In 2006, \( 10.5 \% \) of all live births in the United States were to mothers under 20 years of age. A ociologist claims that births to mothers under 20 years of age is decreasing. She conducts a simple random sample of 134 births and finds that 11 of them were to mothers under 20 years of age. Test the sociologist's claim at the \( \alpha=0.01 \) level of significance.

Given the equation:

Let's assume the denominators are non zero and k is n integer.

Let's find the value of k.

First multiply both sides by the denominator by the left.

Simplify the right side by factoring out x in the parentheses:

Cancel common factors:

Solving further:

Apply distributive property on the left

Divide both sides by x³:

ANSWER:

C. -6

Answer: 8y

Step-by-step explanation:

The values needed to find the length AB will be;

⇒ AB = √(3x)² + (- 8y)²

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The coordinate are,

⇒ A = (- 5x, 4y)

⇒ B = (- 2x, - 4y)

Now,

Since, We know that;

The distance between the points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

So, The distance between the points (- 5x, 4y) and (- 2x, - 4y) is,

⇒ d = √ (- 2x - (- 5x))² + (- 4y - 4y)²

⇒ d = √(3x)² + (- 8y)²

Thus, The values needed to find the length AB is find as;

⇒ AB = √(3x)² + (- 8y)²

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The relation y = (7/8)x is proportional in nature.

In mathematics, two sets of numbers, often experimental data, are proportional- directly or inversely, if their corresponding elements have a constant ratio. This ratio is called the coefficient of proportionality or proportionality constant.

Here, we are given a relation between x and y as follows-

y = (7/8)x

dividing both sides by x we get-

y/x = 7/8

Thus, we see that the ratio y : x will always be equal to 7 : 8. In other words, x and y have a constant ratio. Here, the proportionality constant between x and y is 7 : 8.

This means that they are proportional in nature.

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Answer:

\( - 12288 \div {2}^{11} = - 6 \\ forth \: answer \: is \: correct\)

Answer:

4th option

Step-by-step explanation:

The nth term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

To find a₁ use a₁₂ = - 12288 , then

a₁ \((2)^{11}\) = - 12288 , that is

a₁ × 2048 = - 12288 ( divide both sides by 2048 )

a₁ = - 6

Then the explicit formula is

\(a_{n}\) = - 6 . \(2^{n-1}\)

For safety reasons \theta should not be greater than 70 and with the current scenario\theta= 79.52

the ladder will not be safe at this height

\theta= 79.52

Question Parameters:

Joshua has a ladder that is 18 ft long.

He wants to lean the ladder against a vertical wall so that the top of the ladder is 17.7 ft

Generally the equation for the angle ABC is mathematically given as

Let ∠ABC = \theta

In the right angle triangle ACB,

Hence

sin ∠ABC  = AC / AB

sin \theta = 17.7 / 18

\(\theta = sin-1 (17.7 / 18)\\\\\theta = 79.52\)

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The correct value is f(x) = `(7/4)x^2 + 9sin(x) - 9cos(x) + 2`.

Given: The second derivative of function is `f''(x) = 7x + 9sin(x)`

Initial condition: `f(0) = 2` and `f'(0) = 3`

using the given initial condition:`f''(x) = 7x + 9sin(x)`

Integrating both side, we get:`f'(x) = (7/2)x - 9cos(x) + C1`

Using the initial condition `f'(0) = 3` we get:3 = 0 + C1C1 = 3

Integrating again both side, we get:`f(x) = (7/4)x^2 + 9sin(x) - 9cos(x) + C2`

Using the initial condition `f(0) = 2` we get:2 = 0 + C2C2 = 2

Therefore, the value of the given differential equation is `f(x) = (7/4)x^2 + 9sin(x) - 9cos(x) + 2`

So, the value of `f(x)` is `(7/4)x^2 + 9sin(x) - 9cos(x) + 2`.

Hence, the correct value is f(x) = `(7/4)x^2 + 9sin(x) - 9cos(x) + 2`.

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Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

To find the mass of the surface lamina s with density 2x + 3y + 6z = 12 in the first octant, we need to integrate the density function over the surface.

The surface lamina is defined by the equation z = x^2 + y^2 and is bounded by the coordinate planes and the cylinder x^2 + y^2 = 1 in the first octant.

The mass of the surface lamina can be calculated using the surface integral:

M = ∬s ρ dS

where ρ is the density and dS is the surface area element.

The surface area element in cylindrical coordinates is given by:

dS = √(r^2 + (dz/dθ)^2) dθ dr

Substituting the parameterization and the density into the integral, we have:

M = ∫∫s (2r cosθ + 3r sinθ + 6r^2) √(r^2 + (dz/dθ)^2) dθ dr

Now, we need to determine the limits of integration. Since the surface lamina is in the first octant, we can set the limits as follows:

θ: 0 to π/2

r: 0 to 1

z: 0 to r^2

Finally, we can evaluate the integral:

M = ∫[0 to π/2] ∫[0 to 1] (2r cosθ + 3r sinθ + 6r^2) √(r^2 + (dz/dθ)^2) dr dθ

Simplifying further:

M = ∫[0 to π/2] [(3/7) + (2/3) cosθ + (3/4) sinθ]√2 dθ

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Yes, two samples can have the same range but different means. The range of a dataset is a measure of the spread or dispersion and is determined by the difference between the maximum and minimum values. The mean, on the other hand, represents the average value of the dataset.

To illustrate this concept, let's consider two different samples:

Sample 1: 1, 5, 6, 9, 10

Sample 2: 2, 4, 7, 8, 10

Both samples have a range of 9 (10 - 1).

However, the means of the samples are different. The mean of Sample 1 is

(1 + 5 + 6 + 9 + 10) / 5 = 6.2,

while the mean of Sample 2 is

(2 + 4 + 7 + 8 + 10) / 5 = 6.2.

Despite having the same range, the means differ between the two samples.

The range only considers the extreme values of the dataset, whereas the mean takes into account all values and provides an average measure. It is possible for the individual values within the samples to be distributed differently, resulting in different means, even if the range remains the same.

Therefore, the range and the mean are distinct measures that capture different aspects of the dataset. While it is possible for two samples to have the same range, they can still have different means based on the specific values and their distribution within each sample.

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The total percent of decrease in price of the shares of Selena's stock which Selena first buys and then sold is 11.5 percent.

Percentage decrease in a number is the ratio of total decrease in the original value of a number to the decreased value in the percentage form.

Given information-

The total stock buy by the Selena in $32.

The total stock sold by the Selena in $28.32.

As the total stock buy by the Selena in $32, and the total stock sold by the Selena in $28.32. Thus the total decrease in the price of stock is,

\(C_s=32-28.32\\C_s=3.68\)

Thus the total decrease in the price of stock is $3.68.

As the cost price of the stock is $32 and the total decrease in the price of stock is $3.68. Thus the total percent of decrease in the price of the stock is,

\(\Delta C_s=\dfrac{3.68}{32}\times100\\\Delta C_s=11.5\)

Thus the total percent of decrease in the price of the stock is 11.5 percent.

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y > x - 3

y > x - 1

The above system of inequalities was given from the question

Firstly, we will need to graph the system of inequalities

y > x - 3

Change the inequality sign to equality sign

The equation becomes

y = x - 3

To find y, let x = 0

y = 0 - 3

y = -3

To find x, let y = 0

0 = x - 3

Make x the subject of the formula

0 + 3 = x

x = 3

For the system of inequality, y > x - 3

The points is (3, -3)

For the second system of inequality

y > x - 1

Change the inequality ss

Answer:

6.3/2.5=2.52

Step-by-step explanation:

Answer:

2.52

Step-by-step explanation:

Answer:

Explanation:

Answer:

18 miles driven in a week

Step-by-step explanation:

The dimensions of the rectangle are 7 feet by 9 feet.

Let's use algebra to solve this problem.

Let x be the width of the rectangle in feet. Then, according to the problem, the length of the rectangle is 2 feet longer than the width, or x + 2 feet.

The area of a rectangle is given by the formula\(A = length x width.\) So, we can write:

A = (x + 2) x x

Simplifying this expression, we get:

A = x^2 + 2x

We know from the problem that the area of the rectangle is 63 square feet. So, we can substitute this value for A and solve for x:

63 = x^2 + 2x

Rewriting this equation in standard form:

x^2 + 2x - 63 = 0

Now, we can use the quadratic formula to solve for x:

x = (-2 ± sqrt(2^2 - 4(1)(-63))) / (2(1))

x = (-2 ± sqrt(4 + 252)) / 2

x = (-2 ± sqrt(256)) / 2

x = (-2 ± 16) / 2

x = -9 or x = 7

Since the width of the rectangle cannot be negative, we reject the solution x = -9. Therefore, the width of the rectangle is 7 feet.

The length of the rectangle is 2 feet longer than the width, or x + 2 = 7 + 2 = 9 feet.

So, the dimensions of the rectangle are 7 feet by 9 feet.

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\(\lim \limits_{x \to 1} \sqrt{51 -2x}\\\\=\sqrt{51 -2 (1)}\\\\=\sqrt{51-2}\\\\=\sqrt{49}\\\\=7\)

To determine the t-statistic for determining the significance of the relationship between the midterm score and grade on the final exam, we need information as the sample size (n) and the degrees of freedom (df).

Without these values, we cannot calculate the exact t-statistic.

However, the t-statistic is typically calculated using the formula t = r * sqrt((n-2)/(1-r^2)), where r is the correlation coefficient and n is the sample size. In this case, the correlation coefficient is 0.30.

The t-statistic measures the strength and significance of the relationship between the variables. A larger t-value indicates a stronger relationship and a higher likelihood of statistical significance.

To determine whether the relationship is significant, we compare the calculated t-value to the critical value from the t-distribution for the given degrees of freedom.Without the specific values for sample size and degrees of freedom, we cannot provide the exact t-statistic in this case.

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Answer:

12 batches

Step-by-step explanation:

Total cups of flour = 1 1/2

Flour used per batch = 1/8 cups

What is the maximum number of times (batches) Steve can complete the recipe?

Maximum batches Steve can make = Total cups of flour / Flour used per batch

= 1 1/2 ÷ 1/8

= 3/2 ÷ 1/8

= 3/2 × 8/1

= (3*8) / (2*1)

= 24 / 2

= 12 batches

Maximum batches Steve can make = 12 batches

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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Answer:

We need to see the graph in order to solve this.

Step-by-step explanation:

No graph

By using the concept of maxima, it can be calculated that

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

What is maxima of a function?

Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.

Let the length of the rectangle be l m and width of the rectangle be w m

Perimeter (P) = 2(l + w)

By the problem,

2(l + w) = 72

l + w = \(\frac{72}{2}\)

l + w = 36

w = 36 - l

Area (A) = l \(\times\) w

A = l \(\times\) (36 - l) = \(36l - l^2\)

Differentiation with A with respect to l

\(\frac{dA}{dl} = 36 - 2l\)

For maximum area,

\(\frac{dA}{dl} = 0\)

36 - 2l = 0

2l = 36

l = \(\frac{36}{2}\)

l = 18 m

\(\frac{d^2A}{dl^2} = -2 < 0\)

Hence area is maximum

w = 36 - 18 = 18 m

Length of the  rectangle of perimeter 72 m with maximum area is 18 m

Breadth of the  rectangle of perimeter 72 m with maximum area is 18 m

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According to the question, the closing balance for quarter 2 is £82,750.

A quarter is one fourth of a year. It is typically a three month period, usually consisting of January, February, and March; April, May, and June; July, August, and September; or October, November, and December. The terms of a quarter can vary depending on the context. For example, in the United States, quarters are commonly referred to as “fiscal quarters,” and begin on the first day of October, January, April, and July. In this case, each quarter covers a three-month period.

Inflows for quarter 2: 540,000 x 1.075 = £581,000

Outflows for quarter 2: 495,000 x 1.05 = £519,250

Closing balance for quarter 2:

Opening balance + Inflows - Outflows =

20,000 + 581,000 - 519,250 = £82,750

Therefore, the closing balance for quarter 2 is £82,750.

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The probability that a randomly selected dinner bill will be at least $39.10 is approximately 0.0322.

a. The random variable in this case is the amount of money spent on dinner bills in the local restaurant on a daily basis.

b. To find the probability that a randomly selected bill will be at least $39.10 To do this, we can use the formula  z = (x - μ) / σ

Where

Substituting the values, we get:

z = (39.10 - 28) / 6

z = 1.85

We need to find the probability of getting a z-score of 1.85

The probability can be determined by using a conventional normal distribution table and is as follows:

P(z > 1.85) = 1 - P(z < 1.85) = 1 - 0.9678 = 0.0322

Therefore, the probability that a randomly selected dinner bill will be at least $39.10 is approximately 0.0322.

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The most common type of observational study is a Survey.

Observe the change in behavior of the independent variable. Don't add prejudice. Use surveys to get information about variables.

In the study, the independent variable is observed only for its behavior. Variables naturally exhibit variation. Researchers must not be biased when conducting research. Fundamentally, surveys help us obtain information about social parameters.

Step: 1

An experiment is a well-planned study of any particular cause and effect relationship between variables of interest. A debate is the form of discussion in which a conclusion is to be summarized at last. The statistical inference is a very crucial subject involving the predictions about population parameters based on sample statistics. The survey is the method of collection of information on variables which are not under the control of the experimenter.

The analysis defines various terminologies intermixed with the right answer to the question of interest.

Step: 2

An observational study is mostly conducted in the form of questionnaire. The questionnaire involves question regarding the issue to be studied. The most common type of observational study is a Survey.

Most of the observational studies are carried out in the form of surveys.

The most common type of observational study is a Survey.

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Answer: 3/4ths of an hour.

Step-by-step explanation:

So we know he grows 2/3rd of a mile in half an hour, but we want to find the time to grow 1 mile at his current rate.

Let's make a ratio of miles to hours

2/3 : 1/2

4 : 3

1: 3/4

So, he can grow 1 mile in 3/4ths of an hour.

Answer:

B

Step-by-step explanation:

because  when simplified we get b

Answer:

Step-by-step explanation:

\( {x}^{2} - 4x - 12 \\ {x}^{2} + 2x - 6x - 12 \\ x(x + 2) - 6(x + 2) \\ (x - 6)(x + 2) \\ \)

Lladones had 594 pages of notes left after giving away 155 pages.

To solve this problem, we will use the given information to set up a system of equations and solve for the remaining pages of notes Lladones has left.

Let A represent the initial number of pages of notes Asister had, and L represent the initial number of pages of notes Lladones had. We know that they both had the same number of notes in the beginning, so:

A = L

After Asister gave away 650 pages of notes and Lladones gave away 155 pages of notes, we know that Lladones had 6 times as many pages left as Asister. So we can represent this with the equation:

L - 155 = 6(A - 650)

Now, substitute A with L from the first equation:

L - 155 = 6(L - 650)

Next, simplify and solve for L:

L - 155 = 6L - 3900
3900 - 155 = 6L - L
3745 = 5L
L = 749

Now that we have the initial number of pages Lladones had, we can find out how many pages Lladones had left after giving away 155 pages:

Lladones left = L - 155 = 749 - 155 = 594

So, Lladones had 594 pages of notes left after giving away 155 pages.

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Answer:

I'm not sure, but it looks like there is just one invariable point (3,3)

Step-by-step explanation:

Answer:

How would you represent the expression "any position"?

Step-by-step explanation:

Answer:

I don't know what's I don't know I'm really sorry very very very very very very very very very very very very sorry very sorry