MATHEMATICS COLLEGE

3(5/10)-(4/8) pls asap

Answers

Answer 1
Answer:

Answer:

-51.

Step-by-step explanation:

3 x 5 is 15

3 x 10 is 30

3 x 4 is 12

3 x 8 is 24.

15 - 30 - 12 - 24

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Is 6 a solution of 5(c - 9) = - 15?
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The owner of a grocery store wants to mix two kinds of candy together to make 15 lb that he can sell for $5.00 per lb. He wants to use chocolate candies that he sells for $7.00 per lb and sugar candies that he sells for $2.00 per lb. How many pounds of each should the owner use?_ pounds of chocolate candies
_ pounds of sugar candies
=OWO=

Answers

Answer: 9 pounds of chocolate and 6 pounds of sugar candies

Let's define the variables:

C = pounds of chocolate candies used.

S = pounds of sugar candies used.

We know that he wants to make a total of 15lb, then:

C + S = 15

We also want that the price per pound to be equal to 5$.

This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.

C*$7.00 + $2.00*S = $5.00*15

Then we have a system of equations:

C + S = 15

C*$7.00 + $2.00*S = $5.00*15

To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:

C = 15 - S

now we can replace that in the other equation:

(15 - S)*$7.00 + $2.00*S = $5.00*15

Now we can solve this for S.

$105 - $5.00*S = $75

$105 - $75 = $5.00*S

$30 = $5.00*S

$30/$5 = S = 6

Then there are 6 pounds of sugar candy, and we can use the equation:

C + S = 15

C + 6 = 15

C = 15 - 6 = 9

There are 9 pounds of chocolate candy in the mix.

Step-by-step explanation:

Final answer:

To find the pounds of chocolate and sugar candies the owner should use, set up and solve equations based on the given information.

Explanation:

Let's assume that the owner uses x pounds of chocolate candies and y pounds of sugar candies.

According to the problem, the total weight of the candies should be 15 pounds.

So, we can set up the equation:

  1. x + y = 15

The owner wants to sell the candies for $5.00 per pound. We can set up another equation to represent the total value of the candies:

  1. 7x + 2y = 5 * 15

Now we can solve these equations to find the values of x and y.
By solving the equations, we find that x = 9 and y = 6.

Therefore, the owner should use 9 pounds of chocolate candies and 6 pounds of sugar candies.

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.4 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Answers

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

During that time, his shadow on the wall is y = BC

ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

(AD)/(AB) = (DE)/(BC)

(8)/(12) = (2)/(y)

8y = 24

y = 24/8

y = 3 meters

Let take an integral look  at the distance of the man from the building as x, therefore the distance from the spotlight to the man is  12 - x

∴

(12-x)/(12)=(2)/(y)

1- (1)/(12)x = 2* (1)/(y)

To find the derivatives of both sides ;we have:

- (1)/(12)dx = 2* (1)/(y^2)dy

- (1)/(12) (dx)/(dt) = 2* (1)/(y^2) (dy)/(dt)

During that time ;

(dx)/(dt )= 1.4 \ m/s   and y = 3

So; replacing the value into above ; we have:

-(1)/(12)(1.4) = - (2)/(9) (dy)/(dt)

(dy)/(dt) = \frac{\frac{ 1.4} {12 } }{ (2)/(9)}

(dy)/(dt) = {\frac{ 1.4} {12 } }*{ (9)/(2)}

(dy)/(dt) =0.525 \ m/s

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

(10 points) Starting salaries of 64 college graduates who have taken a statistics course have a mean of $42,500 with a standard deviation of $6,800. Find an 90% confidence interval for ????. (NOTE: Do not use commas or dollar signs in your answers. Round each bound to three decimal places.) Lower-bound: 41101.87 Upper-bound: 43898.13

Answers

Answer:

41101.750 to 43898.250

Step-by-step explanation:

Using this formula X ± Z (s/√n)

Where

X = 42500 --------------------------Mean

S = 6800----------------------------- Standard Deviation

n = 64 ----------------------------------Number of observation

Z = 1.645 ------------------------------The chosen Z-value from the confidence table below

Confidence Interval Z

80%. 1.282

85% 1.440

90%. 1.645

95%. 1.960

99%. 2.576

99.5%. 2.807

99.9%. 3.291

Substituting these values in the formula

Confidence Interval (CI) = 42500 ± 1.645(6800/√64)

CI = 42500 ± 1.645(6800/8)

CI = 42500 ± 1.645(850)

CI = 42500 ± 1398.25

CI = 42500+1398.25 ~. 42500-1398.25

CI = 43898.25 ~ 41101.75

In other words the confidence interval is from 41101.750 to 43898.250

Final answer:

To find a 90% confidence interval for the mean starting salary, use the formula CI = sample mean ± (Z * sample standard deviation / √n).

Explanation:

To find a 90% confidence interval for the mean starting salary, we will use the formula:

CI = sample mean ± (Z * sample standard deviation / √n)

Given that the sample mean is $42,500, the sample standard deviation is $6,800, and the number of college graduates is 64, we can substitute these values into the formula to calculate the confidence interval. The lower-bound is $41,101.87 and the upper-bound is $43,898.13.

Learn more about Confidence Interval here:

brainly.com/question/34700241

#SPJ11

A triangle has sides with lengths of 8 kilometers, 13 kilometers, and 16kilometers. Is it a right triangle?

Answers

No, It’s not a right triangle.
We can prove by using Pythagoras theorem
Let the longest length be hypotenuse and shortest length be base now,

h^2=p^2+b^2
16^2=13^2+8^2
256=169+64
246=233


Hence it is not equal with hypotenuse
In right triangle the sum of the squares of two short sides should be equal to hypotenuse

Find the value of x​

Answers

Answer:

x = 70

Step-by-step explanation:

the sum of the interior angles of a hexagon is 720 degrees. All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 720 degrees.

Now,

102+146+158+120+124+x=720

or,650+x=720

or,x=70

Therefore The value of X is 70 degree.
no x’s have no value

What is the 100th term in the pattern with the formula n+7

Answers

To find it, put 100 where n is in the formula and evaluate
.. n + 7
for n = 100
.. 100 +7
.. = 107

The 100th term is 107.
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