John and Ben each bought school supplies. John bought three pens, and Ben bought two pens. Ben bought three pencils. If each pen cost $1.10 and each pencil costs $0.75, how many pencils did John buy, if together they spent $10.00?

From the given system of linear equations, we have;

a. The system of linear equations can be expressed as follows;

y = 22•x - 9.5

y = 2.5•x + 4.1

Rewriting the equations to have the constants on the right, we have;

y - 22•x = - 9.5

y - 2.5•x = 4.1

Solving the above equations using matrices method on a calculator gives;

By direct solving, we have;

22•x - 9.5 = 2.5•x + 4.1

22•x - 2.5•x = 4.1 + 9.5

19.5•x = 13.6

x = 13.6 ÷ 19.5 ≈ 0.697

y = 22•x - 9.5

y = 22×(13.6/19.5) - 9.5 ≈ 5.84

b. 8•x + y - 18 = 0

5•x + 9•y + 4 = 0

Rewriting gives;

8•x + y = 18

5•x + 9•y = -4

Solving with technology gives,;

Solving directly gives;

Which gives;

18 - 8•x = -(5•x + 4)/9

9×(18 - 8•x) = -(5•x + 4)

162 - 72•x = -(5•x + 4)

5•x - 72•x = -162 - 4 = -166

67•x = 166

x = 166 ÷ 67 ≈ 2.478

y = 18 - 8•x

Therefore;

y = 18 - 8 × (166 ÷ 67) ≈ -1.82

c. 6•x + y = 12

5•x + 8•y = -100

Solving the above linear system using technology, we have;

Solving directly, we have;

y = 12 - 6•x

5•x + 8•y = -100

y = (-100 - 5•x)/8

12 - 6•x = (-100 - 5•x)/8

8 × (12 - 6•x) = (-100 - 5•x)

96 - 48•x = (-100 - 5•x)

48•x - 5•x = 96 + 100

43•x = 196

x = 196/43 ≈ 4.56

y = 12 - 6•x

Therefore;

y = 12 - 6×(196/43) ≈ -15.35

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The amount that will be in the account after 30 years is $188,921.57.

When an amount is compounded annually, it means that once a year, the amount invested and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.

The formula that can be used to determine the future value of the deposit in 30 years is : annuity factor x yearly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$2000 x [{(1.07^30) - 1} / 0.07] = $188,921.57

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Answer:

220

Step-by-step explanation :

11 = 5%

100 ÷ 5 = 20

11 × 20 = 220

0.05 × 220 = 11 ✓

0.05 = decimal multiplier of 5%

Distribute the summation over the sum.

[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]

Now plug in the known sums and simplify.

[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]

Answer: Choice B

[tex]2 = \log_{8}(64)[/tex]

======================================================

Explanation:

The original equation is [tex]8^2 = 64[/tex] with 8 as the base. That is also the base of the log when we get the final answer shown above. Logs are useful to isolate the exponent.

The general rule is that [tex]\text{y} = b^{\text{x}}[/tex] is equivalent to the log form of [tex]\text{x} = \log_{b}(\text{y})[/tex] where b is the base of each.

2 = log Subscript 64 Baseline 8 is the  logarithmic equation which is equivalent to 82 = 64.

Two or more expressions with an Equal sign is called as Equation.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

The logarithmic equation equivalent to 82 = 64 is:

2 = log Subscript 64 Baseline 8

This is because the logarithmic equation relates the base (64) to the result of the exponentiation (8), which in this case is 2.

Hence, 2 = log Subscript 64 Baseline 8 is the  logarithmic equation which is equivalent to 82 = 64.

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A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.

A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.

The area of a circle can be determined by the given expression:

Area = π[tex]r^{2}[/tex]

where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]

So, the area of the shaded region can be determined as:

Area of the shaded region = area of the larger circle - area of the smaller circle

Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]

                                            = π (46.24 - 20.25)

                                            = [tex]\frac{22}{7}[/tex] x 25.99

                                            = [tex]\frac{571.78}{7}[/tex]

Area of the shaded region = 81.683

Thus the appropriate answer to the question is option D. 81.65.

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The ages of Carl and Angela given from the expression is 25 years and 18 years respectively

5(x + 7) + 4x = 197

5x + 35 + 4x = 197

9x = 197 - 35

9x = 162

x = 162/9

x = 18

So,

Angela's age = x

= 18 years

Carl's age = x + 7

= 18 + 7

= 25 years

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$1078.56

The formula of the area of the  rectangle = Length * Breadth

                                               = 18*21 feet

                                              = 378 feet^2

As cost of carpet is given in square yard. so convert area of rectangle in square yard.

1 square feet = 9 square yard

so, 378/9 = 42 square yard

Cost of carpet = $ 25.68 per square yard (given)

Total cost of rectangular floor = 25.68 * 42

                                                = $1078.56 square yard

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$1078.56 is the cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard.

Given:

Find:

Solution:

The formula of the area of the  rectangle = Length * Breadth

                                              = 18*21 feet

                                             = 378 feet^2

As the cost of the carpet is given in square yard. so convert an area of the rectangle into a square yard.

1 square foot = 9 square yards

so, 378/9 = 42 square yard

Cost of carpet = $ 25.68 per square yard (given)

Total cost of rectangular floor = 25.68 * 42

                                               = $1078.56 square yard

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By using excel sheet we can get the answers for the difference t test.

The two kinds of formula are used in the excel . One from the data analysis the t test assuming equal variances as nothing was mentioned.

But if the t test for the means is used there might be slight variation in the values.

The other formula was of descriptive statistics.

The data was

No of feedback (sec) Feedback (sec) Difference

45 54 9

33 50 17

59 58 -1

32 38 6

30 42 12

27 35 8

29 38 9

59 66 7

64 65 1

38 55 17

For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.

The null hypothesis is accepted because t stat= -1.322 is less than t critical which is  t critical= ±2.119  and lies in the acceptance region.

The p- value is 2.04 which is greater than alpha= 0.05

The t stat for 0.01=  4.561578674 and t Critical two-tail 3.249835541

The t stat is greater than t critical at alpha 0.01 so it is rejected.

The difference t test gives

Count=N   9                  9

Mean        41.2             49.67

Mean Difference  8.4

Standard Deviation  14.967       11.97

Variance        223.944  143.25

Standard Error 2.0824

t       = -1.322

df = 16

t Critical two-tail 2.119905285

Confidence Level(95.0%) 4.802039614

Lower CI (95.0%) =  3.6

Upper CI(95.0%)=  13.2

t stat for 0.01=  4.561578674

t Critical two-tail 3.249835541

Confidence Level(99.0%) 6.055710988

Lower CI (99.0%) =  2.345

Upper CI(99.0%)=  14.457

For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.

The null hypothesis is accepted because t stat= -1.322 is less than t critical which is  t critical= ±2.119  and lies in the acceptance region.

The p- value is 2.04 which is greater than alpha= 0.05

The t stat for 0.01=  4.561578674 and t Critical two-tail 3.249835541

The t stat is greater than t critical at alpha 0.01 so it is rejected.

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The scaled copy of the polygon is added as an attachment

The complete question is added as an attachment

The coordinates of the polygon are

A = (-7, 6)

B = (-10, 8)

C = (-10, 10)

D = (-6, 10)

The scale factor is 3.

So, the rule of dilation is

(x, y) = (3x, 3y)

Using the above rule, we have:

A' = (-21, 18)

B' = (-30, 24)

C' = (-30, 30)

D' = (-18, 30)

See attachment for the scaled copy of the polygon

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The term that has a degree of 8 is -2x³y⁵

The polynomial above is a monomial. A monomial is a polynomial with a single term.

Therefore, the degree of a monomial is the sum of the exponents of all its variables.

In other words, a monomial is a number, a variable or a product of a number and a variable where all exponents are whole numbers.

Hence, the term with degree of 8 is -2x³y⁵

Degree = 0 + 3 + 5 = 8

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Answer:

B. 2√3+4

Step-by-step explanation:

3√3+4−√3

=2√3+4 (Decimal: 7.464102)

The pizza originally have 30 slices.

What is linear equation?

An equation in which the highest power of the variable is one is known as linear equation.

We will find number of pizza slices as shown below:

Let pizza originally have x slices.

Adam eats 20% of a pizza

= 0.2x

Bethany eats 1/3 of pizza

=1/3(x)

Charlie eats the remaining 14 slices

0.2x+1/3(x)+14=x

14 = x - 0.2x - 1/3(x)

14 = x - x/5 - x/3

14 = (15x - 3x - 5x)/15

14*15 = 7x

By dividing both sides by 7, we get

30 = x

x = 30

Hence, the pizza originally have 30 slices.

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Answer:

x = 2/7

x = -6

Step-by-step explanation:

You can solve the equation by setting each set of parentheses equal to 0 and simplifying.

7x - 2 = 0                                <----- First set of parentheses

7x = 2                                      <----- Add 2 to both sides

x = 2/7                                    <----- Divide both sides by 7

x + 6 = 0                                 <----- Second set of parentheses

x = -6                                      <----- Subtract 6 from both sides

Answer:

4

Step-by-step explanation:

Since,

The width of the Longer gear is 7, and the smaller gear has a width of 3..

7-3 = 4

Hope it helps...

Marking me as Brainliest would help me... :(

The value of angle TUS based on the information given about the circle will be 49°.

It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Here, the value of TUS will be:

= 1/2 × TRS

= 1/2 × 98°

= 49°

In conclusion, the correct option is 49°.

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Complete question:

Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?

Answer:

  1.14200738982×10^26

Step-by-step explanation:

Substitution can make this integral much easier to evaluate.

Let u = 7x² -x. Then du = (14x -1)dx. The limits on x become different limits for u:

  for x = 1: u = 7(1²) -1 = 6

  for x = 3: u = 7(3²) -3 = 60

  [tex]\displaystyle\int_1^3{(14x-1)e^{(7x^2-x)}}\,dx=\int_6^{60}{e^u}\,du=\left.e^u\right|^{60}_6\\\\=e^{60}-e^6\approx e^{60}\approx\boxed{1.14200738982\times10^{26}}[/tex]

The additional information would you want to know about the survey before you accepted the results of the study will be:

In research of human subjects, a survey is a list of questions aimed for extracting specific data from a particular group of people.

Surveys may be conducted by phone, mail, through the internet or in malls. From the information, a recent survey points to the transformation underway in the automotive retail landscape.

It is important to know the sampling design that was used, the population from which the design was selected and the response rate.

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electronic data interchange

Answer:

both two

Step-by-step explanation:

because it is in alphabetical order

Using the binomial distribution, it is found that:

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

For this problem, the parameters are given as follows:

n = 8, p = 0.09.

Hence the mean and the standard deviation are, respectively:

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The angle which is coterminal with -60 between 0 and 360 is; 300°.

Since, it follows that the representation of the angle -60 corresponds to 60° span in the clockwise direction.

Therefore, by going the conventional anticlockwise direction, the angle which is coterminal with -60 is; 300°.

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Answer:

[tex]\frac{16}{32}[/tex]

Step-by-step explanation:

given

[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )

= [tex]\frac{16}{32}[/tex]

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.

An equation is an expression that shows the relationship between two or more numbers and variables.

System A:

x + 6y = 5 and; 3x - 7y = -35

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.

System B:

x + 6y = 5 and; - 25y = -50

The solution of system B will be the same as the solution of system A.

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The actual value is 250.

Applying simple percentage formula here,

let x be the whole value

x=148.5/ 59 2/5%

x= 148.5/0.594

x=250.

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The actual value is 250.

Applying percentage formula here,

let x be the value:

x=148.5/ 59 2/5%

x= 148.5/0.594

x=250

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Answer:

from looking at this we can see

1*4=4

2*4=8

3*4=12

6*4=24

a

Hope This Helps!!!

Answer:

[tex]f(x) = \frac{1}{2}x + 5[/tex]

Step-by-step explanation:

So you can generally express a linear function use the slope-intercept form as such: [tex]y=mx+b[/tex] where m=slope, and b=y-intercept.

The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: [tex]f(x) = mx+5[/tex]

The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and this can be found using any two points, since the slope is constant.

We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run

[tex]\frac{6-5}{2-0} = \frac{1}{2}[/tex]

So plugging this into the slope-intercept form you get the function

[tex]f(x) = \frac{1}{2}x + 5[/tex]

The computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.

It should be noted that from the information given, we are given the information about three salesmen and their sales.

The total earnings for salesman A will be:

= (1300 × 3) + 65 × (11 + 14 + 16)

= 3900 + 2730

= 6630

The total earnings for salesman B will be:

= 300 × 3 + 40 × (14 + 15 + 13)

= 900 + 1680

= 2580

The total earnings for salesman C will be:

= 900 × 3

= 2700

Therefore, the computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.

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Answer:

3:12:39

Step-by-step explanation:

The ratio of amount for 1 day, number of employee and total number of days is 1 : 4 : 13.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given information are,

Amount for 1 day = $3,

Number of employee = 12,

Total number of days = 39.

The ratio of amount for 1 day, number of employee and total number of days

= 3 : 12 : 39

Simplify the ratio by dividing it to 3,

= 1 : 4 : 13

The required ratio is 1:4:13.

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Answer:

The answer to your question is 125

Step-by-step explanation:

x = 25 X 5= 125.

The required number is 125.

I hope this helps and have a good day!