How to find A and B?

Answer:

This equals (2x-9), you cannot simplify it more because it's a variable and number.  They have to both be numbers without variables or both variables to simplify.

Step-by-step explanation:

? This makes no sensibility.....

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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8/12 -3/8=16/24-9/24=7/24

You should make like numbers then subtract

If you need to simplify at the end

The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8

The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point

The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;

f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8

The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8

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Answer:

20

Step-by-step explanation:

An expression dose NOT have an = sign

An equation dose have an = sign

In this case, the expression 4x+8, replace the x with 3, since x=3

                                  4x + 8

                                4 x 3 + 8         (  don't forget  PEMDAS )

                                  12  + 8

                                     20

Answer:

2. kilograms

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = -x²+4 and y = 2x+1

Therefore,  -x²+4 = 2x+1

x²+2x-3 = 0

x = 1,-3

There are two solutions:

(1,3) and (-3,-5)

The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).

We have,

To solve the system of equations:

Set the expressions for y equal to each other:

-x² + 4 = 2x + 1

Rearrange the equation to bring all terms to one side:

-x² - 2x + 3 = 0

Solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we will use factoring.

Factor the quadratic equation:

(-x - 3)(x - 1) = 0

Set each factor equal to zero and solve for x:

-x - 3 = 0 or x - 1 = 0

Solve the first equation:

-x = 3

x = -3

Solve the second equation:

x = 1

Substitute the values of x back into one of the original equations to find the corresponding values of y.

For x = -3:

y = 2(-3) + 1

y = -6 + 1

y = -5

For x = 1:

y = 2(1) + 1

y = 2 + 1

y = 3

Therefore,

The solutions to the system of equations are (x, y) = (-3, -5) and (1, 3).

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The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

Step-by-step explanation:

Multiply answer = - 106

Divide answer = 1.25

Answer:

y=2x+9

Step-by-step explanation:

Point of intersection of y=3 & x+y=0

Point of intersection of y=3 & x+y=0put x=3 in x+y=0

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2y−3=2[x+3]

Point of intersection of y=3 & x+y=0put x=3 in x+y=0x=−3so the point is (−3,3)2x−y=4m=2y−3=2[x+3]y=2x+6+3

y=2x+9

Answer:

\((11)\ -2x + 5y = 20\)

\((12)\)   \(4x + y= -25\)

\((13)\)   \(3x + 8y = -15\)

\((14)\ -9x + 4y = 2\)

\((15)\ y = - 9\)

Step-by-step explanation:

Required

The line equation

\((11)\ (-5,2); m =\frac{2}{5}\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = \frac{2}{5}(x - (-5)) + 2\)

\(y = \frac{2}{5}(x +5) + 2\)

Open bracket

\(y = \frac{2}{5}x +2 + 2\)

\(y = \frac{2}{5}x +4\)

Multiply through by 5

\(5y = 2x + 20\)

Rewrite as:

\(-2x + 5y = 20\)

\((12)\ (-6, -1);\ m = -4\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = -4(x - -6) - 1\)

\(y = -4(x +6) - 1\)

Open bracket

\(y = -4x -24 - 1\)

\(y = -4x -25\)

Rewrite as:

\(4x + y= -25\)

\((13)\ (3,-3)\ m =-\frac{3}{8}\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = -\frac{3}{8}(x - 3) -3\)

\(y = -\frac{3}{8}x + \frac{9}{8} -3\)

Multiply through by 8

\(8y = -3x + 9 - 24\)

\(8y = -3x -15\)

Rewrite as:

\(3x + 8y = -15\)

\((14)\ (0, \frac{1}{2}); m = \frac{9}{4}\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = \frac{9}{4}(x - 0) + \frac{1}{2}\)

\(y = \frac{9}{4}x + \frac{1}{2}\)

Multiply through by 4

\(4y = 9x + 2\)

Rewrite as:

\(-9x + 4y = 2\)

\((15)\ (\frac{16}{3}, -9); m =0\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 0(x - \frac{16}{3}) - 9\)

\(y = 0 - 9\)

\(y = - 9\)

Answer:

a) The sample mean is of 49 and the sample standard deviation is of 11.7.

b) The range of the true mean at 90% confidence level is of 9.62 hours.

c) The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.

Step-by-step explanation:

Question a:

Sample mean:

\(\overline{x} = \frac{34+40+46+49+61+64}{6} = 49\)

Sample standard deviation:

\(s = sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7\)

The sample mean is of 49 and the sample standard deviation is of 11.7.

b)Determine the range of the true mean at 90% confidence level.

We have to find the margin of error of the confidence interval. Since we have the standard deviation for the sample, the t-distribution is used.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 2.0.150

The margin of error is:

\(M = T\frac{s}{\sqrt{n}}\)

In which s is the standard deviation of the sample and n is the size of the sample. So

\(M = 2.0150\frac{11.7}{\sqrt{6}} = 9.62\)

The range of the true mean at 90% confidence level is of 9.62 hours.

(c)If a seventh sample is tested, what is the prediction interval (90% confidence level) of its failure time.

This is the confidence interval, so:

The lower end of the interval is the sample mean subtracted by M. So it is 49 - 9.62 = 39.38 hours.

The upper end of the interval is the sample mean added to M. So it is 49 + 9.62 = 58.62 hours.

The prediction interval, at a 90% confidence level, of it's failure time is between 39.38 hours and 58.62 hours.

The correct statement is that for each hour, the earnings go up by $7. Option A

If we have the equation of the line, we can substitute the value of 7 for the number of hours into the equation and solve for the earnings. The equation would typically be in the form of "earnings = slope * hours + y-intercept," where the slope represents the rate of earnings per hour and the y-intercept represents the earnings when no hours are worked.

We can find the slope of the graph to know as said above;

m = y2 - y1/x2 - x1

m = 14 - 0/2 - 0

m = 7

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Answer:

m=1

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

the number would simply be

14÷2=7

7²=49

Answer:

12/7

Step-by-step explanation:

Answer:

a) Mean number of beans = 33.4 per coco pad

b) Standard deviation of the  beans = 5.2   per coco pad

Step-by-step explanation:

Step(i):-

a)

Given data  30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.

mean of beans

  x⁻ = ∑x/n

\(x^{-} = \frac{30+ 28+30+35+40+25+32+36+38 + 40.}{10} = 33.4\)

Mean number of beans per coco pad  = 33.4

step(ii):-

b)

standard deviation

∑(xi - x⁻)²  =  (30-33.4)²+ (28-33.4)²+(30-33.4)²+(35-33.4)²+(40-33.4)²+(25-33.4)²+(32-33.4)²+(36-33.4)²+ (38-33.4)²+(40-33.4)²

On calculation , we get

      ∑(xi - x⁻)²  = 242.4

standard deviation

 =        \(\sqrt{\frac{sum((x-x^{-} )^{2} }{n-1} } = \sqrt{\frac{242.4}{10-1} } = 5.189\)

Standard deviation of the  beans  (σ) = 5.2   per coco pad

Answer:

Infinite

Step-by-step explanation:

If you try to solve this equation, the solution is 0 = 0 which means an infinite number of solutions.

Using the relation between acceleration, velocity and distance, it is found that:

a) The differential equation for the velocity is: \(\frac{dV}{dt} = 0.5\)

b) The formula for the velocity is given by: V(t) = 0.5t + 6.

c) The initial value problem to find the position is: \(\frac{dS}{dt} = 0.5t + 6, S(0) = 0\)

d) The formula for the position of the car is S(t) = 0.25t² + 6t.

e) The car is at a velocity of 21 m/s after 30 seconds.

We have that:

For item a, we have that the acceleration is constant of 0.5 m/s², hence the differential equation for the velocity is:

\(\frac{dV}{dt} = 0.5\)

For item b, we apply separation of variables, and find the velocity as follows:

\(\frac{dV}{dt} = 0.5\)

\(\int dV = \int 0.5 dt\)

V(t) = 0.5t + v(0).

v(0) is the initial velocity and is the constant of integration, hence:

The formula for the velocity is given by: V(t) = 0.5t + 6.

For item c, we have that the position is the integral of the velocity, hence:

The initial value problem to find the position is: \(\frac{dS}{dt} = 0.5t + 6, S(0) = 0\)

For item d, applying separation of variables, we have that:

\(\frac{dS}{dt} = 0.5t + 6\)

\(\int dS = \int (0.5t + 6) dt\)

S(t) = 0.25t² + 6t + s(0).

Since s(0) = 0, we have that:

The formula for the position of the car is S(t) = 0.25t² + 6t.

The velocity after 30 seconds is of:

v(30) = 6 + 0.5(30) = 21.

The car is at a velocity of 21 m/s after 30 seconds.

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Answer:

y=−210+5x

Step-by-step explanation: easy

Answer:

-1 ,+1 i hope it helps mark me as brainliest

The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.

Given are the closing prices of two stocks in three days.

If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,

Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25

If the stock is sold in day 2,

Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25

Profit = $1435.25 - $1448.25 = -$13

If the stock is sold in day 3,

Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7

Profit = $1450.7 - $1448.25 = $2.45

The profit is more for day 3 than day 2.

Hence it is best to sell on day 3 by $2.45.

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The solution to the equations are b = 15, b = 22, c = 21 and n = 28

From the question, we have the following equations that can be used in our computation:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Answer:

Step-by-step explanation:

Q3 asks for reasons of statements in a theorem proof.

1 Given is correct

2 Definition of right angle is correct

3 should be sum of interior angles in a triangle

4 is substitution

5 subtracting 90degree from left and right hand side

6 is definition of complementary

The Width of the rectangle be 1 3/4 feet and the length be 2 1/3 feet then the perimeter of given rectangle is 8 1/6 feet.

A rectangle's perimeter (P) is the sum of the lengths of its four sides. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter:

Perimeter = length + length + width + width.

P = l + l + w + w.

Given:

Width of rectangle = 1 3/4 feet

Length of rectangle = 2 1/3 feet

Perimeter of rectangle = 2( Length + Width )

substitute the values in the above equation, then we get

\($& 2 \times\left(1 \frac{3}{4}+2 \frac{1}{3}\right) \\\)

simplifying the equation, we get

\($& =2 \times\left(\frac{7}{4}+\frac{7}{3}\right) \\\)

\($& =2 \times\left(\frac{21+28}{12}\right) \\\)

\($& =2 \times \frac{49}{12}\)

\($$\begin{aligned}& =\frac{49}{6} \\& =8 \frac{1}{6}\end{aligned}$$\)

Therefore, the perimeter of given rectangle is \($8 \frac{1}{6}$\) feet.

The complete question is:

A rectangle has side lengths of 1 3/4 feet and 2 1/3 feet. Find the perimeter of the rectangle. Write your answer as a mixed number in simplest form.

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The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

From the question, we have the following parameters that can be used in our computation:

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

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