Yolanda is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of 'English is Fun' she sells. Suppose that x and y are related by the equation y=1900+80x.

a. What is the change in Yolanda's total pay for each copy of 'English is Fun' she sells?
b. What is Yolanda's total pay if she doesn't sell any copies of 'English is Fun'?

Answer: the total amount that you can earn in 15 years is $737245. Option C

Step-by-step explanation:

You receive an annual salary of $32,900 and each year, you are assured of a 5.5% raise. Assuming there was no raise, you get 100% of your previous salary each year. With a raise of 5.5%, you will get 100 + 5.5 = 105.5% of your previous salary for each year. This is a geometric progression and we want to determine the sum of 15 terms(15 years).

The formula for the sum of terms in a geometric progression is

Sn = [a(r^n - 1)]/ r - 1

Sn = sum of n terms

a = the first term

n = number of terms

r = common ratio

From the information given,

a = 32900

n = 15

r = 105.5/100 = 1.055

S15 = [32900(1.055^15 - 1)] / 1.055 - 1

S15 = [32900(2.23247649 - 1)] / 0.055

S15 = 32900 × 1.23247649) / 0.055

S15 = 737245.0277

S15 = $737245

Tommy must clean at least 76 pools, in addition to mowing 41 lawns, to earn the $1500 he needs to buy a car.

Tommy has a summer job mowing lawns at $20 per lawn and cleaning pools at $9 per pool to save up for a car. To determine how many pools he needs to clean to reach his goal of $1500, we need to calculate his earnings from mowing lawns first and then see how much more he needs to earn from pool cleaning.

First, we calculate Tommy's lawn mowing earnings:
41 lawns × $20 per lawn = $820

After mowing lawns, Tommy will need an additional $1500 - $820 to buy the car. This difference is $680.

Next, to find out how many pools Tommy needs to clean, we divide the remaining amount by the amount he earns per pool:
$680 ÷ $9 per pool ≈ 75.56

Since Tommy can't clean a fraction of a pool, he will need to clean at least 76 pools to make enough money to buy the car. Therefore, the answer is 76 pools.

Answer:

Part (A): it would take 2 seconds to reach maximum height of 264 foot.

Part (B): Ball will hit the ground in about 6.1 seconds

Part (C): S(0) represents the initial height of the base ball or the baseball was thrown  at a height of 200 ft.

Step-by-step explanation:

Consider the provided function.

[tex]s(t)=-16t^2+64t+200[/tex]

Part (A) After how many seconds does the ball reach it's maximum height? What is the maximum height?

The coefficient of t² is a negative number, so the graph of the above function is a downward parabola.

From the given function a=-16, b=64 and c=200

The downward parabola attain the maximum height at the x coordinate of the vertex. [tex]x=\frac{-b}{2a}[/tex]

Substitute the respectives.

[tex]x=\frac{-64}{2(-16)}=2[/tex]

Substitute x=2 in the provided equation.

[tex]s(t)=-16(2)^2+64(2)+200=264[/tex]

Hence, it would take 2 seconds to reach maximum height of 264 foot.

Part (B) How many seconds does it take until the ball finally hits the ground?

Substitute s(t)=0 in the provided equation.

[tex]-16t^2+64t+200=0[/tex]

Use the formula [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] to find the solutions of the quadratic equation.

[tex]t=\frac{-64+\sqrt{64^2-4\left(-16\right)200}}{2\left(-16\right)}\\t=\pm\frac{4+\sqrt{66}}{2}\\t\approx-2.1\ or\ 6.1[/tex]

Reject the negative value as time can't be a negative number.

Hence, ball will hit the ground in about 6.1 seconds

Part (C) Find s(0) and describe what this means.

Substitute x=0 in the provide equation.

[tex]s(0)=-16(0)^2+64(0)+200[/tex]

[tex]s(0)=200[/tex]

S(0) represents the initial height of the base ball or the baseball was thrown  at a height of 200 ft.

Part (D) Use your results from parts (a) through (c) to graph the quadratic function.

Use the starting points (0,200), maximum point (2,264) and the end point (6.1,0) in order to draw the graph of the function.

Connect the points as shown in figure.

The required figure is shown below.

Answer:

40h+125=1205

Step-by-step explanation:

He is paid $40 for an unknown amount of hours which in this case would be considered as (h) plus a 125 service charge. Overall, he was paid $1205

Answer:

Question 1 = $59.85.

Question 2 = 0.45

Step-by-step explanation:

Doug did cleaning for 1 ¾ hours.

Doug did paperwork for 2 1/3 hours.

Doug did serving for 1 5/8 hours.

Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.

=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.

In one hour Doug earns $10.50.

Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.

Hence, the total which Doug earned is $59.85.

Second question answer

5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5

Answer:

Answer:

Question 1 = $59.85.

Question 2 = 0.45

Step-by-step explanation:

Doug did cleaning for 1 ¾ hours.

Doug did paperwork for 2 1/3 hours.

Doug did serving for 1 5/8 hours.

Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.

=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.

In one hour Doug earns $10.50.

Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.

Hence, the total which Doug earned is $59.85.

Second question answer

5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5

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Question 1 = $59.85.

Question 2 = 0.45

Step-by-step explanation:

Doug did cleaning for 1 ¾ hours.

Doug did paperwork for 2 1/3 hours.

Doug did serving for 1 5/8 hours.

Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.

=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.

In one hour Doug earns $10.50.

Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.

Hence, the total which Doug earned is $59.85.

Second question answer

5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Samantha had $620 in her savings. She wanted to have at least $200 in her account after her five days in San Diego. This means that the amount that she can spend in 5 days would be her savings minus the least amount that she wants to have left. It becomes 620 - 200 = $420

If she decides to spend her spendable amount of $420 equally per day, it means that each day, she will spend 420/5 = $84

The inequality representing the amount that she can spend for each day will be

Let y = the amount that she can pend each day. Then, it will be

y lesser than or equal to 84

Answer: -12.286 in/sec

Step-by-step explanation:

Differentiate A=s^2 to get d(A)/d(t) = 2s * d(s)/d(t).

Plug in -43 for d(A)/d(t) since it is the rate of change for area. Plug in 7 for s since it is the value of the side length. -43 = 2(7) * d(s)/d(T).

d(s)/d(T) equals -3.0714286

Differentiate P=4s to get d(P)/d(t) = 4 * d(s)/d(t)

Plug in -3.0714286 to d(P)/d(t) = 4 * d(s)/d(t).

d(P)/d(s)= -12.286 in/sec

Final answer:

To find the rate of change of the perimeter when the square's side length is 7 inches and its area decreases at a rate of 43 square inches/sec, we calculate ds/dt and then use it to find dP/dt. The perimeter is decreasing at a rate of approximately -12.284 inches/sec.

Explanation:

The question involves finding the rate at which the perimeter of a square changes given that the area of the square is decreasing at a rate of 43 square inches per second. To solve this problem, let's denote the side length of the square as s and the area as A, so A = s². The perimeter of the square, P, is given by P = 4s.

Given that the area is decreasing at a rate of -43 square inches per second, we represent this rate of change as dA/dt = -43 inches^2/sec. We also know that at the instant when s = 7 inches, we want to find dP/dt, the rate at which the perimeter is changing.

First, we find the rate of change of the side length, ds/dt, given by differentiating A = s² with respect to time (t), giving 2s(ds/dt) = dA/dt. Substituting the given values, we get 2*7(ds/dt) = -43, solving for ds/dt gives us -43/14 = -3.071 inches/sec.

Finally, since the perimeter's rate of change, dP/dt, is 4(ds/dt), we substitute the value we found for ds/dt, resulting in dP/dt = 4*(-3.071), which equals -12.284 inches/sec. Hence, the perimeter of the square is decreasing at a rate of approximately -12.284 inches per second.

Answer:

The p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to don't reject the claim that the group with DDT have a mean greater than the group for rats not poisoned.

Step-by-step explanation:

1) Data given and notation

P:[12.207 ,16.869, 25.050, 22.429, 8.456, 20.589]

UP:[11.074, 9.686 ,12.064, 9.351, 8.182, 6.642]

[tex]\bar X_{P}=17.6[/tex] represent the mean for the sample poisoned

[tex]\bar X_{UP}=9.50[/tex] represent the mean for the sample unpoisoned

[tex]s_{P}=6.34[/tex] represent the sample standard deviation for the sample poisoned

[tex]s_{UP}=1.95[/tex] represent the sample standard deviation for the sample unpoisoned

[tex]n_{P}=6[/tex] sample size for the group poisoned

[tex]n_{UP}=6[/tex] sample size for the group unpoisoned

t would represent the statistic (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for rats exposed to DDT is greater than that for rats not poisoned , the system of hypothesis would be:

Null hypothesis:[tex]\mu_{P} \leq \mu_{UP}[/tex]

Alternative hypothesis:[tex]\mu_{P} > \mu_{UP}[/tex]

If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{P}-\bar X_{UP}}{\sqrt{\frac{s^2_{P}}{n_{P}}+\frac{s^2_{UP}}{n_{UP}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

In order to calculate the mean and the sample deviation we can use the following formulas:

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

3) Calculate the statistic

We can replace in formula (1) the results obtained like this:

[tex]t=\frac{17.6-9.5}{\sqrt{\frac{(6.34)^2}{6}+\frac{(1.95)^2}{6}}}}=2.99[/tex]  

4) Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{P}+n_{UP}-2=6+6-2=10[/tex]

Since is a unilateral test the p value would be:

[tex]p_v =P(t_{(10)}>2.99)=0.0067[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to don't reject the claim that the group with DDT have a mean greater than the group for rats not poisoned.

Answer:

  v = 2√2i -2√2j

Step-by-step explanation:

  v = ||v||·cos(θ)i +||v||·sin(θ)j

  v = 4cos(315°)i +4sin(315°)j . . . . . . fill in the numbers

  v = 2√2i -2√2j . . . . . . . . . . . . . . . put in desired form

The probability of drawing two pink marbles from a bag with replacement can be calculated using the multiplication rule of independent events as P(pink and pink) = P(pink) x P(pink), where P(pink) is the probability of drawing a pink marble.

The subject of this problem is probability in Mathematics, particularly with replacement. The scenario involves drawing two pink marbles from a bag with replacement. This means that after the first marble is drawn, it is put back into the bag before the second one is drawn.

The probability of drawing a pink marble on the first draw is calculated by dividing the number of pink marbles by the total number of marbles. Similarly, the probability of drawing a pink marble on the second draw, with replacement, stays the same because the total number of marbles in the bag is the same as in the first draw.

To calculate the final probability, you use the multiplication rule of independent events (events where the outcome of the first event does not affect the outcome of the second event). According to this rule, the probability of both events happening is the product of the probabilities of each event. Hence, if P(pink) represents the probability of drawing a pink marble, the probability of drawing two pink marbles (with replacement) is P(pink and pink) = P(pink) x P(pink).

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Answer:

  1.  9 < s < 17

  2.  5 < MN < 19

  3.  AD > BD

Step-by-step explanation:

1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:

Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...

  9 < s < 17

(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)

__

2. Same as (1) using different numbers.

  12 -7 < MN < 12 +7

  5 < MN < 19

__

3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:

  AD > BD

Option C

Domain: {-5, 1, 3, 7); Yes, it is a function

The given relation is :-

{(-5, 2), (7, 7), (3,6), (1, 7)}

It is of form (x, y)

The domain is the set of all the values of  "x" . The range is the set of all the values of  "y"

We need to find domain :-

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Domain is the set of "x" values , in the given relation these are:-

Domain is :-  { -5, 7, 3, 1}

And Range is :- {2, 7, 6, 7}

Since there is one value of y for every value of  "x"

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y.

Hence, the relation is a function

The option C) is correct  

Answer:x

=

5

toppings

Step-by-step explanation:Total cost of cheese pizza:  

$

10.75

Any additional topping adds:  

+

$

1.25

So a cheese pizza with  

1

additional topping is:

$

10.75

+

$

1.25

=

$

12.00

A cheese pizza with  

2

additional toppings is:

$

10.75

+

$

1.25

+

$

1.25

=

$

10.75

+

2

×

$

1.25

=

$

13.25

A cheese pizza with  

3

additional toppings is:

$

10.75

+

$

1.25

+

$

1.25

+

$

1.25

$

10.75

+

3

×

$

1.25

=

$

14.50

If you pay attention to the pattern you can see that, for any number of toppings, say  

x

toppings, the price is going to be:

$

10.25

+

x

×

$

1.25

We are told the final cost is  

$

17.00

. That is

$

10.25

+

x

×

$

1.25

=

$

17.00

Subtract  

$

10.25

from both sides

$

10.25

−

$

10.25

+

x

×

$

1.25

=

$

17.00

−

$

10.25

x

×

$

1.25

=

$

6.25

Divide both sides by  

$

1.25

x

×

$

1.25

$

1.25

=

$

6.25

$

1.25

x

=

5

Answer:

  38

Step-by-step explanation:

The year 2004 is 4 years after the year 2000, so the corresponding value of t is 4. Using that value in the formula, we get ...

  f(4) = 41(0.9842^4) ≈ 38.47 ≈ 38

The estimated number of new HIV cases reported in 2004 is 38.

Answer:

x =  3.53 ft

y - 3.53 ft

z = 3.53 ft

Step-by-step explanation:

given details

volume = 44 ft^3

let cardboard dimension is x and y and height be z

we know that area of given cardboard without lid is given as

A = xy + 2xy + 2yz

xyz   = 44 ft^3

To minimize area we have

A = xy + 2x (44/xy) + 2y(44/xy)

A = xy + (44/y) + (44/x)

we have

[tex]Ax = y - \frac{44}{x^2}[/tex]

[tex]0 = yx^2 = 44[/tex]................1

[tex]Ay = x - \frac{44}{y^2}[/tex]

[tex]0 = x - \frac{44}{y^2}[/tex]

[tex]xy^2 = 44[/tex] ..............2

from 1 and 2

[tex]yx^2 = xy^2[/tex]

xy(y-x) = 0

xy = 0 or y = x

from geometry of probelem

x ≠ 0 and y ≠ 0

so y = x

x^3 = 44

x =  3.53 ft = y

z = 44/xy = 3.53

To find the dimensions of the box that requires the least amount of cardboard, we need to minimize the surface area of the box. Since it doesn't have a lid, the box will have an open top. Let's call the length of the box 'x' and the width and height 'y'. The dimensions of the box that requires the least amount of cardboard are x = 44 ft and y = 0 ft.

To find the dimensions of the box that requires the least amount of cardboard, we need to minimize the surface area of the box. Since it doesn't have a lid, the box will have an open top. Let's call the length of the box 'x' and the width and height 'y'.

The volume of the box is given as 44 ft3, so we have the equation x * y * y = 44.

To minimize the surface area, we can differentiate the surface area function with respect to x or y, set it equal to zero, and solve for the corresponding variable.

Let's differentiate the surface area function with respect to x to find the critical point:

0 = 2y2 + 2xy * dy/dx

Since the box has an open top, the length, x, cannot be zero. Therefore, we can solve the equation 2y2 + 2xy * dy/dx = 0 for dy/dx. This gives us:

dy/dx = -y/x

Now, we can substitute this into the equation for the surface area:

S = x * y2 + 2xy * dy/dx

Simplifying, we get:

S = x * y2 - 2y2

To find the critical point, we set the derivative equal to zero:

0 = y2 - 2y2

0 = -y2

Since y is squared, it cannot be negative. Therefore, the only possible critical point is when y is zero, which means the dimensions of the box are x = 44 ft and y = 0 ft.

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Answer:

  4/5

Step-by-step explanation:

This is a long-winded way to ask you the sum of the three fractions:

  1/10 + 1/5 + 1/2

  = 1/10 + 2/10 + 5/10 = (1 +2 +5)/10 = 8/10

  = 4/5

Janine spends 4/5 hour doing morning activities.

Answer:

The probability is 0.7946

Step-by-step explanation:

Let's call F the event that 16 of the 30 tortillas are failures, A the event that you choose a type 1 part and B the event that you choose a type 2 part.

So, the probability that you picked a Type 1 part given that 16 of the 30 tortillas are failures is calculated as:

P(A/F)=P(A∩F)/P(F)

Where P(F) = P(A∩F) + P(B∩F)

Then, the probability that a type 1 part created 16 failures can be calculated using the binomial distribution as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Where x is the number of failures, n is the total number of tortillas and p is the failure rate, so:

[tex]P(16)=\frac{30!}{16!(30-16)!}*0.4^{16}*(1-0.4)^{30-16}=0.0489[/tex]

Therefore, The probability P(A∩F) that you choose a type 1 part and this part created 16 square tortillas is:

(0.3)(0.0489) = 0.0147

Because 0.3 is the probability to choose a type 1 part and 0.0489 is the probability that a type 1 part created 16 square tortillas.

At the same way, the probability that a type 2 part created 16 failures is:

[tex]P(16)=\frac{30!}{16!(30-16)!}*0.75^{16}*(1-0.75)^{30-16}=0.0054[/tex]

Therefore, P(B∩F) is:  (0.7)(0.0054) = 0.0038

Finally, P(F) and P(A/F) are equal to:

P(F) = 0.0147 + 0.0038 = 0.0185

P(A/F) = 0.0147/0.0185 = 0.7946

Answer:

D is correct

Step-by-step explanation:

2x/(x-2) - (x+5)/(x+3)

2x(x+3)/(x-2)(x+3) - (x+5)(x-2)/(x+3)(x-2)

2x^2+6x/(x-2)(x+3)-(x^2+3x-10)(x+3)(x-2)

(x^2+3x+10)/(x+3)(x-2)

Answer:

x^2+3x+10/(x-2)(x+3)

Step-by-step explanation:

Just took the test

Answer:

$0.1 is the additional fee per mile.

Step-by-step explanation:

Given:

Fixed charge = $35.99

Total Bill charged = $90.99

Number of miles traveled = 550 miles

Let additional fee per mile be x.

Now total bill Charge = Fixed charge + additional fee per mile × Number of miles traveled

The expression can be represented as;

[tex]\$35.99 + 550x = \$90.99\\550x = \$90.99-\$35.99\\550x= 55\\x= \frac{55}{550}=\$0.1[/tex]

Hence, the additional fee per mile is $0.1.

Answer:

B. One can be​ 90% confident that the mean additional tax owed is between the lower and upper bounds.

Step-by-step explanation:

Given:

n= 81

[tex]\bar{x}=3408[/tex]

[tex]\sigma= 2565[/tex]

Solution:

A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. A confidence interval can take any number of probabilities, with the most common being a 95% or 99% confidence level.

Confidence interval = [tex]\bar{x} \pm z * \frac{\sigma}{\sqrt{n}}[/tex]

To Find the z  value:

Degree of freedom = n-1

=>81- 1

=> 80

Significance level = 1- confidence level

=>[tex]\frac{(1-\frac{90}{100})}{2}[/tex]

=>[tex]\frac{(1-0.90)}{2}[/tex]

=> [tex]\frac{0.1}{2}[/tex]

=>0.05

using this value In T- Distribution table we get

z =  1.645

Substituting the values  we have,

confidence interval = [tex]3408\pm 1.645 * \frac{2565}{\sqrt{81}}[/tex]

confidence interval = [tex]3408\pm 1.645 * \frac{2565}{\sqrt{9}}[/tex]

confidence interval = [tex]3408\pm 1.645 * 285[/tex]

confidence interval = [tex]3408\pm 468.825[/tex]

confidence interval= (2939.18, 3876.83)

To construct a 90% confidence interval for the mean additional amount of tax owed for estate tax returns, we need to use a z-score and the formula CI = x ± z * (σ/√n), where CI is the confidence interval, x is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. Plugging in the values from the problem, we can calculate the lower and upper bounds of the confidence interval.

To construct a 90% confidence interval for the mean additional amount of tax owed for estate tax returns, we can use the formula:

CI = x ± z * (σ/√n)

where CI is the confidence interval, x is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Plugging in the values from the problem, we have:

x = $3408

σ = $2565

n = 81

Using a z-score table or a statistical calculator, we can find that the z-score corresponding to a 90% confidence level is approximately 1.645.

Substituting these values into the formula, we get:

CI = $3408 ± 1.645 * ($2565/√81)

Simplifying the expression, we have:

CI = $3408 ± 1.645 * $285

Calculating the upper and lower bounds of the confidence interval, we get:

Lower bound = $3408 - 1.645 * $285 = $2977.82

Upper bound = $3408 + 1.645 * $285 = $3838.18

Therefore, the 90% confidence interval for the mean additional amount of tax owed for estate tax returns is approximately $2977.82 to $3838.18.

Interpreting the confidence interval, we can say that we are 90% confident that the true mean additional amount of tax owed for estate tax returns falls within this range.

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Answer:

Step-by-step explanation:

1:22

Answer:

Step-by-step explanation:

so

b buys a paperback for 5.5, while after natalie purchases 35.35 for membership- her books are 2.50

blake paid 5.5

nat paid 37.85

lets see how many books blake has to pay to reach 37.85 shall we?

5.5*22=121

2.5*35=87.5

35.35+87.5=122.85

i dont think its possible

Answer:

m > 15

Step-by-step explanation:

Let m represent the number of miles ran each week by cross country team members

therefore, every week, m > 15.

Answer: 525 cycles per second.

Step-by-step explanation:

The equation for inverse variation between x and y is given by :-

[tex]x_1y_1=x_2y_2[/tex]       (1)

Given : The length of a violin string varies inversely with the frequency of its vibrations.

A violin string 14 inches long vibrates at a frequency of 450 cycles per second.

Let x =  length of a violin

y=  frequency of its vibrations

To find: The frequency of a 12 inch violin string.

Put [tex]x_1=14,\ x_2=12\\y_1=450,\ y_2=y[/tex] in equation (1) , we get

[tex](14)(450)=(12)(y)[/tex]  

Divide both sides by 12 , we get

[tex]y=\dfrac{(14)(450)}{12}=525[/tex]

Hence, the frequency of a 12 inch violin string = 525 cycles per second.

The frequency of a 12 inch violin string is approximately 388.57 cycles per second.

The length of a violin string varies inversely with the frequency of its vibrations. This means that as the length of the string decreases, the frequency of the vibrations increases, and vice versa. To find the frequency of a 12 inch violin string, we can set up the following proportion:

14 inches / 450 cycles per second = 12 inches / x cycles per second

To solve for x, we can cross multiply:

14 inches * x cycles per second = 12 inches * 450 cycles per second

x = (12 inches * 450 cycles per second) / 14 inches

Simplifying:

x = 388.57 cycles per second

Therefore, the frequency of a 12 inch violin string is approximately 388.57 cycles per second.

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Answer:

E= 3/20

Step-by-step explanation:

Number of blue disk= 3

Number of green disk= 3

Number of orange disk= 4

Total number of disk = 3+3+34

= 10

Let B represent blue disk

Let G represent green disk

Let O represent orange disk

If three disk are selected at random, the possible outcome of one green disk and two orange disks are

OOG, OGO, GOO

Pr(OOG) = Pr(O1) * Pr(O2) * Pr(G3)

= 4/10 * 3/9 * 3/8

= 36/720

= 1/20

Pr(OGO) = Pr(O1) * Pr(G2) * Pr(O3)

= 4/10 * 3/9 * 3/8

= 36/720

= 1/20

Pr(GOOG) = Pr(G1) * Pr(O2) * Pr(O3)

= 4/10 * 4/9 * 3/8

= 36/720

= 1/20

Pr(total) = Pr(OOG) + Pr(OGO) + Pr(GOO)

= 1/20 + 1/20 + 1/20

= 3/20

Answer:

1 foot

Step-by-step explanation:

Set equal:

4w² + 70w = 74

Move to one side:

4w² + 70w − 74 = 0

Simplify:

2w² + 35w − 37 = 0

Factor.  Using the AC method, ac = 2×-37 = -74.  Factors of -74 that add up to 35 are 37 and -2.  Dividing by a, the factors reduce to 37/2 and -1/1.

(w − 1) (2w + 37) = 0

Set each factor to 0 and solve:

w − 1 = 0

w = 1

2w + 37 = 0

w = -18.5

Since w must be positive, w = 1.  The width of the wood border is 1 foot.

Answer:

1 footsie

Step-by-step explanation:

the first thing ur gonna wanna do is set them equal:

4w^2 + 70w = 74

now in order to solve it you are goonna put it all onto one side:

4w^2+ 70w − 74 = 0

Now, you are gonna simplify this:

2w² + 35w − 37 = 0

(w − 1) (2w + 37) = 0

Set each factor to 0 and solve:

w − 1 = 0

w = 1

2w + 37 = 0

w = -18.5

Since w must be positive, w = 1.  so the width must be 1 foot

Answer:

Step-by-step explanation:

Assuming the same number of bowling and mini golf games are played, let x represent the total number of games played, either bowling or mini golf. let y represent the total cost of bowling. Let z represent the total cost of golfing

Bowling cost $2 to rent a club plus $5 per game. It means that the cost, y for x bowling games will be

y = 2 + 5x

Mini golf cost $5 to rent a club, plus $4 per game. It means that the cost, y for x mini golf games will be

z = 5 + 4x

For the total cost to be the same, we will equate both equations(y = zl

2 + 5x = 5 + 4x

5x - 4x = 5 - 2

x = 3

There would be 3 games before total cost would be the same

Answer:

$1300

Step-by-step explanation:

The extruder yields a revenue of $200per hour

Y denotes the number of breakdown per day.

The daily revenue generated is given as

R = 1600 - 50Y^2

We have an average of 2 breakdown per day

Lamda = 2

Represent lamda as β

E(Y) = β

E(Y(Y-1)) = β^2

E(Y^2) = E[Y(Y-1)] + E(Y)

= β^2 + β

E(R) = E(1600 - 50Y^2)

= 1600 - 50E(Y^2)

= 1600 - 50(β^2 +β)

Recall that β = lamda = 2

= 1600 - 50(2^2 + 2)

= 1600 - 50(4+2)

= 1600 - 50(6)

= 1600 - 300

= 1300

$1300

The expected daily revenue of the extruder is $1300

Answer:

t=4 seconds to reach the cannon floor

Step-by-step explanation:

ax^2+bx+c=0

0=-16t^2+255

-255=-16t^2

t^2=15.9375

t= 3.99

round it up...

t=4 seconds to reach the cannon floor

hope this helps!!! :)

Answer:

The number of books left on shelves or in circulation is 1,163 .

Step-by-step explanation:

Given as :

The total number of Books in the Library = 1219

The number of lost or stolen books = 32

The number of books sent fro repair = 24

Now, Let The number of books left on shelves or in circulation = x

So,

The total number of Books in the Library  = The number of lost or stolen books + The number of books sent fro repair  + The number of books left on shelves or in circulation

I.e 1219 = 32 + 24 + x

Or, 1219 = 56 + x

Or, x = 1219 - 56

∴    x = 1,163

Hence The number of books left on shelves or in circulation is 1,163 Answer

Answer: Number of books in circulation or left on the shelf is 1163

Step-by-step explanation:

At the end of the year, 32 books were reported to be lost or stolen and 24 books were sent out for repair. This means that the number of books not in circulation is the sum of the number books that was lost or reportedly stolen and the number of books that were sent out for repair.

Therefore,

Number of books not in circulation = 32+24 = 56

The Library originally had 1219 books.

The number of books left on the shelves or in circulation will be total number of books initially - number of books not in circulation. This becomes

1219 - 56 = 1163 books

Answer:

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