The radius of the inscribed circle is cm, and the radius of the circumscribed circle is cm.

Answer:

Dimensions: 165 feet by 110 feet.

Maximum Area =18,150 Square feet

Step-by-step explanation:

Let the dimension of the playground be x and y.

The rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.

Let the side parallel to one side of the playground =x

Therefore, the total length of fencing =2x+x+2y

P=3x+2y

Six hundred and sixty feet of fencing is used.

We have: 3x+2y=660

3x=660-2y

[tex]x=\dfrac{660-2y}{3}[/tex]

Area of the Playground A=xy

We write the area in terms of y by substitution of x derived above.

[tex]A(y)=y\left(\dfrac{660-2y}{3}\right )\\A(y)=\dfrac{660y-2y^2}{3}[/tex]

We want to maximize the total enclosed area.

To do this, we first find the derivative of A(y).

[tex]A'(y)=\dfrac{660-4y}{3}[/tex]

Next, we solve A'(y) for its critical point.

[tex]A'(y)=\dfrac{660-4y}{3}=0\\660-4y=0\\660=4y\\y=660 \div 4\\y=165$ feet\\[/tex]

Recall that: [tex]x=\dfrac{660-2y}{3}[/tex]

Therefore:

[tex]x=\dfrac{660-2(165)}{3}=\dfrac{660-330}{3}=\dfrac{330}{3}\\x=110$ feet[/tex]

Therefore, the dimensions of the playground that maximize the total enclosed area is 165 feet by 110 feet.

Maximum Area =165 X 110

=18,150 Square feet

Answer:

Dimensions: 165 feet by 110 feet.

Maximum Area =18,150 Square feet

Maximum Area =165 X 110

=18,150 Square feet

Answer:

480 cubic feet

Step-by-step explanation:

The volume of any rectangular prism can be found by multiplying together the length, width and height. In this case, 8*6*10=48*10=480 cubic feet. Hope this helps!

Answer:

[tex]480 {ft}^{3} [/tex]

Step-by-step explanation:

[tex]area \\ = l \times b \times h \\ = 8 \times 6 \times 10 \\ = 48 \times 10 \\ = 480 {ft}^{3} [/tex]

hope this helps

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good luck! have a nice day!

−2(x+3)+6x

Distribute:

=(−2)(x)+(−2)(3)+6x

=−2x+−6+6x

Combine Like Terms:

=−2x+−6+6x

=(−2x+6x)+(−6)

=4x+−6

Answer:

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If [tex]Z \leq 2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered to be unusual.

In this question:

[tex]\mu = 8.21, \sigma = 1.9[/tex]

Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

This is the pvalue of Z when X = 5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 8.21}{1.9}[/tex]

[tex]Z = -1.69[/tex]

[tex]Z = -1.69[/tex] has a pvalue of 0.0455.

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Answer:

Race covers 1911 meters.

Step-by-step explanation:

Triangle ABC represents a race path.

Total distance covered by the race = Perimeter of the triangle ABC

We will apply Sine rule in the given triangle to find the unknown sides.

By Sine rule,

[tex]\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}[/tex]

[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}[/tex]      [Since m∠A = 180° - (85 + 60)° = 35°]

[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}[/tex]

AC = [tex]\frac{450\times \text{Sin85}}{\text{Sin35}}[/tex]

     = 781.57 meters

[tex]\frac{Sin35}{450}=\frac{Sin60}{AB}[/tex]

AB = [tex]\frac{450\times \text{Sin60}}{\text{Sin35}}[/tex]

     = 679.44 meters

Perimeter of the triangle = AB + BC + AC

                                         = 679.44 + 450 + 781.57

                                         = 1911.01

                                         ≈ 1911 meters

Therefore, the race covers 1911 meters.

Answer:

1911

Step-by-step explanation:

yes

Answer:

A trinomial

Step-by-step explanation:

Since there are three terms, x^2, 3x, and 8, it is a trinomial

Answer:

$2

Step-by-step explanation:

Because 3/12 is 0.25 and then you multiply it by 8 to get 2.

Answer: C≈ 37.7cm

Step-by-step explanation: C=2πr=2·π·6≈37.69911cm

Hope this helps.

Answer:

C = 37.7 cm

Step-by-step explanation:

Circumference = 2πr

Where r = 6 cm, π = 3.14

C = 2(3.14)(6)

C = 37.69

C ≈ 37.7 cm

Answer:

graph of exponential rising up to the right, through the point 0, negative 2

Step-by-step explanation:

I graphed the function on the graph below so you can see that it rises to the right and goes through the point (0,-2).

Answer:

graph of exponential rising up to the right, through the point 0, negative 2

Step-by-step explanation:

f(x)=3x-2

f(0)=3*0-2= -2

(0, -2) is the last given option

Answer:

a. The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

b. It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 451, \pi = 0.015[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.015 - 1.96\sqrt{\frac{0.015*0.985}{451}} = 0.0038[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.015 + 1.96\sqrt{\frac{0.015*0.985}{451}} = 0.0262[/tex]

The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

b. Explain in a complete sentence what the confidence interval means

It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).

Answer:

The value of the test statistic = 2.58

Test statistic Z = - 4.805

|Z| = 4.805 > 2.58

Null hypothesis is rejected The value of the test statistic = 2.58

There is  significant difference between in the mean number of times men and women send a Twitter message in a day

Step-by-step explanation:

Step(i):-

Sample size of men  n₁ = 25

mean of the first sample x₁⁻ = 20

Standard deviation of the first sample σ₁ = 5

Sample size of women n₂ = 30

mean of the second sample x₂⁻ = 30

Standard deviation of the first sample σ₂ = 10

Level of significance ∝= 0.01

Step(ii):-

Null Hypothesis : H₀: There is no significant difference between in the mean number of times men and women send a Twitter message in a day

Alternative Hypothesis :H₁:There is  significant difference between in the mean number of times men and women send a Twitter message in a day

Test statistic

[tex]Z = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S.D_{1} ^{2} }{n_{1} }+\frac{ S.D_{2} ^{2}}{n_{2} } } }[/tex]

[tex]Z = \frac{20 - 30 }{\sqrt{\frac{(5)^{2} }{25 }+\frac{ (10)^{2} }{ 30} } }[/tex]

Z =  [tex]\frac{-10}{2.081} = - 4.805[/tex]

The value of the test statistic = 2.58 C

|Z| = 4.805 > 2.58

Null hypothesis is rejected The value of the test statistic = 2.58

Conclusion:-

There is  significant difference between in the mean number of times men and women send a Twitter message in a day

Answer:

I think it is 310 plus 300 and

320 plus 390

Step-by-step explanation:

Answer:

3.25 h = 3 h 15 m

Step-by-step explanation:

156 mi * 1h/48 mi = 3.25 h = 3 h 15 m

Answer: 195 min or 3 hr and 15 min

Step-by-step explanation:

We can set up a proportion to solve this problem.

[tex]\frac{48mi}{60 min} =\frac{156 mi}{x}[/tex]

[tex]48x=156*60[/tex]

[tex]48x=9360[/tex]

[tex]x=195 min[/tex]

We can also write this in terms of hours and minutes.

[tex]\frac{60 min}{1 hr} =\frac{195 min}{x}[/tex]

[tex]60x=195[/tex]

[tex]x=3.25[/tex]

3 hr and 15 min

CLICK ON THE POIN AND SCHROOL DOWN

Answer:

By asking the question.

Answer:

so she saved 82 cents in the interest the month after

Step-by-step explanation:

case 1: payment is $75

interest on 2000 = 0.125/12×2000 = $20.83

so the actual repayment on the balance = (75-20.83) = $54.17

therefore,balance =$(2000-54.7)=$1945.83

interest in the next month = $20.27

case 2: payment is $100

interest on 2000 is still $20.83

repayment = $79.73

balance = $1920.27

interest in the next month = 20.01

so she saved 82 cents in the interest the month after

Answer:

$101

Step-by-step explanation:

Check link explanation.

Answer:

Option (E)

Step-by-step explanation:

In the figure attached,

Given a isosceles right triangle with two equal legs measuring [tex]3\sqrt{2}[/tex] units

By Pythagoras theorem,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Since, hypotenuse = h

Leg 1 = Leg 2 = 3√2

Now we substitute the values,

h² = (3√2)² + (3√2)²

h² = 18 + 18

h = √36

h = 6 units

Therefore, length of the hypotenuse is 6 units.

Option (E) will be the answer.

Using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.

Given that the hypotenuse length of a right triangle is c, and the other legs are a and b, the Pythagorean Theorem states that: c = √(a² + b²).

Thus:

h = √((3√2)² + (3√2)²)

h = √(18 + 18)

h = √36

h = 6

Therefore, using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.

Learn more about Pythagorean Theorem on:

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Answer:

Step-by-step explanation:

Using either the critical value rule or the p-value rule, a conclusion can be drawn at a level of significance (alpha)

The null hypothesis: u = hypothesized mean

Alternative hypothesis: u > u0 or u < u0 for a one tailed test

Alternative hypothesis for a two tailed test: u =/ u0

To draw a conclusion by failing to reject the null hypothesis as stated then: using critical value

Observed z score > critical z score for both the one and two tailed test.

Or using p value:

P-value > alpha for a one tailed test

P-value > alpha/2 for a two tailed test

Thus, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis will also not be rejected at the same significance level.

Answer:

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

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

[tex]a=104.5 -1.282*23.62=74.22[/tex]

And the best answer for this case would be:

b) $74.23

Step-by-step explanation:

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

[tex]X \sim N(104.5,23.62)[/tex]  

Where [tex]\mu=104.5[/tex] and [tex]\sigma=23.62[/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)

As we can see on the figure attached the z value 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=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90

If we use condition (b) from previous we have 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 set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]

And if we solve for a we got

[tex]a=104.5 -1.282*23.62=74.22[/tex]

And the best answer for this case would be:

b) $74.23

Answer:

-37

Step-by-step explanation:

Answer:

-2x/yz

Step-by-step explanation:

You can cancel out terms using division and properties of exponents. x^a/x^b = x^a-b

Answer:

C.

Step-by-step explanation:

the standard form of a QE is ax2+bx+c. This includes x squared, and when graphed, it forms the graph of a QE, a parabola.

Hope this helps!

The parent function of f(x) = x^2 is the quadratic parent function.

We have given that,

f(x) = x^2

We have to determine the parent function of the given function.

Here the highest power of the x is 2.

We remember that the quadratic equation has the highest power is 2.

The standard form of a quadratic equation is ax^2+bx+c.

This includes x squared and when graphed it forms the graph of a quadratic equation is a  parabola.

We have given function is  f(x) = x^2

Therefore the value of the a,b and  c  are,

a=1

b=0 and c=0

Therefore, option C is correct.

The parent function of f(x) = x^2 is the quadratic parent function.

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Answer:

A

Step-by-step explanation:

(f-g)(x) means that the 2 functions are being subtracted.

[tex]3^{x}[/tex] +10x -(5x-3) =[tex]3^{x}[/tex] +10x-5x+3

simplify!

[tex]3^{x}[/tex] +5x+3

the answer is A

Answer:

4/5

Step-by-step explanation:

[tex]y=\dfrac{1}{3}x+\dfrac{11}{15} \\\\1=\dfrac{1}{3}x+\dfrac{11}{15}\\\\\dfrac{4}{15}=\dfrac{1}{3}x\\\\\dfrac{4}{5}=x[/tex]

Hope this helps!

Answer:

x=4/5

Step-by-step explanation:

y=1/3x+11/15

1=1/3x+11/15

4/15=1/3x

multiply both sides by 3

4/5=x

Answer:

H = 49.56 m

Step-by-step explanation:

We have,

A kite is flying in the air has a 91 ft string attached to it.

The angle of elevation of the kite is 57 degrees.

It is required to find the height of the kite. If we consider a right angled triangle, 91 ft is the hypotenuse. Let H is the height of the kite.

[tex]\cos\theta=\dfrac{H}{91}\\\\H=91\times \cos(57)\\\\H=49.56\ m[/tex]

Hence, the height of the kite is 49.56 m.

Answer:

Dear user,

Answer to your query is provided below

The value of f(10) using synthetic division is 396.

Explanation:

Cubic polynomials cannot be factorized by splitting the middle term. Quadratic polynomials can be factorized by splitting the middle term.

A cubic polynomial can have a maximum of three linear factors. To factorize a cubic polynomial, we first find a factor by hit and trial method or using factor theorem and reduce it into the product of a quadratic polynomial and a linear polynomial. The quadratic polynomial can then be factorized in linear factors.

The value of f(10) using synthetic division method is 396.

"The synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division."

The given function is:

f(x) = x³ – 7x² + 8x + 16

Therefore using synthetic division, we get:

(10)    | (1)    (- 7)       (8)      (16)

        |         (10)      (30)    (380)

        |............................................

                                        (396)

Therefore, f(10) = 396.

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Answer:

The probability that the three drivers would wear seat belts is 0.5

Step-by-step explanation:

Given

Percentage of drivers using seat belt = 80%

Number of drivers pulled over = 3

Required

Probability that all three drivers wore seat belt

First, the probability that a driver would wear seat belt has to be calculated.

Let's represent that with P(D)

P(D) is equivalent to the percentage of drivers using seat belt

[tex]P(D) = 80%[/tex]%

[tex]P(D) = \frac{80}{100}[/tex]

[tex]P(D) = 0.8[/tex]

Let the probability that the three drivers would wear seat belts be represented as P(All).

P(All) is calculated as thus;

(Probability that the first driver would wear seat belt) and (Probability that the second driver would wear seat belt) and (Probability that the first driver would wear seat belt).

Mathematically, this means

[tex]P(All) = P(D) * P(D) * P(D)[/tex]

Substitute [tex]P(D) = 0.8[/tex]

[tex]P(All) = 0.8 * 0.8 * 0.8[/tex]

[tex]P(All) = 0.512[/tex]

[tex]P(All) = 0.5[/tex] --- Approximated

Hence, the probability that the three drivers would wear seat belts is 0.5

Answer:

1

Step-by-step explanation:

Answer:

53.375 or 427/8 or 53 3/8

Step-by-step explanation:

To solve this you must find the area of both the carpet and the tiled floor. You use the equation area = length x width

Carpet: 10.5 x 7 = 73.5

Tile: 5.75 x 3.5 = 20.125

The you subtract the area of the tiled floor from the carpet

73.5 - 20.125 = 53.375

(I prefer to work in decimals but most of the time they want fraction answers so 53.375 = 427/8 = 53 3/8

Answer:

77.98% probability that the height of a randomly chosen child is between 38.9 and 61 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 54, \sigma = 8[/tex]

What is the probability that the height of a randomly chosen child is between 38.9 and 61 inches

This is the pvalue of Z when X = 61 subtracted by the pvalue of Z when X = 38.9. So

X = 61

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{61 - 54}{8}[/tex]

[tex]Z = 0.875[/tex]

[tex]Z = 0.875[/tex] has a pvalue of 0.8092

X = 38.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{38.9 - 54}{8}[/tex]

[tex]Z = -1.89[/tex]

[tex]Z = -1.89[/tex] has a pvalue of 0.0294

0.8092 - 0.0294 = 0.7798

77.98% probability that the height of a randomly chosen child is between 38.9 and 61 inches

Answer:

B (2.5, 0)

Step-by-step explanation:

2x - y = 5 (multiply all by 4)

8x- 4y = 20

-8x - 4y = - 20

eliminate the 4y

8x- 4y = 20

-8x - 4y = - 20

-------------------- –

16x = 40

x = 40/16 = 2.5

now we substitute x with 2.5

2x - y = 5

2(2.5) - y = 5

y = 0

Answer:

its B

Step-by-step explanation:

took the test