19. Stephanie has to save at least $860 this
year for a vacation. Write the inequality that
can be used to calculate the amount she needs
to save each week. Calculate the least amount
she must save each week.

The scenario that could be modeled by the graph is:

A. The number of pounds of apples, y, minus two times the number of pounds of oranges, x, is at most 5.

A linear function is defined as a function in the form of f(x) = mx + bc where 'm' and 'c' are real numbers.

It represents the line's slope-intercept form, which is written as y = mx + c.

This is because a linear function represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'c' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable

Looking at the options, the fact that option A has 5, and x is minus two times, 5/2= 2.5, and that is where the second arrowhead is pointing to on the x axis, it means option A is correct.

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Answer:

the simple interest in both cases is 200 and 756 respectively

Step-by-step explanation:

The computation of the simple interest is shown below:

As we know that

Simple interest = P × r% × t

So

a. Simple interest is

= 2,500 × 8% × 1

= 200

b. The simple interest is

= 4,200 × 6% × 3

= 756

Hence, the simple interest in both cases is 200 and 756 respectively

The measure of angle BDC = 100°

The smallest polygon with three sides and three internal angles is known as a triangle. According to the triangle's "angle sum property," a triangle's internal angles add up to 180°.

Sum of angles in a triangle = 180°

Here we have

3 triangles in the given picture

As we know the Sum of angles in a triangle = 180°

From triangle CBD

∠CBD + ∠BDC + ∠DCB = 180°

From figure  ∠DCB = 40° and ∠CBD = 40°

=> 40° + ∠BDC + 40° = 180°  

=> ∠BDC = 180° - 80°

=> ∠BDC = 100°

Therefore,

The measure of angle BDC = 100°

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Answer:

Taco time

Step-by-step explanation:

Now I'm hungry for tacos

Freddy's froze. custard

Answer:

C. 24

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

9 ÷ 3[12 - 4]

3[8] = 24

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

Answer:

0.619

Step-by-step explanation:

Answer:

0.619

Step-by-step explanation:

Fist divide 13/21. I used a claulator since thats allows in my class. When you do that you get 0.619047619. to round we look at the thrid and fourth decimal places, which are 9 and 0. Since zero is less than nine we round down to get the answer.

a) The revenue R as a function of p is given by R(p) = -5p^2 + 100p.

b) This equation has two solutions: p = 0 and p = 20. Since R is nonnegative, the domain of R is the set of all values of p greater than or equal to 20, or {p | p ≥ 20}.

c)  The price that maximizes revenue is $10.

d)  The maximum revenue is $500.

a) The revenue R is given by R = xp. Since x = -5p + 100, we can substitute this into the equation for R to get:

R(p) = p(-5p + 100) = -5p^2 + 100p

Therefore, the revenue R as a function of p is given by R(p) = -5p^2 + 100p.

(b) We are given that the revenue R is nonnegative. To find the domain of R, we need to find the values of p that make R nonnegative. We can do this by finding the zeros of the quadratic equation -5p^2 + 100p = 0:

-5p(p - 20) = 0

This equation has two solutions: p = 0 and p = 20. Since R is nonnegative, the domain of R is the set of all values of p greater than or equal to 20, or {p | p ≥ 20}.

(c) To find the price p that maximizes revenue, we can take the derivative of R(p) with respect to p, set it equal to zero, and solve for p:

R'(p) = -10p + 100 = 0

-10p = -100

p = 10

Therefore, the price that maximizes revenue is $10.

(d) To find the maximum revenue, we can substitute p = 10 into the equation for R(p):

R(10) = -5(10)^2 + 100(10) = $500

Therefore, the maximum revenue is $500.

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All of the criteria's are fulfilled the survey is valid.

We have the information from the question:

The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.

Then, 34% = 0.34

The sample size of the data is = 100

p: the ‘proportion’ of ‘college’

The required conditions for testing the hypothesis of population proportion are,

(i) The population is larger than the sample

(ii) np > 10

=> 100 × 0.34

      =34

(iii) n(1-p) > 10

100 × (1 - 0.34)

=> 100 × 0.66

      =66

iv)The ‘sample’ is drawn randomly from the population.

Since all of the above criteria's are fulfilled the survey is valid.

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(i) The correct statement about the probability of Aadi getting Tails is B - Sue's estimate is best because she gets more Tails. The number of times a coin is flipped affects the accuracy of the probability estimate, but getting more Tails in fewer trials does not necessarily mean that the probability of getting Tails is higher.

(ii) Eric got 3 Tails in 10 trials, so the proportion of Tails is 3/10. Sue got 20 Tails in 50 trials, so the proportion of Tails is 20/50 or 2/5. We can use the average of these two proportions as an estimate for the probability that Aadi will get Tails.

(3/10 + 2/5) / 2 = 0.35

So the estimated probability of Aadi getting Tails is 0.35 or 7/20 in fraction form.

Answer:

1 a

2b

3b

4b

5a

6b

7d

8a

9d

10d

11b

The exponential function, considering the base e, can be written as follows:

\(f(t) = 8000e^{0.02t}\)

The standard definition of an exponential function is given as follows:

\(A(t) = A(0)\left(1 + \frac{r}{n}\right)^{\frac{t}{n}}\).

The parameters are given as follows:

The function for this problem is given as follows:

\(f(t) = 5000(1.4)^{\frac{t}{20}}\)

Considering the base e, the rate of change is obtained as follows:

k = 0.4/20 = 0.02.

Hence the function is written as follows:

\(f(t) = 8000e^{0.02t}\)

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Therefore, the orthogonal projection of the vector X = (2 9 4) onto the subspace W = span [(1 (2 2 1 2), -2) is

\(proj_WX = \begin{pmatrix}\frac{4}{3}\\\frac{14}{3}\\\frac{10}{3}\end{pmatrix}\)

Given,

\(X=\begin{pmatrix}2\\9\\4\end{pmatrix},W= span\begin{pmatrix}1\\2\\2\end{pmatrix},\begin{pmatrix}-2\\1\\2\end{pmatrix}\)

the projection of a vector X onto a subspace W is given by the following formula:

\(proj_WX =\frac{X\cdot w}{\left\|w\right\|^2}w\)

Here, w = the vector of W and \(\left\|w\right\|\) is the norm of the vector w. So, find the projection of vector X onto the subspace W. The projection of X onto W is given by the formula,

\(proj_WX =\frac{X\cdot w}{\left\|w\right\|^2}w\)

Let's begin by finding the orthonormal basis for the subspace W:

\(W = span \left\{\begin{pmatrix}1\\2\\2\end{pmatrix},\begin{pmatrix}-2\\1\\2\end{pmatrix}\right\}\)

\(\begin{pmatrix}1\\2\\2\end{pmatrix},\begin{pmatrix}-2\\1\\2\end{pmatrix} \Rightarrow Orthogonalize \Rightarrow \left\{\begin{pmatrix}1\\2\\2\end{pmatrix},\begin{pmatrix}-\frac{3}{2}\\\frac{1}{2}\\1\end{pmatrix}\right\}\)

\(\left\{\begin{pmatrix}1\\2\\2\end{pmatrix},\begin{pmatrix}-\frac{3}{2}\\\frac{1}{2}\\1\end{pmatrix}\right\} \Rightarrow Orthonormalize \Rightarrow \left\{\frac{1}{3}\begin{pmatrix}1\\2\\2\end{pmatrix},\frac{1}{\sqrt{14}}\begin{pmatrix}-3\\1\\2\end{pmatrix}\right\}\)

So, the orthonormal basis for the subspace W is

\(\left\{\frac{1}{3}\begin{pmatrix}1\\2\\2\end{pmatrix},\frac{1}{\sqrt{14}}\begin{pmatrix}-3\\1\\2\end{pmatrix}\right\}\)

Now, let's compute the projection of X onto the subspace W using the above formula.

\(proj_WX =\frac{X\cdot w}{\left\|w\right\|^2}w\)

\(proj_WX =\frac{\begin{pmatrix}2\\9\\4\end{pmatrix}\cdot \frac{1}{3}\begin{pmatrix}1\\2\\2\end{pmatrix}}{\left\|\frac{1}{3}\begin{pmatrix}1\\2\\2\end{pmatrix}\right\|^2}\frac{1}{3}\begin{pmatrix}1\\2\\2\end{pmatrix} + \frac{\begin{pmatrix}2\\9\\4\end{pmatrix}\cdot \frac{1}{\sqrt{14}}\begin{pmatrix}-3\\1\\2\end{pmatrix}}{\left\|\frac{1}{\sqrt{14}}\begin{pmatrix}-3\\1\\2\end{pmatrix}\right\|^2}\frac{1}{\sqrt{14}}\begin{pmatrix}-3\\1\\2\end{pmatrix}\)

\(proj_WX = \frac{14}{27}\begin{pmatrix}1\\2\\2\end{pmatrix} + \frac{2}{7}\begin{pmatrix}-3\\1\\2\end{pmatrix}\)

\(\Rightarrow proj_WX = \begin{pmatrix}\frac{4}{3}\\\frac{14}{3}\\\frac{10}{3}\end{pmatrix}\)

Therefore, the orthogonal projection of the vector X = (2 9 4) onto the subspace W = span [(1 (2 2 1 2), -2) is

\(proj_WX = \begin{pmatrix}\frac{4}{3}\\\frac{14}{3}\\\frac{10}{3}\end{pmatrix}\)

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In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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225125₆/101₆ = 2225₆

One way to arrive at this is to convert both given numbers to base 10, compute the quotient in base 10, then convert back to base 6.

101₆ = 1×6² + 0×6¹ + 1×6⁰ = 37

225125₆ = 2×6⁵ + 2×6⁴ + 5×6³ + 1×6² + 2×6¹ + 5×6⁰ = 19,277

So we have

225125₆/101₆ = 19,277/37 = 521

Next,

521 = 2×216 + 89 = 2×6³ + 89

89 = 2×36 + 17 = 2×6² + 17

17 = 2×12 + 5 = 2×6¹ + 5×6⁰

and so

521 = 2×6³ + 2×6² + 2×6¹ + 5×6⁰ = 2225₆

Or you can use the long division algorithm. Division in base 6 is the same as in base 10, except numerals range from 0 to 5 instead of 0 to 9. See if you can follow this diagram (replaced with an attachment)

The area of triangle ABC is equal to 48 cm².

In Mathematics, the midpoint theorem states that in a triangle, the line segment which joins the midpoints of any two (2) sides of the triangle must be parallel to the third side and congruent to half of the length of the third side.

3DE = 12

DE = 12/3

DE = 4 cm.

By applying the midpoint theorem to triangle ABC, the measure of side A-F can be calculated as follows;

CD/CA = DE/A-F = 1/2

4/A-F = 1/2

A-F = 4 × 2

A-F = 8 cm.

Mathematically, the area of a triangle can be calculated by using this mathematical expression:

Area of a triangle = 1/2 × base × height

Area of a triangle = 1/2 × A-F × BC

Area of a triangle = 1/2 × 8 × 12

Area of a triangle = 48 cm².

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There are 30 of 1/10's in the number 3

From the question, we have the following parameters that can be used in our computation:

How many 1/10's are in 3?​

The above statement is a quotient expression that has the following features

Dividend = 3

Divisor = 1/10

So, we have

Quotient = Dividend /Divisor

Substitute the known values in the above equation, so, we have the following representation

Quotient = 3/(1/10)

Evaluate

Quotient = 30

Hence, there are 30 1/10's

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A. A sample size of 62 should be taken for a 95% level of confidence.

B. The sample size of 107 should be taken for a 99% level of confidence.

a. To estimate the sample size needed to estimate the mean time a staff member spends with each patient, we can use the formula for sample size calculation:

n = (Z^2 * σ^2) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired level of confidence

σ = population standard deviation

E = desired margin of error

For a 95% level of confidence:

Z = 1.96 (corresponding to a 95% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (1.96^2 * 8^2) / 2^2

n = (3.8416 * 64) / 4

n = 245.9904 / 4

n ≈ 61.4976

Since we can't have a fraction of a sample, we round up the sample size to the nearest whole number. Therefore, a sample size of 62 should be taken for a 95% level of confidence.

b. For a 99% level of confidence:

Z = 2.58 (corresponding to a 99% confidence level)

E = 2 minutes

σ = 8 minutes (population standard deviation)

Substituting these values into the formula:

n = (2.58^2 * 8^2) / 2^2

n = (6.6564 * 64) / 4

n = 426.0096 / 4

n ≈ 106.5024

Rounding up the sample size to the nearest whole number, a sample size of 107 should be taken for a 99% level of confidence.

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The circumference of circle B is about 31.4 centimeters long. That is about 3.14 centimeters larger than the other circle's circumference.

31.40

-28.26

3.14

Answer:

1. B 2. 31.4 3. 3.14

Step-by-step explanation:

1=first blank

2 = second one

3 = third one

The actual selling price of the phone is 360000 Francs.

In order to find the actual selling price of a phone that was marked down by 10% at a kiosk, given the old price of 400000 Francs, let's use the following formula:

Actual selling price = Old price - (Marked down percentage * Old price)

In this case, the marked down percentage is 10%, which can be written as 0.1 in decimal form.

Substituting the given values, we get:

Actual selling price = 400000 Francs - (0.1 * 400000 Francs)

Simplifying the expression on the right side of the equation:

Actual selling price = 400000 Francs - 40000 Francs

Therefore, the actual selling price of the phone is:

Actual selling price = 360000 Francs

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Answer:

B 16 : 24

Step-by-step explanation:

8 : 12 => when multiply by 2 = 16 : 24

Answer:

8 = m, No solution

Step-by-step explanation:

1. -88 = -3(4m + 5) - (1 - 3m)

-88 = -12m - 15 - 1 + 3m : distributed into parentheses

-88 = -9m - 16 : combined like terms

+16           + 16 : adding to cancel out

-72 = -9m

/-9       /-9 : dividing by -9 to cancel

8 = m

2. -4(5k - 7) + 2k = -2(9k + 5)

-20k + 28 + 2k = -18k - 10 : distributed into parentheses

-18k + 28 = -18k - 10 : combined like terms

       + 10            + 10 : adding to cancel out

-18k + 38 = -18k

+18k            +18k : adding to cancel out

38 = 0k (No solution)

Answer:

73

Step-by-step explanation:

g(x)=8x^2-7x+2

g(3)=8(3)^2-7(3)+2 = 53

g(7)=8(7)^2-7(7)+2 = 345

The average rate of change for the function g(x) for the interval [3, 7] is

= [g(7) - g(3)] / (7 - 3)

= (345 - 53) / 4

= 73

Let's see

g(7)

\(\\ \rm\rightarrowtail 8(7)^2-7(7)+2=8(49)-49+2=392-47=345\)

g(3):-

\(\\ \rm\rightarrowtail 8(3)^2-7(3)+2=8(9)-21+2=72-19=53\)

Now rate of change:-

\(\\ \rm\rightarrowtail \dfrac{345-53}{7-3}==\dfrac{292}{4}=73\)