the maximum number of boxes that will fit on the shelf, we need to calculate the area of the shelf and the area of each box, then divide the total area of the shelf by the area of each box.
Given:
- Shelf dimensions: 65 cm x 35 cm
- Box dimensions: 180 mm x 60 mm
First, let's convert all dimensions to the same unit. Let's choose millimeters for consistency:
Shelf dimensions:
- Length: [tex]\(65 \, \text{cm} \times 10 \, \text{mm/cm} = 650 \, \text{mm}\)[/tex]
- Width: [tex]\(35 \, \text{cm} \times 10 \, \text{mm/cm} = 350 \, \text{mm}\)[/tex]
Now, let's calculate the area of the shelf:
[tex]\[ \text{Shelf area} = \text{Shelf length} \times \text{Shelf width} \][/tex]
[tex]\[ \text{Shelf area} = 650 \, \text{mm} \times 350 \, \text{mm} \][/tex]
[tex]\[ \text{Shelf area} = 227,500 \, \text{mm}^2 \][/tex]
Now, let's calculate the area of each box:
[tex]\[ \text{Box area} = \text{Box length} \times \text{Box width} \][/tex]
[tex]\[ \text{Box area} = 180 \, \text{mm} \times 60 \, \text{mm} \][/tex]
[tex]\[ \text{Box area} = 10,800 \, \text{mm}^2 \][/tex]
Now, to find out the maximum number of boxes that will fit on the shelf, we divide the shelf area by the area of each box:
[tex]\[ \text{Maximum number of boxes} = \frac{\text{Shelf area}}{\text{Box area}} \][/tex]
[tex]\[ \text{Maximum number of boxes} = \frac{227,500 \, \text{mm}^2}{10,800 \, \text{mm}^2} \][/tex]
[tex]\[ \text{Maximum number of boxes} \approx 21.06 \][/tex]
Since we can't have a fraction of a box, the maximum number of boxes that will fit on the shelf is 21.
complete question given below:
The campsite shop sells boxes of Funshine Cereal.
The base of each box is a 180 mm x 60 mm rectangle.
The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.
Work out the maximum number of boxes that will fit on the shelf.
the maximum number of boxes that will fit on the shelf is 21.
To find the maximum number of boxes that fit on the shelf, we divide the shelf area by the area of each box.
Given:
- Shelf dimensions: 65 cm x 35 cm
- Box dimensions: 180 mm x 60 mm
First, let's convert the shelf dimensions to millimeters for consistency:
Shelf dimensions:
- Length: [tex]\(65 \, \text{cm} \times 10 \, \text{mm/cm} = 650 \, \text{mm}\)[/tex]
- Width: [tex]\(35 \, \text{cm} \times 10 \, \text{mm/cm} = 350 \, \text{mm}\)[/tex]
Now, calculate the area of the shelf:
[tex]\[ \text{Shelf area} = \text{Shelf length} \times \text{Shelf width} \]\[ \text{Shelf area} = 650 \, \text{mm} \times 350 \, \text{mm} \]\[ \text{Shelf area} = 227,500 \, \text{mm}^2 \][/tex]
Next, calculate the area of each box:
[tex]\[ \text{Box area} = \text{Box length} \times \text{Box width} \]\[ \text{Box area} = 180 \, \text{mm} \times 60 \, \text{mm} \]\[ \text{Box area} = 10,800 \, \text{mm}^2 \][/tex]
Now, find the maximum number of boxes that fit on the shelf:
[tex]\[ \text{Maximum number of boxes} = \frac{\text{Shelf area}}{\text{Box area}} \]\[ \text{Maximum number of boxes} = \frac{227,500 \, \text{mm}^2}{10,800 \, \text{mm}^2} \]\[ \text{Maximum number of boxes} \approx 21.06 \][/tex]
Since we can't have a fraction of a box, the maximum number of boxes that will fit on the shelf is 21.
The probable question maybe:
The campsite shop sells boxes of Funshine Cereal.
The base of each box is a 180 mm x 60 mm rectangle.
The shelf where the boxes are displayed is a 65 cm x 35 cm rectangle.
Work out the maximum number of boxes that will fit on the shelf.
*Will Give Brainliest* Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.
A. (3, 1)
B. (3, 3)
C. (3, 5)
D. (3, 13)
The coordinates of the point on the graph when x=3 are C. (3, 5)
Step-by-step explanation:
Given piece-wise function is:
[tex]y = \left \{ {{4x+1\ \ \ x<3 } \atop {2x-1\ \ \ x\geq 3 }} \right.[/tex]
In order to determine the coordinates of the point on the graph where x=3 we will see which part of the function we have to consider as the function is in two pieces.
By observing we see that the second piece of function will be used as it is for x≥ 3 so it includes 3.
Putting x = 3 in y = 2x-1
[tex]y = 2(3) -1\\y = 6-1\\y = 5[/tex]
Hence,
The coordinates of the point on the graph when x=3 are C. (3, 5)
Keywords: Functions, graph
Learn more about functions at:
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How do the values of the 4s in 64.723 and 9.048 compare?
Select from the drop-down menu to correctly complete the statement.
The value of the 4 in 64.723 is times the value of the 4 in 9.048.
A) 10 B)100 C)1000
Answer:
C.
is the right answer
Step-by-step explanation:
The value of the 4 in 64.723 is 100 times the value of the 4 in 9.048. The correct option is B
What is a number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently using digits or other symbols to represent the numbers in a given set.
It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Given that there are two numbers 64.723 and 9.048. The value of the number 4 in one number is 100 times the other. As it is at one-hundredth place of another number
To know more about the number system follow
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A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)(1) It takes the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.
(2) It takes the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.
Answer:
The distance that the conveyor belt moves the bottle is less than 90 meters
Step-by-step explanation:
Speed of the conveyor belt
120 cm/s
Time it takes to move the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.
But 60s = 1 minute
This gives
1.2 minutes = 1.2×60s seconds = 72 seconds
But speed = distance/time
so that distance = speed × time = 120cm/s ×(<72s)
From where distance = <8640cm<90m (90m×100=9000cm)
Time it takes to move the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.
Again 60s = 1 minute
This gives
1.1 minutes = 1.1×60s seconds = 66 seconds
Time it takes is more than 66s
But speed = distance/time
so that distance = speed × time = 120cm/s × (>66s)
From where distance >7920cm
However
7920cm < 90m (90m×100=9000cm)
So that
The distance that the conveyor belt moves the bottle is less than 90 meters
Mary plants roseas in 1/4 of her garden. She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?
Answer:the fraction of Mary's garden that has tulips is 2/3
Step-by-step explanation:
Let x represent the full area if Mary's garden.
Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4
She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12
The portion of the garden on which she planted tulips would be
x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12
x - x/3 = (3x - x)/3 = 2x/3
Therefore, the fraction of Mary's garden that has tulips would be
(2x/3) /x = 2/3
Final answer:
Mary has 2/3 of her garden planted with tulips.
Explanation:
To find the fraction of Mary's garden that has tulips, we need to first determine the fraction of her garden that she has planted with roses. We are given that Mary plants roses in 1/4 of her garden, so the fraction of her garden that she has planted with roses is 1/4. Since she has 1/12 of her garden left to plant more flowers, the fraction of her garden that she has planted with tulips is the remaining fraction, which is 1 - 1/4 - 1/12.
Let's simplify this expression. First, find a common denominator for 1/4 and 1/12, which is 12. Rewrite 1/4 with the denominator 12 as 3/12, and rewrite 1/12 with the denominator 12 as 1/12. Now we can subtract these fractions:
1 - 3/12 - 1/12 = 12/12 - 3/12 - 1/12 = 8/12 = 2/3
Therefore, 2/3 of Mary's garden has tulips.
Show your work
What are the roots of the polynomial equation?
You can use any method you would like to solve.
0=x^4-3x^3+10x^2-24+16
Answer:
1, 2, and ±i√8
Step-by-step explanation:
0 = x⁴ − 3x³ + 10x² − 24x + 16
Using grouping:
0 = x⁴ − 3x³ + 2x² + 8x² − 24x + 16
0 = x² (x² − 3x + 2) + 8 (x² − 3x + 2)
0 = (x² + 8) (x² − 3x + 2)
0 = (x² + 8) (x − 1) (x − 2)
The roots are 1, 2, and ±i√8.