Mohawk Skywalkers are iron workers who helped build skyscrapers, bridges, and other structures for over 120 years. Which of the following is a statistical question about the Mohawk Skywalkers?

A. How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime?

B. How many New York City skyscrapers were built with the help of Mohawk Skywalkers?

C. How many generations of the Martin family have worked as Mohawk Skywalkers?

D. How many Mohawk Skywalkers helped build the Empire State Building?

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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Answer:

area = 6.5 square units

Step-by-step explanation:

Use the area of a triangle in coordinate geometry formula:

\(\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|\)

where \((x_1,y_1)=(-8,-8) \ \ \ \ (x_2,y_2)=(-6,-7) \ \ \ \ (x_3,y_3)=(-9,-2)\)

      \(\triangle GHI =\frac{1}{2} |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|\)

\(\implies \triangle GHI =\frac{1}{2} |-8(-7+2) -6(-2 +8) -9(-8 +7)|\)

\(\implies \triangle GHI =\frac{1}{2} |40 -36 +9|\)

\(\implies \triangle GHI =6.5\)

The Venn Diagram for these given sets is graphed at the end of the answer.

A Venn Diagram uses circles to show if elements belong to one set, or multiple sets, in the intersection.

For this problem, we have that:

The Venn Diagram showing this is inserted at the end of the answer. There are a two erasers marks because of typing mistakes on my part.

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Answer:

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

Answer: 584 yds

Step-by-step explanation:

3mi-3mi=0

1622-1038=584yds

Answer:

answer is D

Step-by-step explanation:

(2^3)^-2= 2^(3)*(-2)
             = 2^-6
             = 1/2^6
             = 1/64

     

The expressions (a), (d), (e) and (f) have values less 1.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Solving each expression :-

1) 4¹¹ / 4¹⁴        

= 4¹¹ × 4⁻¹⁴

= (4)¹¹⁻¹⁴

= 4⁻³

= 1 / 4³

2) (3⁵)² / 3⁸

= 3¹⁰ / 3⁸

= 3¹⁰⁻⁸

= 3²

= 9

3) 4⁻¹ × 4⁵

= 4⁻¹⁺5

= 4⁴

= 64

4) (2³)⁻²

= 2⁻⁶

= 1 / 2⁶

5) (5⁴)² x 5⁻¹¹

= 5⁸ x 5⁻¹¹

= 5⁻³

= 1 / 5³

6) (6⁻⁴ x 6⁶) / 6³

= 6² / 6³

= 1 / 6

Hence, the expressions (a), (d), (e) and (f) have values less 1.

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Answer:

152

Step-by-step explanation:

a = 3; b = -8

2b² − 4a + 4a² =

= 2(-8)² - 4(3) + 4(3)²

= 2(64) - 12 + 4(9)

= 128 - 12 + 36

= 116 + 36

= 152

Answer:

Length and Width = 10ft

Height = 5ft

Surface Area = 300 square feet

Step-by-step explanation:

Given

\(V = 500ft^3\) -- Volume

Let:

\(L = Length\)

\(W =Width\)

\(H = Height\)

Volume (V) is calculated as:

\(V = L * W * H\)

Substitute 500 for V

\(500 = L * W * H\)

Make H the subject

\(H = \frac{500}{LW}\)

The tank has no top. So, the surface area (S) is:  

\(S = L * W + 2*H*L + 2*H*W\)

\(S = L * W + 2H(L + W)\)

Substitute 500/LW for H

\(S = L * W + 2*\frac{500}{LW}(L + W)\)

\(S = L * W + \frac{1000}{LW}(L + W)\)

\(S = L W + \frac{1000}{L} + \frac{1000}{W}\)

Differentiate with respect to L and to W

\(S'(W) = L - \frac{1000}{W^2}\)

and

\(S'(L) = W - \frac{1000}{L^2}\)

Equate both to get the critical value

\(S'(W) = L - \frac{1000}{W^2}\)and \(S'(L) = W - \frac{1000}{L^2}\)

\(0 = L - \frac{1000}{W^2}\) and \(0 = W - \frac{1000}{L^2}\)

\(\frac{1000}{W^2} = L\) and \(\frac{1000}{L^2} = W\)

\(W^2L = 1000\) and \(L^2W = 1000\)

Make L the subject in  \(W^2L = 1000\)

\(L = \frac{1000}{W^2}\)

Substitute \(\frac{1000}{W^2}\) for L in \(L^2W = 1000\)

\((\frac{1000}{W^2})^2 * W = 1000\)

\(\frac{1000000}{W^4} * W = 1000\)

\(\frac{1000000}{W^3} = 1000\)

Cross Multiply

\(1000000 = 1000W^3\)

Divide both sides by 1000

\(1000 = W^3\)

Take cube roots of both sides

\(\sqrt[3]{1000} = W\)

\(10 = W\)

\(W = 10\)

Substitute 10 for W in \(L = \frac{1000}{W^2}\)

\(L = \frac{1000}{10^2}\)

\(L = \frac{1000}{100}\)

\(L = 10\)

Recall that:\(H = \frac{500}{LW}\)

\(H = \frac{500}{10*10}\)

\(H = \frac{500}{100}\)

\(H = 5\)

So, the dimensions are:

\(L, W=10\) and \(H = 5\)

The surface area is:

\(S = L * W + 2H(L + W)\)

\(S = 10*10 +2*5(10+10)\)

\(S = 10*10 +2*5*20\)

\(S = 100 + 200\)

\(S = 300\)

Answer:

A) 52

Step-by-step explanation:

If < 1 and < 2 are complementary angles, then it means that the sum of their measures add up to 90°.

< 1 + < 2 = 90°

12x + 4 + 9x + 2 = 90°

21x + 6 = 90°

21x + 6 - 6 = 90° - 6

21x = 84°

21x/21 = 84°/21

x = 4

Substitute the value of x = 4 into < 1 and < 2:

m < 1: 12x + 4 = 12(4) + 4 = 52°

m < 2: 9x + 2 = 9(4) + 2 = 38°

Therefore, the correct answer is A) m < 1 = 52°.

Answer: 5km

Step-by-step explanation: 2cm=1 km

10cm divided by 2 is 5km

Luckily, the integral is basically set up for you:

\(\displaystyle \int_{\theta=0}^{2\pi} \int_{\phi=\frac\pi4}^{\frac\pi2} \int_{\rho=2}^6 \cos(\phi) \, d\rho \, d\phi \, d\theta\)

Since the limits on every variable are constant, and we can factorize \(f(\rho,\theta,\phi) = f_1(\rho) f_2(\theta) f_3(\phi)\), we can similarly factorize the integrals. (This is a special case of Fubini's theorem, if I'm not mistaken.)

So the triple integral is equivalent to

\(\displaystyle \left(\int_0^{2\pi} d\theta\right) \left(\int_{\frac\pi4}^{\frac\pi2} \cos(\phi) \, d\phi\right) \left(\int_2^6 d\rho\right)\)

and each of these subsequent integrals are easy to compute:

\(\displaystyle \int_0^{2\pi} d\theta = \theta \bigg|_0^{2\pi} = 2\pi - 0 = 2\pi\)

\(\displaystyle \int_{\frac\pi4}^{\frac\pi2} \cos(\phi) \, d\phi = \sin(\phi) \bigg|_{\frac\pi4}^{\frac\pi2} = \sin\left(\frac\pi2\right) - \sin\left(\frac\pi4\right) = 1 - \frac1{\sqrt2} = \frac{2 - \sqrt2}2\)

\(\displaystyle \int_2^6 d\rho = \rho\bigg|_2^6 = 6 - 2 = 4\)

Taken together, the triple integral evaluates to

\(\displaystyle \int_{\theta=0}^{2\pi} \int_{\phi=\frac\pi4}^{\frac\pi2} \int_{\rho=2}^6 \cos(\phi) \, d\rho \, d\phi \, d\theta = 2\pi \times \frac{2-\sqrt2}2 \times 4 = \boxed{4\pi(2-\sqrt2)}\)

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

After answering the provided question, we can conclude that The slope answer is not listed as a choice, but this is the correct equation.

In mathematics, slope is the slope of the regression of a line or curve. It is a measure of the degree to which a function's y-value varies once the x-value changes. A line's slope is usually expressed as a letter m and is able to be calculated as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) is some two important points on the line. The slope of a line can be favorable, negative, equal to 0, or unknown. A positive slope means the line rises up from left to right, whereas a slope means the line falls back from left to right.

To find the equation of the line passing through the point (4,-5) with slope 2, we can use the point-slope form of the equation of a line.

y - y1 = m(x - x1)

y - (-5) = 2(x - 4)

y + 5 = 2x - 8

y = 2x - 13

y = 2x - 13

The answer is not listed as a choice, but this is the correct equation.

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In the triangle, The lengths of FD, AD, AG, BG, and BF are: FD = 6, AD = 0, AG = 6, BG = 6, BF = 12

A closed, two-dimensional geometric shape known as a triangle is made up of three lines that link three non-collinear points. The line segments are known as sides, and the spots where the line segments intersect are known as vertices. The sides and angles of a triangle can be used to categorize it. By side, a triangle can be categorized as being scalene, isosceles, or equilateral (all sides are equal) (no sides are equal). A triangle can be categorized as acute (all angles are under 90 degrees), right (one angle is precisely 90 degrees), or obtuse (one angle is exactly 90 degrees) (one angle is greater than 90 degrees). In various mathematical and practical contexts, including trigonometry, geometry, and engineering, triangles are used.

First, let's draw a diagram of the triangle ABC and label the given points:

          A

          / \

         /   \

        /     \

     F-------B

    /  \       /

   /    \    /

  /      \ /

D-------C

Since AB = AC and angle A is 120 degrees, triangle ABC is an isosceles triangle with AB = AC = 12 and angle BAC = 120 degrees. To find the lengths of FD, AD, AG, BG, and BF, we can use the following steps:

Step 1: Find the length of BC.

Since triangle ABC is isosceles, we can find the length of BC using the law of cosines:

\(cos(120) = (BC^2 + 12^2 - 2(BC)(12)) / (2(BC)(12))\\-0.5 = (BC^2 + 144 - 24BC) / (24BC)\\BC^2 - 24BC - 288 = 0\\(BC - 12)(BC + 24) = 0\\BC = 12 or BC = -24\\\)

Since BC cannot be negative, we have BC = 12.

Step 2: Find the lengths of FD and BF.

Since F and D are the midpoints of sides AC and BC, respectively, we have FD = (AC)/2 = 6 and BD = (BC)/2 = 6. Therefore, BF = BD + DF = 6 + 6 = 12.

Step 3: Find the length of AD.

Since D is the midpoint of BC, we have AD parallel to FC and AD = 2(DC). Since triangle ABC is isosceles, we have DC = (BC - AC)/2 = (12 - 12)/2 = 0. Therefore, AD = 2(0) = 0.

Step 4: Find the length of AG.

Since G is the intersection of AD and BF, we can use similar triangles to find AG. Specifically, triangle ABG is similar to triangle CFD, so we have:

AG/BG = FD/CD

AG/12 = 6/(BC/2)

AG/12 = 6/(12/2)

AG/12 = 1/2

AG = 6

Step 5: Find the length of BG.

Since G is the intersection of AD and BF, we can use similar triangles to find BG. Specifically, triangle ABG is similar to triangle CFD, so we have:

BG/AG = BD/FD

BG/6 = 6/6

BG = 6

Therefore, the lengths of FD, AD, AG, BG, and BF are:

FD = 6

AD = 0

AG = 6

BG = 6

BF = 12

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Answer:

year 1: 90% × 245000 = 220500

year 2: 90% × 220500 = 198450

year 3: 90% × 198450 = 178605

∴ the car price after 3 years is 178605

explanation:

the value of car decreases 10%. that means the car price is 90%

The price of the car after 3 years will be 178605

We can calculate the value in the following way

Rate of decrease in car's price: 10%

Current price of the car: 245000

Value after 1 year, say value1= current value-10% of current value

\(value1=245000-\frac{10*245000}{100}\)

=245000-24500

=220500

After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.

Value of car after 2 years, say value2= value1- 10% of value1

\(value2=220500- (\frac{10*220500}{100})\)

=220500-22050

=198450

Similarly,

Value of car after 3 years, say value3= value2- 10% of value2

\(value3=198450- (\frac{10*198450}{100})\)

=198450-19845

=178605

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Answer:

p = 6 , q = 43

Step-by-step explanation:

x² + 12x - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

=x² + 2(6)x + 36 - 36 - 7

= (x + 6)² - 43 ← in the form (x + p)² - q

with p = 6 and q = 43

Answer:

B = 31°

a = 18.9

b = 11.3

Step-by-step explanation:

✔️B = 180° - (90° + 59°) (sum of triangle)

B = 31°

✔️Use trigonometric ratio to find a:

Reference angle = 59°

Side opposite to reference angle = a

Hypotenuse = 22

Thus,

Sin 59 = a/22

Multiply both sides by 22

22*sin 59 = a

18.9 = a

a = 18.9 (nearest tenth)

✔️Use trigonometric ratio to find a:

Reference angle = B = 31°

Side opposite to reference angle = b

Hypotenuse = 22

Thus,

Sin 31 = b/22

Multiply both sides by 22

22*sin 31 = b

11.3 = b

b = 11.3 (nearest tenth)

Answer:

1366.66 ft³

Step-by-step explanation:

12ft × 8ft × 12ft = 1152 ft³

214.66 ft³ + 1152 ft³

1366.66 ft³

Answer:

The total volume of the trailer is 1366.6 ft^3

Step-by-step explanation:

12 * 8 = 96

96 * 12 = 1152 ft^3

1152ft^2 + 214.66 = 1366.6 ft^3

sorry I was late.

The formula for y in terms of x is y=160​/x^2.

We are given that;

y = 20 when t=4

And t = 8 when x = 2

Now,

To find the value of k by using the fact that y = 20 when t = 4:

20=k⋅4

k=5

Also, y=5t

Next, we use the fact that t is inversely proportional to the square of x. We can write:

t=x2k​

where k is a constant of proportionality. We can find the value of k by using the fact that t = 8 when x = 2:

8=22k​

k=32

Now we know that:

t=x232​

Substituting this into the equation for y:

y=5t=5⋅x232​=160​/x^2

Therefore, by proportions the answer will be y=160​/x^2.

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Answer:

Hunting and Gathering

Step-by-step explanation:

Men would be in charge of hunting and gathering thus leaving women to bear the brunt of household decisions.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Step-by-step explanation:

If you are talking about an inverse function f-1(x) of the function f(x), you must remember that, by definition,

f(f-1(x)) = x

So given f(x) = x/4 if I apply an arbitrary K which is equal to f-1(x), then

f(K) = x

K/4 = x

K = 4x

But I want to recover f-1(x), so replace it back.

f-1(x) = 4x

Done

Answer:

2+x>24

Step-by-step explanation:

X more than 2 indication addition, which would be 2+x. That value is greater than 24, which means it will be on the open side of the greater than symbol, giving us 2+x>24.

Answer:

Step-by-step explanation:

(9).

3 multiplied by b

the product of 3 and b

(10).

2 + x > 24

The measure of the side OP for the given figure is equal to 6. The correct option is d.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

For the two objects to be similar the ratio of the two corresponding sides of one shape is equal to the ratio of the two corresponding sides of another shape.

Given that in the figure there are two triangles triangle MNP and the triangle QOP both the triangles are similar.

The value of OP will be calculated as below,

MP / NP = PQ / OP

( 3 + 4 ) / ( OP + 8 ) = 3 / OP

7OP = 3( OP + 8 )

7 OP = 3 OP + 24

4 OP = 24

OP = 24 / 4

OP = 6

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Step-by-step explanation:

f(3)=2(3)+1

6+1

7

answer is 7

Answer:

f(3)=15

Step-by-step explanation:

just put 3 instead of x

Answer:

20%

Step-by-step explanation:

When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.

Hence,

8 is 20% of 40.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

The answer is option B.

Step-by-step explanation:

Let the percentage be x

We have

\( \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20\)

Hope this helps you

Answer:

It is 16

Step-by-step explanation:

Because 64÷4=16 80÷5=16 96÷6=16

So to find the constant of portionality you divide the second number by the first number.

Answer:its 16

Step-by-step explanation:

The answer is 0.471 radians.

FORMULA:

Just do 27° × π/180 = 0.4712rad but then cut off the two.