Answer:The expressions for the payment made to Mary are,
(Monday) 90 = 15m + b
(Tuesday) 62 = 8m + b
where m and b are the fee per student and the base fee, respectively. Solving for m and b, the values are 4 and 30.
The equation that represents Mary's earning is
y = 4x + 30
For 20 students,
y = 4(20) + 30 = 110
For Lisa's earnings,
y = 8x + 15
Substituting 20,
y =8(20) + 15 = 175
Thus, Lisa would earn more than Mary by $65.
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Step-by-step explanation:
Jack found bought a apple that was 3 dollars and he also bought a 2 dollar pen what is his total amount
Answer:
5 dollars
Step-by-step explanation:
Answer:
5 dollars
Step-by-step explanation:
A recent study claims that business travelers spend an average of $41 per day on meals. A sample of 16 business travelers found that they had spent an average of $45 per day with a standard deviation of $3.65. If a = 0.05, what are the critical values?
Answer:
[tex] df = n-1= 16-1 =15[/tex]
And the significance level is [tex]\alpha=0.05[/tex] and since we are conducting a bilateral test then the critical values are founded with the t distribution with 15 degrees of freedom and we got:
[tex] t_{\alpha/2}= \pm 2.131[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=45[/tex] represent the sample mean
[tex]s=3.65[/tex] represent the sample standard deviation
[tex]n=16[/tex] sample size
[tex]\mu_o =41[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to determine the true mean is 41 per day, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 41[/tex]
Alternative hypothesis:[tex]\mu \neq 41[/tex]
We need to find the degrees of freedom first:
[tex] df = n-1= 16-1 =15[/tex]
And the significance level is [tex]\alpha=0.05[/tex] and since we are conducting a bilateral test then the critical values are founded with the t distribution with 15 degrees of freedom and we got:
[tex] t_{\alpha/2}= \pm 2.131[/tex]
What is the mean of the data set below? Round to the nearest tenth when necessary. 40, 40, 52, 41, 62
Answer:
47
Step-by-step explanation:
add all the numbers and divide them by however many numbers there are.
Answer: The mean is 47.
There are 5 numbers.
To find the mean of them we add them and divide the sum by 5.
Mean = [tex]\frac{\left(40+40+52+41+62\right)}{5}=\frac{235}{5}=47[/tex]
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Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x<-1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer: C
Step-by-step explanation:
I went w/ my trusty C and got it right on e2020
All real values of x where 1 < x < 3. Therefore, option C is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
The positive regions of a function are those intervals where the function is above the x-axis.
It is where the y-values are positive (not zero).
Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which describes all of the values for which the graph is positive and decreasing?
A.all real values of x where x < −1
B.all real values of x where x < 1
C.all real values of x where 1 < x < 3
D.all real values of x where x > 3
Match the following items.
1. a2 +2ab + b2
factor
2. a2 - b2
(a + b)2
3. a2 -2ab + b2
(a-b)(a2 + ab + b2)
4. a3 - b3
joint variation
5. a3 + b3
(a + b)(a - b)
6. divisor
(a - b)2
7. process
direct variation
8. a simplified procedure that temporarily omits variables
synthetic division
9. y = 10x
combined variation
10. xy = 18
algorithm
11. y = 4xz
(a + b)(a2 - ab + b2)
12. y = 4x/z
inverse variation
Step-by-step explanation:
The following match
* a² + 2ab + b² and (a + b)²
* a² - b² and (a - b)(a + b)
* a² - 2ab + b² and (a - b)²
* a³ - b³ and (a - b)(a² + ab + b²)
* a³ + b³ and (a + b)(a² - ab + b²)
* y = 10x Direct variation
* xy = 18 Algorithm
* y = 4xz Joint variation
* y = 4x/z Inverse variation
how to change the format of the equation y-5=x
Kale can typed 165 words in 3 minutes. How can this ratio be written to show words per minute?
Answer:
55 words per minute
Step-by-step explanation:
165/3
Final answer:
The ratio of words typed per minute for Kale who typed 165 words in 3 minutes is calculated by dividing the number of words by the number of minutes, resulting in 55 words per minute.
Explanation:
To calculate the number of words typed per minute, you take the total number of words typed and divide it by the number of minutes it took to type them. In this case, Kale typed 165 words in 3 minutes, so the ratio of words to minutes is:
165 words / 3 minutes = 55 words per minute
This ratio indicates the typing speed, measured in words per minute (wpm), which is a common way to express typing efficiency.
Mike bought 7 new baseball cards to add to his collection. The next day his dog ate half of his collection. There are now only 41 cards left. How many cards did Mike start with?
Answer: Mike started with 75 cards
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
The number of cards mike started with (x) plus the new cards added (7) must be divided by 2 (since his dog ate half of his collection).
That expression must be equal to the number of cards left (41)
Mathematically speaking:
(x + 7) /2 = 41
Solving for x:
x+7 = 41x2
x+7 = 82
x = 82-7
x = 75 cards
Feel free to ask for more if needed or if you did not understand something.
I'm not the brightest, mind helping me out?
Answer:
C.
Step-by-step explanation:
Opposite means that they are the same value away from 0 just on the opposite side.
4 is opposite to -4
and 7 is opposite to -7
An expression is shown. 3/5÷5/8 What is the value of the expression?
Answer:
24/25
Step-by-step explanation:
3/5×8/5
24/25
Martha made 3 birthday cards, and she wants to make more. If she makes 5 cards an hour, how many cards will she have after 6 hours? REMEMBER TO ADD THE ORIGINAL 3 TO THE NUMBER SHE MAKES IN 6 HOURS. ANSWER WITHOUT UNITS.
Answer:
33
Step-by-step explanation:
just multiply 5*6 and add three to the result
Answer:
33
Step-by-step explanation:
Every hour she makes 5 cards, and she makes them for 6 hours so you need to multiply 6 with 5 to get 30, then add up the 3 she made earlier...33 :D
Evaluate the expression 5^x- 3^x5 x −3 x 5, start superscript, x, end superscript, minus, 3, start superscript, x, end superscript for x=2x=2x, equals, 2.
Question:
Evaluate the expression 5^x - 3^x for x=2
Answer:
5^x - 3^x for x=2 is 16
Step-by-step explanation:
Given
5^x - 3^x
x=2
Required
Evaluate
When fazed with question like this all you need is to substitute the value of x (or any other variable{s} used) in the expression.
Recall that x = 2
So, you have to substitute 2 for x in 5^x - 3^x
This gives
[tex]5^2 - 3^2[/tex]
This can be further solved in 2 ways
1. Solve directly
[tex]5^2 - 3^2[/tex]
= [tex]25 - 9[/tex]
= 16
2. Expand using difference of two squares.
Difference of two squares is represented by
[tex]a^2 - b^2 = (a + b) (a - b)[/tex]
By comparison
[tex]5^2 - 3^2[/tex] becomes
[tex]5^2 - 3^2 = (5 + 3) (5 - 3)[/tex]
[tex]5^2 - 3^2 = (8) (2)[/tex]
[tex]5^2 - 3^2 = 8 * 2[/tex]
[tex]5^2 - 3^2 = 16[/tex]
For both ways, we'll arrive at the same answer.
Hence, 5^x - 3^x for x=2 is 16
Answer:
5^x - 3^x for x=2 is 16
Step-by-step explanation:
Lena tried to solve a system of linear equations algebraically and in process found the equation 5=9. Lena thought something was wrong,so she graphed the equations and found that they were parallel lines. Explain whats Lenas graph and equation could mean.
Answer:
This means that there is no solution
Step-by-step explanation:
When solving for a system of linear equations, we are solving for the intersection point. If we cannot algebraically solve for a system, it automatically means you made a mistake or the lines are parallel. Since the two lines are parallel, there is no intersection point, so there is no solution
Ethan Purchased a gently used minivan 2 years ago. the current value of the van is $8000 the vans value depreciated by 11% each year. how much does Ethan pay for the van?
Answer:
18,736.80
Step-by-step explanation:
Final answer:
To determine the original purchase price of the van, we apply the formula for exponential decay and find that Ethan paid approximately $10,100.45 for the van two years ago, taking into account a depreciation rate of 11% per year.
Explanation:
To find how much Ethan paid for the van, we need to work backwards from the current value and consider the annual depreciation rate.
To do this, we can use the formula for exponential decay which is final value = initial value × (1 - rate of depreciation)number of years. Given the final value ($8000) and the depreciation rate (11% or 0.11), we need to solve for the initial value, which represents the price Ethan paid for the van.
Let's set up the equation:
8000 = initial value × (1 - 0.11)2
8000 = initial value × (0.89)2
8000 = initial value × 0.7921
Initial value = 8000 / 0.7921
Initial value ≈ $10,100.45
Therefore, Ethan paid approximately $10,100.45 for the van.
20 POINTS!!!! PLZ HELP WILL MARK BRAINLEST 20 POINTS!!!!
Answer:
[tex]10\pi[/tex]
Step-by-step explanation:
The penguin swam around half of the perimeter, or circumference, of the pool. The first step is to calculate that. You can find the circumference of a circle by multiplying the diameter by pi. Therefore, the circumference of this island is 20pi. Half of that is [tex]10\pi[/tex] meters. Hope this helps!
Answer:
10 meters
Step-by-step explanation:
20 / 2 = 10
There are 10 students participating in a spelling bee. In how many ways can the students who go first, second, and third in the bee be chosen?
Answer:
90
Solution:
The 1st choice is 1 of 10.
The 2nd is one of 9.
Therefore, 10 times 9= 90
What is the final amount if 457 is decreased by 1% followed by a further 3% decrease? Give your answer rounded to 2 DP.
Answer:
438.86
Step-by-step explanation:
1. 457 x 0.99 = 452.43 - Decreased by 1%
2. We need to decrease 452.43 again but this time by 3% - 452.43 x 0.97
3. This gives us an answer of 438.8571
4. Finally we need to round this to 2DP, the 7 (438.8571) rounds up so the number to the left increases. This leaves an answer of 438.86
Hope this helps :D
Dwayne buys ingredients to make a cake. He buys 112 pounds of flour, 12 ounces of coconut, and 114 pounds of sugar. What is the total weight of the ingredients Dwayne bought? Select all that apply. A. 56 ounces B. 3 pounds 8 ounces C. 13 3/ 4pounds D. 13 3/ 4ounces E. 3 1/2pounds
Answer:
The only correct options are A, B and E.
Step-by-step explanation:
He buys [tex]1\frac{1}{2}[/tex] pounds of flour, 12 ounces of coconut, and [tex]1\frac{1}{4}[/tex] pounds of sugar.
We will add these together, but before that, we convert the 12 ounces to pounds, so that all the units are the same:
1 ounce = 0.0625 pounds
12 ounces = 12 * 0.0625 = [tex]\frac{3}{4}[/tex] pounds
He buys [tex]\frac{3}{4}[/tex] pounds of coconut.
Adding all of them together yields:
[tex]1\frac{1}{2}[/tex] + [tex]\frac{3}{4}[/tex] + [tex]1\frac{1}{4}[/tex] = [tex]3\frac{1}{2}[/tex] pounds
Let us also convert to ounces:
[tex]3\frac{1}{2}[/tex] / 0.0625 = 56 ounces
Let us also convert 1/2 pound to ounces:
1/2 / 0.0625 = 8 ounces
Hence, the total weight of ingredients that Dwayne bought is [tex]3\frac{1}{2}[/tex] pounds or 56 ounces or 3 pounds 8 ounces
Hence, options A, B and E are correct.
after making 20 servings of pasta, a chef has used 30 cloves of garlic. how many cloves are used to make 10 servings?
Answer:
15
Step-by-step explanation:
Need help now please answer
Answer:
10 cm
Step-by-step explanation:
We want to find TS = ST
ST = CD from the second statement of congruence
CD = IJ from the first statement of congruence
We know IJ = 10
That means ST = 10
Easy question, Easy points LIMTED TIME. LOTS OF POINTS
Topic: Volume
Answer:
V = 77 m^3
Step-by-step explanation:
We want the volume of the cylinder
V = pi r^2 h
We know the diameter not the radius
r = d/2 = 7/2 = 3.5
V = 3.14 * (3.5)^2 (2)
V = 76.93 m^3
To the nearest cubic meter
V = 77 m^3
The answer is 77 m^3
Quick question though... Why say "easy" and ask for an answer?
Solve the equation x³ − 5 = 59
Answer:
4 = x
Step-by-step explanation:
x³ - 5 = 59 Add five to both sides of the equation.
x³ = 64 Now find the cubed root of 64
∛64 = 4
x = 4
A cylinder has a base diameter of 10m and a height of 14m. What is its volume in cubic m, to the nearest tenths place?
Answer:
1099.6 m³
Step-by-step explanation:
The formula for the volume of a cylinder of radius r and height h is
V = πr²h. In this case, the radius, r, is half the diameter, 10 m: r = 5 m, and the height is 14 m.
Thus, the volume of this cylinder is
V = π(5 m)²(14 m) = 1099.6 m³ (to the nearest tenths place).
The volume of the cylinder is approximately 1099.6 cubic meters to the nearest tenth place.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
The formula for the volume of a cylinder is:
V = πr²h
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).
To find the radius of the cylinder, we need to divide the diameter by 2:
r = d/2 = 10m / 2 = 5m
Now we can plug in the values:
V = πr²h = π(5m)²(14m) = 350π m³
To approximate the value to the nearest tenths place, we can substitute the value of π as 3.14159 and use a calculator to evaluate the expression:
V ≈ 350 × 3.14159 ≈ 1099.56 ≈ 1099.6
Therefore, the volume is 1099.6 cubic meters.
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What is the measure of x?
115°
105°
15°
285°
Answer: B. 105
Step-by-step explanation:
180 - 75 = 105
Hope this helps!
A rectangle has a length of 4 inches and area of 12 in.² what is the perimeter of the rectangle
Answer:
14 in
Step-by-step explanation:
breadth = 12/4 = 3
perimeter = 3+3+4+4 = 14
Two similar pyramids have base areas of 122 cm? and 16 cm? The surface area of the larger pyramid is 56 cm
What is the surface area of the smaller pyramid?
40.1 cm
42.7 cm
522 cm
59.8 cm
Answer:
42.7 cm sq.
Step-by-step explanation:
small/large = 16 / 122
16/122 = S / 56
S = 56 * (16/122) = 7.34...
however not in the choice
ah ha..
You meant : 12.2 sq. cm : 16 sq. cm = small / large
so 12.2 / 16 = S / 56 cm
S = 42.7 sq. cm
The surface area of the smaller pyramid is approximately 42.7 cm. Answer: B) 42.7 cm
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
If two pyramids are similar, their corresponding linear dimensions (height, slant height, etc.) are in the same ratio as their corresponding base dimensions.
Let the height of the larger pyramid be h, and let the height of the smaller pyramid be x, h, where x is the scaling factor.
The ratio of their base areas is given by:
(xh)² : h² = 16 : 122
Simplifying this equation, we get:
x²h² = 16/122 * h²
x² = 16/122
x = √(16/122)
Now we know that the linear dimensions of the smaller pyramid are
1/√(122/16) = √(16/122) times that of the larger pyramid.
So, the surface area of the smaller pyramid is:
(16/122) * (56 / (√(16/122))²) = 42.7 cm (rounded to one decimal place)
Therefore, the surface area of the smaller pyramid is approximately 42.7 cm. Answer: B) 42.7 cm
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The percentage profit on an MP3 player purchased for $320 and later sold for $350 is
Answer:
The profit percentage in MP3 player is 9.37 %.
Step-by-step explanation:
Cost price of MP3 player is $320
Selling price of MP3 player is $350.
Here, selling price is more than cost price. It means there is profit in MP3 player.
Profit = SP - CP
Profit = 350 - 320
Profit = $30
Profit percentage is given by :
[tex]\% P =\dfrac{{SP}-{CP}}{{CP}}\times 100\\\\\% P=\dfrac{30}{{320}}\times 100\\\\\% P=9.37\%[/tex]
The profit percentage in MP3 player is 9.37 %.
PLEASE HELP ASAP
Fiona must find the length indicated by the dotted line for
the tiles she is installing. She knows that each polygon is a
regular hexagon with a perimeter of 7.5 in.
What is the length of the dotted line? Round to the nearest
hundredth.
2.50 in.
3.75 in.
5.00 in.
6.25 in.
Answer:
3.75 in.
Step-by-step explanation:
Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in.
3 regular hexagons are connected at their sides. A dotted line is drawn through the middle of the 3 hexagons. The top image is a reflection of the bottom image. The dotted line is the length of one side and the distance from one point of the hexagon to the opposite point.
What is the length of the dotted line? Round to the nearest hundredth.
2.50 in.
3.75 in.
5.00 in.
6.25 in.
The length of the dotted line in the hexagon is 3.75 cm.
What is a hexagon?A polygon with 6 sides is called a hexagon.
Finding the length across one entire hexagon :-
We can draw 6 small triangles from the center of the hexagon. The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360.
The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°.
Since the triangle is isosceles, the base angles will be equal to 120/2 = 60
The bottom two angles will also be 60°.
This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.
Hence,
This means across the dotted line we have 1.25+1.25+1.25 = 3.75.
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2. The area of a rectangle is 56 square inches. The rectangle is 8 inches long. How wide is the rectangle?
A.15 inches
B. 7 inches
C.48 inches
D.20 inches
Answer:
B. 7 inches
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
56 = 8*w
Divide each side by 8
56/8 = 8w/8
7 =w
Answer: 7 inches
Step-by-step-Explanation: The formula for the area of a rectangle is below shown below.
Area = length · width
Since we know that the area of the rectangle is 56 in² and the length of the rectangle is 8 inches, we have 56 = 8 · w.
Now to find w or the width of the rectangle, we divide
both sides of the equation by 8 to get 7 = w.
So the width of the rectangle is 7 inches.
Notice that we include inches in our final answer because we were given inches as units in the original problem.
Also notice that we don't ever have to draw a picture of the rectangle in this problem. We can find our answer by simply using the formula for the area of a rectangle.
An elevator started on the 10th floor of a large hospital. it traveled up 4 floors, then down 6 floors, then down 2 more floors, and finally went back up 7 floors. Which floor was the elevator on when it stopped?
After a series of movements starting on the 10th floor, the elevator stopped on the 13th floor.
To determine which floor the elevator was on when it stopped, we need to perform a series of additions and subtractions based on the elevator's movements, as described:
The elevator started on the 10th floor.
It traveled up 4 floors: 10 + 4 = 14th floor.
Then down 6 floors: 14 - 6 = 8th floor.
Then down 2 more floors: 8 - 2 = 6th floor.
Finally, it went back up 7 floors: 6 + 7 = 13th floor.
After completing all these movements, the elevator stopped on the 13th floor.