Please answer ASAP. The question is down below

Answer:

The height of the flag pole is approximately 19 feet and 2 inches.

Step-by-step explanation:

Let suppose that length of the shadow of the object is directly proportional to its height. Hence:

[tex]l \propto h[/tex]

[tex]l = k\cdot h[/tex]

Where:

[tex]h[/tex] - Height of the object, measured in inches.

[tex]l[/tex] - Shadow length of the object, measured in inches.

[tex]k[/tex] - Proportionality constant, dimensionless.

Now, let is find the value of the proportionality constant: ([tex]h = 5\,\frac{1}{4} \,ft[/tex] and [tex]l = 2\,ft\,\,10\,\frac{1}{2}\,in[/tex])

[tex]h = \frac{21}{4}\,ft[/tex]

[tex]h = \left(\frac{21}{4}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)[/tex]

[tex]h = 63\,in[/tex]

[tex]l = (2\,ft)\cdot \left(12\,\frac{in}{ft} \right) + \frac{21}{2}\,in[/tex]

[tex]l = 24\,in + \frac{21}{2}\,in[/tex]

[tex]l = \frac{48}{2}\,in+\frac{21}{2}\,in[/tex]

[tex]l = \frac{69}{2}\,in[/tex]

Then,

[tex]k = \frac{l}{h}[/tex]

[tex]k = \frac{\frac{69}{2}\,in }{63\,in}[/tex]

[tex]k = \frac{69}{126}[/tex]

[tex]k = \frac{23}{42}[/tex]

The equation is represented by [tex]l = \frac{23}{42}\cdot h[/tex]. If [tex]l = 10\,\frac{1}{2}\,ft[/tex], then:

[tex]l = \frac{21}{2}\,ft[/tex]

[tex]l = \left(\frac{21}{2}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)[/tex]

[tex]l = 126\,in[/tex]

The height of the flag pole is: ([tex]l = 126\,in[/tex], [tex]k = \frac{23}{42}[/tex])

[tex]h = \frac{l}{k}[/tex]

[tex]h = \frac{126\,in}{\frac{23}{42} }[/tex]

[tex]h = \frac{5292}{23}\,in[/tex]

[tex]h = 230\,\frac{2}{23}\,in[/tex]

[tex]h = \frac{115}{6}\,ft\,\frac{2}{23}\,in[/tex]

[tex]h = 19\,\frac{1}{6}\,ft \,\frac{2}{23}\,in[/tex]

[tex]h = 19\,ft\,\,2\,\frac{2}{23}\,in[/tex]

[tex]h = 19\,ft\,\,2\,in[/tex]

The height of the flag pole is approximately 19 feet and 2 inches.

Answer: The frog fell asleep for 4 nights.

Step-by-step explanation: First, he climbs up 3m every night. there are 16 nights before he gets to 29m. He has not climbed up for the 16th day so 15*3= 45. 45-29= 16. 16/4=4. The frog slept for 4 nights.

Answer:

Step-by-step explanation:

The function is f(x)=x^2 + ax + b

Derivate the function:

● f'(x)= 2x + a

Solve the equation f'(x)=0 to find a

The minimum is at (3,9)

Replace x with 9

● 0 = 2×3 + a

● 0 = 6 + a

● a = -6

So the value of a is -6

Hence the equation is x^2 -6x+b

We have a khown point at (3,9)

● 9 = 3^2 -6×3 +b

● 9 = 9 -18 + b

● 9 = -9 +b

● b = 18

So the equation is x^2-6x+18

Verify by graphing the function.

The vetex is (3,9) and it is a minimum so the equation is right

Answer:

Option (B).

Step-by-step explanation:

From the figure attached,

There are two pieces of the function defined by the graph.

1). Curve with the domain (-∞, 2)

2). Straight line with domain (2, ∞)

1). Function that defines the curve for x < 2,

  f(x) = |4 - x²|

2). Linear function which defines the graph for x ≥ 2 [Points (2, 2), (4, 4), (6, 6) lying on the graph]

  f(x) = x

Therefore, Option (B) will be the answer.

Answer:

unsimplified improper fraction

Step-by-step explanation:

8/2 could be simplified into 4 and its an improper fraction bc proper fraction form is 4/1 or just 4

Answer:

Step-by-step explanation:

[tex]Midpoint = (3,-2)\\1st \: endpoint = (1,6)\\2nd \: endpoint = ?\\\\\\Let \: (1,6) \:be \:x_1y_1\\Let\:(3,-2)\: be\:x\:and\:y\\\\x=(x_1+x_2)/2\\y=\frac{(y_1+y_2)}{2} \\\\3 =\frac{1+x_2}{2} \\\\3\times 2 =1+x_2\\\\6 = 1+x_2\\6-1=x_2\\\\x_2 =5\\\\y=\frac{(y_1+y_2)}{2} \\-2 = \frac{6+y_2}{2}\\\\ -2 \times 2= 6+y_2\\\\-4 = 6+y_2\\\\-4-6=y_2\\\\y_2 = -10\\\\Answer = (5 ,-10)[/tex]

Answer:

6x

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

Answer:

Least common denominator = (x - 1)²(x - 2)

Step-by-step explanation:

Least common denominator of two rational expressions = LCM of the denominator of the expressions.

[tex]\frac{x^3}{x^2-2x+1}[/tex] and [tex]\frac{-3}{x^{2}-3x+2}[/tex]

Factorize the denominators of these rational expressions,

Since, [tex]x^{2}-2x+1[/tex] = x² - 2x + 1

                             = (x - 1)²

And x² - 3x + 2 = x² - 2x - x + 2

                         = x(x - 2) -1(x - 2)

                         = (x - 1)(x - 2)

Now LCM of the denominators = (x - 1)²(x - 2)

Therefore, Least common denominator will be (x - 1)²(x - 2).

Answer:

C!

Step-by-step explanation:

Answer:

y=-12+2x

Step-by-step explanation:

The equation was transformed step-by-step to isolate y on one side, and we obtained y = 2x - 12 as the final solution.

Hence, the correct answer is A. y = 2x - 12.

Given is an equation 6x - 3y = 36, we need to solve for y.

To solve the equation 6x - 3y = 36 for y, we need to isolate y on one side of the equation.

Here's the step-by-step process:

Start with the given equation: 6x - 3y = 36

Get rid of the constant term (36) on the right side by subtracting 36 from both sides:

6x - 3y - 36 = 36 - 36

6x - 3y = 0

Divide both sides of the equation by -3 to isolate y:

(6x - 3y) / -3 = 0 / -3

(6x)/(-3) - (3y)/(-3) = 0

-2x + y = 0

Add 2x to both sides to isolate y:

-2x + y + 2x = 0 + 2x

y = 2x

So, the equation was transformed step-by-step to isolate y on one side, and we obtained y = 2x - 12 as the final solution.

Hence, the correct answer is A. y = 2x - 12.

Learn more about Equations click;

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Answer:

[tex]Net\ Change = \$13997.53[/tex]

Step-by-step explanation:

Given

[tex]Debt = \$15,234.68[/tex]

[tex]Monthly\ Payment= \$247.43[/tex]

[tex]Duration = 5\ months[/tex]

Required

Determine the net change

First, we need to determine the total repaid amount;

[tex]Amount = Monthly\ Payment * Duration[/tex]

Substitute values for Monthly Payment and Duration

[tex]Amount = \$247.43 * 5[/tex]

[tex]Amount = \$1237.15[/tex]

The net change is the difference between the loan amount and the repaid amount

[tex]Net\ Change = Loan\ Amount - Repaid\ Amount[/tex]

[tex]Net\ Change = \$15,234.68 - \$1237.15[/tex]

[tex]Net\ Change = \$13997.53[/tex]

Hence, the net change over the period of 5 months is $13997.53

Answer: Quiana's initial loan amount is -15, 234.68. This is the total amount of money she must pay back to the lender.

Answer:

72

Step-by-step explanation:

As you can see the top - view is a rectangle of 2 by 9 dimensions. Respectively the right - side view is a rectangle of 2 by 4 dimensions. The common dimension among both rectangles would be 2, making this rectangular prism have dimensions 2 by 4 by 9.

Therefore the rectangular prism will have a volume of 2 [tex]*[/tex] 4 [tex]*[/tex] 9

2 [tex]*[/tex] 4 [tex]*[/tex] 9 = 8( 9 ) = 72 cubic units

Solution : 72 unit cubes

Answer:

The outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

Step-by-step explanation:

The outcomes provided are:

(A) 0, 1, 2, 6, 7, 8

(B) 0, 1, 2, 7, 8

(C) 0, 1, 7, 8

(D) 0, 1, 2, 8

Solution:

The random variable X can be defined as the number of employees who judge their co-workers by cleanliness.

The probability of X is:

P (X) = 0.65

The number of employees selected is:

n = 8

An unusual outcome, in probability theory, has a probability of occurrence less than or equal to 0.05.

Since outcomes 0 and 1 are contained in all the options, we will check for X = 2.

Compute the value of P (X = 2) as follows:

[tex]P(X=2)={8\choose 2}(0.65)^{2}(0.35)^{8-2}[/tex]

                [tex]=28\times 0.4225\times 0.001838265625\\=0.02175\\\approx 0.022<0.05[/tex]

So X = 2 is unusual.

Similarly check for X = 6, 7 and 8.

P (X = 6) = 0.2587 > 0.05

X = 6 not unusual

P (X = 7) = 0.1373 > 0.05

X = 7 not unusual

P (X = 8) = 0.0319

X = 8 is unusual.

Thus, the outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

Answer:

Surface area of a cone = 461.58 In²

Step-by-step explanation:

Surface area of a cone = πrl + or

Surface area of a cone = πr(r+l)

Where r = radius

Radius= diameter/2

Radius=14/2

Radius= 7 inch

And l slant height= 14 inch

Surface area of a cone = πr(r+l)

Surface area of a cone = π*7(7+14)

Surface area of a cone = 7π(21)

Surface area of a cone = 147π

Surface area of a cone = 461.58 In²

Answer:

4/20

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The probability of landing on tails for any fair coin is [tex]\frac{1}{2}[/tex], or 50%. It doesn't matter how many times you've landed on heads/tails before, it always remains at [tex]\frac{1}{2}[/tex].

Hope this helped!

Answer:

two games must be won by the team

Step-by-step explanation:

Let the no. of games played by x, since  team

does not lose any more games.

Then total game won = 6+x

total game lost = 4

win: loss = 6+x : 4

given ratio of win and loss = 2:1

6+x : 4 = 2: 1

6+x = 8

=> x = 8-6 = 2

Thus, two games must be won by the team

then total win will be = 6+2 = 8

and loss = 4

ration of win : loss = 8:4 = 2:1

Answer:

I would gues c because brown is the hardest to see in the dark

Answer:

C dark brown

Step-by-step explanation:

Answer:

m=48

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

m = 48

▹ Step-by-Step Explanation

Rewrite:

m/8 = 6

Use the inverse operation:

8 * 6 = 48

m = 48

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer: 180x5y2

Hope this helps!

Answer:

[tex]180x^5y^2[/tex]

Step-by-step explanation:

[tex]5x^3y^4(6xy^-^1)^2\\5x^3y^4(6^2x^2y^-^1^(^2^))\\5x^3y^4(36x^2y^-^2)\\180x^5y^2[/tex]

Answer:

I hope it helps.

The solutions in photo ^_^

Answer:

5 -3 = 2

3-5 = -2

Step-by-step explanation:

In this question, we want to examine the validity of the statement by the use of an example.

Firstly, we need to understand the meaning of the fact that they are ‘closed’

By saying these numbers are closed under this arithmetic operation i.e subtraction, we directly mean that they obey the closure property.

Now, to obey the closure property means that if we move either way i.e by switching the numbers and performing the same arithmetic operation of subtraction, we are supposed to get same answer.

What this means in terms of examples is as follows;

Consider two positive numbers, 5 and 3

Now we know that 5-3 = 2

To check if the closure property is obeyed, switch the place of the numbers.

This means we would have;

3-5 = -2

We can see that both results are not the same. We can then conclude that the arithmetic operation of subtraction is not closed or does not obey the closure property for positive numbers.

Answer:75

Step-by-step explanation:54+21

Answer:

15 bicycles, 6 skateboards

Step-by-step explanation:

We are looking for the number of skateboards and the number of bicycles. Those two numbers are our unknowns.

We define variables for those two numbers.

Let s = number of skateboards.

Let b = number of bicycles.

A skateboard has 4 wheels. s number of skateboards have 4s wheels.

A bicycle has 2 wheels. b bicycles have 2b wheels.

The total number of wheels is 4s + 2b.

The total number of wheels is 54, so our first equation is

4s + 2b = 54

The total number of skateboards and bicycles combined is s + b.

We are told the total number of skateboards and bicycles combined is 21.

The second equation is

s + b = 21

We have a system of two equations in two unknowns.

4s + 2b = 54

s + b = 21

We can solve it by the elimination method.

Rewrite the first equation below.

Multiply both sides of the second equation by 2 and write it below that. Then add the equations.

          4s + 2b = 54

(+)      -2s - 2b = -42

-----------------------------

          2s         = 12

s = 6

There are 6 skateboards.

Now we substitute 6 for s in the second original equation and solve for b.

s + b = 21

6 + b = 21

b = 15

There are 15 bicycles.

Answer: 15 bicycles, 6 skateboards

Answer:

2/3

Step-by-step explanation:

Hey there!

Well in the equation,

y = 2/3x - 3

the slope is 2/3 because the equation shows 2/3x and wherever the x is in slope intercept that the slope.

Hope this helps :)

6:40 or 6 hour 40 minutes,

if you go back(subtract) 1 hour and 40 minutes

i.e. 6hours 40 minutes- 1 hour 40 minutes

subtract minutes from minutes and hours from hours,

5:00

note that here the minutes value is not negative so it was not a problem, what If it was 6:40-1:50?

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion [tex]\hat p[/tex]= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]

the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]

[tex]S,E = 0.0144[/tex]

Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: [tex]\hat p - E[/tex]

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: [tex]\hat p + E[/tex]

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Answer:

0.5625 ft^2

Step-by-step explanation:

area of square = side * side

A = s^2

A = (0.75 ft)^2 = (0.75 ft)(0.75 ft) = 0.5625 ft^2

Answer:

30.51 meters

Step-by-step explanation:

Given that:

The distance from the point to the base of the tower = 42 m, the angle of elevation = 36°.

According to sine rule if a,b,c are the sides of a triangle and its respective opposite angles are A, B, C. Therefore:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Let the height of the tower be a and the angle opposite the height be A = angle of elevation = 36°

Also let the  distance from the point to the base of the tower be b = 42 m, and the angle opposite the base of the tower be B

To find B, since the angle between the height of the tower and the base is 90°, we use:

B + 36° + 90° = 180° (sum of angles in a triangle)

B + 126 = 180

B = 180 - 126

B = 54°

Therefore using sine rule:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}\\\\\frac{a}{sin(36)}=\frac{42}{sin(54)}\\\\ a=\frac{42*sin(36)}{sin(54)}\\ \\a=30.51\ meters[/tex]

The height of the tower is 30.51 meters

Answer:

Step-by-step explanation:

7x - 21 + 12 - 3x = -8

4x - 9 = -8

4x = 1

x = 1/4

Answer:

x= 0.25, or x=1/4

Step-by-step explanation:

First, use the distributive property and multiply 7 within the parenthesis:

7x -21

Next, use the distributive property again, and multiply 3 within the parenthesis:

12 -3x

Combine Like terms: 7x - 21 + 12 - 3x

4x - 9

Add 9 to both sides: 4x - 9 = -8

-8 + 9 = 1

Divide 4 by both sides: 4x = 1

1 / 4 = .25 or 1/4

Answer:

-3x + y = 8.

3y = 9x.

Step-by-step explanation:

To find the slope of the lines we convert to slope-intercept form, which is

y = mx + c   (m is the slope.)

The slope of y = 3x + 5 is therefore 3.

Parallel lines have the same slope.

Finding the slope of the given lines:

-3x + y = 8

y = 3x + 8  - slope is 3 so this is parallel to  y = 3x + 5.

3y = 9x

Divide through by 3:

y = 3x  - so this is also parallel to 3x + 5.

y = -jx  The slope is -j so it is not parallel.

16x + 2y = 12

2y = -16x + 12

y = -8x + 6  - Not parallel.

Answer:

12 mangoes

Step-by-step explanation:

Two types of boxes contains mangoes

The larger box contain 4 mangoes than the number of mangoes that is present in 8 smaller box

Each of the box have a total of 100 mangoes

Let y represent the number of mangoes that is present in the smaller box

Therefore, the number of mangoes in the smaller box can be calculated as follows

8y + 4= 100

Collect the like terms

8y= 100-4

8y= 96

Divide both sides by the coefficient of y which is 8

8y/8= 96/8

y= 12

Hence the number of mangoes that is present in the smaller box is 12