Answer:
[tex]0.5\frac{lb}{person}[/tex]
Step-by-step explanation:
we know that
To find out how many pounds of fries each person will receive, divide the total pounds of fries by the total number of people.
so
[tex]\frac{2}{4} \frac{lb}{persons}=0.5\frac{lb}{person}[/tex]
Each person will receive 0.5lb of fries.
To solve this problem, we need to divide the total weight of the French fries by the number of people sharing them. Carmen has prepared a 2lb bag of French fries for 4 people. To find out how much each person will get, we divide the total weight of the fries by the number of people:
[tex]\[ \text{Fries per person} = \frac{\text{Total weight of fries}}{\text{Number of people}} \][/tex]
[tex]\[ \text{Fries per person} = \frac{2 \text{lb}}{4} \] \[ \text{Fries per person} = 0.5 \text{lb} \][/tex]
So, each person will receive 0.5lb of fries.
Angenita drives to work at 50 mph and arrives 1 minute late. she drives to work at 60 mph and arrives 5 minutes early.
Answer:
2 mpm
Step-by-step explanation
One part of a circle is shaded 1/3 and another is shaded 1/2. How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
5/6
Step-by-step explanation:
1/3 + 1/2 = 5/6
Solve the equation by using tu basic properties of logarithms log(2x)=3 (Picture provided)
Answer:
Option b
Step-by-step explanation:
According to the property of sum of logarithms we know that
[tex]log(ab) = log(a) + log(b)[/tex].
In this case we have the equation:
[tex]log(2x) = 3[/tex]
Using the property of sum of logarithms:
[tex]log(2) + log(x) = 3[/tex]
[tex]log(x) = 3 - log(2)[/tex]
We also know that:
[tex]10 ^{(logx)} = x[/tex] -------- Inverse logarithm
So:
[tex]x = 10 ^{3-log(2)}[/tex]
[tex]x = 500[/tex]
Another easiest way to solve it is the following:
Make [tex]w = 2x[/tex].
Then:
[tex]log(2x) = log(w)[/tex]
[tex]log(w) = 3[/tex]
[tex]w = 10^3[/tex] -------- Inverse logarithm property
[tex]w = 1000[/tex]
but [tex]w= 2x[/tex]. Then:
[tex]2x = 1000\\\\x = 500[/tex]
The point (4, -2) lies on a circle and the center of the circle is at the point (4, 1).
What is the equation of this circle?
A. (x - 1)2 + (y - 4)2 = 9
B. (x - 1)2 + (y - 4)2 = 3
C. (x + 4)2 + (y + 1)2 = 9
D. (x - 4)2 + (y - 1)2 = 9
Answer:
D
Step-by-step explanation:
The equation of the circle is (x-x0)^2 + (y-y0)^2 = r^2, where (x0,y0) is the center of the circle. Radius is the distance from any point to the center. Using distance formula you get r = 3.
The equation of the circle having center at point (4,1) and passing through the point (4,-2) is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Equation of circle in parametric form -A circle having radius r and having center at (x0,y0) can be represented by the parametric equation as -
[tex](x - x0)^{2} + (y - y0)^{2} = r^{2}[/tex]
Any point say (x1,y1) which lies on the circle, must satisfy the given parametric equation of the circle.
How to frame the equation of circle from the information given in the question ?Given that the point (4,-2) lies on the circle. Also the center of circle is at (4,1). Therefore, calculating the radius of the circle which is the distance from the center to the point lying on the circle.
Using distance formula,
radius = [tex]\sqrt{(4 - 4)^{2} + (-2 - 1)^{2} }[/tex] = [tex]\sqrt{9 }[/tex] = [tex]3[/tex]
Thus forming the equation of circle from the general parametric equation,
⇒ [tex](x - 4)^{2} + (y - 1)^{2} = 3^{2}[/tex]
∴ [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
Therefore the equation of circle is Option (D) [tex](x - 4)^{2} + (y - 1)^{2} = 9[/tex]
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A car of the same type and make is 3 1/2 years old. Estimate the value of the car.
The values in the scatter diagram indicate;
a) The graph of the data showing the location of the car that costs £2600 and is 4 years of age created with MS Excel is attached
b) The value of the cars decreases as the age increases
c) £3687.9
To address the question, plot the new car data on a scatter diagram, describe the trend of decreasing value with increasing age, and estimate the value of a car based on its age by interpolating between data points.
The question requests steps on how to represent data on a scatter diagram as well as how to interpret and estimate values from it.
a. Add the new point to the scatter diagram for a car that's 4 years old and valued at £2600. This point (4, £2600) should be plotted on the graph along with the other data points.
b. Describe the relationship by observing how the value tends to change as the age of the cars increases. Generally, as cars age, their value decreases, which suggests a negative relationship between the age and the value of the cars.
c. For estimating the value of a car that is 3.5 years old can be found as follows; The equation of the trend line for the scatter diagram obtained usinfg MS Excel is; y = -1290.2·x + 8203.6, indicates that when x = 4, we get;
y = -1290.2 × 3.5 + 8203.6
-1290.2 × 3.5 + 8203.6 =
The estimated price of the car is £3687.9
The complete question found through search is presented as follows;
The scatter diagram shows information about 10 cars.
The 10 cars are of the same type and make
Another car is 4 years old and has been valued at £2,600
a) Show this information on the graph
b) Describe the relationship between the age and the values of the cars
A car of the same type and age is 3¹/₂ years old
c) Estimate the value of the car
Brian and Carlos are sharing a large sub sandwich. Brian ate 2 / 5 of the sandwich, and Carlos ate 1 / 5 of the sandwich. How much of the sandwich is left over?
if I'm right it would be 2/5. you get your answer by adding 2/5 and 1/5 then subtract 5/5- 3/5 to get 2/5
Name the different forms of linear equations you learned. If (1, 2) and
(3, 4) lie on the same line, give the slope-intercept equation of the line.
2
Explain how to find the inverse of f(x) = (x-1)/4
2
What is average rate of change? How do you calculate it? What can you tell about the average rate of change for linear functions? Compare the slopes of horizontal and vertical lines.
3/4
Compare the processes of graphing linear equations and inequalities with examples of your own.
3/4
Create a real-life scenario in which you show how you interpret key features of functions and graphs such as slope and y-intercept?
Module 2
1
What is the definition of “i”? What do we use it for? Demonstrate with an example of your own.
2
Why are radicals simplified before adding and subtracting? Explain your reasoning by adding sqrt8 and sqrt32. Compare the process to multiplying and dividing.
2
Give an example of an expression with a rational exponent and explain how to convert it into radical form.
3/4
A good practice in mathematics is to always check your work. Explain why it is very important to do so when you are solving equations that involve radical expressions?
Where in real life do you work with radical expressions and functions? Give an example of your own.
Module 3
Webbs DOK
Discussion Prompt
1
How many different ways can you solve a quadratic equation? List them.
2
Create a trinomial that can be factored and write it in standard form.
2
Factor x^2 – 7x + 10, 4x^2 – 81 and p(x)=3x^3-12x
3/4
What key features of a quadratic graph can be identified and how are the graphs affected when constants or coefficients are added to the parent quadratic equations? Compare the translations to the graph of linear function. Create examples of your own to explain the differences and similarities.
3/4
A ball is kicked into the air and follows the path described by
h(t)= -4.9t^2+6t+0.6, where t is the time in seconds and h is the height in meters above the ground. Find the maximum height of the ball. What value would you have to change in the equation if the maximum height of the ball is more than 2.4 meters?
The solution to this exercise has been attached below. The problem has been solved in this way:
________________
1. Different forms of linear equations. Point slope-intercept equation of the line that passes through two points.2. Inverse Function. 3. Average Rate of Change.4. Comparison of linear equations and inequalities5. Real-life problems6. Imaginary Number7. Radicals8. Rational exponent and radical form9. Radical expressions10. Quadratic equation11. Trinomial12. Factoring expressions13. Quadratic and linear graph14. A problem of heightAnswer:
Everything he said was correct!
Step-by-step explanation:
I hope this helps!
- sincerelynini
HELP PLEASE!!! NEED FAST ANWER!!
Identify the slope of a line that described by:
down 3 and right 5
m=3/5
m=-3/5
m=5/3
m=-5/3
which one is it???
Answer: second option.
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope of the line and b the y-intercept.
We know that we can calculate the slope with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, keeping the above on mind, you have that:
- If the line moves upward from the left to right, then the slope is positive.
- If the line moves down from the left to right, then the slope is negative.
Then, if the slope described moves 3 units down and 5 units to the right, the it is negative. Therefore:
[tex]m=-\frac{3}{5}[/tex]
Answer:
[tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
We are to identify the slope of a line which is described as:
'down 3 and right 5'
We know that a straight line which is sloping downwards from left to right has a negative slope.
And a straight line which goes upwards from left to right side has a positive slope.
According to the describe slope of a line, it goes 3 units down and 5 units right so it makes a negative slope which is equal to [tex]-\frac{3}{5}[/tex].
FIND ST OF THIS CIRCLE.
[tex]\bigtriangleup RSP \cong\bigtriangleup RQT\Rightarrow \frac{RS}{RQ}=\frac{RP}{RT}\Leftrightarrow RS=3 \\ \Rightarrow ST=RT-RS=5[/tex]
What are the tangent ratios for Y and Z? The triangle is not drawn to scale. Please help I selected an answer but I’m sure it’s wrong
Answer:
[tex]tanY = \frac{4}{5}[/tex] and [tex]tanZ=\frac{5}{4}[/tex]
Explanation:
The tan of an angle in a triangle is equal to [tex]\frac{opposite}{adjacent}[/tex] for the side lengths. Opposite side is the one found directly across the triangle and the adjacent is the side touching the angle that is not the hypotenuse. This means the tan for Y is 4 over 5 and the tan for Z is 5 over 4.
The tangent ratios are:
tan(Y) = 5/4
tan(Z) = √41/4
In a right triangle with sides labeled X, Y, and Z, and angles labeled x, y, and z, you can use the trigonometric ratios to find the tangent ratios for angles Y and Z.
The tangent ratio is defined as:
For angle Y (opposite to side XY): tan(Y) = opposite / adjacent = XY / ZX
For angle Z (opposite to side ZY): tan(Z) = opposite / adjacent = ZY / XZ
Given the following values:
ZX = 4
XY = 5
ZY = √41
Let's calculate the tangent ratios:
For angle Y (opposite to XY):
tan(Y) = XY / ZX = 5 / 4
For angle Z (opposite to ZY):
tan(Z) = ZY / XZ = √41 / 4
So, the tangent ratios are:
tan(Y) = 5/4
tan(Z) = √41/4
for such more question on tangent ratios
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Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares share one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answer:
18 cm
Step-by-step explanation:
Let the width of the rectangle be x cm, then the length of the rectangle is x+5 cm.
The area of the ractangle is
[tex]x\cdot (x+5)\ cm^2.[/tex]
The area of the square with side's length of x cm is
[tex]x^2\ cm^2.[/tex]
The area of the square with side's length of x+5 cm is
[tex](x+5)^2\ cm^2.[/tex]
The area of constructed figure is
[tex]x(x+5)+2x^2+2(x+5)^2\ cm^2.[/tex]
Since the total area of the constructed figure is 120 cm², you have
[tex]x(x+5)+2x^2+2(x+5)^2=120.[/tex]
Solve this equation:
[tex]x^2+5x+2x^2+2x^2+20x+50=120,\\ \\5x^2+25x-70=0,\\ \\x^2+5x-14=0,\\ \\D=5^2-4\cdot (-14)=25+56=81,\\ \\x_{1,2}=\dfrac{-5\pm\sqrt{81}}{2}=-7,\ 2.[/tex]
The width of the rectangle cannot be negative, so x=2 cm and x+5=7 cm and the perimeter of the rectangle is
[tex]2x+2(x+5)=2\cdot 2+2\cdot 7=4+14=18\ cm.[/tex]
There are 45 members on the board of directors for a certain non-profit institution. if they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?
Answer:
1,221,759.
Step-by-step explanation:
This is the number of combinations of 5 from 45.
This = 45! / 40! 5!
= 1,221,759.
Answer:
1,221,759
Step-by-step explanation:
Question 2(Multiple Choice Worth 4 points) (08.02)A pair of equations is shown below. x + y = 5 y = one halfx + 2 If the two equations are graphed, at what point do the lines representing the two equations intersect? (2, 5) (5, 2) (2, 3) (3, 2)
Answer:
[tex](2,3)[/tex]
Step-by-step explanation:
The first equation is [tex]x+y=5[/tex]
The second equation is [tex]y=\frac{1}{2}x+2[/tex]
When we graph these two equations, they will meet at a point which represent the solution of the two equations.
We can solve the two equations simultaneously to determine their point of intersection.
Let us substitute the second equation into the first equation to get;
[tex]x+\frac{1}{2}x+2=5[/tex]
Multiply through by 2 to get;
[tex]2x+x+4=10[/tex]
Group similar terms to obtain;
[tex]2x+x=10-4[/tex]
Simplify;
[tex]3x=6[/tex]
Divide both sides by 3;
[tex]\Rightarrow x=2[/tex]
Put [tex]x=2[/tex] into the second equation;
[tex]y=\frac{1}{2}(2)+2[/tex]
[tex]\Rightarrow y=1+2[/tex]
[tex]\Rightarrow y=3[/tex]
Therefore the graphs of the two functions intersect at (2,3)
See graph in attachment.
Josh took out a payday loan for $1300 that charged a $75 fee. If the loan matures in 2 weeks, what is the approximate effective interest rate of the loan?
A. 430%
B. 33%
C. 43%
D. 330%
(Apex)
The approximate effective interest rate of the loan is 330%.
What is Interest?The cost of borrowing money or the fee you charge to lend it is known as interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
Given:
The amount owed increases by $75 in two weeks.
n= 52/2 = 26 periods
If the loan applied with same interest rate, then the total amount owed
=[tex](1375/1300)^{26}[/tex] x $1300
Now, If we subtract the original principle $1300, then the compounding interest as a percentage of that principle is
= [[tex](1375/1300)^{26}[/tex] x $1300 - $1300] / $1300
= 5,493.8 - 1300 / 1300
= 330%
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Final answer:
To find the effective interest rate of Josh's payday loan, you divide the interest ($75) by the principal ($1300) and multiply by 100 to get a two-week rate. Then you annualize it by multiplying by the number of two-week periods in a year (26), resulting in an approximate annual interest rate of 150%. The options provided in the question appear to be incorrect considering this calculation.
Explanation:
To calculate the effective interest rate of Josh's payday loan, we first need to determine the interest he's paying compared to the principal. The fee associated with the loan can be considered the interest, which in this case is $75. Since the loan is for $1300, we can calculate the interest rate for the two-week period by dividing the interest by the principal and then multiplying by 100 to get a percentage:
Interest Rate for 2 Weeks = ($75 ÷ $1300) × 100
Then, to annualize this rate, since there are 26 two-week periods in a year, we multiply the result by 26:
Annualized Interest Rate = Interest Rate for 2 Weeks × 26
Performing the calculations gives us:
Interest Rate for 2 Weeks = (75 ÷ 1300) × 100 ≈ 5.769%
Annualized Interest Rate = 5.769% × 26 ≈ 150%
However, the options given in the question do not match this calculation. It seems there might be a mistake with the options provided. The effective interest rate calculated here is approximately 150%, which is much lower than the options given. It is crucial to double-check the information or the methodology if this seems inconsistent with expected results. Note that payday loans typically have extremely high-interest rates, so a very high annual percentage rate (APR) is possible, but it may be calculated in a different manner.
What is 0.36 expressed as a fraction in simplest form? Enter your answer in the box. Repeating 36
Answer: 9/25
Step-by-step explanation: .36 equals 36/100 in decimal form.
Reducing it into its simplest form:
Both numbers are divisible by 4-
36/100 = 9/25 - which is the simplest form.
what quadrilateral always has 4 congruent angles and opposite sides that are congruent and parallel?
Answer:
See below.
Step-by-step explanation:
A rectangle has 4 * 90 degree angles and opposite sides are congruent and parallel. A square also fits the bill.
The figures below are similar. Compare the larger figure to the smaller. which of the following is the ratio of the areas of the figures?
Answer:
4:3
Step-by-step explanation:
The ratio is 8:6, which simplifies to 4:3.
Answer:
16:9
Step-by-step explanation:
PLEASE HELP! URENT!
What is the measure of ∠R ?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R=
°
Answer:
R = 48.59 degrees
Step-by-step explanation:
We know that
sin theta = opposite / hypotenuse
sin R = 30/40
sin R = 3/4
Taking the inverse sin of each side
sin^-1 (sin R) = sin ^-1(3/4)
R = 48.59037789
To the nearest hundredth
R = 48.59 degrees
The probability assigned to each experimental outcome must be
Answer:
Between 0 and 1
Step-by-step explanation:
The probability for each outcome in experimental probability must be a value between 0 and 1. A probability of 0 means the event did not happen; the probability of 1 means it is certain. We cannot have probabilities smaller than 0 or greater than 1.
All of the probabilities in an experiment must sum to 1 whole.
The probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.
The probability of extremely certain event is 1 and the probability of extremely uncertain event is 0. The sum of all the probabilities in an experiment is always equals to 1.
Hence the probability assigned to each experimental outcome must be greater than 0 or less than 1 or lies in between 0 and 1.
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You are buying shoes online.The selling price is $29.99. Round to the nearest penny if necessary.
it's 30 dollars because it's the closest whole number
Final answer:
To calculate the total cost of an online purchase, round the sales tax to the nearest penny and add it to the item's price. When combining multiple items, sum their prices and add the rounded sales tax to find the total cost.
Explanation:
When buying shoes or any item online and encountering a selling price that includes cents, you may need to perform rounding if further calculations are required. For example, to round $6.375 to the nearest penny, we would get $6.38 because the third digit after the decimal is 5 or more, thus we increase the second digit by one. From there, we would add the rounded sales tax to the original price of the item to find the total cost.
In a different scenario where you are adding two prices together, like $8.99 and $11.99, you get the subtotal of $20.98 before tax. Then calculate the sales tax by converting the percent to a decimal and multiplying by the subtotal, rounding again to the nearest cent if necessary. Finally, add the sales tax to the subtotal to get the total cost. For instance, if the sales tax was $1.47, adding this to the subtotal of $20.98 would give you a total of $22.45.
When you multiply expressions with the same base, you ______ the exponents. Add multiply
Answer:
... you add the exponents
Step-by-step explanation:
An exponent is a way of showing repeated multiplication. For example, ...
x^2 means x·x
and
x^3 means x·x·x
If we multiply these two expressions together, we get ...
(x^2)·(x^3) = (x·x)·(x·x·x) = x·x·x·x·x
This is a product in which x appears as a factor 5 times, so we can write it using an exponent as ...
x·x·x·x·x = x^5
___
That is, when we multiply the expressions, we add the numbers of times the factor appears in the product:
2 + 3 = 5
x^2 · x^3 = x^(2+3) = x^5
Answer: Add
Step-by-step explanation: When you multiply expression with the same base you ADD the exponents. The exponent tells you how many times you multiply the base by itself. This means the exponent corresponds to the amount of base replications. If you add the exponents you are adding the replications of the base.
Lines p and q are perpendicullllar if the slope of line p is 2 what is the slope of line q
q= -1/2
perpendicular slopes are those that are opposite sign and reciprocal of the original given slope
At school 95% of students arrive on time.If there are 200 students how many are expected to be late
Answer:
10 students (late)Step-by-step explanation:
total students = 200
95% of students arrived on time
5% of students were late.
95% x 200 = 190 students (on time)
5% x 200 = 10 students (late)
-------------------------------------
200 students
The bus from Karen's house to school runs 26 to 75 minutes of the bus runs on Monday at 7:05am at which time could the bus run next
I’m pretty sure the answer is 8:25 a.m
Find the product of x^2+2x-4 and 3x.
a. 3x^3+6x^2+12x
b. 3x^3+6x^2-12x
c. 3x^3+2x-4
d. -3x^3
[tex] 3x({x}^{2} + 2x - 4)[/tex]
[tex]3x \times {x}^{2} = {3x}^{3} [/tex]
[tex]3x \times 2x = 6 {x}^{2} [/tex]
[tex]3x \times - 4 = - 12x[/tex]
[tex]b. \: 3 {x}^{3} + 6 {x}^{2} - 12x[/tex]
Find the area of the trapezoid. leave your answer in simplest radical form.
Answer:
Area[tex]=70in^2[/tex]
Step-by-step explanation:
The given diagram is a tra-pezoid.
The area of a tra-pezoid is calculated using the formula;
Area[tex]=\frac{1}{2} (Sum\:of\:parallel\:sides)\times height[/tex]
This implies that;
Area[tex]=\frac{1}{2} (8+12)\times 7[/tex]
Area[tex]=\frac{1}{2} (20)\times 7[/tex]
Area[tex]=(10)\times 7[/tex]
Area[tex]=70in^2[/tex]
The last choice is correct.
Use the x-intercept method to find all real solutions of the equation.
x^3-7x^2+4x+12=0
Answer:
the answer is c for apex
Step-by-step explanation:
Answer:
a. [tex]x=-1,2,\:or\:6[/tex]
Step-by-step explanation:
The given equation is
[tex]x^3-7x^2+4x+12=0[/tex]
To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.
The corresponding function is;
[tex]f(x)=x^3-7x^2+4x+12[/tex]
The real solutions to [tex]x^3-7x^2+4x+12=0[/tex], are the x-intercepts of the graph of the corresponding function.
From the graph the x-intercepts are
(-1,0),(2,0) and (6,0).
Therefore the real solutions are
[tex]x=-1,2,\:or\:6[/tex]
Given the following sets, which of the following is false? A={4, 6, 8} B={-2, 0, 2, 4} C={13, 23, 33, 43}
Answer:
gfjhgfterjrjtryuyrt
Step-by-step explanation:
hgfdjjrfdsfdjuytitdfgfdsuygeryauvfudsgygwerauyerwaguyfdsguyagsuydzgfuygewsabfuyguyeravcuyeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraeraerajhbfcds
What value of k causes the terms 5, 2k, 13 to form an arithmetic sequence?
2
4
9/2
13/4
Answer:
[tex]k=\frac{9}{2}[/tex]
Step-by-step explanation:
The given sequence is
[tex]5,2k,13[/tex]
For the sequence to be arithmetic, then
[tex]2k-5=13-2k[/tex]
We group similar terms to get;
[tex]2k+2k=13+5[/tex]
[tex]4k=18[/tex]
Divide both sides by 4;
[tex]k=\frac{18}{4}[/tex]
Simplify;
[tex]k=\frac{9}{2}[/tex]
Answer:
The correct answer is 3rd option 9/2
Step-by-step explanation:
From the given sequence, 5, 2k, 13
Which are in AP.
We can consider a₁ = 5 , a₂ = 2k and a₃ = 13
To find the value of k
We have,
a₂ = (a₁ + a₃)/2
Here,
2k = (5 + 13)/2 = 18/2 = 9/2
Therefore the correct answer is option 3
9/2
Find the total area of the solid figure.
60 sq. in.
78 sq. in.
90 sq. in.
Answer:
245.04
Step-by-step explanation:
The equation to a cylinder for area is A=2πrh+2πr^2
Fill in and solve.
A=2(3.14)(3)(10)+2(3.14)(3)^2
So using PEMDAS you get the answer 245.04
While taking @Jtakes700's answer and putting it into the form your asking, or putting into one of your options, you would get 78pi sq. in.