Miriam was testing � 0 : � = 18 H 0 ​ :μ=18H, start subscript, 0, end subscript, colon, mu, equals, 18 versus � a : � < 18 H a ​ :μ<18H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 18 with a sample of 7 77 observations. Her test statistic was � = − 1.9 t=−1.9t, equals, minus, 1, point, 9. Assume that the conditions for inference were met.

The columns of A are linearly independent if and only if A has n pivot columns.

Fill in the blank:

If A is an m x n matrix, then the columns of A are linearly independent if and only if A has n pivot columns.

Explanation:

A pivot column of a matrix A is a column that contains a pivot element in the row echelon form of A.

In other words, a pivot column is a column that has a leading non-zero entry in the row echelon form of A.

Suppose A is an m x n matrix with columns. [tex]a1, a2, ..., an[/tex].

If the columns of A are linearly independent, then there is no non-trivial solution to the equation. [tex]c1a1 + c2a2 + ... + cnan[/tex] [tex]= 0[/tex], where [tex]c1, c2, ..., cn[/tex]are not all zero.

This implies that the coefficient matrix.[tex][a1, a2, ..., an][/tex]has full rank n, and so the row echelon form of A has n pivot columns.

Tthe row echelon form of A has n pivot columns, then the coefficient matrix [a1, a2, ..., an] has full rank n.

This implies that the columns of A are linearly independent, because if there were a non-trivial linear combination of the columns of A that gave the zero vector, then the coefficient matrix would not have full rank n.

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Hence ,the surface area of the trapezoid is  173 [tex]ft^{2}[/tex] .

In geometry,  a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American and Canadian English, or a  trapezium in British and other  forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by  definition. The bases of the  trapezium are the parallel sides.

The amount  of space that a trapezoidal prism is surface takes up is known as its surface area. A three-dimensional solid called a trapezoidal  prism is composed of two  trapezoids on opposing faces connected by four  rectangles known as the lateral faces. You will learn how to determine the surface area of a trapezoidal prism, as with  all three-dimensional shapes.

We know that ,surface area of trapezoid is,

Surface Area= [tex]\frac{1}{2}[/tex] x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

In given figure,

∵ value of parallel sides is 10 ft and 13 ft ,

So, the sum of the lengths of the parallel sides= 10+13=23 ft

∵ perpendicular distance between parallel sides= 15 ft

∴ The Surface Area of trapezoid = [tex]\frac{1}{2}[/tex] x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

⇒The Surface Area of trapezoid = [tex]\frac{1}{2}[/tex] x 23 x 15

⇒The Surface Area of trapezoid = [tex]\frac{1}{2}[/tex] x 345

⇒The Surface Area of trapezoid = 172.5 [tex]ft^{2}[/tex] ≅ 173 [tex]ft^{2}[/tex]

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Answer:

66/5 or 13.2

Step-by-step explanation:

..........

The type of skewness that can be observed in an histogram are positive and negative skewness.

An histogram can display both positive and negative skewness.

A positive skew means that the tail of the histogram is longer on the positive side of the distribution, indicating that there are more data points with smaller values, and fewer data points with larger values.

A negative skew, on the other hand, means that the tail of the histogram is longer on the negative side of the distribution, indicating that there are more data points with larger values, and fewer data points with smaller values.Read more about histogram at

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Answer:

A byte is 8 bits.

The total quantity produced when p = 5 is 26 in the long run.

In the short run, each firm will produce where its marginal cost equals the market price, which we'll denote as p.

So, for Type A firms, the short-run supply curve is:

q4(p) = (p-2)/2

And for Type B firms, the short-run supply curve is:

qB(p) = (p-2)/6

The short-run market supply is simply the sum of the quantities supplied by each type of firm at a given price level. So, if there are 10 Type A firms and 6 Type B firms, the short-run market supply at a price level of p is:

Qs(p) = 10q4(p) + 6qB(p)

= 10(p-2)/2 + 6(p-2)/6

= 8p - 20

The total quantity produced when p=5, we can substitute p=5 into the market supply equation we just derived:

Qs(5) = 8(5) - 20

= 20

So, the total quantity produced when p=5 is 20.

The long run, firms can enter or exit the market, and as a result, the number of firms in each market may change.

In this case, we'll assume that the number of Type A and Type B firms can adjust freely in the long run, and that each firm earns zero economic profit in the long run.

If there are zero economic profits, each firm's total revenue (TR) must equal its total cost (TC), which means that price must equal average total cost (ATC).

For Type A firms, ATC4(q) = TC4(q)/q = 1/q + 2 + q, so:

5 = 1/q + 2 + q

Rearranging and solving for q, we get:

q4 = 2

So each Type A firm will produce 2 units of output in the long run.

For Type B firms, ATCB(q) = TCB(q)/q = 6/q + 2 + 3q, so:

5 = 6/q + 2 + 3q

Rearranging and solving for q, we get:

qB = 1

So each Type B firm will produce 1 unit of output in the long run.

If there are 10 Type A firms and 6 Type B firms, the total quantity produced in the long run when p=5 is:

Qlr = 10q4 + 6qB

= 10(2) + 6(1)

= 26

So, the total quantity produced when p = 5 is 26 in the long run.

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The surface area of the rectangular prism is 35.5 square feet.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The surface area of a rectangular prism is expressed as;

SA = 2lw + 2lh + 2wh

Where l, w, and h are the length, width, and height of the rectangular prism, and SA is the surface area.

Given that:

Length l = 2.5 ft

Width w = 1.5 ft

Height h = 3.5 ft

Substituting the given values, we get:

SA = 2lw + 2lh + 2wh

SA = 2(2.5 ft × 1.5 ft) + 2(2.5 ft × 3.5 ft) + 2(1.5 ft × 3.5 ft)

SA = 7.5 ft² + 17.5 ft² + 10.5 ft²

SA = 35.5 ft²

Therefore, the surface area is 35.5 ft².

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Answer:

Let's start by using algebra to represent the given information.

Let the son's current age be "s" and the mother's current age be "m". We know from the problem that:

m = 3s (the mother is 3 times as old as her son is now)

and

m - 14 = 10(s - 14) (fourteen years ago, the mother was 10 times as old as her son was then)

Now we can solve for the son's age:

m - 14 = 10s - 140 (distribute the 10)

m = 10s - 126 (add 14 to both sides)

3s = 10s - 126 (substitute m = 3s)

7s = 126

s = 18

Therefore, the son is currently 18 years old. To check this answer, we can use the first equation to find the mother's current age:

m = 3s = 3(18) = 54

So the mother is currently 54 years old, and 14 years ago the son was 4 years old and the mother was 40 years old, which is 10 times as old as the son.

Step-by-step explanation:

Answer:

Let's denote Sydney's age as S. According to the given information, Devaughn is 12 years younger than Sydney, so Devaughn's age would be S - 12.

The sum of their ages is 78, which can be expressed as:

S + (S - 12) = 78

Now we can solve this equation for S, which represents Sydney's age.

Simplifying the equation:

2S - 12 = 78

Adding 12 to both sides:

2S = 90

Dividing both sides by 2:

S = 45

So Sydney's age is 45 years.

Kendrick's basil plant is now 6 inches tall.

If the basil plant was originally 4 inches tall and grew to a height of 1 foot (12 inches), then its total growth is 12 - 4 = 8 inches.

If Kendrick then cuts off 6 inches from the plant, the new height of the plant is 12 - 6 = 6 inches.

Therefore, Kendrick's basil plant is now 6 inches tall.

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Answer:The term used for the $400 difference in Alex and Alecia's tax liability is known as the marriage penalty. Option C

The marriage penalty refers to the situation in which a married couple pays more taxes than they would if they were both single and filing separately. This penalty arises due to the progressive tax system in which the tax rate increases as the income increases. When two individuals with similar income levels get married and file jointly, their combined income puts them in a higher tax bracket, resulting in a higher tax liability.

In this case, Alex and Alecia's joint tax liability is $9,300, which is higher than the sum of their individual tax liabilities ($3,900 + $5,000 = $8,900). Therefore, they are paying an extra $400 due to the marriage penalty. This penalty can be significant for couples with similar incomes, as it can impact their financial planning and budgeting. However, there are also cases in which couples may benefit from the marriage tax advantage, such as when one spouse earns significantly less than the other.

Overall, it is essential for couples to understand their tax liability and to explore different filing options to determine the most advantageous one for their particular situation. Therefore option C is correct.

Step-by-step explanation:

Answer:

neither

$0

No

Step-by-step explanation:

The equation that represents the situation is 1/3x + 3/4(2/3x) + 4 = x, where x is the total distance. The athlete is planning to run a total distance of 24 miles.

Let x be the total distance the athlete is planning to run in three days. Then, the distance he plans to run on the first day is 1/3 of x, the distance he plans to run on the second day is 3/4 of the distance left after the first day, which is (2/3)x.

Finally, the distance he plans to run on the third day is 4 miles. The equation that represents the situation is

1/3x + 3/4(2/3x) + 4 = x

To solve for x, we can simplify the equation obtained in Part A

1/3x + 1/2x + 4 = x

Multiplying both sides by 6 to get rid of the fractions, we get

2x + 3x + 24 = 6x

Simplifying and solving for x, we get

x = 24

Therefore, the athlete is planning to run a total distance of 24 miles in the three days.

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The measure of angle ABP from the given circle is 90°.

From the given figure,

11) Measure of angle ABP is 90°.

12) Measure of angle BAK is 180°-(90°+25°)

= 180°-115°

= 65°

13) Measure of angle AQP is 90°.

14) Measure of angle QAK is 180°-(90°+25°) (Because ∠BPA=∠QPA=25°)

15) Measure of Arc BK = Measure of angle BAK = 65°

16) Measure of Arc BQ = Measure of angle BAQ = 65°×2

= 130°

17) m∠CAD=m∠BAK=65°

Therefore, the measure of angle ABP from the given circle is 90°.

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Answer:

y + 21 = - 4(x - 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, - 21 ) and (x₂, y₂ ) = (- 4, 23 )

m = [tex]\frac{23-(-21)}{-4-7}[/tex] = [tex]\frac{23+21}{-11}[/tex] = [tex]\frac{44}{-11}[/tex] = - 4

using (a, b ) = (7, - 21 ) , then

y - (- 21) = - 4(x - 7) , that is

y + 21 = - 4(x - 7)

What percentage of 1.23 is 2.17?  The amount over 100% will be the increase:

[tex]2.17 = \huge \text(\dfrac{x}{100}\huge \text )(1.23)[/tex]

[tex]x =\dfrac{ 2.17(100)}{1.23}[/tex]

[tex]x = 176.4\%[/tex]

The increase is 76.4%

AC is congruent to DF by the definition of congruency. Applying SSS Congruency, Triangle ABC is congruent to DEF, and since Triangle DEF is a right angled triangle, Triangle ABC is also a right angled triangle with angle B as 90 degrees.

AB is congruent to DB because segment DE was constructed so that DE = AB, BC is congruent to EF, because segment EF was constructed so that EF = BC, and since Triangle DEF is a right angled triangle, we have:

DE² + EF² = DF² (Pythagoras Theorem)

We are also given that:

AB² + BC² = AC²

Since DE = AB and EF = BC, we can substitute these values in the above equation to get:

DE² + EF² = AC²

Thus, we can substitute the above value of AC² in the equation DE² + EF² = DF² to get:

DE² + EF² = DF² = AB² + BC²

Taking the square root on both sides, we get:

DF = √(AB² + BC²)

Since AC² = AB² + BC², we can write:

DF = √AC²

Therefore, AC is congruent to DF by the definition of congruency. Applying SSS Congruency, Triangle ABC is congruent to DEF, and since Triangle DEF is a right angled triangle, Triangle ABC is also a right angled triangle with angle B as 90 degrees.

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Your question is incomplete; most probably, your complete question is this:

Prove that △ABC is a right triangle. Select the correct answer from each drop-down menu.

The volume of the cylinder is 90π cubic units.

To calculate the volume of a cylinder with a radius of 3 and a height of 10, you can use the following formula:

Volume = π × r² × h

Where:

- Volume represents the volume of the cylinder,

- π (pi) is a mathematical constant approximately equal to 3.14159,

- r is the radius of the cylinder (in this case, 3), and

- h is the height of the cylinder (in this case, 10).

Now, plug in the given values:

Volume = π × (3)² × 10

Simplify the expression:

Volume = π × 9 × 10

Volume = 90π

So, the volume of the cylinder is 90π cubic units.

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The mercury will not be the same in all the fishes it will depend on various factors such as the species of fish, the location where it was caught, and the size of the fish.

In any case, in common, the mercury levels in angle can change broadly depending on different components such as the species of angle, the area where it was caught, and the measure of the angle.

A few angle species are known to construct up">to construct up more mercury in their tissues than others.

whereas a few angles caught in certain ranges may be uncovered to higher levels of mercury due to contamination or other environmental factors.

It is additionally worth noticing that the  U.S. Food and Drug Administration (FDA) has issued rules on the greatest levels of mercury that are considered secure for utilization in angle.

The FDA exhorts that pregnant ladies, nursing moms, and youthful children ought to dodge devouring angles that are known to be tall in mercury, such as shark, swordfish, ruler mackerel, and tilefish.

Other sorts of angles that are lower in mercury, such as salmon, shrimp, pollock, and catfish, can be devoured in balance.

By and large, it is vital to be aware of the potential dangers of expanding fish which will contain tall levels of mercury, and to form educated choices approximately which sorts of angle to expend. 

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The values that are equivalent to the fraction -10/7 are -(-10/7) and -13/7 which makes options D and E correct.

Equivalent fractions are fractions that have different numerators and denominators, but represent the same amount or quantity. In other words, equivalent fractions are different ways of representing the same fraction.

-10/-7 = 10/7 {not equivalent to - 10/7}

-3 1/7 = -22/7 {not equivalent to - 10/7}

1 3/7 = 10/7 {not equivalent to - 10/7}

- -10/-7 = - (-10/-7) = - 10/7 {equivalent}

- 1 3/7 = - 10/7 {equivalent}

Therefore, the values that are equivalent to the fraction -10/7 are -(-10/7) and -13/7.

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As a result, for the two schools, the measures of variability are:

Mountain View School:

Range = 4, Variance = 9.1733, Standard deviation = 3.029

Bay Side School:

Range = 10, Variance = 7.84, Standard deviation = 2.8.

The degree of variance or dispersion in a set of data values is measured by standard deviation. The degree to which the data values deviate or vary from the mean or average value of the data set is indicated by this statistical indicator.

We must ascertain the range, variance, and standard deviation for each dataset in order to determine the measures of variability for the two schools.

Mountain View School:

Range: The smallest class size is 5 and the largest is 9, so the range is 9-5 = 4.

Variance: To calculate the variance, we need to find the mean first.

Mean = (5+6+8+9+8+2+0+10+2+4+5+6+8)/15

= 5.6

Then, we can find the variance using the formula:

Variance = Σ(xi - μ)²/n

= [(5-5.6)² + (6-5.6)² + (8-5.6)² + (9-5.6)² + (8-5.6)² + (2-5.6)² + (0-5.6)² + (10-5.6)² + (2-5.6)² + (4-5.6)² + (5-5.6)² + (6-5.6)² + (8-5.6)²]/15

= 9.1733

Standard deviation = √(9.1733) = 3.029

Bay Side School:

Range: The smallest class size is 0 and the largest is 10, so the range is 10-0 = 10.

Variance: To calculate the variance, we need to find the mean first.

So,

Mean will be = (8+7+6+5+5+4+4+3+1+0+2+0+0+2+3+5)/15

= 3.6

Then, we can find the variance using the following formula:

Variance = Σ(xi - μ)²/n

= [(8-3.6)² + (7-3.6)² + (6-3.6)² + (5-3.6)² + (5-3.6)² + (4-3.6)² + (4-3.6)² + (3-3.6)² + (1-3.6)² + (0-3.6)² + (2-3.6)² + (0-3.6)² + (0-3.6)² + (2-3.6)² + (3-3.6)² + (5-3.6)²]/15

= 7.84

Standard deviation will be = √(7.84)

= 2.8

As a result, for the two schools, the measures of variability are:

Mountain View School:

Range = 4, Variance = 9.1733, Standard deviation = 3.029

Bay Side School:

Range = 10, Variance = 7.84, Standard deviation = 2.8

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Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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Answer: s = p - 0.25p; $30

Step-by-step explanation:

      First, we need to know that a percent divided by 100 becomes a decimal.

          25% / 100 = 0.25.

      Next, we will use this equation because it takes 25% off of the original price (p) by subtracting 0.25p from p.

          s = p - 0.25p

      Lastly, we will substitute 40 in for 0 and solve.

          s = ($40) - 0.25($40)

          s = $30

If you are trying to predict Y scores from X scores, X is referred to as the a. predictor variable. Therefore, option a. predictor variable is correct.

The predictor variable, also known as the independent variable or explanatory variable, is a variable that is used to explain the changes or variations in another variable. In this case, the predictor variable (X) is used to predict the value of the dependent variable (Y).

For example, if you are trying to predict the score of a student on a test (Y) based on the number of hours they study (X), then the number of hours studied is the predictor variable. The predictor variable is what you manipulate or control to see its effect on the dependent variable. In other words, the predictor variable is what you believe influences the outcome variable.

It is important to note that the predictor variable does not necessarily cause changes in the dependent variable. There may be other variables at play that can affect the outcome variable. Therefore, it is important to consider other potential confounding variables in your analysis.

In summary, when trying to predict Y scores from X scores, X is referred to as the predictor variable. It is the variable that is manipulated to explain the changes in the dependent variable, Y.

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Answer:

3.6

Step-by-step explanation:

a^3+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

square root to get c alone

3.6055512754639=c

rounded= 3.6

Answer: 3.6

Step-by-step explanation: pythagorean theorem

A^2 + B^2 = C^2

3^2=9

2^2=4

13

Square root of 13 rounded to nearest 10th

3.6

Raw answer: 3.60555127546

The quotient of 30y³ + 50y² - 35y divided by 5y is: 6y² +10y - 7

Hence option c is the correct answer.

Applying long division rule to find quotient,

Dividend is  30y³ + 50y² - 35y and divisor is 5y

Dividing   30y³ + 50y² - 35y  by 5y step by step we get ( +) 30y^3  is divisible by 5y as the remainder is zero and the quotient is (+) 6y^2.

Then at second step we get (+) 50y^2 is divisible 5y as the remainder is zero and the quotient is (+) 10y.

And at the last step we get (-) 35y is divisible by 5y as the remainder is zero and the quotient is (-) 7.

Thus adding up the quotients found at each step of division of   30y³ + 50y² - 35y by 5y is 6y² +10y - 7.

Hence option c is the correct answer.

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The measure of the supplementary angle of the given angle would be = 175.2°

A supplementary angles are those angles that sums up to 180° when added up together.

To calculate the supplementary angle represented by X;

That is,

X+ 4.8° = 180

X = 180-4.8 = 175.2°

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The percentage of pens that are blue =18%

Let's assume that r represents the red pens, b represents the blue pens and g represents the green pens.

From the statements we can observe that the blue appears in both ratio.

The ratios are,

r:b=5:9 and b:g=1:4

Consider ratio b:g,

b:g

= 1:4

= (1×9) : (4×9)

=9:36

i.e., b:g = 9:36 and r:b = 5:9

So, we can conclude that, b=9, g=36, r=5

so, the total number of pens would be,

n = b + g + r

n = 9 + 36 + 5

n = 50

Now we need to find the percentage of pens that are blue.

Using percentage formula,

p = (b/n) × 100

p = (9/50) × 100

p = 18%

Hence, the percentage of blue pens are 18%.

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Given that biology is the subject, the Probability of being on time is 32.8%.

In this case:

P(on-time arrival in class | biology) = P(on-time arrival in class and biology) / P(biology) is the result of applying the conditional probability formula.

According to the table, 82.4% of students will be on time for biology class. Since there are four topics listed, each with an equal weight, the likelihood of biology is 25%. Therefore, we have:

P(on-time arrival in class | biology) = 82.4% / 25% = 0.328 = 32.8%

Therefore it can be concluded that the probability of on-time arrival in class given that the subject is biology is 32.8%.

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Answer:

on what

Step-by-step explanation: