Adam wants to plant flowers in a triangular plot. He has three lengths of plastic edging that measures 8 feet, 15 feet, and 17 feet. Determine whether these pieces fit for a right triangle. Explain.

a) The null hypothesis: H0: μ >= 1000

alternate hypothesis Ha: μ < 1000

b) The value of the test statistic is -3.12.

a) The null hypothesis, denoted by H0, is a statement of no difference or no effect. The alternate hypothesis, denoted by Ha, is a statement of a difference or effect that we want to test.

In this case, the null hypothesis would be that the average bulb life is greater than or equal to 1000 hours:

H0: μ >= 1000

The alternate hypothesis would be that the average bulb life is less than 1000 hours:

Ha: μ < 1000

where μ is the population mean bulb life.

b) To calculate the test statistic, we need to use the formula:

t = (x - μ) / (s / √(n))

where x is the sample mean, μ is the hypothesized population mean (under the null hypothesis), s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (950 - 1000) / (160 / √(30))

t = -3.12

Therefore, the value of the test statistic is -3.12.

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The area of the triangle is given as follows:

17 cm².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

Considering the image presented for this problem, the dimensions for the triangle are given as follows:

b = 5 cm, h = 6.8 cm.

Applying the multiplication of these dimensions, the area of the triangle is given as follows:

A = 0.5 x 5 x 6.8

A = 17 cm².

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a. The average rate of change for the temperature from 0 minutes to 20 minutes is 2.2.

b. The average rate of change for the temperature from 30 minutes to 60 minutes is 2.7.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function g(t) over the interval [0, 20]:

a = 20; f(a) = 140.3

b = 0; f(b) = 184.3

By substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (184.3 - 140.3)/(20 - 0)

Average rate of change = 44/20

Average rate of change = 2.2

Part b.

a = 30; f(a) = 109.3

b = 60; f(b) = 28.3

By substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (109.3 - 28.3)/(60 - 30)

Average rate of change = 81/30

Average rate of change = 2.7

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After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

The value of the car 4 years after it was purchased is  $16,270.86.

Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.

The equation that would be used to determine the value of car with the passage of time would be an exponential equation.

Value of the car after t years = [tex]p(1 -r)^{\frac{t}{3}[/tex]

Where:

Value of the car after 4 years  = [tex]41,000(1 -0.5)^{\frac{4}{3}[/tex] = $16,270.86

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Answer:

-0.5. is 5

Step-by-step explanation:

i need the poits

Answer:

5/12

Step-by-step explanation:

add 12 y to both sides:

5x = 24 + 12y

subtract 24 from both sides:

12y = 5x - 24

divide all by 12:

y = (5/12)x - 2.

slope is the number in front of x.

slope is (5/12).

There will be about 21 cm³ of empty space in the cylindrical container.

The formula for the volume of a sphere is V = (4/3)πr³ where r is the radius of the sphere. Since the diameter of each bouncy ball is 3 cm, the radius is 1.5 cm.

V = (4/3)π(1.5)³

= 14.13 cm³

The volume of three bouncy balls is 3 times this amount:

= 3 × 14.13

= 42.39 cm³

Since the diameter of each cylinder is 3 cm, the radius is 1.5 cm. We also know that the height of the cylinder is 9 cm, since each cylinder is 3 cm tall and there are three cylinders stacked on top of each other.

= π(1.5)^2(9)

= 63.62 cm³

Empty space = Vcontainer - Vtotal

= 63.62 - 42.39

= 21.23 cm³

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Answer: 30.6 km away

Step-by-step explanation:

The main thing this problem requires is Pythagoras' theorem. So set the problem up by marking the airport as (0,0) on a graph. Then move 19 units to the right, and 24 units down and make a point. Now you have the two short lengths of a right-angle triangle, so all that's left is to solve for the hypotenuse. So using the formula [tex]a^{2} + b^{2} = c^{2}[/tex] you would end up with [tex]19^{2} + 24^{2} =c^{2}[/tex]. Then you get: 361+576=[tex]c^{2}[/tex]

solve for c and you get about 30.6 km!

Hope this helps!

The perimeter of the field is 4x + 6/(x + 1)(x - 1).

Given that a field has a width of 5/x²-1 and the length is 2/x+1,

We need to find the perimeter,

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle,

Perimeter of a rectangle = 2(l+w)

= 2(5/x²-1+2/x+1)

= 2((2(x-1)+5)/(x + 1)(x - 1)

= 4x + 6/(x + 1)(x - 1)

Hence the perimeter of the field is 4x + 6/(x + 1)(x - 1).

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Answer:

Do you wish for the mistake to be pointed out? If so, can you please provide the dot plot so I can answer this question?

Step-by-step explanation:

Answer:

[-infinity, 4]

Step-by-step explanation:

-9x + 3 >= -33
-9x >= -36

x<=4 (sign switched because of dividing both sides by a negative integer in an inequality)
Therefore, x is less than or equal to 4

[ - infinity, 4]

The additional tax (liability) that Lynn owes after her employer withheld $3,150 from her pay is D. $399.

Tax liability refers to the amount that a taxpayer owes.

We can determine the tax liability as the difference between the total tax and the employer-withheld tax.

The total tax is computed by applying the rate to the taxable income, which is the difference between the total income and the total deductions.

Lynn's total income last year = $38,900

Total deductions = $11,450

Employer withheld taxes = $3,150

Taxable income = $27,450 ($38,900 - $11,450)

From the tax table, when taxable income is at least $27,450 but less than $27,500, the total tax is $3,549, based on being a head of household.

The tax liability = $399 ($3,549 - $3,150)

Thus, Lynn is expected to remit an additional $399 to settle her tax liability.

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(a) The distribution of X is X ~ N(130, 49)

(b) The probability that the average number of friends is less than 135 is 0.610

(c) The first quartile for the average number of friends is 96.925

(d) The assumption of normal distribution is necessary

Given that

Mean = 130

Standard deviation = 49

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(130, 49)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (135 - 130)/18

Evaluate

z = 0.278

So, we have

P = P(z < 0.278)

Evaluate

P = 0.60949

Approximate

P = 0.610

This is calculated as

Q₁ = Mean - 0.675 * Standard deviation

So, we have

Q₁ = 130 - 0.675 * 49

Evaluate

Q₁ = 96.925

Hence, the first quartile for the average friends for this sample size is 96.925

Yes, the assumption is necessary

This is because

The distribution has a sample size greater than 25 as required by the central limit theorem

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The value of f(2) is 40.5

The given function is f(x) = 1/x + 5[tex]x^3[/tex], and we need to find the value of f(2).

To do this, we substitute x=2 into the function and simplify:

f(2) = 1/2 + 5([tex]2^3[/tex])

= 1/2 + 5(8)

= 1/2 + 40

= 40.5

Therefore, the value of f(2) is 40.5.

The function f(x) has two parts: 1/x and 5[tex]x^3[/tex]. The first part of the function, 1/x, is a decreasing function that approaches zero as x gets larger. The second part of the function, 5[tex]x^3[/tex], is an increasing function that grows rapidly as x gets larger.

When we substitute x=2 in the function f(x), we get f(2) = 1/2 + 5([tex]2^3[/tex]) = 40.5. This means that at x=2, the value of the function is 40.5.

This result tells us that the function f(x) has a positive value at x=2. Moreover, since the second part of the function grows faster than the first part, the value of the function f(x) will increase as x gets larger. This means that as x increases, the value of f(x) will increase more and more rapidly.

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The magnitude of the complex number -10 + 24i is 26.

We have,

Complex numbers can be represented as a combination of a real number and an imaginary number, in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Now,

To find the magnitude of a complex number, we take the square root of the sum of the squares of its real and imaginary parts.

For -10 + 24i, the real part is -10 and the imaginary part is 24.

So the magnitude:

| -10 + 24i | = √((-10)^2 + (24)^2) = √(100 + 576) = √676 = 26

Therefore,

The magnitude of -10 + 24i is 26.

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After considering all the given data we conclude that the measure of m∠E is 54.46° under the condition that ADEF is a right angled triangle.

We already know that ADEF is a right angled triangle having sides EF = 6 and FD = 4, we can apply the Pythagorean theorem to evaluate the length of the hypotenuse AD.
AD = √(6² + 4²)
= √52)
≈ 7.21
Now we can apply the sine function to find the measure of angle E.
sin(E) = opposite/hypotenuse = EF/AD
E = arcsin(EF/AD)
≈ 54.46°
Therefore,  m∠E  ≈ 54.46°.
The Pythagorean Theorem is considered a fundamental relation in the context of Euclidean geometry comparing the three sides of a right triangle.
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Answer:

The correct answer is b) f^-1(n)= 4/-n-1 +1.

b

Step-by-step explanation:

I think parentheses are missing :

y = -4/(n-1)  - 1       switch n and y   then solve for y

n = -4/(y-1) - 1         add 1 to both sides of the equation

n+1 = - 4/(y-1)         multiply through by y -1

(y-1)(n+1) = - 4         divide through by (n+1)

y -1   = - 4/ (n+1)      add 1 to both sides

y = - 4/ (n+1 )  + 1     <=====this is the inverse function  y = -4/(n-1) -1

   equivalent to   4 / (-1-n)  + 1        by putting the ' - ' in the denominator

Step-by-step explanation:

x y^3 z^2      =   x^1  y^3  z^2  

                           the x   exponent is '1'

Ans4863

Step-by-step explanation:

The option that is not equivalent to x ¹⁸ is D. x ¹⁹

As a means to simplify option 1, we can incorporate the rule of multiplying two powers with an identical base to add their exponents. For instance, by doing x³ × x¹⁵ , we would end up with x¹⁸, which ultimately leads to x ¹⁸ as an equivalent result.

By applying the understood concept that when raising a power to itself,exponents must be multiplied together, option 2 becomes more understandable. Specifically, (x ² ) ⁹ = x ¹⁸,the same equivalence as x¹⁸.

Similarly, option 3 assimilates this approach; (x ⁶ ) ³ = x¹⁸,leading to x¹⁸ once again as an equal resonance.

In contrast, option 4, i.e., x¹⁹, comprises an exponent one higher than x¹⁸ and thus, is dissimilarly unequal in comparison.

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Options for this question are:

x³ × x¹⁵

(x²)⁹

(x⁶)³

x¹⁹

The area under the curve over [0, 1] is 15.75.

To find the Riemann sum, divide [0, 1] into n equal subintervals of width Δx = 1/n.

Using the right endpoint, c = iΔx = i/n. The Riemann sum is:

Σ[f(c)Δx] = Σ[(21(i/n) + 21(i/n)³)(1/n)] from i=1 to n.

To find the area under the curve, take the limit as n→∞:

Area = lim(n→∞) Σ[(21(i/n) + 21(i/n)³)(1/n)].

Find the answer by using the method of definite integration.

Area = ∫(21x + 21x³)dx from 0 to 1 = [10.5x² + 5.25x⁴] from 0 to 1 = 10.5(1)² + 5.25(1)⁴ - 0 = 15.75.

The area under the curve over [0, 1] is 15.75.

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The illustration of p - q and p + (-q) using a number line is added as an attachment

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

p - q

Also, we have

p + (-q)

The above expressions mean that

To add two numbers (positive and negative), we can start from a point p, and then count backwards on the number line in q terms

Using the above as a guide, we have the following:

The illustration using a number line is added as an attachment

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The required probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.

The probability that a student is taking calculus or French is calculated by adding the number of students taking calculus and the number of students taking French and then subtracting the number of students taking both calculus and French. This gives us the number of students taking either calculus or French. We then divide this number by the total number of students, which is 100.

So, the number of students taking either calculus or French is 27 + 26 - 13 = 40.

The probability that a student is taking either calculus or French is 40 / 100 = 0.40 = 40%.

Therefore, the probability that a student is taking calculus or French, rounded to two decimal places, is 0.40.

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The ordered pairs representing the amount of money left after playing variable number of games is :

(Number of games played, Amount of money left)

(0, 8)

(1, 6)

(2, 4)

(3, 2)

(4, 0)

Ordered pairs gives a tabular description of data as the values of two or more variables change.

Here, the amount Gabe has before playing a game is $8 and the cost per game is $2 .

Hence, the amount he has left decreases by $2 for every increase in number of games played.

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Answer:

113.1 in²

Step-by-step explanation:

A = 2πrh + 2πr²

r = 2 in

h = 7 in

A = 2π(2)(7) + 2π2² = 113.1 in²

$1356.52 is the cost price of the article.

To find the cost price of the article, we can utilize the concept of calculating the original amount based on a percentage increase.

Let's assume the cost price of the article is "x" dollars.

The trader gained a 15% interest, which means the selling price is 115% of the cost price. In other words, the selling price is 115% of "x".

To calculate the selling price, we can set up the following equation:

115% of x = 1560

To convert the percentage to a decimal, we divide it by 100:

1.15 * x = 1560

Now we can solve for x by dividing both sides of the equation by 1.15:

x = 1560 / 1.15

Using a calculator, we find:

x ≈ 1356.52

Therefore, the approximate cost price of the article is $1356.52.

This means that the trader purchased the article for around $1356.52 and then sold it for $1560.00, resulting in a 15% gain.

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