What is the solution to this inequality?
-2x-3 ≥ 6 or 3(x-4) < -6
OA. * > - 2/1
OB.
Oc. or x > 2
C.
OD.
-/<< 2
x
<2
-

ANSWER

EXPLANATION

We want to rewrite the division problem into a multiplication one.

To do this, we have to change the division sign to a multiplication sign, and then, we invert the fraction on the right.

That is:

That is the answer.

The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

Answer:

angle B=122degree

Step-by-step explanation:

straight line AC =180degree, then 180-(21+37)=122 degree

a=b*sinA/sinB=84.5

c=b*sinC/sinB=141.9

Answer:

radius

Step-by-step explanation:

The probability that the student chosen at random was male OR got an "A" is 31/58.

To find the probability that the student was male OR got an "A," we need to calculate the probability of each event separately and then add them together.

Let's calculate the probability of the student being male:

Total number of males = 11

Total number of students = 58

Probability of the student being male = Number of males / Total number of students = 11/58

Now, let's calculate the probability of the student getting an "A":

Total number of students who got an "A" = 20

Probability of the student getting an "A" = Number of students who got an "A" / Total number of students = 20/58

To find the probability of the student being male OR getting an "A," we add the two probabilities together:

Probability (Male OR A) = Probability (Male) + Probability (A) = 11/58 + 20/58 = 31/58

Therefore, the probability that the student chosen at random was male OR got an "A" is 31/58.

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Answer:

37

Step-by-step explanation:

106+37+x= 180( being sum of angle of triangle)

143+x= 180

x= 180-143

= 37

•°•x= 37°

Answer:

37

Step-by-step explanation:

106+37+x-180

x-180-143

x+-37

To show that the point (å, ä) is on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ), we need to demonstrate two things: that the point lies on the line segment, and that it is equidistant from the endpoints.

1. Determine the midpoint of the line segment:

  - The midpoint coordinates (\(x_{mid, y_{mid\)) can be found using the midpoint formula:

    \(x_{mid\) = (x1 + x2) / 2 and \(y_mid\) = (y1 + y2) / 2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

    In this case, we have (x1, y1) = (Ů, ü) and (x2, y2) = (ĝ, ġ).

2. Calculate the midpoint coordinates:

  - Substitute the values into the midpoint formula to find (x_mid, y_mid).

3. Find the slope of the line segment:

  - Use the slope formula: slope = (y2 - y1) / (x2 - x1).

    Apply the formula to the endpoints (Ů, ü) and (ĝ, ġ) to determine the slope of the line segment.

4. Determine the negative reciprocal of the line segment's slope:

  - Take the negative reciprocal of the slope calculated in the previous step. The negative reciprocal of a slope m is -1/m.

5. Write the equation of the perpendicular bisector:

  - Using the negative reciprocal slope and the midpoint coordinates (\(x_{mid\), \(y_{mid\)), write the equation of the perpendicular bisector in point-slope form: y - \(y_{mid\) = \(m_{perp\) * (x - \(x_{mid\)), where \(m_{perp\) is the negative reciprocal slope.

6. Substitute the point (å, ä) into the equation:

  - Replace x and y in the equation of the perpendicular bisector with the coordinates of the point (å, ä). Simplify the equation.

7. Verify that the equation holds true:

  - If the equation is satisfied when substituting (å, ä), then the point lies on the perpendicular bisector.

By following these steps, you can demonstrate that the point (å, ä) lies on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ).

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Answer:

36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²

Step-by-step explanation:

This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.

Answer:

Equation: y= -3/4x+15/2

Step-by-step explanation:

The points given: (-2,9) and (2,6)

Slope ,m=y2-y1/x2-x1=6-9/2-(-2)= -3/(2+2)

slope ,m= -3/4

Equation: y-y1=m(x-x1)

Equation: y-6= -3/4(x-2)

y-6= -3/4x+3/2

y= -3/4x+3/2+6

y= -3/4x+15/2

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From the given question, Option 2 and 3 i.e., \(5(x^{2} +4x)=7\)  and \(5(x^{2} +4x+4)=7+20\) are correct for the given equation \(5x^{2} +20x-7=0\).

Given quadratic equation is

\(5x^{2} +20x-7=0\)

Firstly, we will add of 7 in both sides

\(5x^{2} +20x-7+7=0+7\)

Now, same variable of opposite sign is cancelled

\(5x^{2} +20x=7\)

Now, taking 5 common from left side

\(5x(x+4)=7\)

\(5(x^{2} +4x)=7\)

Case (II):

Given equation

\(5x^{2} +20x-7=0\)

Firstly, we will add of 7 in both sides

\(5x^{2} +20x=7\)

Now, we will add of 20 in both sides

\(5x^{2} +20x+20=7+20\)

Now, taking common of 5 from left side

\(5(x^{2} +4x+4)=7+20\)

So, The next step on solving completing square is \(5(x^{2} +4x)=7\) and \(5(x^{2} +4x+4)=7+20\) .

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Answer:

1

Step-by-step explanation:

To divide 2 fractions, you have to use the reciprocal of the latter fraction.

The reciprocal of 12/38 is 38/12

Now you can multiply

6/19*38/12 = 1

Answer:

(p + 2)(3b - 7)

Step-by-step explanation:

3b(p + 2) - 7(p + 2) ← factor out common factor (p + 2) from each term

= (p + 2)(3b - 7)

Answer:

\( P(0.55 <X<1.1)= F(1.1) -F(0.55) \)

And replacing we got:

\( P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})\)

\( P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457\)

And rounded the answer would be 0.246

Step-by-step explanation:

For this case we can define the random variable X as "The commute time for people in a city" and for this case the distribution of X is given by:

\( X \sim exp (\lambda = \frac{1}{0.66}= 1.515)\)

And for this case we want to find the following probability:

\( P(0.55 <X<1.1)\)

And we can use the cumulative distribution function given by:

\( F(x) =1- e^{-\lambda x}\)

And using this formula we got:

\( P(0.55 <X<1.1)= F(1.1) -F(0.55) \)

And replacing we got:

\( P(0.55 <X<1.1)= (1-e^{-\frac{1}{0.66} *1.1}) -(1-e^{-\frac{1}{0.66} *0.55})\)

\( P(0.55 <X<1.1)=e^{-\frac{1}{0.66} *0.55}- e^{-\frac{1}{0.66} *1.1}=0.2457\)

And rounded the answer would be 0.246

9514 1404 393

Answer:

  f(-x) = x^2 -3x +9

Step-by-step explanation:

Use -x as the argument of the function.

  f(-x) = (-x)^2 +3(-x) +9

  f(-x) = x^2 -3x +9 . . . . . . . . simpify

We make expressions for each afirmation

Where X is the first day, Y second day and Z the third

1. the sum of the 3 days gives us 30

2. Second day is 4/5 of the first day

3.Third day is 3/2 of the second day

Whit the expressions I try to represent everything as a function of X

I must represent Z in function of X, for this I can replace Y of the second expression in the third expression

So I have:

And I can replace on the first expression

I must find X

So, if I have X I can replace on this expressions to find de value:

Where X is 10

To check:

The result is correct, therefore:

let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly

\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)

Answer:

the answer is true! :)

Step-by-step explanation:

The statement "a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions" is true .

A linear equation is an algebraic equation of the form \(y= mx+b.\)involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

We define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is , \(y = ax^2 + bx + c\)

where a, b, and c are numbers and a cannot be 0.  

According to the question

A system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions.​

This statement is true as

if we see graphically  

A quadratic equation is a parabola and a linear equation is a straight line.

There could be 3 situations of intersection of line and parabola

1. straight line never crosses the parabola

i.e line passing above or below parabola without touching

it is called zero solution

2. where the straight line is a tangent to the parabola, 'touching' it at only one point.

i.e single point lies in both line and parabola

it is called one solution

3. the line cuts across the parabola, it will cut the parabola at 2 points

it is called two solution .

Hence, The statement " a system that consists of a linear equation and a quadratic equation can have zero, one, or two solutions "is true .

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Answer:   The intersections of the graphs of a system of equation correspond to the solutions of the system. Since we saw that a line can intersect a parabola zero, one, or two times, a linear-quadratic system can have zero, one, or two solutions.

Step-by-step explanation:PLATO

Answer:

A opens upward

Step-by-step explanation:

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

she filled 80 pages with 5 left over

Step-by-step explanation:

Answer: z = 7 or z=-5

Step-by-step explanation:

First you need to factor the polynomial.

To factor \(z^{2}\)  - 2z -35       You will need to find two numbers that their product is -35 and their sum is -2  and the numbers -7 and 5  works out.

Rewrite the polynomial as,

\(z^{2}\) - 7z + 5z - 35  = 0   factor the left by grouping

(\(z^{2}\) -7z) (5z -35)  = 0

z(z -7)  5(z - 7) = 0      Factor out z-7

(z-7)(z+5) = 0        Now apply the zero product by setting each of them equal 0.

z-7= 0      or  z+5=0

 +7  +7             -5  -5

z = 7     or  z= -5  

Answer:

lo i just gto 100 %

Step-by-step explanation:

lets do dad i love you

Answer:

285

Step-by-step explanation:

570/2=285

true or false means theres a 1/2 possibility you guess right thats why you divide by 2

The mean number of correct answers to 570 true or false questions will be 285.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

For the true or false, the probability of getting correct is given as,

p = 1/2

There are 570 true or false questions in a quiz. If the pupil guesses for each inquiry. Then the expected value is given as,

E = 570 x (1/2)

E = 285

The mean number of correct answers will be 285.

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The  quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x\(10^1\)

Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)

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Answer:

  (c)  Credit unions are nonprofit financial institutions

Step-by-step explanation:

A bank is a financial institution owned by stockholders. It has the intention of making a profit, a portion of which benefits the stockholders. A full-service bank offers loans (at interest), savings and checking accounts, credit and debit cards, and access to ATMs. It may also offer safe deposit boxes. Fees may be charged for any or all of these services.

__

A credit union is a non-profit financial institution. It is owned by its members, who obtain the benefit of lower fees for services. A full-service credit union offers loans (at interest), savings and checking accounts, and credit and debit cards. It will generally offer access to one or more networks of ATMs. Many of these services are free to members.

__

Banks and credit unions are subject to different regulatory requirements.