How far up the building does the top of the ladder reach?

H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.

Let [tex]\mathcal{H}[/tex]  be a non-empty directed family of subgroups of a group G. We need to show that the union [tex]H=\bigcup_{H_i\in\mathcal{H}}H_i[/tex] is a subgroup of G.

First, note that H is non-empty since[tex]\mathcal{H}[/tex] is non-empty. We also have [tex]1_G \in H_i[/tex] for all [tex]H_i\in\mathcal{H}[/tex], so [tex]1_G \in H.[/tex]

To show that H is closed under multiplication, let [tex]h_1,h_2\in H[/tex]. Then there exist [tex]H_{i_1},H_{i_2}\in\mathcal{H}[/tex] such that [tex]h_1\in H_{i_1}[/tex] and [tex]h_2\in H_{i_2}.[/tex] Since [tex]\mathcal{H}[/tex] is directed, there exists[tex]H_{i_3}\in\mathcal{H}[/tex] such that [tex]H_{i_1}\cup H_{i_2} \subseteq H_{i_3}[/tex]. Thus, [tex]h_1,h_2\in H_{i_3},[/tex]and since [tex]H_{i_3}[/tex] is a subgroup, we have [tex]h_1h_2\in H_{i_3} \subseteq H[/tex]. Therefore, H is closed under multiplication.

Finally, to show that H is closed under taking inverses, let h\in H. Then there exists [tex]H_i\in\mathcal{H}[/tex] such that [tex]h\in H_i[/tex]. Since [tex]H_i[/tex]is a subgroup, we have [tex]h^{-1}\in H_i \subseteq H[/tex]. Therefore, H is closed under taking inverses.

Since H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.

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The additional tax (liability) that Lynn owes after her employer withheld $3,150 from her pay is D. $399.

Tax liability refers to the amount that a taxpayer owes.

We can determine the tax liability as the difference between the total tax and the employer-withheld tax.

The total tax is computed by applying the rate to the taxable income, which is the difference between the total income and the total deductions.

Lynn's total income last year = $38,900

Total deductions = $11,450

Employer withheld taxes = $3,150

Taxable income = $27,450 ($38,900 - $11,450)

From the tax table, when taxable income is at least $27,450 but less than $27,500, the total tax is $3,549, based on being a head of household.

The tax liability = $399 ($3,549 - $3,150)

Thus, Lynn is expected to remit an additional $399 to settle her tax liability.

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Answer:

X=-√7 and √7

Step-by-step explanation:

To solve the equation 6x² - 42 = 0, we can begin by rearranging it to isolate the variable term:

6x² = 42

Then, we can divide both sides by 6:

x² = 7

To get the exact values of x, we need to take the square root of both sides:

x = ±√7

Therefore, the exact values of x are √7 and -√7.

The family would need to bring home an additional $2400 annually to cover the increased cost of housing.

The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.

The current monthly cost of housing is $1600 so the annual cost is:

$1600/month x 12 months = $19,200/year

Let's assume the family needs to cover an increased housing cost of $200 per month.

The new monthly cost of housing would be:

$1600/month + $200/month = $1800/month

The new annual cost of housing would be:

$1800/month x 12 months = $21,600/year

The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:

$21,600/year - $19,200/year = $2400/year

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The area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.

From the given figure, legs of triangle measure the same, that is 10 units.

Let the diameter of the circle be x.

By using Pythagoras theorem,

x²=10²+10²

x²=100+100

x²=200

x=10√2 units

Radius = 5√2 units

We know that, area of a circle = πr²

= 3.14×(5√2)²

= 3.14×50

= 157 square units

We know that, circumference of a circle = 2πr

= 2×3.14×5√2

= 31.4√2 units

Therefore, the area of a circle is 157 square units and the circumference of a circle is 31.4√2 units.

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Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

[tex]v = {s}^{2} ( \frac{h}{3} )[/tex]

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

[tex]v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196[/tex]

28. The volume of a rectangular prism

[tex]v = l \times w \times h[/tex]

where l is length

w is width

h is height

[tex]v = 11 \times 11 \times 8 = 968[/tex]

29.

Use the same formula in 27

[tex]v = 100(3) = 300[/tex]

30.

Volume of a Cylinder is

[tex]v = \pi {r}^{2} h[/tex]

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

[tex]v = {11}^{2} (8)(\pi)[/tex]

[tex]v = 968\pi[/tex]

pi is approximately 3.14

[tex]v = 3041.06[/tex]

31. Volume of A Sphere

[tex] \frac{4}{3} \pi {r}^{3} = v[/tex]

The radius is half of diamter, thus r=7

[tex] \frac{4}{3} \pi( {7}^{3} ) = 1436.76[/tex]

Answer: 11x16x5=880

This means the answer is C

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

Option B is the correct answer.

We have,

Dilation is a transformation that changes the size of an object.

When a figure is dilated with a scale factor between 0 and 1, the resulting figure is smaller than the original.

The scale factor indicates how much smaller the image is compared to the original.

For example, a scale factor of 0.5 would mean that the image is half the size of the original.

Now,

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

This is because the side lengths of the second rectangle are half of the side lengths of the first rectangle, which means that the second rectangle is a dilation of the first rectangle with a scale factor of 0.5.

Thus,

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

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a. The average rate of change for the temperature from 0 minutes to 20 minutes is 2.2.

b. The average rate of change for the temperature from 30 minutes to 60 minutes is 2.7.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function g(t) over the interval [0, 20]:

a = 20; f(a) = 140.3

b = 0; f(b) = 184.3

By substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (184.3 - 140.3)/(20 - 0)

Average rate of change = 44/20

Average rate of change = 2.2

Part b.

a = 30; f(a) = 109.3

b = 60; f(b) = 28.3

By substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (109.3 - 28.3)/(60 - 30)

Average rate of change = 81/30

Average rate of change = 2.7

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Answer:

-0.5. is 5

Step-by-step explanation:

i need the poits

The monthly payment added to your mortgage for property taxes is $270.25, rounded to the nearest cent. It is a good idea to budget for property taxes when purchasing a home, as they can be a significant expense that should not be overlooked.

To calculate the monthly payment added to your mortgage for property taxes, we can use the following steps:

1) Find the taxable value of the home by subtracting the exemption from the appraised value:

Taxable value = $315,000 - $50,000 = $265,000

2) Calculate the annual property tax by multiplying the taxable value by the tax rate:

Annual property tax = $265,000 x 0.0122 = $3,243

3) Divide the annual property tax by 12 to get the monthly payment:

Monthly property tax payment = $3,243 / 12 = $270.25

It's important to note that property tax rates can vary depending on where you live, so it's a good idea to check with your local tax authority to get an accurate estimate of your property tax bill.

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The area of the triangle is given as follows:

17 cm².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

Considering the image presented for this problem, the dimensions for the triangle are given as follows:

b = 5 cm, h = 6.8 cm.

Applying the multiplication of these dimensions, the area of the triangle is given as follows:

A = 0.5 x 5 x 6.8

A = 17 cm².

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Seattle's sales were approximately 33.33% larger than Portland's.

Portland's sales were approximately 25% smaller than Seattle's.

Portland's sales were approximately 75% of Seattle's sales.

We have,

a)

Seattle's sales were larger than Portland's by:

= (380,000 - 285,000)

= $95,000.

To calculate the percentage difference, we can use the formula:

Percentage difference = (Difference / Original value) x 100

Percentage difference = (95,000 / 285,000) * 100 ≈ 33.33%

b)

Portland's sales were smaller than Seattle's by (380,000 - 285,000) = $95,000.

To calculate the percentage difference, we can use the formula:

Percentage difference = (Difference / Original value) x 100

Percentage difference = (95,000 / 380,000) x 100 ≈ 25%

c)

Portland's sales were a certain percentage of Seattle's sales.

To calculate this percentage, we can use the formula:

Percentage = (Portland sales / Seattle sales) * 100

Percentage = (285,000 / 380,000) * 100 ≈ 75%

Therefore,

Seattle's sales were approximately 33.33% larger than Portland's.

Portland's sales were approximately 25% smaller than Seattle's.

Portland's sales were approximately 75% of Seattle's sales.

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The measures are given as follows:

On a parallelogram, the opposite sides are congruent, hence the value of x is obtained as follows:

2x = 4

x = 2.

Opposite angles are congruent, meaning that they have the same measure, hence the measure of angle A is given as follows:

m < A = m < C = 110º.

Consecutive angles are supplementary, meaning that the sum of their measures is of 180º, hence the measure of angle B is given as follows:

m<B = 180º - 110º = 70º.

Considering the angle addition postulate, the measure of angle ABD is given as follows:

m < ABD = 70 - 36

m < ABD = 34º.

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Answer:

60°

Step-by-step explanation:

180-78-42=60

The magnitude of the complex number -10 + 24i is 26.

We have,

Complex numbers can be represented as a combination of a real number and an imaginary number, in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Now,

To find the magnitude of a complex number, we take the square root of the sum of the squares of its real and imaginary parts.

For -10 + 24i, the real part is -10 and the imaginary part is 24.

So the magnitude:

| -10 + 24i | = √((-10)^2 + (24)^2) = √(100 + 576) = √676 = 26

Therefore,

The magnitude of -10 + 24i is 26.

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The area of the regular polygon is 311.5 in2.

We are given that;

A polygon

Now,

To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.

To find the apothem length, we need to use some trigonometry.

The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.

To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.

A = (1/2)708.9 ≈ 311.5 in2.

Therefore, by the area the answer will be 311.5 in2.

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Answer:

Step 4

Step-by-step explanation:

In step 3, 16 + 9 = 25, so step 4 should subtract 25 from both sides. Also, y² became -y² in step 4 which is incorrect.

Answer: Step 4

a) The null hypothesis: H0: μ >= 1000

alternate hypothesis Ha: μ < 1000

b) The value of the test statistic is -3.12.

a) The null hypothesis, denoted by H0, is a statement of no difference or no effect. The alternate hypothesis, denoted by Ha, is a statement of a difference or effect that we want to test.

In this case, the null hypothesis would be that the average bulb life is greater than or equal to 1000 hours:

H0: μ >= 1000

The alternate hypothesis would be that the average bulb life is less than 1000 hours:

Ha: μ < 1000

where μ is the population mean bulb life.

b) To calculate the test statistic, we need to use the formula:

t = (x - μ) / (s / √(n))

where x is the sample mean, μ is the hypothesized population mean (under the null hypothesis), s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (950 - 1000) / (160 / √(30))

t = -3.12

Therefore, the value of the test statistic is -3.12.

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Hello!

area

= (b x h)/2

= (18in x 7in)/2

= 126in²/2

= 63in²

Answer:

63 in²

Step-by-step explanation:

1/2 bh=area of the triangle

(a) The distribution of X is X ~ N(130, 49)

(b) The probability that the average number of friends is less than 135 is 0.610

(c) The first quartile for the average number of friends is 96.925

(d) The assumption of normal distribution is necessary

Given that

Mean = 130

Standard deviation = 49

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(130, 49)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (135 - 130)/18

Evaluate

z = 0.278

So, we have

P = P(z < 0.278)

Evaluate

P = 0.60949

Approximate

P = 0.610

This is calculated as

Q₁ = Mean - 0.675 * Standard deviation

So, we have

Q₁ = 130 - 0.675 * 49

Evaluate

Q₁ = 96.925

Hence, the first quartile for the average friends for this sample size is 96.925

Yes, the assumption is necessary

This is because

The distribution has a sample size greater than 25 as required by the central limit theorem

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The option that is not equivalent to x ¹⁸ is D. x ¹⁹

As a means to simplify option 1, we can incorporate the rule of multiplying two powers with an identical base to add their exponents. For instance, by doing x³ × x¹⁵ , we would end up with x¹⁸, which ultimately leads to x ¹⁸ as an equivalent result.

By applying the understood concept that when raising a power to itself,exponents must be multiplied together, option 2 becomes more understandable. Specifically, (x ² ) ⁹ = x ¹⁸,the same equivalence as x¹⁸.

Similarly, option 3 assimilates this approach; (x ⁶ ) ³ = x¹⁸,leading to x¹⁸ once again as an equal resonance.

In contrast, option 4, i.e., x¹⁹, comprises an exponent one higher than x¹⁸ and thus, is dissimilarly unequal in comparison.

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Options for this question are:

x³ × x¹⁵

(x²)⁹

(x⁶)³

x¹⁹

After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.

The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted  measurement regarding the distance around the outside of a two-dimensional shape. In this system  the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m

There will be about 21 cm³ of empty space in the cylindrical container.

The formula for the volume of a sphere is V = (4/3)πr³ where r is the radius of the sphere. Since the diameter of each bouncy ball is 3 cm, the radius is 1.5 cm.

V = (4/3)π(1.5)³

= 14.13 cm³

The volume of three bouncy balls is 3 times this amount:

= 3 × 14.13

= 42.39 cm³

Since the diameter of each cylinder is 3 cm, the radius is 1.5 cm. We also know that the height of the cylinder is 9 cm, since each cylinder is 3 cm tall and there are three cylinders stacked on top of each other.

= π(1.5)^2(9)

= 63.62 cm³

Empty space = Vcontainer - Vtotal

= 63.62 - 42.39

= 21.23 cm³

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Answer:

The estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is 0.25.

The estimated probability that it takes at least four guests to find one who is staying for personal reasons is 0.125.

Step-by-step explanation:

x y^3 z^2      =   x^1  y^3  z^2  

                           the x   exponent is '1'

so first I would move -6x to the other side and -2 at the same time it would look like this

24+2=6x+7x

and simplify

26= 13x

divide both sides by 13 to find x

2= x

The measures of NP and AP equals 8

First, it is important to note that;

From the information given, we have that;

The centroid of the triangle divides AN in the ratio of 1: 2

Hence, the length of AN is twice that of line NP

So;

AN = 2NP

Substitute the value

18 = 2NP

Divide by the coefficient

NP = 9

But;

AN = NP + AP

Substitute the values, we get;

AP = 18 - 9

AP = 9

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