To measure the height of a mountain, a surveyor took two sightings, one 1000 feet farther from the mountain of the other. The first angle of elevation was 85° and the second was 83°.
What is the mountain’s height?

Answer: P = 96 - 30 + 9.48

Step-by-step explanation:

The price of the jacket is $96.

The discount is 31.25% and

The sales tax is 9.875%

To find the price paid, we subtract the discount from the original price and add the sales tax. This will be:

P=96 - (31.25% × 96)+(9.875% × 96)

P = 96 - 0.3125(96) + 0.09875(96)

P = 96 - 30 + 9.48

P = 75.48

Where,

P stands for the final price.

The first term (96) shows the initial price.

The second term (-30) is about the discount which has to be negative.

The final term (+9.48) is about the sales tax which must be added to have the total price.

Answer:

Sunflower because it has the fewest number of them all

Sunflower is having the fewest number of 8 amongst all.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Ruby has a basket of roses, lilies, orchids, and sunflowers. She picks a flower by chance and replaces it. She repeats this experiment 80 times and gets the results shown in the table.

rose            -       16

lily               -       24

orchid         -       32

sunflower   -       8

From the above table we can see that the sunflower has the fewest number.

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Answer:

It was colder on Wednesday morning than Monday morning.

Step-by-step explanation:

(How I know)

-Friday did not have the coldest temperature because Wednesday did.

-it became warmer after Wednesday

-It was colder on Wednesday morning than on Tuesday morning

--8 degrees is colder than -2 degrees.

It was colder on Wednesday morning than Monday morning. Then the correct option is D.

The degree of warmness and coldness is determined by the temperature.

Anna sees a thermometer each morning when she walks out of her house to get on the school bus.

In the following table, she recorded the outdoor temperature each morning for five days.

      Days                         Temperature

   Monday                               -2 °C

  Tuesday                               -3 °C

Wednesday                            -8 °C

  Thursday                             -5 °C

    Friday                                 0 °C

If temperature is negative, then it means more coldness.

It was colder on Wednesday morning than Monday morning.

Then the correct option is D.

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Answer:

Larger hose will take 18 minutes and 45 seconds

Step-by-step explanation:

ONE smaller hose fills the pool in 5*15 = 75 minutes.One large hose can do this job in  75/4 minutes = 18 3/4 minutes = 18 minutes and 45 seconds

The larger hose will take 18 minutes and 45 seconds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

One smaller hose fills the pool in 5 x 15 = 75 minutes.

One large hose can do this job,

Time = 75/4 minutes = 18 3/4 minutes

Time = 18 minutes and 45 seconds

Therefore, the larger hose will take 18 minutes and 45 seconds.

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Answer:

E

Step-by-step explanation:

Answer: "x" : 3, "star" : 2/3, "circle" : 2 1/3, "square" : 4 2/3

Step-by-step explanation:

The number line is divided into segments that are thirds of a whole number. The question is asking where the shapes fall on the number line. For shapes that do not fall on a whole number, they fall on a fractional portion of a whole number, hence why they are a mixed number.

Answer:

Magda is incorrect

Step-by-step explanation:

Given

Formula:

[tex]K = \frac{P}{2.59M}[/tex]

Population Density of Canada = 3.57 people per km²

Population of Russia = 143.96 million

Land Mass of Russia = 6.593 million square miles

Required

Which country has a greater population density.

First, the population density of Russia needs to be calculated using the given formula;

[tex]K = \frac{P}{2.59M}[/tex]

Here, P = 143.96 million

M = 6.593 million square miles

Substitute these values in the above formula;

[tex]K = \frac{143.96}{2.59 * 6.593}[/tex]

[tex]K = \frac{143.96}{17.07587}[/tex]

[tex]K = 8.43[/tex] people per square miles

Before we can make any comparison, we have to convert the unit of K to people per square kilometre.

From unit of standard conversion;

1 square miles = 2.58999 square kilometre

Hence;

[tex]K = \frac{8.43}{2.58999}[/tex]

[tex]K = 3.25483882177[/tex]

[tex]K = 3.25[/tex] people per km²

Given that the Population Density of Canada = 3.57 people per km²

And We solved for the Population Density of Russia = 3.25 people per km²

By Comparison, the Population Density of Canada is greater than the Population Density of Russia;

Hence, Magda is incorrect

Answer: 24%

Step-by-step explanation:

A company is expanding its building area from 16,500 square feet to 20,460 square feet. To calculate the percentage increase in the area of the building space, we first find the difference. This will be:

20,460 - 16,500 = 3960

We then divide the difference by the former building area and then multiply by 100. This will be:

3960/16500 × 100

= 0.24 × 100

= 24%

The percentage increase of the area of the building space is 24%.

Answer:

She ordered 85.7 packages as dog food

Step-by-step explanation:

Let b represent bird food, d represent dog food and c represent cat food.

The bird food is 4 times as much dog food. This can be represented as b = 4d

Also, the dog food is half the amount of cat food, it can be represented as d = 1/2c. Therefore, c = 2d

The total feed is 600.

Therefore dog feed + cat feed + bird feed = 600

d + 2d + 4d = 600

7d = 600

d = 600/7 = 85,7

She ordered 85.7 packages as dog food.

Answer:

62

Step-by-step explanation:

hope this helps

Answer:

12cm

Step-by-step explanation:

Answer:

16A. 42 cm

16B. 7 cm  

Step-by-step explanation:

Answer:

g(-5) = -6

Step-by-step explanation:

g(-5) is the value of the function when x = -5

When x = -5 the function ( or y value) is -6

Answer:14.58 miles.

Step-by-step explanation:

Matthew is training to participate in a half marathon.

The distance covered by Matthew on the first day is 12.5 miles.

The distance covered by Matthew on the second day is 13.5 miles.

The distance increased on the second day is, 13.5-12.5=1 mile.

The percentage will be,

=\dfrac{1}{12.5}\times 100\%

=0.08\times 100\%

=8\%

Hence, each day he runs 8% more. So the distance covered by him on day 3 will be,

=13.5+\left(13.5\times \dfrac{8}{100}\right)

=13.5+1.08

=14.58 miles

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Step-by-step explanation:

Answer:

Basic consensus is that that other answer is wrong. The actual answer is 19.22

Step-by-step explanation:

To find the common ratio you just do this, last number = 15.5, and first number = 12.5.

15.5/12.5 equals 1.24.

^That's the common ratio.^

using A(n) = a * r ^ n - 1,

you get 12.5 * 1.24 ^ 3 - 1, or just 12.5 * 1.24 ^ 2

and solving that problem, you get 19.22.

Confirm this by doing the same thing earlier, 19.22/15.5 is 1.24. Which is the ratio found earlier. So it checks out.

Answer:

87.92 ft

Step-by-step explanation:

The circumference of a circle can be found using the formula: c = 2pi(r) OR c = pi(d).

r stands for the radius, d stands for the diameter. Because you're given the diameter of the circle, you can simply multiply 28 by pi (3.14), and you'll get the circumference!

Answer:

10,000-500=9,500 is  what it is worth

Step-by-step explanation:

-3× - 5= 10+5

-3×=15

15÷-3 = -5

x= -5

Answer:

9

Step-by-step explanation:

9X6

=54

63-54

=9

Answer:

The correct answer is 6.

Step-by-step explanation:

There are "six" blue marbles in the given bag, which is the correct answer would be an option (D).

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Given that bag contains 15 marbles. The probability of randomly selecting a green marble is One-fifth.

The probability of randomly selecting a green marble and then randomly selecting a blue marble is 1/5 x P(blue), where P(blue) is the probability of selecting a blue marble.

As per the question, the probability of this event is 2/25, so we can set up the equation 1/5 x P(blue) = 2/25.

Solving for P(blue), we find that P(blue) = 2/5.

Since the probability of selecting a blue marble is 2/5, and there are 15 marbles in the bag, the number of blue marbles in the bag must be 15 x (2/5) = 6.

Therefore, the number of blue marbles in the bag must be 6.

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Answer:

5a + 5b - 6b

Step-by-step explanation:

In an equation -

2a + 8b + 10  - x  =   -3a + 7b +16

-x = -3a + 7b +16 -2a - 8b - 10

-x = -5a -b + 6

x = -(-5a -b + 6)

x = 5a + 5b - 6b

Answer:

(8.5, - 2 )

Step-by-step explanation:

Given the 2 equations

6x + 4y = 43 → (1)

2x - 3y = 23 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the term in x

- 6x + 9y = - 69 → (3)

Add (1) and (3) term by term to eliminate x, that is

13y = - 26 ( divide both sides by 13 )

y = - 2

Substitute y = - 2 in either of the 2 equations and solve for x

Substituting into (1)

6x + 4(- 2) = 43

6x - 8 = 43 ( add 8 to both sides )

6x = 51 ( divide both sides by 6 )

x = 8.5

Solution is (8.5, - 2 )

Answer:

16 notebooks

Step-by-step explanation:

I think you are asking how many notebooks she bought? just do 52/3.25=16

Answer:

The answer is 16 notebooks or in this case C

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Given

x² + 12x

To make the polynomial a perfect square

add ( half the coefficient of the x- term)²

= x² + 12x + 6²

= x² + 12x + 36

= (x + 6)² ← a perfect square

Answer:

1st sphere has r1 = 6

=> Surface area S1 = 4 x pi x r1^2 = 4 x pi x 6^2 = 144pi

=> Volume V1 = (4/3) x pi x r1^3 = (4/3) x pi x 6^3 =288pi

2nd sphere has r1 = 15

=> Surface area S1 = 4 x pi x r1^2 = 4 x pi x 15^2 = 900pi

=> Volume V1 = (4/3) x pi x r1^3 = (4/3) x pi x 15^3 =4500pi

=> S1/S2 = 144pi/900pi = 0.16

=> V1/V2 = 288pi/4500pi = 0.064

Hope this helps!

:)

The percentage change in temperature is 19.0%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the temperature rises from 21c to 29c.

The change in temperature is:

29c - 21c

= 4c

The percentage change in temperature from 21c is:

percentage change = (4c/21c)×100

                                 =4/21×100

                                 = 19.0%

Therefore, the percentage change in temperature is 19.0%.

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Given Information:

Principle amount = P = $6,000

Interest rate = r = 4% = 0.04

Period in years = t = 5

Required Information:

How much interest will he earn in 5 years = ?

Answer:

Amount of interest = $1,299.92

Step-by-step explanation:

Using the formula given in the question,

[tex]B = P(1 + r )^{t}[/tex]

Where B is the final amount, P is the initial amount, r is the interest rate and t is the number of years

[tex]B = P(1 + r )^{t}\\\\B = 6,000(1 + 0.04)^{5}\\\\B = 7,299.92[/tex]

The amount of interest earned is

[tex]Amount \:of\: interest = B - P \\\\Amount \:of \:interest = 7,299.92 - 6,000\\\\Amount \:of \:interest = 1,299.92[/tex]

Therefore, Quincy has earned $1,299.92 in terms of interest by investing  $6,000 in a savings account at the rate of 4% annual interest for a period of 5 years.

Answer:

(7, 5)

Step-by-step explanation:

9-2=7 x-coordinate

0+5=5 y-coordinate

Answer:

4.8

Step-by-step explanation:

Answer:

4.8 miles

Step-by-step explanation:

Let's make a proportion using this setup:

miles/minutes=miles/minutes

We know that Nicole runs 6 miles in 55 minutes. We don't know how many miles she runs in 44 minutes, so we can say she runs x miles in 44 minutes.

6 miles/55 minutes=x miles/44 minutes

6/55=x/44

Now, we have to find x. To do this, we need to get x by itself. x is being divided by 44. To undo this, multiply both sides by 44, since multiplication is the opposite of division.

44*(6/55)=(x/44)*44

The 44s on the right cancel, so we are left with:

44*6/55=x

4.8=x

Nicole can run 4.8 miles in 44 minutes