the measure of the angles of a triangle are shown in the figure below. solve for x

64°
x°
40°

a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]

The rental price of the house after 10 months = $16117.629

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Answer:

[tex]-2\sqrt{} 6x^{8}[/tex]

Step-by-step explanation:

Answer is y=1/2x+2 because the slope is 1/2 and the starting point is +2

Answer:B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It is given that lines k and p are parallel. You also know that angles 2 and 3 are equal because of vertical angles. Due to the parallel lines, you can say that angles 1 and 2 are equal because they are corresponding angles (same-side).

These two angles are not alternate interior angles because angle 1 is exterior and on the same side as angle 2. The third option would not make sense because you are trying to prove two angles are equal, not that lines are parallel.

From the given values, we know there are 2 defective resistors and 9 not defective. then, we have

where

denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,

denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.

Then, we have

then, the answer is

Answer:

1000000

Step-by-step explanation:

100000000:    2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5

100000:    2 2 2 2 2       5 5 5 5 5      

GCF:    2 2 2 2 2       5 5 5 5 5      

The Greates Common Factor (GCF) is:   2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 = 100000

Each child will receive the 1.1 cup of milk.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;

8  -  [tex]1\frac{2}{5}[/tex] = 8 -  7/5

= 40- 7/5

= 33/5

= 6.6

The the rest cups of milk = 6.6

Then the rest evenly among his three children 6.6/3 = 1.1

Hence, Each child will receive the 1.1 cup of milk.

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A family taking a road trip vacation travels 126 miles in 3 hours.

We can calculate the constant of proportionality as:

Then, in 5 hours they would travel:

In 5 hours they would travel 210 miles.

If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.

Using this formula to determine the monthly payment

P = A ×r × ( 1 +r)^n  ÷( 1+ r)^n -1

Where:

P = Principal = ?

A = Amount = $29,000 × ( 1- .10) = 26,100

r = Interest rate = 4.5% / 12 = 0.00375

n = number of months = 48 months

Let plug in the formula

P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1

P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1

P = 26,100 × 0.00375 × 1.196814377  ÷  1.196814377 -1

P = 26,100 × 0.00375 × 1.196814377  ÷  0.196814377

P = $117.1382456  ÷  0.196814377

P = $595.17

Therefore $595.17 is the monthly payment.

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Answer: 19

Step-by-step explanation:

[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]

[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]

without given any restriction x is all the numbers greater than 0.

NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

The researcher draws a random sample using a Multistage cluster sample

At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.

In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.

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Answer:

a₉₀ = 168

Step-by-step explanation:

there is a common difference between consecutive terms, that is

- 8 - (- 10) = - 6 - (- 8) = 4 - (- 6) = 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 10 and d = 2 , then

a₉₀ = - 10 + (89 × 2) = - 10 + 178 = 168

Answer:

F (false)

Step-by-step explanation:

i hope this helps! Have a good day! c:

Answer:

9 + 7 + 7.2 = 23.2

23.2 x 2 = 46.4

Step-by-step explanation:

The probability of getting a green of a yellow marble can be determined like this:

Probability = (yellow marbles + green marbles) / total number of marbles

Probability = (1 + 4) / 10

Probability = 5 / 10

Probability = 1/2

By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:

Number of predictions = 150 × 1/2

Number of predictions = 75

Then, the answer is 75 times

Answer:

75 times.

Step-by-step explanation:

There are a total of 10 marbles in the bag.

Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.

In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.

Probability a yellow marble is drawn (in 1 draw) = 1/10.

In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.

So, the number of times for a green or yellow marble

= 60+15= 75.

Answer: -2 1/2 or -2.5

Step-by-step explanation:

Yes, it can be simplified.

-5/2 can be simplified to -2 1/2 which can be as a decimal as -2.5

Answer: A.

Step-by-step explanation:

1. The function is even (symmetric about the y-axis)

2. The function F(x) is positive

[tex]\displaystyle\\Hence,\\F(x)=\frac{1}{x^2}[/tex]

Answer:

1)

b = 42° (corresponding angles, parallel lines)

2)

b + 31 + 90 = 180 (sum of angles on a straight line=180)

b = 59°

3)

b + 34 = 180 (sum of angles on a straight line=180)

b = 146°

4)

b + 30 + 90 = 180 (sum of angles on a straight line=180)

b = 60°

5)

b + 35 + 90 = 180 (sum of angles on a straight line=180)

b = 55°

6)

b = 58° (alternate angles, parallel lines)

The greatest possible integer of the inequality is 19.902.

What is the inequality?

In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, as to if it is less than or greater than. The different inequality symbols, properties, and methods for resolving linear inequalities inside one variable and two variables will all be covered in this article along with examples.

Given that,

3.806< 19.902

In which, less than inequality is used.

The given numbers are in decimal form.

comparison be between the given numbers and check which one is greater.

3.806< 19.902

19.902 is the greater than 3.806

Hence, the greatest possible integer is 19.902.
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Using the normal distribution, the probabilities are given as follows:

a) Between 210 and 220 for a single egg: 0.2586 = 25.86%.

b) Between 210 and 220 for the average of 25 eggs: 0.8164 = 81.64%.

c) Third quartile for the average of 25 eggs: 213 milligrams.

d) Less than 220 if less than 210: 0.1011 = 10.11%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the cholesterol levels are given as follows:

[tex]\mu = 215, \sigma = 15[/tex]

For item a, the probability is the p-value of Z when X = 220 subtracted by the p-value of Z when X = 210, hence:

X = 220:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (220 - 215)/15

Z = 0.33

Z = 0.33 has a p-value of 0.6293.

X = 210:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (210- 215)/15

Z = -0.33

Z = -0.33 has a p-value of 0.3707.

Hence the probability is:

0.6293 - 0.3707 = 0.2586.

For item b, we are dealing with a sample of 25, hence we apply the Central Limit Theorem as follows:

n = 25, s = 15/sqrt(25) = 3.

X = 220:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (220 - 215)/3

Z = 1.33

Z = 1.33 has a p-value of 0.9082.

X = 210:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (210 - 215)/15

Z = -1.33

Z = -1.33 has a p-value of 0.0918.

Then the probability is:

0.9082 - 0.0918 = 0.8164 = 81.64%.

The third quartile is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:

[tex]Z = \frac{X - \mu}{s}[/tex]

-0.675 = (X - 215)/3

X - 215 = -0.675 x 3

X = 213.

The conditional probability in item d is calculated as follows:

P(X < 210)/P(X < 220) = 0.0918/0.9082 = 0.1011 = 10.11%.

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The rate of change of angle of elevation between the radar station and airplane is

                       [tex]\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]

The airplane is flying at the speed of 200 mph

The airplane is at an altitude of 3 miles over the radar station

The distance travelled by the airplane after 3 mins

      distance = speed x time

                     = 200 mi/hr x 3 min

Since the speed is hour let us convert it to mins

                     = 200 x 3 x 1/60

                     = 600 / 60

                    = 10 miles

So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles

Then the elevation angle of the between radar station and airplane can be find by

                              tan θ = O / A
where O is the opposite side to the angle of elevation

          A is the adjacent side to the angle of elevation.

But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time

                                [tex]\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}[/tex]

                                        [tex]\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}[/tex]

                                       [tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}[/tex]

The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.

                                   [tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}[/tex]

We had found the value of sec²θ = (hyp/adj)²

                                    [tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}[/tex]

Now , let us convert in terms of rad/min

                                   [tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)[/tex]

                                  [tex]\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]    

Therefore , the rate of change of angle of elevation is -10/109 (rad/min)    

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Vector a = (3, 2), then;

Also, vector b = (-5, 6), then;

Then, -3a + 2b = (-9, -6) + (-10, 12)

The answer is (-19,6)

Equation (B) "y = 3x + 10" represents the growth of the puppy.

So, the equation that represents the situation:

Then:

For example, Salomon checks the weight for the 6th time then:

So, the equation is correct.

Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.

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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}

Which equation represents the growth of the puppy? Select one:

A. y = x + 3

B. y = 3x + 10

C. y = 10x + 3

D. y = x + 10

Answer:

Let's break down the given information.

Car A

Speed - 30 mph

Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.

Car B

Speed - 36 mph

The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.

Initial distance between the cars is 10 Miles

Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.

Hence to calculate the distance between the 2 cars we need to calculate

Initial distance - Distance travelled by Car A - Distance traveled by Car B

Which is

10 - 1 - 1.2

7.8 Miles distance between the 2 cars

The rate of the slowest car is 86 km/hr using the concept of relative velocity.

Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.

Let the speed of 1st car is v₁.

Let the speed of 2nd car is v₂.

v₁- v₂ = 18 km/hr --- (1)

And using the concept of relativity.

S(rel) = D(rel)/time

S(rel) = 360 / 2

S(rel) = 190

v₁ + v₂ = 190 --- (2)

Adding equations 1 and 2 we get

v₁ = 104 km/hr

v₂ = 86 km/hr

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The two linear equations are perpendicular.

Here we have the two linear equations:

12y - 4x = 84

y = -3x + 8

If we write both of them in the slope-intercept form (as the second one) we will get:

12y - 4x = 84

12y = 4x + 84

y = (4x + 84)/12

y = (1/3)*x + 7

Now, if we take the product of the slopes of the two lines, we get:

p = -3*(1/3) = -1

when this product is -1, the lines are perpendicular, so that is the relation between our lines.

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Solution:

From the given diagram;

The statements that are correct about the given diagram are

b)

d) The sum of exterior angles of a polygon is 360°,

Hence, the sum of the exterior angles of polygon ABCDE and the sum of exterior angles of polygon DEHGF is 720°

e)