Aftor and increased of 10% a Clercks
Salary was $13,250. Calcolate her salary
if an increase of 15% was given instead

The equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.

If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation is given below.

4x + 5y = 15

5y = −4x + 15

y = −(4/5)x + 3

The slope of the equation is −4/5. Then the slope of the perpendicular line will be 5/4. Then the equation is given as,

y = (5/4)x + c

The equation that passes through (−10, 2) will be

2 = (5/4)(−10) + c

2 = −12.5 + c

c = 14.5

Then the equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.

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Using the conversion of a fractional exponent to a rational expression, the equivalent expression to  x^(2/3) is given by:

K. [tex]\sqrt[3]{x^2}[/tex]

A fractional exponent is converted to a rational expression applying the law of indices, in which the numerator, which is the top term of the fraction, will be the power of the base, while the denominator, which is the bottom term of the fraction, represents the root.

The law of indices is illustrated as follows:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

In the context of this problem, the expression is:

x^(2/3).

Hence the coefficients are n = 2 and m = 3, and thus the equivalent expression is:

[tex]x^{\frac{2}{3}} = \sqrt[3]{x^2}[/tex]

Meaning that option K is correct.

The possible options for the question are missing, and are given by the image at the end of the answer.

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iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855%  of the population has an iq score between 70 and 115

What is z-score?

The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.

Using z tables, you may calculate the proportion of the population that is either below or above the score.

Now, according to the question;

IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.

A z score is determined as follows:

z = (x - μ)/σ

μ = mean of the distribution

σ = standard distribution of the sampling.

Calculation for the z score for x = 70 and  115

z= (70-100)/15

= -30/15

=-2

and x=115

z = (115 - 100)/15

= 15/15

z = 1.0

Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,

P( -2 < z < 1)= P(z<1) - P(z< -2)

                   =  0.8413 - 0.02275

                  = 0.81855

Therefore, the percent of the population has an iq between 70and 115 is 81.855%.

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Okay, here we have this:

Considering the provided information, we are going to calculate the speed at which he runs, so we obtain the following:

So we have the following equation:

Distance Traveled Walking + Distance Traveled Running = Total Distance

Distance Traveled Walking + Distance Traveled Running = 20 miles

And taking into account that speed is equal to distance over time, if we take speed to which runs as x we have:

((x/2) mi/h * 2h) + (x mi/h* 1.5h) = 20 miles

x mi+ 1.5x mi= 20 mi

2.5x mi=20mi

x = 20mi/2.5mi

x=8

Finally we obtain that he runs at 8 miles per hour.

Answer:

[tex]-5x^2 + 3x+9[/tex]

Step-by-step explanation:

Let the polynomial be p(x).

[tex]p(x)+(5x^2 -3x-9)=0 \\ \\ p(x)=-(5x^2 -3x-9) \\ \\ =-5x^2 + 3x+9[/tex]

If Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots

The total quantity of potting soil that she has =  [tex]5\frac{1}{3}[/tex] pounds

Convert  the mixed fraction to the simple fraction

[tex]5\frac{1}{3}[/tex] pounds = 16/3 pounds

The quantity of potting soil that required to fill one flowerpot = 1/4 pounds

Number of flowerpot that she can fill = The total quantity of potting soil that she has / The quantity of potting soil that required to fill one flowerpot

= 16/3 ÷ 1/4
= 16/3 × 4

= 64/3

= 21.33

≈ 21 flowerpot

Hence, if Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots

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By probability , An average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .

Describe probability using an example?

Suppose that, in a strand f DNA ,mutations occur randomly and independently of other mutations .

at an average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .

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Answer:

308

Step-by-step explanation:

Based on the given conditions, formulate: 7 x 572/13

Cross out the common factor: 7 x 44

Calculate the product or quotient: 308

Answer:

308

Step-by-step explanation:

572 divided by 13 is 44 which means there is 44 miles per gallon. So multiply 44 x 7 and you get 308 miles.

The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed = 8 : 4 : 1

Total numbers of words Li Zhen, Kara and Rose typed = 156 words

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Since, it's given that

    the number of words Kara typed = 48

number of words Li Zhen typed = 2 x 48

                                                      =96words

a)  The ratio of the number of words Kara typed to the number of words Rose typed = 4:1

Since, it's given that

    the number of words Kara typed = 48

let, the number of words Rose typed = x

then, by equating them we get,

4/1 = 48/x

       4x = 48

          x = 48/4

          x = 12

The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed :

=  96 : 48 : 12

= 8 : 4 : 1

b) Now we know that,

  The number of words Li Zhen typed = 96words

  The number of words Kara typed = 48words

  The number of words Rose typed = 12words

Then, the total numbers of words Li Zhen, Kara and Rose type altogether

                               = 96 + 48 + 12

                               = 156 words

Hence, the total numbers of words Li Zhen, Kara and Rose type altogether is 156 words

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James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. time  left after he finished cleaning is 4 hour 36 minutes

James took 97 minutes to clean his house.

there were 12 rooms in the house,

and it took him the same amount of time to clean each room

how much time did he have left after he finished cleaning?

one room clean =97 minutes

12 room clean = 97*12 amount of minutes

                        = 1164 minutes

                       = 19hour 24 minutes

James took 19 hour 24 minutes to clean 12 room

amount of time left = 24 hour - 19 hour 24 minutes

             = 4 hour 36 minutes

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Answer:

Step-by-step explanation:

Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years

Let the ages be x and x + 2 since they're consecutive odd integers.

We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:

x² + 4(x + 2) = 85

x² + 4x + 8 = 85

Collect like terms

x² + 4x + 8 - 85

x² + 4x - 77 = 0

x² + 11x - 7x - 77 = 0

x(x + 12) - 7(x + 11) = 0

x - 7 = 0

x = 0 + 7

Therefore, the age is 7 years.

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We will see that the slope of function B is 2, and the slope of function A is 1. This means that the correct equation is:

Slope of function B = 2*Slope of Function A

First, a general linear equation is:

y = a*x + b

Where a is the slope and b the y-intercept.

Here the function A is:

f(x) = x - 9

Then the slope is equal to 1.

We know that function B is a line that passes through (-1, -3) and (2, 3)

Then the slope is:

s = (3 + 3)/(2 + 1) = 6/3 = 2

So the slope of function B is 2, and the slope of function A is 1. Then the equation is:

Slope of function B = 2*Slope of Function A

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even if an independent variable has an effect on the dependent variable, it fail to reject the null hypothesis and make a type II error

Even if a treatment is effective in the real world (it has an effect), it is still possible to obtain a sample mean that is so similar to the population mean that the sample mean doesn't fall in the critical, or rejection, region. If this happens, you are likely to fail to reject the null hypothesis and make a type II error.

Since that sample mean is so similar to the population mean, the treatment effect may not be detected on analysis even though it is in fact significant, this will cause the research to erroneously concluded that the treatment effect is zero and accept the null hypothesis when it is actually not zero. This is a type II error. Type II error in statistics means the non-rejection of a false null hypothesis and type I error is the rejection of a correct null hypothesis.

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Answer:

22 cups in total

Step-by-step explanation:

In order to solve this problem we need to know how much money Mimi makes by just selling 1 cup of lemonade. We can find this by dividing

38/19 = 2

Now that we know how much money Mimi makes by just selling 1 cup of lemonade, we can use this to find how many cups she needs to sell in total to earn $44. We can use this equation

2x = 44 (x = cups of lemonade)

Now we solve for x

2x =44

/2    /2

x = 22

So Mimi needs to sell 22 cups in total to earn $44 dollars. Hope this helps :)

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

Bonus: she need to sell 3 more cups lol incase you need to know

Damien score on the fourth day is 86.

Damien played golf on each of the four days of his vacation and the average for the four days of was 90.

so, his score on the fourth day.

so firstly let, X, be his score on the fourth day. then, the other four day's score is already given so, by using the formula for average.

the average for four numbers is given by, the sum of all numbers divided by the total numbers. so, by using this formula we have

=>(93+92+89+X)/4=90.and ,

on solving this we got,

X=86.

that is our answer.

so, His score on the fourth day is 86

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Answer:

Step-by-step explanation:

[tex]\stackrel\ell{\boxed{\boxed{\begin{minipage}{7cm}\\\begin{aligned}\sf{3k-8=7}\\\downarrow\\\sf{3k=7+8}\\\downarrow\\\sf{3k=15}\\\downarrow\\\boxed{\boxed{\sf{k=5}}}\end{aligned}\end{minipage}}}}}[/tex]

I hope this helps!!

Answer:

5

step by step explaination

first side change -8=+8

7+8

now divide 15 by 3

Then

K=5

Rising or growing steadily and quickly: a city in exponential expansion. noun. Mathematics the value of the constant e raised to the power of a given expression, represented as the exponential of 3x, e3x. something that is positive and raised in power.

In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.

The values of f(x) and g(x) in the table for various values of f(x) = 9x + 7 and g(x) = 5x

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Ann must bowl 119 in the sixth game to have an average score of 120.

What is average?

Average is defined as the mean value that is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

According to question,

155+121+125+118+112+x= 6(120)

601+x=720

x= 720-601

x= 119

Hence, she must bowl 119 in the sixth game.

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The absolute value inequality represents the difference between the rope lengths cut and the specifications are | x - 10 | ≤ 0.5.

Modulus value always outputs a positive value irrespective of the input value sign.

Julian needed to cut ropes for her school project and their length should be 10 inches long with a difference of 0.5 inches.

∴ The maximum allowable length of the rope should be (10 + 0.5) = 10.5 inches and the minimum allowable length of the rope should be

(10 -0.5) = 9.5 inches.

The absolute value of inequality that represents this condition is,

| x - 10 | ≤ 0.5.

x - 10 ≤ 0.5.

x ≤ 10.5, And

- ( x - 10) ≤ 0.5.

-x + 10 ≤ 0.5.

- x ≤ - 9.5.    ( think of moving the terms on either side to make x positive).

x ≥ 9.5.

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The number 3 will come 20 times in 1 to 100 .

In mathematics, a number serves as both a unit of measurement and a label.

We know that the number 3 will come up in 3 ,13 ,23,30 , 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93.

Therefore the number 3 will come up 20 times.

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The angle pairs can be classified as follows

∠1 and ∠5       →  Alternate exterior angles

∠2 and ∠10    →  Corresponding angles

∠10 and ∠14   →  Alternate interior angles  

∠6 and ∠7      →  Consecutive interior angles

∠5 and ∠12    →  Consecutive interior angles

∠3 and ∠13    →  Alternate exterior angles

From the question, we are to classify each of the angle pairs as corresponding, alternate interior, alternate exterior, or consecutive interior angles.

Considering the given diagram, and applying the appropriate angle theorems, we can write that

∠1 and ∠5 are alternate exterior angles

∠2 and ∠10 are corresponding angles

∠10 and ∠14 are alternate interior angles  

∠6 and ∠7 are consecutive interior angles

∠5 and ∠12 are consecutive interior angles

∠3 and ∠13 are alternate exterior angles

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Answer:

8

Step-by-step explanation:

Let the number be “X"

Solution:

4 + (X/2) = 8

(X/2) = 8-4

(X/2) = 4

X = 4×2

X = 8

THEREFORE THE ANSWER IS “8”

Answer:

This is a simultaneous equation.

Step-by-step explanation:

let the first number be x and second be y

Lets make an equation first:

3x-y = 8 .....(1)

x+y = 12........(2)

Solve by elimination.

Dass

3x+x= 8+12

4x=20

x=5

find y

x+y=12

5+y=12

y=12-5

y= 7

Therefore the two numbers are 5 and 7

Answer:

ABC =146.5

ACB=67

ACD=127

CAB=146.5

Step-by-step explanation:

ABD=127

ACD=127

BCD=60 ( Being equilateral triangle)

60+x=127

x=67

ACB=67

CAB=CBA=y (let)

y+y+ACB = 360 ( Sum of int angles of triangle)

2y+67=360

2y=293

y=146.5

CAB=146.5

ABC=146.5

The woodworker should make atmost 4 rocking kitchen chair and 3 simple kitchen chair to maximize the profit under given conditions of 192 woodworking hours and 21 painting hours.

Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.

inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to etc.

Given,

Time needed to woodwork a rocking kitchen chair= 30 hours

Time needed to paint a rocking kitchen chair=3 hours

Time needed to woodwork a simple kitchen chair= 24 hours

Time needed to paint a simple kitchen chair=3 hours

Maximum time given by worker= 192 hours for woodwork and 21 hours to paint

Let x and y be the maximum number of chairs created by woodworker of both the types.

so the system of inequality would be,

30x+24y<192      ......(1)

3x+3y<21             ......(2)

To find x and y,

multiply the (2) by 10

30x+30y<210

subtract (1) from (2)

30x+24y-(30x+30y)<192-210

-6y<-18

y<3

3x+3y<21

3x+3*3<21

3x<12

x<4

By this, he can make maximum 4 rocking and 3 simple kitchen chair to earn the maximum profit.

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The value of the expression y³ = 1 is y = 1.

Expression:

An expression also known as algebraic expression consisting of variables, numbers and an arithmetic operation between them.

Given,

Here we have the expression y³ = 1.

Now, we need to find the value of y.

While we looking into the expression, when we have to find the value of y then we have to move the cube vale to the other side.

When we move the cube to the other side then it will be the cube root of the number.

While we simplify the cube root of the number then we get the result.

Therefore,

y³ = 1

Move the cube to the other side,

y = ∛1

We know that,

∛1 = 1

So, the value of y = 1.

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[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}[/tex]

Answer: h(x)=-15

Step-by-step explanation: First: We plug in h(6) for x. Gives us -2(6)-3. When we solve -12-3. -15.

Answer:

h(6) = 9

Step-by-step explanation:

h(x) = 2x – 3,

Let x = 6

h(6) = 2*6 -3

      = 12 -3

      = 9

Answer:

9+9b

Step-by-step explanation:

Answer:

9 +9b

Step-by-step explanation:

     Like terms are terms that have same variable with same power.

2b and 7b are like terms.

7 and 2 are like terms (constants).

7 + 2b + 7b + 2 = 7 + 2 + 2b +7b

                           = 9 + 9b

Answer:

Image result for the government

The Federal Government is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.S. Constitution in the Congress, the President, and the Federal courts, respectively.

Step-by-step explanation: