solve the inequality

-2x-8>3x+12

a x<-4
b x>-3
c x>-4
d x<-3​

The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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Answer:

g = 3

Step-by-step explanation:

(x+7)(x-4) = x²+ gx -28

Multiply the two parenthesis

(x+7)(x-4)= x² -4x +7x -28

Combine like terms

(x+7)(x-4)= x²+3x-28

Compare the equations

x²+ gx -28 =  x² +3x -28

g = 3

Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

Answer: Should be about a 20.4% chance

Step-by-step explanation:

17 times 6 divided by 5

Answer: 0.05

Step-by-step explanation:

Since 95 out of 100 were closed, the closed window is 95% = 0.95.

5 open windows = 5% = 0.05

Answer:

1/6 that's the answer

Step-by-step explanation:

so you do 43/6-7=43/6-42/6=1/6

Answer:

Actually the answer is -⅙

Step-by-step explanation:

43/6 written differently is 7 ⅙, because the fraction 42/6 is the same as 7 (42÷6=7). But since your number is 43/6 you get

7 1/6.

your original number is larger than 7 but the question was what number you have to "add" to get to 7. so they number has to be a negative number.

like this:

43/6 + (-1/6) = 42/6. which you rewrite now as

43/6 - 1/6 = 42/6. and I explained that 42/6 is the same as 7.

Answer:

Center ( -8, 1 )

Radius ( 13 )

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$975\\ r=rate\to \text{\LARGE 5.7\%}\to \frac{5.7}{100}\dotfill &0.057\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years \end{cases} \\\\\\ A = 975\left(1+\frac{0.057}{1}\right)^{1\cdot t} \implies A = 975(1.057)^t\)

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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Reason: Multiply both sides by 7

The inequality sign doesn't flip. It only flips if you multiplied both sides by a negative number.

Answer:

196

Step-by-step explanation:

147/3 x4

Answer:

All except the 3rd

Step-by-step explanation:

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

the answer was 7.71

Step-by-step explanation:

hope this helps

A fraction is usually split into two parts: the first part is the number on top, called the numerator; and the second part is the number on the bottom, called the denominator. These are both separated by a line called the “divisor line”. We can use the division method help to solve this question: to get a decimal, simply divide the numerator 54 by the denominator 7 (which you can enter in any calculator):

54 (numerator) ÷ 7 (denominator) = 7.71

And finally, you get 7.71 as your answer when you convert 7 5/7 (or 54/7) to a decimal.

Answer:

7.71

Step-by-step explanation:

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

0,5

Step-by-step explanation:

Missing number 5 or it can be a 0

This is beacause a number that ends with 0 or 5 is divisible by 5. Divisibilitiy rules state that!

Ex: 5 x 5 = 25

5 x 4 = 20

Answer:

\(s = cB- 8 \\ cB = s + 8 \\ \\ c = \frac{s + 8}{B} \\ \\ c = \frac{s}{B} + \frac{8}{B} \)

I hope I helped you^_^

There are 9 balls to be sure of having at least three blue balls, and there are 5 balls having at least three balls of the same color.

As per the question, the woman selects the balls at random without looking at them, so there is a possibility that the first 6 balls that she selects are all red. Then to have at least 3 blue balls she has to pick three balls from the rest of the 6 balls.

As all of them are blue only 3 picks are needed for that. Hence 6+3=9 balls she needs to pick to be sure of having at least 3 blue balls.

There are 2 colors of balls that are present in the bowl, Red and Blue. Now Consider there is a Red bucket and a Blue bucket outside the bowl and after picking each ball from the bowl, each ball must go to either of the buckets.

so apply the pigeonhole principle to be sure of having at least 3 balls of the same color

she needs to pick 2+2+1=5 balls from the bowl.

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1) Answer: Option C. 225

2) Answer: Option C. 4.5

Answers are:

8. 225

9. 50

Answer:

Hdhd

Step-by-step explanation:

Usu

Answer:

Ummmmmmm

Step-by-step explanation:

Answer:

i think the answer is D becasue if you do the vertical line test the line passes through alot of times

Step-by-step explanation:

\(\text{Given that,}\\\\\sin \theta = -\dfrac{12}{13}\\\\\implies \sin^2 \theta = \dfrac{144}{169}\\\\\implies 1- \cos^2 \theta = \dfrac{144}{169}\\\\\implies \cos^2 \theta = 1- \dfrac{144}{169}\\\\\implies \cos^2 \theta = \dfrac{25}{169}\\\\\implies \cos \theta = \pm \sqrt{\dfrac{25}{169}} = \pm \dfrac 5{13}\\\\\\\text{Since,}~ \tan \theta >0,\\\\\cos \theta =- \dfrac{5}{13}\)

Answer: a- (7,7) (4,19) b- m=-12/3=-4/1=-4 c- y=4x+35 d- 48min, it increases by 12min a day

Step-by-step explanation:

i did the assignment

Mr. Waxman's delivery is an illustration of a linear function.

(a) Two points on the graph

The points are: (4,19) and (6,11)

(b) The slope of the graph

The slope (m) is calculated as:

\(\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

So, we have:

\(\mathbf{m = \frac{11 - 19}{6- 4}}\)

\(\mathbf{m = \frac{-8}{2}}\)

\(\mathbf{m = -4}\)

The slope of the graph is -4

(c) The equation of the graph

In point-slope form, we have:

\(\mathbf{y -y_1 = m(x - x_1)}\)

So, we have:

\(\mathbf{y -4 = -4(x -19)}\)

In slope intercept form, we have:

\(\mathbf{y = -4(x -19) + 4}\)

Open brackets

\(\mathbf{y = -4x +76 + 4}\)

\(\mathbf{y = -4x +80}\)

The equation of the graph is: \(\mathbf{y = -4x +80}\)

(d) The value of the function at day 0

This means that x = 0

So, we have:

\(\mathbf{y = -4(0) +80}\)

\(\mathbf{y = 0 +80}\)

\(\mathbf{y = 80}\)

Hence, it will take 80 minutes to deliver the package on day 0

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Answer:

y - 2 = 3(x + 1)

Step-by-step explanation:

The slope is 3 and the point is (-1,2)

From the plot pointed, you go up three unit and 1 unit to the right to get back on the line.  This is 3/1 or 3.

y - \(y_{1}\) = m( x - \(x_{1}\))  

Replace m =3

Replace \(y_{1}\) = 2

Replace \(x_{1}\) = -1

y - 2 = 3(x - -1)

y - 2 = 3(x +1)

The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer\(x = (739 - 625) / 3 = 38\) surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

\(CS = \int_0^{38} [D(x) - 25] dx\)

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

\(CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83\)

Therefore, the consumer surplus is approximately $145.83.

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The identity in question is

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

so that

cos(a - b) = 12/37 cos(a) + 3/5 sin(b)

Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,

cos²(x) + sin²(x) = 1,

that

cos(a) = √(1 - sin²(a)) = 4/5

and

sin(b) = √(1 - cos²(b)) = 35/37

So,

cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185