Evaluate the expression 2x-7 for x = -4

The linear equation that passes through the two given points is

3y - 2x = 22

Remember that a linear equation that passes through the points (x₁, y₁) and (x₂, y₂) has a slope:

a = (y₂ - y₁)/(x₂ - x₁)

In this case the points are  (-5,4) and (10,14), then the slope is:

a = (14 - 4)/(10 + 5) = 10/15 = 2/3

Then the line is something like:

y = (2/3)*x + b

To find the value of b, you can replace the values of one of the points there.

14 = (2/3)*10 + b

14 - 20/3 = b

22/3 = b

Then the line is:

y = (2/3)*x + 22/3

3y = 2x + 22

3y - 2x = 22

That is the line that passes through the two points.

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Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed

Answer:

a) 263,158

b) $164,500

c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...

Step-by-step explanation:

a)

Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000

Total revenue = 1.40x

Setting the two equations equal to each other and solving for x, we get:

(0.45)x + 250,000 = 1.40x

0.95x = 250,000

x ≈ 263,158

b)

If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:

270,000 * $1.40 = $378,000

The total cost of producing 270,000 candy bars is:

(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500

Therefore, the company's profit is:

$378,000 - $213,500 = $164,500

c)

Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...

Answer:

8 significant figures should be provided.

Step-by-step explanation:

I believe I am correct, but check your answer anyways.

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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Answer:

A ≥ D

Step-by-step explanation:

Answer:

If Im NOT MISTAKEN its 7.41

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

31+4 × [11-(1+3)]

31+4*[11-4]

31+4*(7)

31+28

59

The easy Answer is 59. When doing these types of questions remember:

Parentheses

Exponents

Multiplication

Divionsion

Add

Subtract

Answer:

The speed of Todd's snowmobile was 22 miles an hour

Step-by-step explanation:

:))

The speed of Todd's automobile is 31 miles per hour.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours.

For the first journey,

v₁ + v₂ = 330 / 11    ......................( 1 )

For the return journey,

v₂ - v₁ = 330 / 15 .........................( 2 )

From equation ( 1 ) and equation ( 2 ),

2v₂ = ( 330 / 11 ) + ( 330 / 15 )

2v₂ = ( 330 ) ( 31 / 165 )

v₂ = 165 ( 31 / 165 )

v₂ = 31 miles per hour

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The formula for calculating distance that Ben covered will be \(500 m/minute * Time.\)

The distance between 2 points in physical space is the length of a straight line between them.

In physics and math, to calculate the distance covered by Ben while cycling, we can use the formula for distance which is: Distance = Speed × Time.

Given:

Ben cycles at average speed of 500 m/minute.

We will substitute the values into the formula which is:

Distance = 500 m/minute × Time.

Therefore, the formula for calculating distance that Ben covered will be \(500 m/minute * Time.\)

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Answer:

4 and 3/2

Step-by-step explanation:

\(x = 4 \)

\(2x = 3 \\ x = \frac{3}{2} \)

Answer:

\(Given: AC=1\)

∠A=0

\(Cos0=\frac{B}{H} =\frac{AB}{AC}\)

\(Cos0=\frac{AB}{1}\)

\(AB=Cos0\)

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

hope it helps...

have a great day!!

Answer:

AB = AC×cos theta= cos theta

Using the Venn diagram to determine the roster form of set (A-C)'  =  { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }.

The difference of the sets A and C in this order is the set of elements which belong to A but not to C.

A - C = elements in set A but not in set C

A - C = { 3, 4 , 8 }

The A minus C complements include the following;

(A - C)' = { 1, 2, 5, 6, 7, 9, 10, 11, 12, 13, 14 }

Thus, using the Venn diagram to determine the roster form of set (A-C)' depends on the number of elements in the universal set.

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Answer:

n = 6

Step-by-step explanation:

Represent the unknown number by n.  Then 8 - n/3 = 6.

Consolidate the constants on the left side:  2 - n/3 = 0, or n/3 = 2.

Multiplying both sides by 3 results in:  n = 6

Answer:

\(\textsf{45.} \quad \log_5\left(\dfrac{x^3y}{w^2}\right)\)

\(\textsf{46.} \quad \log 12\)

\(\textsf{47.} \quad \ln(x-4)+2\ln(2x+5)\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Quotient law:\;\;\;$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\end{minipage}}\)

\(\begin{aligned}3\log_5x + \log_5y - 2\log_5w&=\log_5x^3 + \log_5y - \log_5w^2\\&=\log_5\left(x^3 \cdot y\right)- \log_5w^2\\&=\log_5\left(\dfrac{x^3y}{w^2}\right)\end{aligned}\)

\(\begin{aligned}\log21 - 2 \log7 + \log28 &=\log21 - \log7^2 + \log28\\&=\log21 - \log49 + \log28\\&=\log\left(\dfrac{21}{49}\right) + \log28\\&=\log\left(\dfrac{3}{7} \cdot 28\right)\\&=\log\left(\dfrac{84}{7}\right)\\&=\log12\end{aligned}\)

\(\begin{aligned}\ln \left[(x - 4)(2x+5)^2\right]&=\ln(x-4)+\ln(2x+5)^2\\&=\ln(x-4)+2\ln(2x+5)\\\end{aligned}\)

Answer: w = -3u/2  +  2

Step-by-step explanation:

-12u + 13 = 8w - 3

-12u + 13 + 3 = 8w -3 + 3

-12u + 16 = 8w

w = -3u/2   +   2

Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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For one to isolate the variable by using equation rules. Inverse inequality sign if multiplying/dividing by negative. Steps to isolate variable in inequality: Simplify, move constants with inverse operations. Divide coefficient to isolate variable. Reverse direction if using negative number.

Inequalities require you to apply the same principles as those used in equations when isolating a variable. For example, if there is an inequality 3x - 5 < 7. one can isolate the variable, by first:

Add 5 to both sides to be: 3x < 12.

Then divide both sides by 3: x < 4.

So, the variable x is one that is isolated, and the solution to the inequality is one where x < 4.

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Answer:

Step-by-step explanation:

(x + 4)^2 - 2 = 7 simplifies to

(x + 4)^2 = 5

We must isolate x.  To do this, take the square root of both sides, obtaining:

x + 4 = ±√5

There are two roots/solutions.  They are:

x = -4 + √5 and x = -4 - √5            

You must include the square root operator (√).  Use "  ^  " to denote exponentiation.

The solutions to the given equation (x + 4)² - 2 = 7 when calculated are; 1 and 7

We are given the equation as;

(x + 4)² - 2 = 7

Add 2 to both sides to get;

(x + 4)² = 9

Find the square root of both sides to get;

x + 4 = ±3

Thus;

x = 3 + 4 and x = -3 + 4

x = 1 and 7

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Answer:

Kindly check attached picture

Step-by-step explanation:

Data:

Prior experience :

5

12

0

2

5

9

6

11

12

0

5

9

1

0

5

3

12

3

11

10

8

1

0

6

7

0

8

13

7

0

Annual salary:

37500

50912

29356

27750

97844

48442

40207

42331

87489

26118

40025

88763

35829

17784

54199

36932

93279

22100

49987

85471

52220

36109

23105

39455

49861

30327

31008

90874

57966

16500

Using the data above, the scatter plot obyaoon using statistical software is attached below, from the line of best fit, the regression equation which models the relationship between the two variables is ŷ = 4003.257X + 25172.868.

The trend of the best fit line shows a positive correlation between prior experience and annual salary. The correlation Coefficient value which shows the strength of the association gives a value of 0.7225 ; hence, depicting a strong positive correlation.

Answer:

There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.

Step-by-step explanation:

We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.

Let \(\mu\) = population mean market value of houses in the neighborhood.

So, Null Hypothesis, \(H_0\) : \(\mu\) = $250,000      {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}

Alternate Hypothesis, \(H_A\) : \(\mu\) > $250,000      {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}

The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;

                              T.S. =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean market value = $259,860

            s = sample standard deviation = $24,922

            n = sample of houses = 35

So, the test statistics  =  \(\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }\)  ~ \(t_3_4\)

                                     =  2.34

The value of t-test statistic is 2.34.

Also, P-value of the test statistics is given by;

            P-value = P(\(t_3_4\) > 2.34) = 0.0137

Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.

The number which represents the situation of a withdrawal of $36 is -$36.

In this question, we have to find out the number or integer which represents the situation of a withdrawal of $36. This question is from integers topic and for that we should have the definition of integers in our mind. So, an integer is defined as number which can be represented without the fractional form. It contains whole numbers and negative of natural numbers. The integers are generally denoted by the symbol 'Ζ'. And, the integers can be negative or positive.

In this question we have asked withdrawal of $36 from any source. So, withdrawal basically means money will decrease, so it will become negative.

To represent a withdrawal of $36, we will use the negative sign.

Hence, -$36 is the correct representation of the situation of a withdrawal of $36.

Therefore, -$36 is the required answer.

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Answer:

p - 70

Step-by-step explanation:

70 less than p

Answer:

p - 70

Step-by-step explanation:

We're looking for the number of drawings Nora made, which is 70 fewer than Elise's, p. In instances like this, always subtract the number of less drawn from the quantity drawn by the other person, which is 70 - p. However, this would almost certainly result in a negative response, which isn't feasible. If you flip them over, you'll get p - 70.

Answer:

just multiply everything together, to get volume.

Answer:

The general volume of a pyramid formula is given as: Volume of a pyramid = 1/3 x base area x height.

Step-by-step explanation:

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Step-by-step explanation:

Answer: 21,135.08

Step-by-step explanation: because

22,450.89+5,676.63+15 ,670.25+10,067.15=53,864.92

so now 75,000 - 53,864.92 = 21,135.08 that's it

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.