three friends went to a restraunt and ordered two orders of wings and three soft drinks. their bill totaled $22.50. later that day, five friends went to the same restraunt and ordered three orders of wings and a soft drink each. their bill totaled $34.50. write and solve a system of equations to determine the price of one order of wings.

Answer:

81/64

Step-by-step explanation:

(9/8)²=9²/8²=81/64

Answer:

[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=45-1=44[/tex]  

The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]  

We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.

Step-by-step explanation:

Information given

[tex]\bar X=18.4[/tex] represent the sample mean

[tex]s=2.2[/tex] represent the sample standard deviation

[tex]n=45[/tex] sample size  

[tex]\mu_o =17.5[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

We want to test if the true mean is higher than 17.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 17.5[/tex]  

Alternative hypothesis:[tex]\mu > 17.5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=45-1=44[/tex]  

The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4

The p value would be given by:

[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]  

We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.

Answer:

The number of days the cat food will last is 8 days.

Step-by-step explanation:

In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.

Assume that each cat consumes x portions of food each day.

Then the four cats will consume, 4x portions of food each day.

Then in 12 days the amount of food consumed by the 4 cats will be:

Total amount of cat food = 12 × 4x

                                          = 48x.

Now, it is provided that she on her way home she brought back two stray cats.

Then the six cats will consume, 6x portions of food each day.

Compute the number of days the cat food will last as follows:

[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]

                                                           [tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]

Thus, the number of days the cat food will last is 8 days.

Answer:

[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl

Step-by-step explanation:

For each bead that you draw, there are only two possible outcomes. Either it is a pearl bead, or it is not. The sum of these probabilities = 100% = 1.

So

2/3 probability of drawing a pearl bead.

p probability of drawing a non pearl bead.

What is the probability of drawing a bead which is not a pearl?

[tex]p + \frac{2}{3} = 1[/tex]

[tex]p = 1 - \frac{2}{3}[/tex]

[tex]p = \frac{3*1 - 2}{3}[/tex]

[tex]p = \frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl

Answer:

About 38 feet

Step-by-step explanation:

The formula for a circle's circumference is 2 times pi times r, which is the radius.

Since the diameter is 12, the radius is half the diameter, so the radius is 6.

2 times pi times 6 is about 37.7 feet, or 38 feet.

Hope this helped.

Answer:

[tex]y=100[/tex]

Step-by-step explanation:

I don't know if by the 10 you mean the base is 10 or it's being logged with the y, but I'm assuming the base is 10. If that's not right, message me and I'll fix my answer. If,

[tex]log_an=x\\a^x=n[/tex]

Then,

[tex]log_1_0y=2\\10^2=y\\100=y[/tex]

Answer:

30 years old

Step-by-step explanation:

Joe's age can be set to x. Since Billy is twice as old as Joe, his age can be set to 2x. They add up to 45. You can set up an equation, 2x+x=45.

Simplify the equation.

3x=45, x=15

Joe is 15. Billy is 2(15)=30.

Answer:

0=0

Step-by-step explanation:Let's solve your equation step-by-step.

3(x+1)−1=3x+2

Step 1: Simplify both sides of the equation.

3(x+1)−1=3x+2

(3)(x)+(3)(1)+−1=3x+2(Distribute)

3x+3+−1=3x+2

(3x)+(3+−1)=3x+2(Combine Like Terms)

3x+2=3x+2

3x+2=3x+2

Step 2: Subtract 3x from both sides.

3x+2−3x=3x+2−3x

2=2

Step 3: Subtract 2 from both sides.

2−2=2−2

0=0

mp

Answer:

4 sqrt(6)

Step-by-step explanation:

sqrt(96)

We know sqrt(ab) =sqrt(a) sqrt(b)

sqrt(16*6)

sqrt(16) sqrt(6)

4 sqrt(6)

Answer:

[tex]z=-1.28<\frac{a-23.1}{2.9}[/tex]

And if we solve for a we got

[tex]a=23.1 -1.28*2.9=19.388[/tex]

And for the 90 percentile we can do this:

[tex]z=1.28<\frac{a-23.1}{2.9}[/tex]

And if we solve for a we got

[tex]a=23.1 +1.28*2.9=26.812[/tex]

The P10 would be 19.388 and the P90 26.812

Step-by-step explanation:

Let X the random variable that represent the chocolate chip cookies of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(23.1,2.9)[/tex]  

Where [tex]\mu=23.1[/tex] and [tex]\sigma=2.9[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.90[/tex]   (a)

[tex]P(X<a)=0.10[/tex]   (b)

We can find a z score value who that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28.

Using this value we can do this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]

And we can solve for the value of interest

[tex]z=-1.28<\frac{a-23.1}{2.9}[/tex]

And if we solve for a we got

[tex]a=23.1 -1.28*2.9=19.388[/tex]

And for the 90 percentile we can do this:

[tex]z=1.28<\frac{a-23.1}{2.9}[/tex]

And if we solve for a we got

[tex]a=23.1 +1.28*2.9=26.812[/tex]

The P10 would be 19.388 and the P90 26.812

Answer:

2 2/5

Step-by-step explanation:

12/5

5 goes into 12 2 times

12 - 5*2

12-10 =2

There is 2 left over.  This goes over the denominator

2 2/5

Answer:

all real numbers

Step-by-step explanation:

The domain is the input values

All values for x are valid as inputs to the function

Answer:

160 units and $6400

Step-by-step explanation:

We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2

the price per unit is 100, therefore revenue for each unit would be 100 * x

However:

profit = revenue - cost

p (x) = 100 * x - 20 * x - 0.25 * x ^ 2

for the maximum value profit we must derive and equal 0:

p '(x) = 100 - 20 - 0.5 * x

0 = 80 - 0.5 * x

0.5 * x = 80

x = 80 / 0.5

x = 160

Therefore, the maximum profit occurs when there are 160 units, replacing we have:

p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2

p (x) = 6400

that is to say that the $ 6400 is the maximum profit.

Answer:

[tex]y-x = 16[/tex]

Step-by-step explanation:

Given

Set 1: (9,5,y,2,x)

Set 2: (8,x,4,1,3)

Required

(y - x)

First the mean values of set 1 and set 2 has to be calculated

For set 1

[tex]Mean _1 = \frac{(9+5+y+2+x)}{5}[/tex]

Collect like terms

[tex]Mean _1 = \frac{9+5+2+y+x}{5}[/tex]

[tex]Mean _1 = \frac{16+ y+x}{5}[/tex]

For set 2

[tex]Mean _2 = \frac{(8+x+4+1+3)}{5}[/tex]

Collect like terms

[tex]Mean _2 = \frac{8+4+1+3+x}{5}[/tex]

[tex]Mean _2= \frac{16+ x}{5}[/tex]

Given that the mean of set 1 is twice the mean of set 2;

[tex]Mean_1 = 2Mean_2[/tex]

[tex]\frac{16+ y+x}{5} =2 * \frac{16+x}{5}[/tex]

Multiply both sided by 5

[tex]5 * \frac{16+ y+x}{5} = 5 * 2 * \frac{16+x}{5}[/tex]

[tex]16+ y+x = 2 * (16+x)[/tex]

Open bracket

[tex]16+ y+x = 32 + 2x[/tex]

Subtract 16 from both sides

[tex]16+ y+x- 16 = 32 + 2x - 16[/tex]

[tex]16 - 16 + y+x = 32 - 16 + 2x[/tex]

[tex]y+x = 16 + 2x[/tex]

Subtract 2x from both sides

[tex]y+x-2x = 16 + 2x-2x[/tex]

[tex]y-x = 16[/tex]

Answer:

I think its C. All students in each grade

Step-by-step explanation:

because it should be the students choice.

Answer:

A) MP(q) = -3q² + 440q - 13

B) 146.64 units.

Step-by-step explanation:

The profit function is given by the revenue minus the cost function:

[tex]P(q) = R(q) - C(q)\\P(q) = -q^3+220q^2-500-13q[/tex]

A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:

[tex]P(q) = -q^3+220q^2-500-13q\\MP(q) = \frac{dP(q)}{dq} \\MP(q)=-3q^2+440q-13[/tex]

B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:

[tex]MP(q)=0=-3q^2+440q-13\\q=\frac{-440\pm \sqrt{440^2-(4*(-3)*(-13))} }{-6}\\q'=146.64\\q'' = - 0.03[/tex]

Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.

Answer:

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

 B. F(x) = 2(x+3)^2 + 3

 D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

75

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

3

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.

Answer:

The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.

The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].

And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]

And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]

Step-by-step explanation:

We need to take in count that we are conducting a regression model with just one dependent variable and 3 independent variables

The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.

The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].

And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]

And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]

Answer:

(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Step-by-step explanation:

The  cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:

[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]

(a)

Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:

[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]

The probability is:

[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]

                  [tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b)

The probability density function of X is:

[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]

Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:

[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]

                  [tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Answer=6 . S/R . 4T

This is the answer because u have to simplify so to do this u have to divide all of this by R

Answer:

Step-by-step explanation:

A=πr^2

But A=88/63

88/63=πr^2

88/63π=r^2

√88/63π=r

Answer:

B) (1,2,3,4,5,6,7,8)

Step-by-step explanation:

The answer is B because the union of a set represents everything thing that is within the sets.

Answer: D  180 degrees rotation about the origin.then a dilation by a scale factor of one-third.

Step-by-step explanation:

A( -9,3)    B(-9,6)  C (0,3)  

After a rotation of 180 degrees you will have the new points as

A (9,-3)   B( 9,-6)  C (0, -3)

The you after dilating it by a scale factor of 1/3

you will get the coordinates

A ( 3,-1)  B( 3,-2)   C(0,-1)  

which match is what was given in the question.

Answer:

a 180° rotation about the origin, then a dilation by a scale factor of One-third

Step-by-step explanation:

took the test

Answer:

4/25

Step-by-step explanation:

The probability the first spin lands on gray is 8/10 = 4/5.

The probability the second spin lands on blue is 2/10 = 1/5.

The probability of both events is 4/5 × 1/5 = 4/25.

Answer:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13        for the function.

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4         for the inverse.

Step-by-step explanation:

we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:

g(y) = x.

now we have

y=4x-3

y=(1/4)x+3/4

The only table that works for our first function is:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13

You can see this by replacing the values of x and see if the value of y also coincides.

Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.

The second table is that one:

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4

Answer: B and D

x:-23, -15, -3, 1, 13

y:-5, -3, 0, 1, 4

x:-5, -3, 0, 1, 4

y:-23, -15, -3, 1, 13

Step-by-step explanation:

the answer is 180°

Step-by-step explanation:

because it rotated 2x and 90+90 is 180

Answer: ( 77.27 , 83.93)

Therefore at 95% confidence/prediction interval is

= ( 77.27 , 83.93)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 80.6 words per minute

Standard deviation r = 7.2

Number of samples n = 18

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

80.6+/-1.96(7.2/√18)

80.6+/-1.96(1.697056274847)

80.6 +/- 3.33

= ( 77.27 , 83.93)

Therefore at 95% confidence/prediction interval is

= ( 77.27 , 83.93)

Answer:

$70,000

Step-by-step explanation:

Profit = Revenue - Costs

x = 120,000 - 50,000

x = 70,000

Answer:

The total repair cost was around $300 .

Step-by-step explanation:

I wasn't sure when you were saying to round, so here are two options.

(For rounding at the end) :

82+157+58 = 297

Rounds to 300.

(For rounding as he's adding everything up) :

80+160+60= 300.

So either way it's 300!

Hope this helped!