solve for x
3x + 7 = -2​

Let f(x) = ax ³ + bx ² + cx + d.

The graph of f(x) passes through (4, -22) and (3, -26), which means f (4) = -22 and f (3) = -26, so that

64a + 16b + 4c + d = -22

27a + 9b + 3c + d = -26

When the question says it has tangents at some point, I take that to mean the slope of the tangent line at that point is the given number. So f ' (4) = 11 and f ' (3) = -2. We have

f '(x) = 3ax ²+ 2bx + c

so that

48a + 8b + c = 11

27a + 6b + c = -2

Solve the system:

• Eliminate d :

(64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -22 - (-26)

→   37a + 7b + c = 4

• Eliminate c :

(48a + 8b + c) - (27a + 6b + c) = 11 - (-2)

→   21a + 2b = 13

(48a + 8b + c) - (37a + 7b + c) = 11 - 4

→   11a + b = 7

• Eliminate b, then solve for a and the other variables:

(21a + 2b) - 2 (11a + b) = 13 - 2 (7)

-a = -1

a = 1   →   b = -4   →   c = -5   →   d = -2

Then

f(x) = x ³ - 4x ² - 5x - 2

Answer:

The standard error of the sample mean  (S.E) = 0.7835

Step-by-step explanation:

Explanation:-

Given mean of the Population = 62.95 inches

Given standard deviation of the Population = 5.65 inches

The standard error of the sample mean is determined by

                  \(S.E = \frac{S.D}{\sqrt{n} }\)

                \(S.E = \frac{5.65}{\sqrt{52} } = 0.7835\)

The standard error of the sample mean  is approximately (S.E) = 0.7835.

It is an estimate of the standard deviation of the sampling distribution. It measures the variability of a considered sample statistic.

Supopse that we're given that:

Population standard deviation =\(\sigma\)

Size of sample we're working on = n

Then, the standard error can be calculated as:

\(SE = \dfrac{\sigma}{\sqrt{n}}\)

where SE denotes the standard error.

A track coach is gathering data on the stride length of each of her 52 team members when running a distance of 500 meters.

The population means is 62.95 inches with a standard deviation of 5.65 inches.

The mean of the Population = 62.95 inches

The standard deviation of the Population = 5.65 inches

The standard error of the sample mean can be determined by

\(= \dfrac{Standard deviation }{\sqrt{sample size}}\\\\\\= \dfrac{5.65 }{\sqrt{52}}\\= 0.7835140\)

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Answer:

Linear

Step-by-step explanation:

Both top and bottom are going up at a constant rate

x is going up by 9 and

y is going up by 7

Answer:

%52.87

Step-by-step explanation:

:)

Answer:

Option B, \(-2\)

Step-by-step explanation:

Step 1:  Substitute x with 6 and solve

\(f(x) = \frac{1}{2}x - 5\)

\(f(6) = \frac{1}{2}(6)-5\)

\(f(6) = 3 - 5\)

\(f(6) = -2\)

Answer: Option B, \(-2\)

The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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Answer:

31

Step-by-step explanation:

First you would subtract -12 and 19, which would get you to  -31. The absolute value of a number is the distance between the number and zero. For example, -31 is 31 spaces away from 0, so your answer would be 31.

Answer: The answer is -7.

Step-by-step explanation: First of all to do the difference between them we should remove the absolute value. The absolute value of any number is positive therefore, The absolute value of -12 is 12. So the difference between 12 and 19 is -7.

I think the answer is 1008

Step-by-step explanation:

To add integers with different signs, subtract the lesser absolute value from the greater absolute value. Use the sign of the integer with the greater absolute value for the sum. The following steps will be useful to find the sum of two numbers with different signs.

a. The best point of estimate of the population of portion p is given by the formula:

where x is the number of successes x=545 and n is the sample n=1047.

Replace these values in the formula and find p:

b. The value of the margin of error E is given by the following formula:

Where z is the z-score at the alfa divided by 2, q'=1-p'.

As the confidence level is 95%=0.95, then alfa is 1-0.95=0.05, and alfa/2=0.025

The z-score at 0.025 is 1.96.

Replace the known values in the formula and solve for E:

c. The confidence interval is then:

d. We estimate with a 95% confidence that between 49% and 55.1% of the people felt vulnerable to identity theft.

the value of x is 20

Step-by-step explanation:

hope it helps you!

Answer:

i think x=20

An equation is an expression containing an equals sign (=) that states that two expressions are equal. An inequation is an expression containing an inequality sign (<, >, ≤, or ≥) that states that two expressions are not equal. Equations and inequations are used to describe relationships between two or more values.

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Answer: no one cares

Step-by-step explanation:

Answer:

The standard error of your estimate of the average height in the city is 0.5 inches.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

You begin by collecting the heights of a random sample of 196 people from the city.

This means that \(n = 196\)

The standard deviation of the heights in your sample is 7 inches.

This means that \(\sigma = 7\)

The standard error of your estimate of the average height in the city is

\(s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5\)

The standard error of your estimate of the average height in the city is 0.5 inches.

Answer:

C

Step-by-step explanation:

The asymptote is located at \(x=-2\).

Hence, the answer is C as the denominator cannot be equal to zero.

Answer:

B c < 27.50

Step-by-step explanation:

The cost c of a shirt is less than $27.50

In representing equality

< Represent less than

= Represent equal to

> Represent greater than

Other representation includes

< = Less than or equal to

>= Greater than or equal to

/= Not equal to

The cost c of a shirt is less than $27.50

C< 27.50

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

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The simplified expression of (x¹² ÷  x⁴). x³ is x¹¹

The expression can be solved as follows:

(x¹² ÷  x⁴). x³

The law of indices can be used to solve the expression.

Therefore,

\(\frac{x^{a} }{x^{b} } = x^{a - b}\)  and \((x^{a} )^{b} = x^{ab}\) and \(x^{a} .x^{b} = x^{a+b}\)

Hence,

(x¹² ÷  x⁴) = x¹² / x⁴ = x¹²⁻⁴ = x⁸

Therefore,

(x⁸). x³ = x⁸⁺³

Finally,

x⁸⁺³ = x¹¹

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Step-by-step explanation:

Option (e) is the right answer.

Answer:

C {(0,2), (2,0), (4,6), (6,4)}, {(0,2), (2,0), (4,6), (6,4)}

Step-by-step explanation:

Hey, there!

So, a function is generally speaking referring to an input, and an output. With a function, an input can have many outputs, but an output can only trace back to a specific singular (one) input.

A {(0,3), (3,0), (0,4), (4,0)}, {(0,3), (3,0), (0,4), (4,0)}

Here, you have two of the same inputs (0), that share multiple outputs. In a function, you can only have ONE of same inputs. That means, you cannot have shared x-values in any function.

B {(6,2), (2,0), (4,6), (6,4)}, {(6,2), (2,0), (4,6), (6,4)}

Here, you have two of the same inputs (6), that share multiple outputs. In a function, you can only have ONE of same inputs. That means, you cannot have shared x-values in any function.

C {(0,2), (2,0), (4,6), (6,4)}, {(0,2), (2,0), (4,6), (6,4)}

Here, there are no shared x-values within the two functions. Therefore, this IS A FUNCTION!  (0, 2, 4, 6) are not the same value for x, therefore it is a function.

D {(0,4), (0,9), (12,6), (-3,9)}, {(0,4), (0,9), (12,6), (-3,9)}

Here, you have two of the same inputs (0), that share multiple outputs. In a function, you can only have ONE of same inputs. That means, you cannot have shared x-values in any function.

E {(2,6), (3,6), (4,6), (2,0)}

Here, you have two of the same inputs (2), that share multiple outputs. In a function, you can only have ONE of same inputs. That means, you cannot have shared x-values in any function.

The conclusion to find out if there has been a significant change in the homework habits of grade-school children is that;

There is insufficient evidence to support the claim that there has been significant change in the homework habits of grade-school children.

The seven steps are below.

Step 1; State the null and alternative hypotheses;

We are given;

Population mean; µ = 8 hours

Thus;

Null hypothesis; H\(_{o}\): µ = 8

Alternative hypothesis; H\(_{a}\) \(\neq\) 8

Step 2. We will set the level of risk that is associated with the null hypothesis;

The level of risk associated with the null hypothesis is simply the level of statistical significance. Thus, α = 0.05 = 5%

Step 3. Select the appropriate test statistic;

The question follows normal distribution and so the test statistic to use is z-test

Step 4. The value of the test statistic would be computed;

Formula for z-score is;

z = (x' - µ)/(σ/\(\sqrt{n}\))

z = (7.4 - 8)/(2.5/\(\sqrt{100}\) )

z = -2.4

Step 5. The value needed for rejection of the null hypothesis would be determined from the z-score table;

From z-score table, with z = -2.4; α = 0.05, two tailed hypothesis;

p-value = 0.0164

Step 6. Compare the p-value with the level of significance;

The p-value is less than the significance value

Since the p-value is less than the significance value, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that significant change in the homework habits of grade-school children.

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Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

P = 4/13 = 0.308

Step-by-step explanation:

3 cards 3

13 spade cards (includes the card 3 of spades)

\(P=(3+13)/52= 16/52 = 4/13=0.308\)

Hope this helps.

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

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

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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Answer:

you need three pencil cases to hold all of your pencil

Answer:

3

Step-by-step explanation:

18 = 7 +7 + 4

Since each box can carry 7 pencils, we need three to hold all of them.

Hope this helps!!

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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The addition of the given fraction expression is 7/8.

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. It can be a simple combination of numbers or a more complex combination involving variables, functions, or other mathematical constructs.

When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same.

In this case, both fractions have a denominator of 8, so we can add their numerators:

5/8 + 2/8 = (5 + 2)/8 = 7/8

Thus, the sum of 5/8 and 2/8 is 7/8.

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The unknown number is x .

An equation to find the value of x :-

\(x + 5 = - 4\)

Let us solve this equation :-

\(x + 5 = - 4\)

\(x = - 4 - 5\)

\(x = - 9\)

The value of x is -9 . Let us place -9 in the place of x , to check whether or not we have found out the correct value of x .

So :-

\( - 9 + 5 = - 4\)

\( - 4 = - 4\)

\(LHS = RHS \)

As the left hand side of the equation is equivalent to the right hand side of the equation, we can conclude that we have found out the correct value of x .

Therefore , -9 + 5 = -4 and ( x = -9 ) .

5+x=-4 is equation of sentence 5 more than a number x is -4 and -9 is the solution of equation.

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

The given sentence is 5 more than a number x is -4.

Whenever there is a more than in a sentence means added with some number.

Let us consider the number be x.

5 more than a number x is -4 means 5 is added to number x which gives -4.

5+x=-4

This is the equation for the sentence.

Now let us solve the equation.

5+x=-4

Subtract 5 from both sides

x=-4-5

x=-9

Hence, 5+x=-4 is equation of sentence 5 more than a number x is -4 and -9 is the solution of equation.

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