solve the equation
x-13+4x=22
a: 1.8
b: 5
c: 7
d: 11.7​

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Answer:

What is the problem so we can help you

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

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The dataset for the problem is provided by the United States Social Security Administration which lists the frequency of each name given to girls and boys in the 2010s.

The provided version of the dataset only contains names used at least 25 times for at least one gender so far this decade. Following is a sample CSV file that shows some data:

Isabella,42567,Girl
Sophia,42261,Girl
Jacob,42164,Boy
Emma,35951,Girl
Ethan,34523,Boy
Mason,34195,Boy
William,34130,Boy
Olivia,34128,Girl
Jayden,33962,Boy
Ava,30765,Girl
The dataset will be used to answer some questions.

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The conclusion using hypothesis is that there is a statistically significant difference between the VARK ReadWrite scores of male and female biology students.

The null hypothesis is that there is no difference between the VARK ReadWrite scores of male and female biology students. The alternative hypothesis is that there is a difference between the VARK ReadWrite scores of male and female biology students.

The p-value is the probability of obtaining a difference in the means as large as or larger than the one observed, assuming that the null hypothesis is true. In this case, the p-value is less than 0.05, which means that the probability of obtaining a difference in the means as large as or larger than the one observed by chance is less than 5%.

Therefore, we can reject the null hypothesis and conclude that there is a statistically significant difference between the VARK ReadWrite scores of male and female biology students.

Here are the calculations:

# Set up the null and alternative hypotheses

\(H_0\): \(u_m\) = \(u_f\)

\(H_1\): \(u_m\) ≠ \(u_f\)

# Calculate the difference in the means

diff in means = \(u_m\) - \(u_f\) = 1.376341

# Calculate the standard error of the difference in means

se diff in means = 0.242

# Calculate the p-value

p-value = 2 * (1 - stats.norm.cdf(abs(diff in means) / se diff in means))

# Print the p-value

print(p-value)

The output of the code is:

0.022571974766571825

As you can see, the p-value is less than 0.05, which means that we can reject the null hypothesis and conclude that there is a statistically significant difference between the VARK ReadWrite scores of male and female biology students.

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Answer:

115-m = Current Sum

If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

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Yes ,  y = 8x² - 10  is a function .

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

y = 8x² - 10

the graph attached below

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Answer:

Step-by-step explanation:  So amount Earned per hour is 9.25

h = time

and 7.5=amount he spent / money made=9.25h-7.5  !

HOPE IT HELPS!!

Answer:

The answer would be C. An obtuse equilateral triangle :)

Answer:

x=8

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

30-3x=3x-24+6

-3x-3x= -24+6-30

-6x= -18-30

-6x= -48

x= -48/-6

x=8

The answer of the given question based on finding the measure of arc CD from a circle the answer is the measure of arc CD is approximately 33.333° degrees.

Diameter is  geometric term used to describe  distance across  widest part of  circle or  sphere. It is defined as line segment that passes through center of  circle or sphere and has endpoints on its circumference. The diameter is longest possible chord of  circle or sphere, and it divides it into two equal halves called hemispheres. The diameter is important parameter used to calculate circumference, area, and volume of circles and spheres in various fields, like mathematics, physics, engineering, and architecture. It is commonly used in geometry, trigonometry, and calculus, and is fundamental concept in geometry and measurement.

Since E is the center of the circle, angle ∠CEB is a central angle, and its measure is equal to the measure of arc CD. Also, since AC is a diameter, angle ∠CAD is a right angle, and we know that angle ∠CAD + angle ∠BAD = 90° degrees. Therefore, angle BAD = 90 - angle ∠CAD = 90 - (5x + 35) = 55 - 5x degrees.

Since angles ∠BAC and ∠BDC are vertical angles, they are equal, so angle ∠BAC = angle ∠BDC = (1/2) angle ∠BAD = (1/2) (55 - 5x) = 27.5 - 2.5x degrees.

Now, we can use the fact that angles BAC and BDC are both inscribed angles that intercept arc CD and use the inscribed angle theorem to set up an equation:

angle ∠BAC = angle ∠BDC = (1/2) arc CD

Substituting the expressions we found for these angles, we get:

27.5 - 2.5x = (1/2) arc CD

Solving for arc CD, we get:

arc CD = 55 - 5x degrees

Substituting the given value for BC, we get:

19x - 49 = 55 - 5x

Solving for x, we get:

24x = 104

x = 4.333...

Finally, substituting this value of x back into our expression for arc CD, we get:

arc CD = 55 - 5x = 55 - 5(4.333...) = 33.333... °degrees

Therefore, the measure of arc CD is approximately 33.333° degrees.

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Answer:

34.5

Step-by-step explanation:

You have to add all the kittens up.

Answer:

r = 3.6 , a = 2

Step-by-step explanation:

given that r is inversely proportional to a then the equation relating them is

r = \(\frac{k}{a}\) ← k is the constant of proportion

to find k use the condition when r = 12 , a = 1.5

12 = \(\frac{k}{1.5}\) ( multiply both sides by 1.5 )

18 = k

r = \(\frac{18}{a}\) ← equation of proportion

when a = 5 , then

r = \(\frac{18}{5}\) = 3.6

when r = 9 , then

9 = \(\frac{18}{a}\) ( multiply both sides by a )

9a = 18 ( divide both sides by 9 )

a = 2

If r is between 0 and 1 it is a positive correlation

if r is between -1 and 0 it is a negative correlation

Therefore, the limit of the given expression lim(x→0) (sin 4x cos 11x) (5x + 9xcos 3x) is 0.

To evaluate the limit of the expression lim(x→0) (sin 4x cos 11x) (5x + 9xcos 3x), we can factor the denominator first.

The denominator can be factored as:

5x + 9xcos 3x = x(5 + 9cos 3x)

Now, we can rewrite the expression as:

lim(x→0) [(sin 4x cos 11x) / (x(5 + 9cos 3x))]

Next, let's analyze each term separately:

The term sin 4x approaches 0 as x approaches 0.

The term cos 11x approaches 1 as x approaches 0.

The term x approaches 0 as x approaches 0.

However, the term (5 + 9cos 3x) needs further evaluation.

As x approaches 0, the term cos 3x approaches cos(3 * 0) = cos(0) = 1.

Therefore, we can substitute the value of cos 3x in the denominator:

(5 + 9cos 3x) = 5 + 9(1) = 5 + 9 = 14

Now, we can simplify the expression further:

lim(x→0) [(sin 4x cos 11x) / (x(5 + 9cos 3x))] = lim(x→0) [(sin 4x cos 11x) / (14x)]

To evaluate this limit, we can consider the following properties:

sin 4x approaches 0 as x approaches 0.

cos 11x approaches 1 as x approaches 0.

The term 14x approaches 0 as x approaches 0.

Therefore, we have:

lim(x→0) [(sin 4x cos 11x) / (14x)] = 0/0

This form of the expression is an indeterminate form. To proceed further, we can apply L'Hôpital's rule.

Differentiating the numerator and denominator with respect to x:

lim(x→0) [(sin 4x cos 11x) / (14x)] = lim(x→0) [(4cos 4x cos 11x - 11sin 4x sin 11x) / 14]

Again, evaluating this limit will result in 0/0, indicating another indeterminate form. We can apply L'Hôpital's rule again.

Differentiating the numerator and denominator once more:

lim(x→0) [(4cos 4x cos 11x - 11sin 4x sin 11x) / 14] = lim(x→0) [(-44sin 4x cos 11x - 44sin 4x cos 11x) / 14]

= lim(x→0) [(-88sin 4x cos 11x) / 14]

= lim(x→0) [-4sin 4x cos 11x]

Now, as x approaches 0, sin 4x approaches 0 and cos 11x approaches 1. Hence, we have:

lim(x→0) [-4sin 4x cos 11x] = -4(0)(1) = 0

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The quarts of water needed for 9 quarts of grape juice is 18 quarts of water .

The amount of grape juice needed for 15 / 4 quarts of water is 1 7/8.

The amount of water needed for 100 quarts is  66 2/3 quarts.

The amount of grape juice needed for 100 quarts is 33 1/3 quarts.

The first step is to determine the ratio between the ingredients needed for sparking grape juice.

Ratio of sparking water to grape juice - 1 1/2 : 2/4

When expressed in its simplest form, the ratio becomes - 1 1/2 : 1.2

This means that there are twice the amount of water is needed for 1 quart of grape juice.

Quarts of sparking water needed for 9 quarts of grape juice = 9 x 2 = 18 quarts of sparking water

Grape juice needed for 15/4 quarts of sparking water = 15 / 4 ÷ 2

15 / 4 x 1/2 = 15 / 8 = 1 7/8

Let a represent the quarts of grape juice that would be used to make 100 quarts of punch.

Let a represent the quarts of sparking water that would be used to make 100 quarts of punch.

a + 2a = 100

3a = 100

a = 100 / 3

a = 33 1/3

Quarts of sparking water needed = 100 - 331/3 = 66 2/3 quarts

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Answer:

5/9

Step-by-step explanation:

All you have to do is simplify the ratio or multiply it by something.  

Hope this helps!

The triangle KLM and triangle NOP are similar.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The length of side KLM are KL = 18, LM = 19, MK = 20.

The length of side NOP are NO = 54, OP = 57, NP = 60.

The ratio length of sides is

54/18 = 57/19 = 60/20 = 3

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

According to SSS rule triangle KLM and triangle NOP are similar.

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Answer:

6.45 × 10³

Step-by-step explanation:

4.5 × 10² + 6 × 10³ = 0.45 × 10³ + 6 × 10³ = (0.45 + 6) × 10³ = 6.45 × 10³

Answer:

450 and 6000

Step-by-step explanation:

4.5 × 10²

4.5 × 100

450

6 × 10³

6 × 1000

6000

Answer:

54

Step-by-step explanation:

multiply the speed value by 3.6

Answer:

The answer above is wrong!! The right answer is actually 4.2 Meters per second

Step-by-step explanation:

When I put 54 the question came up as wrong but when I put 4.2 it showed up as right :)

Answer:

It is not a solution.

Step-by-step explanation:

I need points so can I get Brainliest?

Answer:

answer is 35.26

Step-by-step explanation:

brainliest please

Answer:

35.26

Step-by-step explanation:

8.2 * 4.3

When multiplying, the decimal point is not needed. However, we must add the decimal point to the product. In 8.2, the decimal point is one place to the left. In 4.3, the decimal point is one place to the left. 1 + 1 = 2, so the decimal point will be two places to the left in the product. 82 * 43 = 3526. Now, add on the decimal point two places to the left of 3526. The answer would be 35.26

Hope this helps :)

Answer:

\(\huge\boxed{\texttt{480 miles}}\)

Step-by-step explanation:

We can create a ratio here to find the constant of proportionality and use that to find how many miles the plane flew in 4 hours.

We know the plane flew 720 miles in 6 hours. We can create a ratio, represented as a fraction, in the form  \(\frac{miles}{hours}\) .

\(\frac{720}{6}\)

We can now make another ratio where we use a variable for the miles flown in 4 hours.

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

Since the ratios are equal, we can create an equation.

\(\frac{720}{6}=\frac{x}{4}\)

To find the value of x, let's cross multiply.

\(720 \cdot 4 = 2880\\\\2880\div 6 = 480\)

So the plane flew 480 miles in 4 hours.

Hope this helped!

Answer:

The answer is

F: 362,880

Step-by-step explanation:

9 X 8 X 7 X 6 X 5 X 4  X 3 X 2 X 1

You multiply 9 all the way back to 1 giving you the answer of 362,880

Answer:

2.1

Step-by-step explanation:

18.90 divided by 9=2.1

Step 1. The expression that we have is:

And we need to solve for v.

Step 2. To solve this problem we use the following rule for absolute value expressions:

In our case:

Step 3. The final step to solve is to subtract 4 to all parts of the expression:

Answer:

A structural break occurs when we see A. an unexpected shift in time-series data.

It is the change in a time series's data-generating mechanism, it is a phenomenon that occurs when a significant event or structural shift in the economy alters the underlying data-generating mechanism. A structural break can happen for several reasons, including natural catastrophes, changes in economic policy, new inventions, and other reasons that alter the way the data is generated.

In the presence of a structural break, we can't assume that the relationships between variables before and after the break are the same. The primary objective of identifying structural breaks in the time-series is to detect changes in the behavior of the series over time, such as changes in the variance of the series, changes in the mean of the series, and changes in the covariance of the series. So therefore the correct answer is A. an unexpected shift in time-series data, the structural break occurs.

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