Kristi went to the coffee shop and got each of
her 3 kids a $4 cake pop. She also got herself
a $5 chai tea latte. How much did Kristi spend
at the coffee shop?

Answer:

600

Step-by-step explanation:

math

Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

The degree of the given polynomial is 5.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given is a polynomial, 4x²y³-2x²+7y-8

We know that, A polynomial of two variable x and y, like ax^ry^s is the algebraic sum of several terms of the prior mentioned form, where r and s are possible integers.

Here, the degree of the polynomial is r+s where r and s are whole numbers.

Therefore, in the given polynomial, the degree will be

4x²y³

Taking the powers,

2+3 = 5

Hence, the degree is 5

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Answer:

Quadrilateral: 20.5 units

Triangle: 8.6 units

Step-by-step explanation:

Quadrilateral:
We can use the following formula to find the perimeter of a quadrilateral.

Perimeter = AB + BC + CD + DA

where AB, BC, CD, and DA are the lengths of the four sides of the quadrilateral.

In your case, the coordinates of the vertices of the quadrilateral are A(-3,-1), B(-3,3), C(2,3), and D(4,-1).

Using the distance formula, we can find the lengths of the four sides of the quadrilateral as follows:

\(AB = \sqrt{(-3 - (-3))^2 + ((-1) - 3)^2} = \sqrt{16} = 4\)

\(BC = \sqrt{(-3 - 2)^2 + ((3) - 3)^2} = \sqrt{25}= 5\)

\(CD = \sqrt{(2 - 4)^2 + ((3) - (-1))^2} = \sqrt{4+16} = 2\sqrt{5}\)

\(DA = \sqrt{(4 - (-3))^2 + ((-1) - 1)^2} = \sqrt{49} =7\)

Therefore, the perimeter of the quadrilateral is:

Perimeter = AB + BC + CD + DA

= \(4+5+2\sqrt5+7=20.5\) units

Triangle

The perimeter of a triangle is the total length of all three sides of the triangle. To find the perimeter of a triangle, we can use the following formula:

Perimeter = AB + BC + CA

where AB, BC, and CA are the lengths of the three sides of the triangle.

In your case, the coordinates of the vertices of the triangle are

E(-4,1), F(-2,3), and G(-2,4). Using the distance formula, we can find the lengths of the three sides of the triangle as follows:

\(EF = \sqrt{(-4 - (-2))^2 + ((1) - (3))^2} = 2\sqrt{2}\)

\(FG = \sqrt{(-2 - (-2))^2 + ((3) - (4))^2} = 1\)

\(EG = \sqrt{(-4 - (-2))^2 + ((1) - (4))^2} = \sqrt{4 + 9} = \sqrt{13}\)

Therefore, the perimeter of the triangle is:

Perimeter = EF + FG + EG

= 4 + 1 + \(\sqrt{13}\)

=8.6 units

Therefore, the perimeter of the quadrilateral is 20.5 units and the perimeter of the triangle is 8.6 units

Therefore, there is a 68.75% chance that Reese will win at least two of his next four games, assuming that each game is independent and has a 50-50 chance of winning.

Assuming that each game is independent and has a probability of winning of 0.5 (since there are two cups and Reese has a 50-50 chance of choosing the correct one), we can model Reese's wins in four games as a binomial distribution with n=4 and p=0.5.

The probability of Reese winning at least two games can be calculated as the sum of the probabilities of winning two, three, or four games. We can use the binomial probability formula or a binomial probability calculator to find these probabilities:

\(P(X=2) = 6/16 = 0.375\)

\(P(X=3) = 4/16 = 0.25\)

\(P(X=4) = 1/16 = 0.0625\)

So, the probability of Reese winning at least two of his next four games is:

\(P(X\geq 2) = P(X=2) + P(X=3) + P(X=4) = 0.375 + 0.25 + 0.0625 = 0.6875\)

Therefore, there is a 68.75% chance that Reese will win at least two of his next four games, assuming that each game is independent and has a 50-50 chance of winning.

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After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times  (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.

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Answer:

The population reached a total of 19880 people in 1967.

Step-by-step explanation:

The population in t years after 1951 is given by:

\(P(t) = 130t + 17800\)

Which year the population reached a population of 19880 people.

This is t years after 1951

t is found when \(P(t) = 19880\)

So

\(P(t) = 130t + 17800\)

\(19880 = 130t + 17800\)

\(130t = 2080\)

\(t = \frac{2080}{130}\)

\(t = 16\)

1951 + 16 = 1967

The population reached a total of 19880 people in 1967.

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

Answer:

40

Step-by-step explanation:

Hope that helped have a nice day!

Answer:5

Step-by-step explanation:

The range of the function g(x) = a[x], where a < 0, is y ≤ 0.

The function f(x) = [x], where [x] represents the greatest integer less than or equal to x, has a range of y ≤ 0. This means that the output of the function f(x) can be any number less than or equal to zero, including negative integers, zero, and non-negative fractions.

Consider the function g(x) = a[x], where a is a negative constant. When we multiply the input x by a the output of the function is also multiplied by a. Since a is negative, the sign of the output is flipped. Moreover, the output is an integer, as [x] is an integer for all x.

Here, the range of the function g(x) = a[x] is y ≤ 0.

This means that the output of the function g(x) can be any negative integer, zero, or any non-positive fraction, as these are the numbers that are less than or equal to zero.

Thus, the range of the function g(x) = a[x], where a < 0, is y ≤ 0.

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Answer:

A

Step-by-step explanation:

Answer:

6x - 5

Step-by-step explanation:

distribute

6x - 12 + 7

combine like terms

6x - 5  

Answer:

step 1: open bracket

6x - 12 + 7

= 6x -5

Answer:

The probability that the proportion of persons with a retirement account will be less than 57%=31.561%

Step-by-step explanation:

We are given that

n=570

p=58%=0.58

We have to find the probability that the proportion of persons with a retirement account will be less than 57%.

q=1-p=1-0.58=0.42

By takin normal approximation to binomial  then sampling distribution of sample proportion  follow normal distribution.

Therefore,\(\hat{p}\sim N(\mu,\sigma^2)\)

\(\mu_{\hat{p}}=p=0.58\)

\(\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}\)

\(\sigma_{\hat{p}}=\sqrt{\frac{0.58\times 0.42}{570}}\)

\(\sigma_{\hat{p}}=0.02067\)

Now,

\(P(\hat{p}<0.57)=P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.57-0.58}{0.02067})\)

\(P(\hat{p}<0.57)=P(Z<-0.483)\)

\(P(\hat{p}<0.57)=0.31561\times 100\)

\(P(\hat{p}<0.57)\)=31.561%

Hence,  the probability that the proportion of persons with a retirement account will be less than 57%=31.561%

The given value 48,60,75 can be shown  in continous proportion as  48: 60 :: 60: 75.

In mathematics, a continuous proportion is a series of numbers that are proportional to each other, meaning that the ratio of any two adjacent numbers in the series is constant. For example, the numbers 2, 4, 8, 16 are in continuous proportion because the ratio of any two adjacent numbers is 2:1.

We can consider the fraction as  48/60

If we make the division of the the fraction by 12, then we have

48/60 = 4/5

same thing can be done with the fraction 60/75

we can make the division by fraction by 15, so we have

(60/75) = 4/5

Therefore, we have 48: 60 :: 60: 75.

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Answer:

33.51

Step-by-step explanation:

You need to use the equation \(\frac{4}{3} \pi r\)³.

Hope this helps.

Answer:10.7π

Step-by-step explanation:

radius=r=2

volume of sphere=4/3 x π x r x r x r

Volume of sphere=4/3xπx2x2x2

Volume of sphere=(4xπx2x2x2) ➗ 3

Volume of sphere=32π ➗ 3

Volume of sphere=10.7π

Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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Answer:

A)

Student       Test Score     z-score

A                       126               1.25

B                        98                  -2.772

C                        97                -0.26

D                        88                  -2.984

E                        66                -1.88

F                        95                  -2.801

G                        111                  0.47

H                        105                -2.539

B)For z = 2.00, test score =278.4

For z - -2.00, test score =125.6

Step-by-step explanation:

Student       Test Score     z-score

A                       126               1.25

B                        98

C                        97                -0.26

D                        88

E                        66                -1.88

F                        95

G                        111                  0.47

H                        105

Mean = \(\mu = 202\)

Standard deviation = \(\sigma = 38.2\)

For Student B

x= 98

\(Z=\frac{x-\mu}{\sigma}=\frac{98-202}{38.2}=-2.722\)

For Student D

x= 88

\(Z=\frac{x-\mu}{\sigma}=\frac{88-202}{38.2}=-2.984\)

For Student F

x= 95

\(Z=\frac{x-\mu}{\sigma}=\frac{95-202}{38.2}=-2.8010\)

For Student H

x= 105

\(Z=\frac{x-\mu}{\sigma}=\frac{105-202}{38.2}=-2.539\)

Now we are supposed to find test scores :

For z = 2.00

\(Z=\frac{x-\mu}{\sigma}\\2=\frac{x-202}{38.2}\\(2 \times 38.2)+202=x\\278.4=x\)

For z = -2.00

\(Z=\frac{x-\mu}{\sigma}\\-2=\frac{x-202}{38.2}\\(-2 \times 38.2)+202=x\\125.6=x\)

Hence ,For z = 2.00, test score =278.4

For z - -2.00, test score =125.6

Answer:

18.9c - 11.2d + 9.3f

Step-by-step explanation:

First, write the equation as adding all the parentheses together like so:

(9.7c - 1.9d) + (9.2c + 1.1f) + (8.2f - 9.3d)

Remove the parentheses:

9.7c - 1.9d + 9.2c + 1.1f + 8.2f - 9.3d

Collect like terms (9.7c and + 9.2c):

18.9c - 1.9d + 1.1f + 8.2f - 9.3d

Collect like terms again (1.9d and - 9.3d):

18.9c - 11.2d + 1.1f + 8.2f

Collect like terms again (1.1f + 8.2f)

18.9c - 11.2d + 9.3f

Hope this helped!

The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²

We will use the following points to find the area of the sector;

First of all, the angle that is formed in a full rotation is 2π.

The area of a circle is given by the formula; A = πr²

The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π

Thus, the area of a sector is given by the formula;

A = (θ/2π) * πr²

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The different 2-member groups that are possible is 28

From the question, we have

Total number of members, n = 8

Numbers to selection, r = 2

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 2

Substitute the known values in the above equation

Total = ⁸C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 8!/(6! * 2!)

Evaluate

Total = 28

Hence, the number of ways is 28

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The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Jabari's average speed exceed the speed limit by 17 miles per hour

Given:

Total distance = 20.4 miles

Time taken = 17 minutes

convert minutes to hour

60 minutes = 1 hour

17 minutes = 0.283333 hour

Average speed = Total distance ÷ Time taken

= 20.4 ÷ 0.283333

= 72.00008470598200

Approximately, 72 miles per hour

Speed limit = 55 miles per hour

Exceeded speed limit = 72 - 55

= 17 miles per hour

Therefore, Jabari's average speed exceed the speed limit by 17 miles per hour

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The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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-80 is your answer it help you

10-10*10+10

=10-100+10

= - 80

Where the daily growth factor is 1.15 and the starting height in inches is 7.

a. Given by, the function that calculates the height of the beanstalk in relation to the time since Gregory planted it.

\(f(t) = 7(1.15)^t\)

where the daily growth factor is 1.15 and the starting height in inches is 7.

B). The following ratios can be calculated using the formula from section (a):

f(1)/f(0) = (71.15¹)/(71.15⁰) = 1.15

f(2)/f(1) = (71.15²)/(71.15¹ = 1.15

f(1)/f(1) = (71.15¹)/(71.15¹) = 1

\(f(9.56)/f(8.56) = (71.15^{9.56})/(71.15^{8.56})\) ≈ 1.15

\(f(8.56)/f(8.55) = (71.15^{8.56})/(71.15^{8.55})\) ≈ 1.15

c. For the any value of z, we have:

\(f(z+1)/f(z) = (71.15^{(z+1)})/(71.15^z)\) = 1.15

and

\(f(z)/f(z-1) = (71.15^z)/(71.15^{(z-1)})\) = 1.15

For question 6:

a. As a increases throughout the function's domain, f(z) [Select an answer]

Since the base of the exponential function is less than 1 (0.69 < 1), as x increases, f(x) will approach 0.

b. The 1-unit growth factor of f is

The 1-unit growth factor for f is 0.69, since f(x+1)/f(x) = 0.69.

c. The -unit growth factor of f is

The 1/2-unit growth factor for f is (0.69)¹/₂, since f(x+1/2)/f(x) = (0.69)¹/₂.

d. The 6-unit growth factor of f is

The 6-unit growth factor for f is (0.69)⁶, since f(x+6)/f(x) = (0.69)⁶.

e. The 6-unit percent change of  f is

The 6-unit percent change for f is ((0.69)^6 - 1) * 100%, which is approximately -38.77%.

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Answer:

Side of the square (a) = 3½ = 7/2 m

Area of the square

= a²

= (7/2)²

= 49/4

= 12.25 m²

Hope it helps ⚜