Write each as an algebraic expression.

10) the product of 10 and a number n

12) the difference of 19 and a number n

14) The product of 7 and the sum of × and 2

15) The difference of 11 and the quotient of x and 3

11) the sum of a number n and 5

13) a number n squared

Answer:

[tex]x < 13[/tex]    and    [tex]x > 5[/tex]

Step-by-step explanation:

Take a look at the attachments...

Hope this helps! :)

Answer:

7 periods.

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function:

[tex]f(x) = A \cos(B(x + C)) + D[/tex]

where:

Therefore, for y = cos x:

The maximum of the function is when x = 0 + 2πn.

The minimum of the function is when x = π + 2πn.

To find the number of periods, first find the difference between the two given values:

⇒ 9π - (-5π) = 9π + 5π = 14π

As the period of the function is 2π, then the number of periods is:

⇒ 14π ÷ 2π = 7 periods.

Answer:

a x=10

b x=7

Step-by-step explanation:

(a) 2(x+3) = x  -  4

    2x+6 = x - 4

    2x+6-6= x-4-6

    2x=x-10

     2x-x=x-10-x

    x=10

(b) 4(5x-2) = 2(9x+3)

     20x-8  =18x+6

     20x-8+8=18x+6+8

     20x=18x+14

     20x-18x =18x+14-18x
     2x=14

      /2  /2

     x = 7.

The area of the semi circle with radius 2mm is 2[tex]\pi[/tex][tex]mm^{2}[/tex]

A semicircle is formed when a lining passing through the centre touches the two ends on the circle. Thus, by joining two semicircles we get a circular shape.

When a circle is cut into two halves or when the circumference of a circle is divided by 2, we get a semicircular shape.

Area of a semi-circle = [tex]\frac{\pi r^{2} }{2}[/tex]

but radius r = 2mm

substitute r into the area equation, we have

Area of semicircle = [tex]\frac{\pi 2^{2} }{2}[/tex]

Area of semicircle is = 2[tex]\pi[/tex][tex]mm^{2}[/tex]

In conclusion the area of the semicircle is  2[tex]\pi[/tex][tex]mm^{2}[/tex]

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The image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).

Given:

A(3,7) under a translation along the vector (-4, 2).

A' = A + (-4,2)

= (3,7) + (-4,2)

= (3+(-4), 7+2)

= (3-4, 9)

= (-1, 9)

Therefore the image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).

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The slope of the linear equation of the entire data set is -720.98

1. Bring data in to excel sheet

2.Select both x and y variable and insert scatter plot chart. Select any data point in the chart and add trend line. In the format trend line option choose "Linear" and also select "Display an equation on chart" & "Display R-squared value on chart"

To find: What is the slope of the linear equation of the entire data set? Round to nearest hundredth.

Regression equation : y = -720.98x + 15,90,277.32

Slope = -720.98 (Round to nearest hundredth.)

Intercept = 15,90,277.32

So, the slope of the linear equation of the entire data set is -720.98

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The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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The equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.

We are given;

y = 3x³ - 7x² + 5

y = 7x^4 + 2x

We will solve the given equation by substitution method:

Using the substitution method, let us substitute y = 7x^4 + 2x in the equation y = 3x³ - 7x² + 5, we get,

3x³ - 7x² + 5 = 7x^4 + 2x

So, 3x³ - 7x² + 5 = 7x^4 + 2x will be solved by using the given system of equations.

Thus, the equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.

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Answer:

56

Step-by-step explanation:

Number with two digits = 10y + x

x > y

x-y = 1

10y + x = 5(x+y) + 1

x = y + 1

10y + y + 1 = 5(y+1 +y) + 1

11y + 1 = 5(2y+1) + 1

11y + 1 = 10y + 5 + 1

11y - 10y = 5

y = 5

x = 5 + 1 = 6

Answer:

n=7

Step-by-step explanation:

-6n-9=25-8n

2n=34

n=17

1000 paperclips would weigh equal to the dictionary.

Weight of the dictionary = 1 kg

weight of one paper clip = 1 gm

according to the mathematical conversion system of weights

1 kilogram = 1000 grams

on the basis of the statement

1 gram is the weight of = 1 clip

so , 1000gm would be the weight of = 1 x 1000

         1000 gm would be the weight of = 1000 clips

to weigh equal to the dictionary , we would require 1000 clips .

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For given inequality 2y-x>1 point (-7,-3) is not the solution set of given inequality.

Inequality:

               Inequalities are mathematical sentences formed by relating two expressions to each other.

Different inequality sign are:

            x>y ,

                  x is greater than y

           x≥y

                x is greater than or equal to y

           x<y

                 x is less than y

          x≤y

                 x is less than or equal to y

Given inequality is,

             2y - x > 1

In the given inequality

       L.H.S (Left hand Side) = 2y - x

       R.H.S (Right Hand Side) = 1

and the given point is (-7,-3)

Left hand Side at point (-7,-3)

L.H.S  = 2y - x

          = 2 (-3) - (-7)

          = -6 + 7

          = 1

and

       Right Hand Side = 1

Here we can see both L.H.S and R.H.S are equal,but in the given inequality there is no equality,so the point (-7,-3) is not the solution set.

Thus we conclude,

                            (-7,-3) is not the solution set of given inequality.

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The greatest total area, length will be 300 ft. and width will be 200 ft.

Given,

In the question:

A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1200 feet of fencing is used.

Now, According to the question:

Lets assume, the length of the playground is l ft. and width is w ft.

Suppose, the playground is divided into two parts by a fence parallel to width. That means the length of the divider fence will be w ft.

So, the total length of the fence needed = (2l+ 3w)ft.

It is given in the question that 1200 feet of fencing is used.

2l + 3w = 1200

2l = 1200 - 3w

l = 600 - [tex]\frac{3}{2}w[/tex]  ......(1)

Now, the area of the playground....

A = l × w

A = ( 600 - [tex]\frac{3}{2}w[/tex]  ) × w

A = 600w - [tex]\frac{3}{2}w^2[/tex]

Taking derivative on both side in respect of "w" ,

we will get:

dA/dw = 600 - [tex]\frac{3}{2} (2w)[/tex]

dA/dw = 600 - 3w

A will be maximum when dA/dw = 0

600 - 3w = 0

600 = 3w

w = 600/3

w = 200

Now plugging this w = 200 into equation (1)...

l = 600 - [tex]\frac{3}{2}[/tex] × 200

l = 600 - 300

l = 300

Hence, for the greatest total area, length will be 300 ft. and width will be 200 ft.

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$57 is the amount of the tip the server hopes to receive.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

A server at a restaurant is hoping for a 15% tip from a large party.

The party's bill at the end of the night was $312.00.

Now we need to find 15% of $312

15% is converted to decimal by dividing with 100

15/100=0.15

Now multiply 0.15 with 380

0.15×380

57

Hence $57 is the amount of the tip the server hopes to receive.

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The linear equation y = 5 · x - 14 is a possible equation that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4),

To generate a system of linear equations, we need to derive an additional that intercepts the line 2 · x + y = 0 at point (x, y) = (2, - 4). We need to find an equation of the form:

y = m · x + b

Where:

Please notice that there are more than a single choice. First, choose the slope of the line:

m = 5

Second, substitute the slope and the independent and dependent variables:

b = y - m · x

b = - 4 - 5 · 2

b = - 14

Third, write the resulting linear equation:

y = 5 · x - 14

The linear equation y = 5 · x - 14 is a possible equation of the system of equations.

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Answer:

D

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] = [tex]\frac{9}{15}[/tex]  It is the only one that you can multiply the top and the bottom of the fraction with the same number to get an equivalent fractions.  Multiply the top and the bottom of the first fraction by 3 to get the top and the bottom of the second fraction.

Using scientific notation, the number 1240000 can be expressed as 1.24×10⁶

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.

Converting the number 1,240,000 to scientific notation, we will get

1,240,000 = 1.24×10⁶

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Answer:

B

Step-by-step explanation:

The rule means to subtract 3 from the x-coordinate and add 7 to the y-coordinate.

The percent of medical residents less than 28 years old is 69.15%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 28

μ = mean = 27

σ = standard deviation = 2

z-score = (28 - 27) / 2

z-score = (1) / 2

z-score = 0.5

Find the probability that corresponds to the z-score in the z-table. (see attached images)

at z = 0.5,     p = 0.6915

Multiply the probability by 100 to get the percentage.

% = p x 100

% = 0.6915 x 100

% = 69.15

Hence, the percent of medical residents that are less than 28 years old is 69.15%.

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Answer:

B. x=3/k

Step-by-step explanation:

5kx+6=7kx

first you can simplify the kx terms

6=7kx-5kx

6=2kx

now get x by itself

6/2k=x

3/k=x

Answer:

Step-by-step explanation:

An inequality which represents all possible values for x in -2x>-48 is: B. x < 24.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:

Next, we would find the solution and possible values to this given inequality as follows:

-2x > -48

Dividing both sides of the inequality by -2, we have:

-2x/-2 > -48/-2

x < 48/2

x < 24.

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The set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers is given as below as

Cars, Are cars up to date, Select the car to check, Stopped cars, Convenience sampling ,The cars that are not stopped might be having more problems

Given that,

The Population

The Population parameter of interest

The Sampling frame

The Sample

The Sampling Method, Including whether or not randomization was employed.

Any potential source of bias you can detect any problems you see in generalizing to the population of interest.

To find : The set up a roadblock

A. Cars

B. Are cars up to date

C. Select the car to check

D. Stopped cars

E. Convenience sampling

F. The cars that are not stopped might be having more problems

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Answer: (9t + 10)(t - 2)

Step-by-step explanation:

9t (t − 2) + 10(t − 2)

9t^2 − 8t − 20

= (9t + 10)(t − 2)

The value of z statistics is -1.878,  

Given,

In the question:

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Now, According to the question:

Estimated proportion of return rate;

To find the value of p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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Answer:

X=-2

Step-by-step explanation:

5+0.1x=3(1-0.3x)

5+0.1x=3-0.9x

    +0.9x         +0.9x

5+x=3

-5.   -5

x=-2

Hopes this helps

Answer:

the answer is B

Step-by-step explanation:

5+0.1x=3(1-0.3x)=}

5+0.1x=3-0.9x=}

0.1x+0.9x=3-5=}

x= - 2

a) The function that represents the given situation is (x - 11) ÷ 4 = -1.2 and the number thought by Dakari is 6.2

b)  The inverse function (y - 11) ÷ 4 = -1.2

Function:

The function that is from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

Given,

Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.

Here we need to find the following

a) function that map the function and the number though by Dakarai

b) inverse of the function

Let us consider the number thought by Dakarai as "x"

First, he subtracted 11 from the number,

So it can be written as,

=> x - 11

After that, he divided it by 4

So, the it can be written as,

=> (x - 11) ÷ 4

Now, the result was -1.2

So the function is

=> (x - 11) ÷ 4 = -1.2

Now we have to solve this equation, in order to find the value of x,

=> (x - 11) ÷ 4 = -1.2

=> x - 11 = -1.2 × 4

=> x - 11 = -4.8

=> x = -4.8 + 11

Therefore, the value of x is 6.2

And the inverse of the function can be written as by change the x as y,

Then we get,

=> (y - 11) ÷ 4 = -1.2

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A C - chart is used for Number of defects per unit.

What is C - chart?

In statistical quality control, the c-chart is a sort of control chart used to track "count"-type data, often the total number of nonconformities per unit. On rare occasions, it is also used to keep track of all the events that take place in a given period of time.

C-charts are used to assess if a process is predictable and stable as well as to track the results of process improvements before and after they have been made. The C - chart is particularly useful when there are few actual flaws in the subgroup but many potential for defects exist.

Count type data, such as the number of non-conformities per unit, are monitored using a statistical quality control chart known as a C-Chart.

Hence, a C - chart is used for Number of defects per unit.

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The minimal cost of the box is $96.

Given data;

The volume of the box (v) = x²y

Given that, volume = 16 m³

So, 16 = x²y

y = 16/x² → (I)

Material for the base costs $8 per square meter, and material for the sides costs $2 per square meter.

Total cost (C) = 8 (x²) + 2*(xy)(4)

                      = 8x² + 8xy

Using (I),

C(x) = 8x² + 8x(16/x²)

C (^) = 8x² + 128/x

Now find critical points from

∴ [tex]\frac{d}{dx} = [8x^2+\frac{128}{x} ]=0[/tex]

  x³ = 8

  x = 2

So, the minimal cost will be given by x= 2,

Now, y = 16/x²

            = 16/4

            = 4

Dimension of the box that minimizes the cost is;

height = 4m, width=2m and breadth = 12m

Now,

Minimum cost = 8 (2)² + 128/2 = 32 + 64

                        = 96

Hence, The minimal cost of the box is $96.

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