Fareed is making a rectangular garden in his backyard. He wants the length of the garden to be 5 feet longer tha
the width. Which type of function can Fareed write to model the possible areas of his garden?

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

Step-by-step explanation:

−UPDATE!! The answer is 1/3 so harray

Answer: 18.125 lbs

Explanation: The baby weighed 18.125 pounds at the end of eight months.

The baby weighed 7.25 lbs at birth. Eight months later, he weighed 2.5 or 2½ times its birth weight. Multiply 7.25 by 2.5  (which equals 18.125).

So now eight months later, he's 18.125 pounds.

Answer:

1.25 IB of sugar, 3.75 IB of water

Answer:

1.25lb of sugar , 3.75lb of water

Step-by-step explanation:

just trust me on this one :)

Answer:

Correct choice is 4, f(6) = 15

Step-by-step explanation:

f(6) means x = 6. If you look at the piecewise function, x = 6 meets the criteria for the second equation which is just 15. You need the first equation ONLY if x is less than 4.

Answer:

Option 4

The answer is 10.8

Step-by-step explanation:

5/6 = 9/c

5c = 9 × 6

5c = 54

5c/5 = 54/5

c = 10.8

Thus, The value of c is 10.8

5/6 = 9/c

5/6 = 9/10.8

0.833 = 0.833

Hence, L.H.S = R.H.S

-TheUnknownScientist 72

The graph of g(x) is a vertical stretch by a factor of 3/4 of the graph of f(x)

The formulas are given as

g(x) = 3/4x²

f(x) = x²

As a general rule of transformation, we have

g(x) = kf(x)

The above means that

The graph of g(x) is a vertical stretch by a factor of k of the graph of f(x)

By comparing

g(x) = kf(x) and g(x) = 3/4x²

We have

k = 3/4

Hence, the graph of g(x) is a vertical stretch by a factor of 3/4 of the graph of f(x)

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Answer:

The sample size is of 366.

Step-by-step explanation:

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

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The margin of error is of:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

A preliminary sample showed that 30.0% of the families in this sample own this company's product.

This means that \(\pi = 0.3\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The sample size that would limit the margin of error to be within 0.047 of the population proportion is:

This is n for which \(M = 0.047\). So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.047 = 1.96\sqrt{\frac{0.3*0.7}{n}}\)

\(0.047\sqrt{n} = 1.96\sqrt{0.3*0.7}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.047}\)

\((\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.047})^2\)

\(n = 365.2\)

Rounding up:

The sample size is of 366.

Answer:

Step-by-step explanation:

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer: 30%

Step-by-step explanation:

Given, Percent of families subscribe to the morning newspaper =  50%

Percent of families subscribe to the afternoon newspaper = 65%

Percent of families subscribe to at least one of the two newspapers. = 85%

Now, percentage of the families subscribe to both newspapers = % for morning newspaper  +   % for afternoon newspaper - % for at least one of the two newspapers

= (50+65 - 85) %

=  30 %

Hence, the percentage of the families subscribe to both newspapers = 30%

Hi there!

Answer:

2.5/5

Step By Step Explanation:

Given function:

Therefore, 2 3/15 rounded to the nearest half is 2.5/5.

Answer:

2

Step-by-step explanation:

:)

Answer:

-3x\4

Step-by-step explanation:

multiply the number 3x(-1/4)= -3/4x

the combine -3/4x to -3x/4

Answer:

Numbers are not right

.......

Answer:

2080

Step-by-step explanation:

Answer:

75 adults

Step-by-step explanation:

Let

x = number of children

y = number of adults

x + y = 200 (1)

9x + 18y = 2,475 (2)

From (1)

x = 200 - y

9x + 18y = 2,475

9(200 - y) + 18y = 2,475

1800 - 9y + 18y = 2,475

- 9y + 18y = 2,475 - 1800

9y = 675

y = 675/ 9

y = 75 adults

Substitute y = 75 into (1)

x + y = 200

x + 75 = 200

x = 200 - 75

x = 125 children

The maximum number of adults who could attend if the event fills the venue to capacity is 75

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Answer:

Step-by-step explanation:

Explicit

a_n = a1 * r^(n - 1)

Find r by dividing term (n)/(n - 1)

r = 250 / 50

r = 5

a_n = a * r^(n - 1)

Recursive

a_n = a_(n-1)*r

Try an example

Find a_6

a_6 = 2 * 5^(6 - 1)

a_6 = 2 * 5^5

a_6 = 2 * 3125

a_6 = 6250

recursive

a_n = a_(n - 1)*r

r = 5

n = 6

a_n = 1250 * 5

a_n = 6250

The explicit method looks a whole lot easier, but not for a machine made by Dell and programed by Microsoft. A computer doesn't really mind doing a whole lot of calculations that are repetitive. And in many cases recursive is easier to program and is faster.

Answer:

Step-by-step explanation:

The given sequence is exponential with a first term of a1 = 2 and a common ratio of r = 10/2 = 5.

The explicit equation for an exponential sequence is ...

  a(n) = a(1)×r^(n -1)

So, for the given parameters, the explicit equation is ...

  a(n) = 2×5^(n -1)

__

The recursive equation for any series defines the next term as a function of previous terms. For a geometric sequence the next term is the previous term multiplied by the common ratio. For this sequence, the recursive definition is ...

  a(1) = 2

  a(n) = 5×a(n-1)

Answer:

To find Diane's initial investment, we need to use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = 7,872.86 (final amount)

P = initial investment

r = 3.4% (annual interest rate)

n = 4 (number of times interest is compounded per year)

t = 20 (number of years)

We can now rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Plugging in the values, we get:

P = 7,872.86 / (1 + 3.4% / 4)^(4 * 20)

P = 7,872.86 / 1.008622^80

P = 7,872.86 / 1.854148

P = 4,228.44

So Diane's initial investment was $4,228.44.

Step-by-step explanation:

Answer:

the price although will be 47,926

Answer: 198 total people

Step-by-step explanation:

so there are 11 floors and each obtain 9 rooms so if there are two people in each of the 9 rooms there will 18 total people in one floor and since there are 11 floors multiply it by 18 to find out how many people live in the apartment.

11 * 18 = 198

Answer:

Lynn age: 7x+2. That's if you wanted an equation.

Answer:

x = { - 2, \(\frac{1}{4}\) }

Step-by-step explanation:

8x² + 7x = 4x² + 2 ( subtract 4x² from both sides )

4x² + 7x = 2 ( subtract 2 from both sides )

4x² + 7x - 2 = 0 ← in standard form

to factor

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 2 = - 8 and sum = + 7

the factors are + 8 and - 1

use these factors to split the x- term

4x² + 8x - x - 2 = 0 ( factor the first/second and third/fourth terms )

4x(x + 2) - 1(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(4x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ( subtract 2 from each side )

x = - 2

----------

4x - 1 = 0 ( add 1 to both sides )

4x = 1 ( divide both sides by 4 )

x = \(\frac{1}{4}\)

solutions are { - 2, \(\frac{1}{4}\) }

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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The total area of all exposed surfaces of a geometric solid is called surface area .

The area is the entire amount of space filled by flat or two-dimensional objects. In other words, the number of square units that cover the surface of a closed figure is used to represent its area.

It is quantified in square inches, or square units. The area only has length and width since 2-dimensional shapes can be measured using them.

The area is a two-dimensional measurement of the size of a flat surface, whereas surface area is a measurement of a solid shape's exposed surface (three-dimensional).

The main distinction between area and surface area is this. However, both amounts are expressed in square units, which is the same for both. Learn the distinction between area and volume as well.

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