When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.

The population means are known
The population variances are assumed equal but unknown
The population variances are known and equal
The population variances are assumed unequal and unknown

The statement if A ⊂ B, then A ∩ B = ∅ is false.

First, let us understand the set:

A set is a mathematical model for a collection of different things; a set contains elements or members that can be any mathematical object: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

We are given;

A ⊂ B

We need to find A ∩ B.

Let us understand the given set;

A ⊂ B means A is a proper subset of B.

All the elements of set A are in set B.

So, A ∩ B = A

But, A ∩ B = ∅ is given.

So, the statement is false.

Thus, the statement if A ⊂ B, then A ∩ B = ∅ is false.

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Answer:

  y = -x -1

Step-by-step explanation:

You want an equation of the line parallel to y=-x+8 through point (3, -4).

The parallel line will have the same slope as the given line. That slope is the coefficient of x: -1.

The point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

You have m=-1, (h, k) = (3, -4), so the desired line has equation ...

  y -(-4) = -1(x -3)

  y +4 = -x +3 . . . . . . point-slope form

Add -4 to get this to slope-intercept form.

  y = -x -1 . . . . . . . . . slope-intercept form

Answer:

3^3

Step-by-step explanation:

Exponents

9^3 can be rewritten as

3^2 ^3

Using exponent rules a^b^c = a^ (b*c)

3^2^3 = 3^6

3^6 / 3^3

We know that a^b / a^c = a^(b-c)

3^6 / 3^3  = 3^(6-3) = 3^3

Answer:

2nd answer is correct

Step-by-step explanation:

We know that,

[tex] \rightarrow \sf {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \rightarrow \sf \frac{{x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \rightarrow \sf( {x}^{a} )^{b} = {x}^{ab} [/tex]

Accordingly, let us solve it now.

[tex] \sf \frac{ {9}^{3} }{ {3}^{3} } \\ \\ \sf \frac{ {3}^{2 \times 3} }{ {3}^{3} } \\ \\ \sf\frac{ {3}^{6} }{ {3}^{3} } \\ \\ \sf {3}^{6 - 3} \\ \sf {3}^{3} [/tex]

Answer:

18243.906

Step-by-step explanation:

Find how much water is used in 1 hour and then multiply that by 3

24325.208/4

6081.302

6081.302x3

18243.906

The number of angles that are formed by the intersection of the diagonals is 4.

A square is a four-equal-sided figure with diagonals cut perpendicular to each other, with a total of four angles formed by diagonals.

It is a geometrical figure with four sides, each of which must be equal, and an angle of 90 degrees between two adjacent sides.

Square area = Side²

The square's perimeter = 4 sides

Every square contains two diagonals. The intersection angle of both diagonals is 90 degrees. The number of diagonal angles equals four.

Therefore, the correct option is 4.

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Complete question

How many angles are formed by the intersection of the diagonals in a square?

Answer:

22 + h = 53

Step-by-step explanation:

I don't know if I am correct

Answer:

The answer is 31, H=31

Step-by-step explanation:

53-22=31 :)

Answer:

Step-by-step explanation:

1. The measured height is the exact value therefore it is to be considered as actual height.

2. The error is the difference between actual and estimated values:

3. Percent error is:

or

The quantity of violas Kiara collected is 76

From the question, we are to determine the quantity of violas Kiara collected.

From the given information,

"Kiara and Lee are collecting violas in a ratio of 2:5"

First, we will determine the sum of ratios

Sum of ratios = 2 + 5 = 7

Also, from the given information

The total number of violas they collected is 266

Thus,

The quantity of violas Kiara collected will be

2/7 × 266

= 2 × 38

= 76

Hence, the quantity she collected is 76

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Answer:

105/8 = 13 1/8 = 13.125

Step-by-step explanation:

The first step is to turn the (-5 5/8) into a mixed number. The mixed number you should be getting is - 45/8. The second step is to convert the (-2 1/3) into a mixed number as well, your second mixed number should be -7/3. Next multiply the two fractions, - 45/8 x (-7/3) = 315/24.

We can simplify 315/24 by dividing by 3, so you'll divide 315 divided by 3 and 24 divided by 3 and you should get ... 105/8. So 105/ 8 is equal to

13 1/8. If you need this fraction in decimal form it is 13.125.

The actual area of the park in square miles is 21600 miles².

A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.

* Lets explain how to solve the problem

- A drawing that shows a real object with accurate sizes reduced or

 enlarged by a certain amount called the scale

- Drawing scale is a ratio between the drawing length and the

 actual length

- To find the actual dimensions from the drawing dimensions use the

scale drawing

* Lets solve the problem

- A map of a rectangular park has a length of 4 inches and a width

 of 6 inches

∴ The drawing dimensions are:

# length = 4 inches

# width = 6 inches

- The scale of the map is 1 inch for every 30 miles

∴ The scale drawing is 1 : 30

- To find the actual area find the actual dimensions

∵ The scale drawing is 1 : 30

∵ The length = 4 inches and the width = 6 inches

- By using cross multiplication

∴  1        :        30

  4       :  actual length

  6       :  actual width

∴ Actual length = (4 × 30)/1 = 120

∴ Actual length = 120 miles

∴ Actual width = (6 × 30)/1 = 180

∴ Actual Width = 180 miles

∴ The actual dimensions are 120 miles and 180 miles

∵ The area of any rectangle = length × width

∴ The actual area = 120 × 180 = 21600

∴ The actual area 21600 miles²

Hence the answer is the actual area of the park in square miles is 21600 miles².

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The probability that the spinner will land on grey and then purple is 1/18.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of grey regions = 1

Number of purple regions = 2

Total number of regions = 6

Now,

The probability that the spinner will land on grey.

= Number of grey regions / Total number of regions

= 1 / 6

The probability that the spinner will land on purple.

= Number of purple regions / Total number of regions

= 2 / 6

The probability that the spinner will land on grey and then purple.

= 1/6 x 2/6

= 1/6 x 1/3

= 1/18

Thus,

The probability that the spinner will land on grey and then purple is 1/18.

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Answer:

Step-by-step explanation:

You want the steps to writing the equation of a line parallel or perpendicular to a given line through a given point.

Given line ax+by=c and point (h, k), you can write equations for the desired lines using the forms:

  a(x -h) +b(y -k) = 0 . . . . . . parallel line

  b(x -h) -a(y -k) = 0 . . . . . . . perpendicular line

If you eliminate parentheses and collect terms, you will have the general form equation of the desired line(s). If you solve for y, you will have the slope-intercept form of the equation.

To use these forms, it is helpful to start with the equation of the given line in standard form, as shown. (It could also be in general form ax+by-c=0.)

Using the above solution, the steps are ...

You will note that the same coefficients are used on the same variables for a parallel line. This is because parallel lines have the same slope.

The coefficient of the variables are swapped, and one of them is negated in the equation for the perpendicular line. This is because perpendicular lines have opposite reciprocal slope.

When the given line is in slope-intercept form, y = mx +b, the slope is readily identified as m, the coefficient of x. For the parallel line, this slope can be used directly in the point-slope equation for a line through a given point:

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

This can be rearranged to the slope-intercept form:

  y = mx +(k -mh)

The perpendicular line has opposite reciprocal slope. The line perpendicular to the given line with slope m will have slope -1/m. Then the two forms of equation are ...

  y -k = -1/m(x -h) . . . . . . . . . point-slope form

  y = (-1/m)x +(k +h/m) . . . . . slope-intercept form

__

Additional comment

A standard form equation (ax +by = x) has mutually prime integer coefficients, with a positive leading coefficient. When you have written your equation, you may find it necessary to multiply the equation by some value to put it in this form. For example, -2x +4y = -8 must be multiplied by -1/2 to get the standard form equation x -2y = 4.

You need to be aware of the form required by your grader. The wording "the equation" often means slope-intercept form, or the form matching the given equation or the answer box format.

Answer:

5

Step-by-step explanation:

Multiples of 1: 1, 2, 3, 4, 5, 6, 7, ...

Multiples of 5: 5, 10, 15, 20, 25, ...

The smallest number that appears in both lists is 5, and that is the least common multiple.

Answer: Alright, lets get started.

Roberto has already run miles = 16

Total miles for marathon = 26.2

As per percentage formula :

So, percentage completed =

Rounding the answer to whole number 62 %

62 percent of the marathon  he has completed.   :  Answer

Hope it will help :)

Step-by-step explanation:

Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

There is Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x represent Watusi's speed,

y represent Ubangi's speed,

And z represents Pigmy's speed.

According to the given information, we can write the system of equations as

x + y + z = 30  .....(i)

z + 2x/3 = 22 - y  .....(ii)

4x + 3y - z = 12  .....(iii)

The above system of equations gives the values of x, y, and z when solving

x = 6, y = 3, z = 21

This means Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

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By using the concept of depreciation, it is obtained that

New population  after 9 years = 24012

What is Depreciation?

Depreciation is the decrease in the value of a population or any asset over a period of time at a certain rate.

The concept of depreciation has been used here

Original population = 28800

Rate of decrease of population = 2%

Time = 9 years

New population  after 9 years = [tex]28800(1 - \frac{2}{100})^9[/tex]

                                                  = [tex]28800({1 - \frac{1}{50})^9\\[/tex]

                                                  = [tex]28800(\frac{49}{50})^9[/tex]

                                                  = 24011.94

                                                  = 24012

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The smallest number among the given options is 0.07.

To determine the smallest number, we compare the given options. Among the numbers 0.5, 0.17, 0.07, 1.7, and 0.071, the smallest number is 0.07. This can be determined by examining the decimal places. The number 0.07 has the fewest decimal places and is the smallest value.

When comparing decimal numbers, the digits after the decimal point are crucial.

In this case, we observe that 0.07 has the smallest digit in the hundredths place, while the other numbers have larger digits in that place. Therefore, 0.07 is the smallest number among the given options.

It is important to note that the order of magnitude (the number before the decimal point) does not affect the comparison when determining the smallest number among decimal values.

In summary, by comparing the decimal places, we find that 0.07 is the smallest number among the given options.

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Answer:

1) Slope: 2 ; y-intercept: (0, -6)

2) Slope: -5; y-intercept: (0, 16)

Step-by-step explanation:

8x-4y=24 is also y=2x-6

Slope: 2

y-intercept: -6

y= -5x+16

Slope: -5

y-intercept: 16

[tex]a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}[/tex]

The number of laps around the lake that Latrell jogs is 5 1/4 laps.

A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

From the information he jogs 7 miles and each lap is 4/3 miles. The number of laps will be:

= Total laps / Number of miles

= 7 ÷ 4/3

= 7 × 3/4

= 21 / 4.

= 5 1/4 laps.

He jogs 5 1/4 laps.

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The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1      .

In the question ,

it is given that ,

the specification of the furniture , is 17.9 ≤ w ≤ 18.1 ,

where w is the width of the desk drawer in inches .

we need to write the given inequality in absolute inequality form ,

we know that the a-b < x < a+b , then the absolute inequality is |x-a|<b ,

On comparing the given inequality with a-b < x < a+b ,

we get

a - b = 17.9 and

a + b = 18.1

adding both the equations , we get

2a = 36

a = 36/2

a = 18

Substituting a = 18 in a + b = 18.1 , we get

18 + b = 18.1

b = 18.1 - 18

b = 0.1

The required inequality is |x-a| ≤ b .

|x - 18| ≤ 0.1

Therefore , The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1   .

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Answer:

[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]-3x+9          

Step-by-step explanation:

(x-3)([tex]x^{2}[/tex]-3) = 0

x = -[tex]\sqrt{3}[/tex], [tex]\sqrt{3}[/tex], 3

The 30 feet by 14 feet by 8 feet, filled in 3.5 hours by two pipes in which one pipe is 1 more than twice the other, indicates;

1. The rational equation from which the time the smaller pipe takes to fill the pool is; [tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]

2. The solution of the equation is t ≈ 10.51 hours

3. The time it takes to fill the pool using only the small pipe is about 10.51 hours

Rational equation are equations that have rational polynomial expressions.

The dimensions of the pool are;

Length = 30 feet

Width = 14 feet

Depth = 8 feet

1. Let x represent the flow rate of the slower pipe

The flow rate of the faster pipe = 2·x + 1

Time it will take both pies to fill the pool = 3.5 hours

The volume of the pool, V = 30 × 14 × 8 = 3360

The volume of the pool is 3360 cubic feet

The rate equation is therefore;

[tex]\dfrac{x}{3360} +\dfrac{2\cdot x+1}{3360} =\dfrac{1}{3.5}[/tex]

[tex]\dfrac{x}{3360} =\dfrac{1}{3.5} - \dfrac{2\cdot x+1}{3360}[/tex]

From the rate equation above, the time it takes the smaller pipe to fill the pool is; t = 3360/x therefore;

[tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]

2. Solving for x from the volume of water in the pool, V, therefore;

The volume of water that fills the pool, V, is found from the equation;

V = 3.5 × (2·x + 1 + x) = 10.5·x + 3.5

V = 10.5·x + 3.5

Therefore;

3360 = 10.5·x + 3.5

[tex]x = \dfrac{3360-3.5}{10.5} =319.\overline 6[/tex]

t = 3360/319.[tex]\overline 6[/tex] ≈ 10.51

The time it takes to fill the pool using only the smaller pipe is approximately 10.51 hours

Aliter;

[tex]\dfrac{3\cdot x}{3360} =\dfrac{1}{3.5}-\dfrac{1}{3360}[/tex]

[tex]t = \dfrac{3360}{x} =\dfrac{3}{\left(\dfrac{1}{3.5}-\dfrac{1}{3360}\right)} \approx 10.51[/tex]

3. The interpretation of the solution is that it takes about 10.51 hours for the smaller pipe working alone to fill the pool

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Answer:

Step-by-step explanation:

the equation of the cone is given already

r=6 inches

h=7 inches

Substitute in the equation =84pi=263.89

for the sphere substitute the radius r= 6 inches in the equation, and then divide by 2. This is because the spherical shale in top of the cone is half a sphere, as it can be clearly seen.

So It’s 288pi= 904.78 /2 =452.39

add the volume of cone and volume of sphere

The final answer is 716.28 inches^3

The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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The value of x in the given triangle is x = 2 .

In the question ,

it is given that ,

a triangle is given ,

let us name the triangle as triangle ABC ,

So , By Basic Proportionality Theorem , which states that ,

The line drawn parallel to one side of triangle and cuts the other two sides divides the other two sides in equal proportion.

So , By Basic Proportionality Theorem

AD/AB = AE/AC

substituting the value from the triangles , we get

4/12 = 6/(6+6x)

1/3 = 1/(1+x)

1 + x = 3

x = 3 - 1

x = 2

Therefore , The value of x in the given triangle is x = 2 .

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The constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.

We know that the constant of proportionality is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given:

The numbers below are what the dots are plotted-

10, 50

20, 100

30, 150

40, 200

50, 250

Take any two points.

Let us choose (20, 100) and (30, 150).

Put the values in the slope formula;

Slope = (150 - 100) / (30 - 20) = 50 / 10 = 5

So, the slope of the line is 5.

Thus, the constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.

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