A rectangular park measuring 32 yards by 24 yards is surrounded by a trail of uniform width. If the area of the park and the trail combine is 1748 square yards, what is the width of the park

Answer:

line passes through the vertex

Step-by-step explanation:

f(x)=-3(x+2)^2+4

x=-2 it is the x of the vertex

Answer:  18 in²

Step-by-step explanation:

S(fig1)=32 in² . We know that the figures are similar and  the correspondonding sides are a1=12  and a2=9

So the coefficient of similarity is k=9/12=3/4

S(fig2)=S(fig1)*k²

S(fig2)=32*(3/4)²=32*9/16=18 in²

The solution is A = 18 inches²

The proportion relation is given by k = 3/4 and the value of A = 18 inches²

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A

Now , the constant of proportionality be k

From the figures , the two figures are similar

Constant of proportionality k = ( side of first figure / side of second figure)

k = 9/12

k = 3/4

Now , the area of the first figure A = 32 ( k )²

On simplifying the equation , we get

A = 32 ( 3/4 )²

A = ( 32 x 9 ) / 16

A = 2 x 9

A = 18 inches²

Therefore , the value of A is 18 inches²

Hence , the proportion is A = 18

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Answer:

[tex] P(X=8)[/tex]

And using the probability mass function we got:

[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=20, p=1-0.42=0.58)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=8)[/tex]

And using the probability mass function we got:

[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]

The probability of exactly eight successful trials is 0.0486 and this can be determined by using the formula of the probability mass function.

Given :

According to the binomial distribution, the probability mass function is given by:

[tex]\rm P(X) = \; (^nC_x )(p^x)(1-p)^{n-x}[/tex]

where the value of n is 20 and the value of (p = 1 - 0.42 = 0.58).

Now, substitute the values of known terms in the above expression of probability mass function.

[tex]\rm P(X=8) = \; (^{20}C_8 )((0.58)^8)(1-0.58)^{20-8}[/tex]

Simplify the above expression in order to determine the probability of exactly eight successful trials.

P(X = 8) = 0.0486

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Answer: Albert is wrong

Step-by-step explanation:

You first have to subtract Plant B's measurement from Plant A's measurement.

3 7/8-2 1/4 => 3 7/8-2 2/8

If you solve it you get 1 5/8. Since it cannot be reduced this is the final answer.

Answer:

Step-by-step explanation

p - the price of pizza

c- the price of a bottle of coke

p = c+3.2

3p + c=19.4

3* (c+3.2)+c=19.4

3*c+3*3.2+c=19.4

3c+c+9.6=19.4

4c+9.6=19.4

-9.6 -9.6

4c=9.8

:4. :4

c=2.45

p=2.45+3.2=5.65

verify : 3*5.65+2.45=16.95+2.45=19.40

The length of the MK is 5 units if the length of MK = length of HK - length of HM.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

We have a number line shown in the picture.

From the number line:

Length of MK = Length of HK - length of HM

MK = 26 - 21

MK = 5 units

Thus, the length of the MK is 5 units if the length of MK = length of HK - length of HM.

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Answer:

75 %

Step-by-step explanation:

1500 - 375 =1125

So 1125 is spent on the gaming system

Take this over the total amount to get the decimal form

1125/1500 =.75

Change to percent form

75 %

Answer:

75%

Step-by-step explanation:

First we have to find the amount he is using for the gaming system which is

$1500 - $375 = $1125

Now we will express $1125 as a percentage of the total amount and we do that like this;

[tex]\frac{1125}{1500}[/tex] * 100%

= [tex]\frac{1125}{15}[/tex]

=75%

Answer:

24

Step-by-step explanation:

=> (-8)(-3)

So, Here is the rule for it => ( - )( - ) = ( + )

=> +24

Answer:

  (x, y, z) = (45°, 57°, 78°)

Step-by-step explanation:

The problem statement tells you ...

  x + y + z = 180

  -3x +y +z = 0

  0x -y +z = 21

__

Subtracting the second equation from the first gives ...

  4x = 180

  x = 45 . . . . . . divide by 4

Substituting this into the first equation and adding the third equation gives ...

  (45 +y +z) +(-y +z) = (180) +(21)

  2z = 156 . . . . simplify, subtract 45

  z = 78 . . . . . . divide by 2

  y = z -21 = 57

The angle measures are ...

  (x, y, z) = (45°, 57°, 78°)

Answer:

Step-by-step explanation:

The z-score corresponding to a given area of a distribution, is the number of standard deviations that the values in that area have/are from the mean.

In this case, we have a STANDARD normal distribution. In a standard normal distribution, the mean is 0 and the standard deviation is 1.

The Z-score corresponding to a given area, say the 30th percentile is

X = 0 + (-0.524)(1)

Hence, the X (number of values in the given percentile - in this case, 30th) is same as the z-table or z-calculator value for the 30th percentile in ANY normal distribution.

Answer:

We conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.

Step-by-step explanation:

We are given that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2.

Let [tex]\mu[/tex] = population mean score

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 29.5      {means that the students that took the Kaplan tutoring have a mean score less than or equal to 29.5}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 29.5      {means that the students that took the Kaplan tutoring have a mean score greater than 29.5}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean MCAT score = 32.2

            s = sample standard deviation = 4.2

            n = sample of students = 40

So, the test statistics =  [tex]\frac{32.2-29.5}{\frac{4.2}{\sqrt{40} } }[/tex]  ~  [tex]t_3_9[/tex]

                                    =  4.066

The value of t-test statistics is 4.066.

Now, at 0.05 level of significance, the t table gives a critical value of 1.685 at 39 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 4.066 > 1.685, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.

Answer:

9 - 4 1/2 = 4 1/2.

To calculate this you can do (9 - 4 - 1) + (1 - 1/2).

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▹ Answer

4 1/2 or 4.5

▹ Step-by-Step Explanation

[tex]9 - 4\frac{1}{2} \\= 9 - \frac{9}{2} \\Common denominator = 2\\\\\frac{18}{2} - \frac{9}{2} \\= \frac{9}{2} \\\\= 4 \frac{1}{2} or 4.5[/tex]

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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The answer is Ferris wheel, since it is a circular object and will display symmetry even when rotated.

Answer:

A. y=-2x-4

Step-by-step explanation:

The slope is negative when the line is going down from up.

Options B and D are wrong.

The y-intercept is (0, -4) as shown in the graph.

Option C is wrong.

y = mx + b

y = -2x - 4

Answer:

z-test.

Step-by-step explanation:

We want to perform an hypothesis test for a population mean.

In the case that the standard deviation of the population is known and the population distribution is normal, even if the sample is small, we will use a z-test.

The usual case is to not know the standard deviation of the population, in which case a t-test is adequate instead of a z-test, taking into account the degrees of freedom of the sample.

Answer:

[tex]\boxed{\sf \ \ \text{Jori is 42} \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's not J Jori's age

Pamela is 7 years older than Jori so here age is J + 7

The sum of their age is 91 so

J + ( J + 7 ) = 91

<=>

2J + 7 = 91  subtract 7

2J = 91 - 7 = 84  divide by 2

J = 84/2 = 42

So Jori is 42 and Pamela is 49

hope this helps

Answer:

  b = 64/a³

Step-by-step explanation:

Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.

Since a varies inversely as the cube root of b, we have ...

  a = k/∛b

Multiplying by ∛b lets us find the value of k:

  k = a·∛b = 1·∛64 = 4

Taking the cube of this equation gives ...

  64 = a³b

  b = 64/a³ . . . . . divide by a³

The value of b is ...

  b = 64/a³

Answer:

Mean increase or decrease (same quantity) according to the quantity of the increment or reduction

As all elements were equally affected the standard deviation will remain the same

Step-by-step explanation:

For the original set of salaries: ( In thousands of $ )

51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46

Mean = μ₀ = 47,92

Standard deviation  =  σ = 9,56

If we raise all salaries in the same amount  ( 5 000 $ ), the nw set becomes

56,58,53,67,39,39,56,58,53,35,67,56,51

Mean   =  μ₀´  = 52,92

Standard deviation  =  σ´ = 9,56

And if we reduce salaries in the same quantity ( 2000 $ ) the set is

49,51,46,60,32,32,49,51,46,28,60,49,44

Mean μ₀´´ = 45,92

Standard deviation  σ´´ = 9,56

What we observe

1.-The uniform increase of salaries, increase the mean in the same amount

2.-The uniform reduction of salaries, reduce the mean in the same quantity

3.-The standard deviation in all the sets remains the same.

We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the  data spread around the mean will be the same

Any uniform change in the data will directly affect the mean value

Uniform changes in values in data set will keep standard deviation constant

Answer:

Answer: (0.4356,0.4844)

Step-by-step explanation:

Use Ti 84

use function "1-PropZInt".

Enter x = 736

         n = 1600

         c= 0.95

Answer: (0.4356,0.4844)

Answer:

  2.908 s

Step-by-step explanation:

The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.

For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...

  h(t) = -16t² +v₀t +s₀

where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.

  0 = -16t² +65sin(44°) +4

Dividing by -16 gives ...

  0 = t^2 -2.82205t -0.2500

Using the quadratic formula, we find ...

  t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099

  t ≈ 2.90802

It will take about 2.908 seconds for the discus to reach the ground.

_____

Comment on the question

You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.

The table of the probability is missing, so i have attached it.

Answer:

μ = 0.919

The interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

Step-by-step explanation:

The expected value which is also called mean value is denoted by the symbol μ. It is defined as the sum of the product of each possibility x with it's probability P(x) as the formula;

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Thus, the interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

The interpretation of the mean of the random variable X is 0.919.

Here the interpretation should represent the average and it should be individual aged 15 years or more so it should be involved in 0.919 marriage.

Now the mean is

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Hence, The interpretation of the mean of the random variable X is 0.919.

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Answer:

t = 5.6 day

t =5 days 14 hours 24 minutes

Step-by-step explanation:

Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.

N = N•e(-kt)

N• = 25

K = 0.1229

Then

N = 25/2 = 12.5

The reason because at the half life , it's original value will decrease to half.

Let's solve for the half life t

N = N•e(-kt)

12.5 = 25e(-0.1229t)

12.5/25 = e(-0.1229t)

0.5 = e(-0.1229t)

In 0.5 =-0.1229t

-0.69314 = -0.1229t

-0.69314/-0.1229 = t

5.6399 = t

To the nearest tenth

5.6 days = t

Answer:

No, because one X value corresponds to two different y- values.

Step-by-step explanation:

Function has only one output for each input.

Hope this helps..

Good luck on your assignment..

Answer:

all real numbers greater than or equal to zero

Step-by-step explanation:

The domain of the real function f(x) = sqrt(x) is

all real numbers greater than or equal to zero

because when x < 0, then f(x) will become complex, which does not belong to a real function.

Answer:

the driver tried to fix it by lighting up the engine thinking it would start again. it didnt and the entire engine set on fire. the bus doors were closed and everyone was trapped inside. everybody inside burnt to a crisp as the fire spread and local residents heard their screams as their skin melted. the end...

Step-by-step explanation:

If they have the same shape, the red graph is a translation of the blue, which is given to be y=x^2.

Since the red graph stays on the y axis at two units above the blue (y=x^2) curve, therefore the red curve is given by y=x^2+2.

The equation of the red graph is f(x) = x² + 2.

Option B is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The graphs of f(x) = x² and f(x) = x² + 2 are both quadratic functions, which means they have a parabolic shape.

The graph of f(x) = x^2 is an upward-opening parabola with its vertex at the origin (0,0).

The parabola is symmetric about the y-axis and the x-axis.

The graph of f(x) = x² + 2 is also an upward-opening parabola, but it has been shifted upward by 2 units compared to the graph of f(x) = x².

This means that the vertex of the parabola has been shifted from (0,0) to (0,2).

Thus,

The equation of the red graph is f(x) = x² + 2.

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Answer:

16 square meters is equivalent to 19.14 square yards

Hope this helps you

Answer:

1.875

Step-by-step explanation:

To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.

In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:

[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]

[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]

[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]

Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:

[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]

[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]

[tex]E_2 = 1 + \frac{7}{8}[/tex]

[tex]E_2 = \frac{15}{8} = 1.875[/tex]