What is the equation of the line graphed below?
5
- 5
5
(3,-1)
1
-5
O A. y=-3x
1
O B. y = -
O c. y =
C. 5
-X
What is the equation of the line graphed below

Answer:

The absolute change was of -21,665 people.

Step-by-step explanation:

Absolute change:

Final value subtracted by the initial value.

In this question:

Initial value: 699,710

Final value: 678,045

What is the absolute change from 2012 to 2016?

678045 - 699710 = -21,665

The absolute change was of -21,665 people.

Answer:

262.5 miles

Step-by-step explanation:

Correct me if I am wrong

Answer:

-3a+3bx+2ab

Step-by-step explanation:

Answer:

Approximately [tex]4.75[/tex].

Step-by-step explanation:

Remark: this approach make use of the fact that in the original solution, the concentration of  [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] are equal.

[tex]{\rm CH_3COOH} \rightleftharpoons {\rm CH_3COO^{-}} + {\rm H^{+}}[/tex]

Since [tex]\rm CH_3COONa[/tex] is a salt soluble in water. Once in water, it would readily ionize to give [tex]\rm CH_3COO^{-}[/tex] and [tex]\rm Na^{+}[/tex] ions.

Assume that the [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] ions in this solution did not disintegrate at all. The solution would contain:

[tex]0.3\; \rm L \times 0.2\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COOH[/tex], and

[tex]0.06\; \rm mol[/tex] of [tex]\rm CH_3COO^{-}[/tex] from [tex]0.2\; \rm L \times 0.3\; \rm mol \cdot L^{-1} = 0.06\; \rm mol[/tex] of [tex]\rm CH_3COONa[/tex].

Accordingly, the concentration of [tex]\rm CH_3COOH[/tex] and [tex]\rm CH_3COO^{-}[/tex] would be:

[tex]\begin{aligned} & c({\rm CH_3COOH}) \\ &= \frac{n({\rm CH_3COOH})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].

[tex]\begin{aligned} & c({\rm CH_3COO^{-}}) \\ &= \frac{n({\rm CH_3COO^{-}})}{V} \\ &= \frac{0.06\; \rm mol}{0.5\; \rm L} = 0.12\; \rm mol \cdot L^{-1} \end{aligned}[/tex].

In other words, in this buffer solution, the initial concentration of the weak acid [tex]\rm CH_3COOH[/tex] is the same as that of its conjugate base, [tex]\rm CH_3COO^{-}[/tex].

Hence, once in equilibrium, the [tex]\rm pH[/tex] of this buffer solution would be the same as the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex].

Calculate the [tex]{\rm pK}_{a}[/tex] of [tex]\rm CH_3COOH[/tex] from its [tex]{\rm K}_{a}[/tex]:

[tex]\begin{aligned} & {\rm pH}(\text{solution}) \\ &= {\rm pK}_{a} \\ &= -\log_{10}({\rm K}_{a}) \\ &= -\log_{10} (1.76 \times 10^{-5}) \\ &\approx 4.75\end{aligned}[/tex].

Answer:

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

A manufacturer of nails claims that only 4% of its nails are defective.

At the null hypothesis, we test if the proportion is of 4%, that is:

[tex]H_0: p = 0.04[/tex]

At the alternative hypothesis, we test if the proportion is more than 4%, that is:

[tex]H_a: p > 0.04[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

4% is tested at the null hypothesis

This means that [tex]\mu = 0.04, \sigma = \sqrt{0.04*0.96}[/tex]

A random sample of 20 nails is selected, and it is found that two of them, 10%, are defective.

This means that [tex]n = 20, X = 0.1[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.1 - 0.04}{\frac{\sqrt{0.04*0.96}}{\sqrt{20}}}[/tex]

[tex]z = 1.37[/tex]

P-value of the test and decision:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Answer:

Considering an standard significance level of 0.05.

The p-value of the test is the probability of finding a sample proportion above 0.1, which is 1 subtracted by the p-value of z = 1.37.

Looking at the z-table, z = 1.37 has a p-value of 0.9147

1 - 0.9147 = 0.0853

The p-value of the test is 0.0853 > 0.05, which means that there is not enough evidence to reject the manufacturer's claim based on this observation.

Step-by-step explanation:

Answer:

a.) m⁴n²

Step-by-step explanation:

( -m)⁴ × n ²

A negative base raised to an even powers equals a positive.

m ⁴ × n²

multiply the terms

m⁴n²

Answer:

a.) m⁴n²

Step-by-step explanation:

yea

Answer:

1.25. It would be 1.25 if ur just talking about dividing in general which is pretty tough

Answer:

\dfrac54=-4c+\dfrac14 4 5 ​ =−4c+ 4 1 ​ start fraction, 5, divided by, 4, end fraction, equals, minus, 4, c, plus, start fraction, 1, divided by, 4, end fraction

Step-by-step explanation:

C. The two statements agree in point of truth or falsehood in virtue of their logical structure alone, i.e. the two statement are true or false in exactly the same conditions.

For two statements to be logically equivalent, their truth values (true or false) must be the same for every variation of their constituent variables. In other words, if the truth tables of both statements are the same for every possible value of their variables, then they are logically equivalent.

For example;

The two statements P ∩ (Q U R) and (P ∩ Q) ∪ (P ∩ R) are logically equivalent.

If P, Q and R are all true, then;

P ∩ (Q U R) = true

(P ∩ Q) ∪ (P ∩ R) = true

If P, Q and R are all true, then;

P ∩ (Q U R) = false

(P ∩ Q) ∪ (P ∩ R) = false

If P = false, Q = true and R = true, then;

P ∩ (Q U R) = false

(P ∩ Q) ∪ (P ∩ R) = false

Checking for all other possible combinations of truth values of P, Q and R will always give the same results for the two statements, therefore, they are logically equivalent.

Answer:

Step-by-step explanation:

                    Statements                                        Reasons

1). ΔABC with side lengths a, b, c, and h      1). Given

2). Area = [tex]\frac{1}{2}bh[/tex]                                                 2). Triangle area formula

3). [tex]\text{sin}C=\frac{h}{a}[/tex]                                                    3). Definition of sine

4). asin(C) = h                                                4). Multiplication property of

                                                                          equality.

5). Area = [tex]\frac{1}{2}ba\text{sin}C[/tex]                                         5). Substitution property

6). Area = [tex]\frac{1}{2}ab\text{sin}C[/tex]                                         6). Commutative property of

                                                                           multiplication.

Hence, proved.

Answer:

n(B) = 1350

Step-by-step explanation:

Using Venn sets, we have that:

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

Three values are given in the exercise.

The other is n(B), which we have to find. So

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)[/tex]

[tex]2290 = 1300 + n(B) - 360[/tex]

[tex]940 + n(B) = 2290[/tex]

[tex]n(B) = 2290 - 940 = 1350[/tex]

So

n(B) = 1350

Answer:

150 dollars. if I am wrong correct me

Answer:

C and D

Step-by-step explanation:

15 to 30 galons at $9.95 to $21.00

the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25

the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630

there are 2 choices that are between 149.25 and 630, C, and D

Answer:

[tex]2\frac{3}{4} +(-4\frac{1}{4} )=-1\frac{2}{4}[/tex]

Step-by-step explanation:

That's the only equation that makes sense to the number line

Answer:

The correct answer is "1668". A further solution is provided below.

Step-by-step explanation:

According to the question,

Estimated proportion,

[tex]\hat{p} = \frac{574}{1007}[/tex]

  [tex]=0.57[/tex]

Margin of error,

E = 0.02

Level of confidence,

= 90%

= 0.90

Critical value,

[tex]Z_{0.10}=1.65[/tex]

Now,

⇒  [tex]0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }[/tex]

 [tex]0.0004=2.7225\times \frac{0.2451}{n}[/tex]

         [tex]n=\frac{2.7225\times 0.2451}{0.0004}[/tex]

             [tex]=1668.21[/tex]

or,

         [tex]n \simeq 1668[/tex]

Answer:

5 + c > -22

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Sum of 5 and c is greater than -22

↓ Identify

Sum = addition

Is greater than = inequality

Add them all together:

5 + c > -22

Answer:

[tex]{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) = {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =( \frac{a}{a'})x {}^{2} + ( \frac{b}{b'}) x} + \frac{c}{c'} } = 0[/tex]

Answer:

sin²2θ. (cos θ sin θ). cos 2θ

Step-by-step explanation:

finding g'(x)

g'(x)

= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }

= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}

= 4 (cosθsinθ)³{ cos²θ - sin²θ}

= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}

= sin²2θ. (cos θ sin θ). cos 2θ

Answer:

108 meters with the formula lxhxw

Answer:

6 : 24

Step-by-step explanation:

If we are in the ratio of 1 to 4, the total is 1+4 = 5

Divide 30 by 5

30/5 = 6

Multiply each term in the ratio by 6

1  :4

1*6 : 4*6

6 : 24

Answer:

total ratio:

[tex] = 1 + 4 \\ = 5[/tex]

For the portion of 1:

[tex] = 30 \div \frac{1}{5} \\ = 30 \times 5 \\ = 150[/tex]

For the portion of 4:

[tex] = 30 \div \frac{4}{5} \\ = 30 \times \frac{5}{4} \\ = 37.5[/tex]

= 30 : 7.5

Answer:

b.

Graph B

Step-by-step explanation:

We are given the following linear equation:

[tex]6x = y + 8[/tex]

When x = 0:

[tex]6(0) = y + 8[/tex]

[tex]y = -8[/tex]

Thus, the line goes through (0,-8).

When y = 4:

[tex]6x = y + 8[/tex]

[tex]6x = 4 + 8[/tex]

[tex]6x = 12[/tex]

[tex]x = \frac{12}{6} = 2[/tex]

So also through (2,4).

Thus means that the correct answer is given by Graph B.

Answer:

A. c = -7

Step-by-step explanation:

Standard form of a quadratic equation is given as ax² + bx + c = 0, where,

a, b, and c are known values not equal to 0,

x is the variable.

Given a quadratic equation of -x² + 4x - 7, therefore,

a = -1

b = 4

c = -7

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I believe your answer is:  

Quadrant III

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

RA = 24

Step-by-step explanation:

Since the triangle is isosceles ( 2 equal sides ) , then LU is a perpendicular bisector , so

AU = RU , that is

4r = 18 - 2r ( add 2r to both sides )

6r = 18 ( divide both sides by 6 )

r = 3

Then

RA = 18 - 2r + 4r = 18 + 2r = 18 + 2(3) = 18 + 6 = 24

Answer:

[tex]A=603.18\ cm^2[/tex]

Step-by-step explanation:

The length of a blade, r = 24 cm

The sweeping angle is 120°.

We need to find the total area cleaned at one sweep of the blade. The area of sector is given by :

[tex]A=\dfrac{\theta}{360}\times \pi r^2[/tex]

[tex]A=\dfrac{120}{360}\times \pi \times 24^2\\\\=603.18\ cm^2[/tex]

So, the total area cleaned at one sweep of the blade is [tex]603.18\ cm^2[/tex].

Answer:

78.81%

Step-by-step explanation:

We are given;

Population mean; μ = 149

Sample mean; x¯ = 147.8

Sample size; n = 88

standard deviation; σ = 14

Z-score is;

z = (x¯ - μ)/(σ/√n)

Plugging in the relevant values;

z = (147.8 - 149)/(14/√88)

z = -0.804

From z-distribution table attached, we have; p = 0.21186

P(X > 147.8) = 1 - 0.21186 = 0.78814

In percentage gives; p = 78.81%

Answer:

[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Addition/Subtraction]:                                                            [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                               [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

0.9984

Step-by-step explanation:

we have shape parameter for the first component as 2.1

characteristics life = 100000

for this component

we have

exp(-2000/100000)².¹

= e^-0.0002705

= 0.9997

for the second component

shape parameter = 1.8

characteristic life = 80000

= exp(-2000/80000)¹.⁸

= e^-0.001307

= 0.9987

the reliability oif the system after 2000  events

= 0.9987 * 0.9997

= 0.9984

Answer:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Step-by-step explanation:

The transformation is a horizontal dilation

The general transformation is defined as:

For a given function f(x), a dilation of scale factor K is written as:

g(x) = f(x/K)

If K > 1, then we have a dilation (the graph contracts)

if 0 < K < 1, then we have a contraction (the graph stretches)

Here we have m(x) = f(5*x)

Then we have a scale factor:

K = 1/5

So this is a contraction.

Then the transformation is:

m(x) is a dilation of scale factor K = 1/5 of f(x).