A man 1.75 meters tall cast a shadow 5.25 meters long. At the same time, a flagpole casts a shadow 120 meters long. How tall is the flagpole?

Answer:

30

Step-by-step explanation:

You can have any number on the first die, and any number besides the first one on the second. 6*5=30

Answer:

Yes! Extrapolation is fine. Don't worry about it.

Step-by-step explanation:

Because the data we have ranges from 8 to 22 inches, an extrapolation should be made, which is the process of estimating beyond the original observation interval, the value of the variable based on its relationship to another variable. It is similar to interpolation, which produces estimates between known observations, unlike this, extrapolation is subject to greater uncertainty and a higher risk of producing insignificant results, but because the value is 24 inches, it is not too far away. of the upper limit which is 22, the error should not be very big, therefore the answer is: Yes! Extrapolation is fine. Don't worry about it.

The right answer is 9 units.

please see the attached picture for full solution

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Answer:

fifth angle = 102°

Step-by-step explanation:

A pentagon is a polygon that have 5 sides. A pentagon can be divided into 3 triangles .And the sum of angle in a triangle is 180°. Therefore the sum of interior angle in a pentagon will  be 180 × 3 = 540°. The sum of interior angles of a pentagon = 540°.

The general rule for calculating sum of the interior angles of a polygon is

sum of interior angle = (n−2) × 180°

where

n = number of sides

n = 5 since we are dealing with a  pentagon.

sum of interior  angle of a pentagon = 540°

The fifth angle can be computed when you subtract the sum of the 4 angles from 540°.

fifth angle = 540 - (88 + 118 + 132 + 100)

fifth angle = 540 - 438

fifth angle = 102°

Answer:

its C on edg

Step-by-step explanation:

Step-by-step explanation:

The way i like to remember it is that the exponent inside of the radical will be the numerator of the fraction and the index of the radical will be the denominator so the answer is 2^(-5/3).

Answer:

0.6

Step-by-step explanation:

4/7 can be considered a suspended division problem.  To find the answer, 4 must be divided by 7.  This yields the result 0.57142, which can be rounded to 0.6.

Answer:

P=48 millimeters

Step-by-step explanation:

p=4l

p=4 x 12

p=48 mm

Answer:

The solution to [tex]3x\:-\:1\ge 12[/tex] is [tex]x\ge \frac{13}{3}[/tex].

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following symbols: inequalities involving "<", "≠" or ">" are referred to as "strict inequalities", while inequalities involving "≤" or "≥" are not.

Solving an inequality means finding all of its solutions. A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.

To find the solution to [tex]3x\:-\:1\ge 12[/tex]

[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\\\3x-1+1\ge \:12+1\\\\\mathrm{Simplify}\\\\3x\ge \:13\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}\ge \frac{13}{3}\\\\\mathrm{Simplify}\\\\x\ge \frac{13}{3}[/tex]

Step-by-step explanation:

[tex]sin(1 \div 4a + 20) = \sqrt{3} \div 2 \\ sin(1 \div 4a + 20) =sin 60[/tex]

1÷4a+20=60

1÷4a=4

a=1/160

Answer:

displacement x = - 0.046sin4t +0.006cos4t

Step-by-step explanation:

The model of the equation of motion is a forced motion equation and to determine the displacement of the weight as a function of time; we have:

the weight balances of the  elastic force in the spring  to be expressed by the relation:

mg = kx

where;

x=4 in (i.e  1/3 ft )

mass m = 6lb

let make k the subject; then:

k = mg/x = 6×32/(1/3) = 576

assuming  x to be the displacement form equilibrium;

Then;

[tex]F = 27sin 4t-3cos4t +k(x+1/3) - mg -3v[/tex]

(since F(t)=27sin 4t-3cos4t somehow faces downwards, mg=downwards and k(x+1/3)= upwards and medium resistance 3v =  upwards)

SO;

[tex]d2x/dt2 = 27sin 4t-3cos4t +kx - 3dx/dt[/tex]

[tex]d2x/dt2 +3dx/dt - 576x = 27sin 4t-3cos4t[/tex]

Assuming : [tex]x = asin4t + bcos4t[/tex]

[tex]dx/dt = 4acos4t - 4bsin4t[/tex]

[tex]d2x/dt2 = -16asin4t - 14bcos4t[/tex]

replacing  these values in the above equation

[tex]= -16asin4t - 14bcos4t + 12acos4t - 12bsin4t -576asin4t-576bcos4t = 27sin 4t-3cos4t[/tex]

[tex]= sin4t (-592a-12b) + cos4t(12a -590b) = 27sin 4t-3cos4t[/tex]

equating sin and cos terms

a = - 0.046 ;  b = 0.006

displacement x = - 0.046sin4t +0.006cos4t

Answer:

48.30

Step-by-step explanation:

First determine the tip

42 *15%

42 *.15 =6.30

Add this to the amount of the tip

42 + 6.30 =48.30

The total amount is 48.30

Answer:

Step-by-step explanation:

$48.30

Answer:

(a)  0.2650

(b)  0.0111

(c)  0.0105

(d)  0.0006

Step-by-step explanation:

Given that:

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.

Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15.       &;

If the area of the agar plate is 75cm²;

what is the probability  of observing fewer than 4 CFUs in a 25 cm² area of the plate.

We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;

75cm²/25cm² = 3

Since;

mean  μ = 15  

mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs

Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:

= P(X < 4)

Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )

we have ;

P(X < 4) = 0.2650

b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?

Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates =  15×5 = 75 CFUs

The probability is therefore = P( X > 95 )

= 1 - P(X ≤ 95)

= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)

= 0.0111

c) Repeat the probability calculation in part (b) but now use the normal approximation.

Let assume that the mean and the variance of the poisson distribution are equal

Then;

[tex]X \sim N (\mu = 75 , \sigma^2 = 75)[/tex]

We are to repeated the probability calculation in part (b) from above;

So:

P( X > 95 )

use the normal approximation

From standard normal variable table:

P(Z > 2.3094)

Using normal table

P(Z > 2.3094) = 0.0105

(d)  Find the difference between this value and your answer in part (b).

So;

the difference between the value in part c and part b is;

=  0.0111 - 0.0105

[tex]= 6*10^{-4}[/tex]

= 0.0006 to four decimal places

Answer:

B:

Step-by-step explanation:

IN THE ATTACHED FILE

Answer:

44.70 USD

Step-by-step explanation:

250÷1.3687

=182.655074158

182.655074158-150

=32.655074158

32.655074158×1.3687

=44.6950000001

The 44.70 US dollars Phelan now has if Phelan exchanged 250 US dollars for euros option (A) is correct.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip.

After returning to the United States he converts his money back to US dollars. H

Let x be the total original 250 US dollars Phelan now have:

The value of x can be found as follows:

x = (250/1.3687 - 150)x1.3687

After simplification:

x = 44.69 ≈ 44.70 US dollars

Thus, the 44.70 US dollars Phelan now has if Phelan exchanged 250 US dollars for euros option (A) is correct.

Learn more about the unit conversion here:

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Answer:

what is this it is not understand able

Answer:

11

Step-by-step explanation:

<TKF = 90° ( BECAUSE OF THE BISECTOR)

BUT

<TKF = 5(x+7)

So

5(x+7) = 90

5x+35 = 90

5x = 90-35

5x = 55

Dividing by 5(both sides)

x = 11

Answer:

$ 44

Step-by-step explanation:

If we analyze the statement well, we can observe something very crucial to solve it, the jumbo biscuits require 2 oz of flour and give a profit of $ 0.08, the Regular one that only requires 1 oz of flour leaves a profit of $ 0.11, which means that requiring a smaller quantity of flour leaves a greater profit, so in terms of profit it is not profitable to make Jumbo, only Regular.

Therefore, since you can make 400 biscuits, they would all be regular since there are 600 oz of flour available, it is enough to make 400, therefore the maximum profit would be:

$ 0.11 * 400 = 44

The maximum possible profit is $ 44

Answer:

A) 0.386

B).0.325

Step-by-step explanation:

probability p will not work = 0.15

Q probability w5ill work = 0.85

Number of flashlight = 3

Probabilty of at least one=

1- probability of none

But probability of none= 3C0(p)^0(q)^3

= 1*(0.15)^0(0.85)^3

= 1*1*(0.614)

= 0.614

Probability of at least one=1-0.614

= 0.386

Probability of two flashlight work

= 3C1(0.15)^1(0.85)^2

= 3*(0.15)*(0.7225)

= 0.325

Steps:

Shape: Cube

Solved for side length of the cube

Volume: 343 cubic feet

Formula: a=V⅓

Description:

Using the formula for the volume of the cube a=V⅓. We are going to calculate the side length of the cube. Your answer will be 7 feet. Meaning the correct answer for this question is C.

Answer: a≈7ft

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Hope this helps.

Answer:

f(x) = 15

Step-by-step explanation:

"If f(x)= 5x + 40, what is f(x) when x = -5?"

Substitute x for -5:

f(x) = 5x + 40

f(x) = 5(-5) + 40

f(x) = -25 + 40

f(x) = 15

Answer:

A

Step-by-step explanation:

2/3x=1-5

2/3x=-4

x=-4/2/3

x=-6

Answer:

40+5x=y

60+3x=y

Step-by-step explanation:

The first park is 40+5x

The second park is 60+3x

Now set them both equal to y

Answer: 573.75 meters^3

Step-by-step explanation:

Volume = Length x width x height

Volume = 17 x 13.5 x 2.5

Answer:

18.7 km

Step-by-step explanation:

3 cm >>>  7 km

1 cm >>> 7/3 km

8 cm >>> 8*7/3 km= 18.7 km

Answer:

18.7

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

32-6 = 26

Answer:

1/5x = h(x)

Step-by-step explanation:

6x+y = 4x+ 11y

Subtract y from each side

6x+y -y = 4x+ 11y-y

6x = 4x+10y

Subtract 4x from each side

6x-4x = 4x+10y-4x

2x = 10y

Divide each side by 10

2x/10 = 10y/10

1/5x = y

1/5x = h(x)

Answer:

T15 = 31

Step-by-step explanation:

Its in the picture

I hope it helps :)

Answer:

a. It is not likely that a winning ticket will be selected

b. The probability of winning enough to pay for the ticket expressed as a simplified fraction is 13/71

Step-by-step explanation:

To answer this question, there are some important notes to know.

1. The selection is only once

2. To win, you have to select a note which has a greater value than $8

Now, the total number of notes that we have = 38 + 20 + 7 + 5 + 1 = 71

The number of bills present that are greater than $8 are; 7 $10 bills , 5 $20 bills and 1 $100 bill

This makes a total of 7 + 5 + 1 = 13

Thus, the probability of selecting a bill which would pay for the charges is 13/71

Now, the probability of not selecting is 1- probability of selecting = 1-13/71 = 58/71

Since the probability of not selecting is greater than the probability of selecting, it means that it is not likely that a winning ticket will be selected

The requried equations that are equivalent to each other are,
(A)  2 + x = 5    (B) x + 1 = 4   (E) -5 + x = -2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Given equations,
(A) 2 + x = 5
Simplifying the above expression,

x = 5 - 2
x = 3

Similarly, simplify all the equations,
(B) x = 3
(C) x = -3
(D) x = 11
(E) x = 3

Therefore, equations that give x = 3, after simplification is equivalent equations.

Thus, the requried equations that are equivalent to each other are,
(A)  2 + x = 5    (B) x + 1 = 4   (E) -5 + x = -2.

Learn more about simplification here:

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