Solve the following compound inequality. Graph the solution.
5x2-30 and 5x ≤ 15
What is the solution? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. xs
OB. xs
OC. x2
OD. SXS (Type integers or decimals.)
E. The compound inequality has no solution.
OF. The solution is all real numbers.
XXXB
or x2 (Type integers or decimals.)
(Type an integer or a decimal.)
(Type an integer or a decimal.)

Answers in bold:

Problem 4) Shift 6 units left, 1 unit down

Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.

The graphs are below.

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Explanation:

In problem 4, the parent function is y = x^2

Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.

Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.

So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.

I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.

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

For problem 5, the parent function is y = |x|

Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.

The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).

Answer:

4.  Translated 6 units left and 1 unit down.

5.  Translated 3 units right and stretched vertically by a factor of 2.

Step-by-step explanation:

Transformations

[tex]\textsf{For $a > 0$}[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Parent function:

[tex]f(x)=x^2[/tex]

Translated 6 units left:

Add 6 to the x-variable of the function:

[tex]\implies f(x+6)=(x+6)^2[/tex]

Translated 1 unit down:

Subtract 1 from the function:

[tex]\implies f(x+6)-1=(x+6)^2-1[/tex]

Parent function:

[tex]f(x)=|x|[/tex]

Translated 3 units right:

Subtract 3 from the x-variable of the function:

[tex]\implies f(x-3)=|x-3|[/tex]

Stretched vertically by a factor of 2:

Multiply the function by 2:

[tex]\implies 2f(x-3)=2|x-3|[/tex]

The 95% confidence interval for p is (0.333, 0.480).

If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.

The formula for calculating the confidence interval is expressed as shown below;

CI = p±Z * √p(1-p)/n±0.5/n

Where Z is the z-score at 95% confidence

p is the sample proportion

n is the sample size

Given that n = 144, p = 0.7 and z-score at 95%  

CI = 1.645 (from z table)

Now Substituting this values;

CI = p ± 1.645*√0.7(1-0.4)/144 ±0.5/n

CI = 0.4 ± 1.645*√0.7(0.6)/144 ± 0.5/144

CI = 0.4 ±1.645 * √0.24/144 ± 0.00347

CI = 0.4 ±1.645 * 0.04087± 0.00347

CI = 0.4±0.06723±0.00347

CI =(0.333, 0.480)

Hence, The 95% confidence interval for p is (0.333, 0.480).

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About 25 percent of the data are greater than 20.(option a)

About 50 percent of the data are less than 15. (option b)

20 is wrongly interpreted as the median. 20 is the third quartile. The data between 11 and 20 is 50%.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

The box plot consists of two whiskers and a box. The first whisker represent the minimum value. The second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

20 is the third quartile. Score greater than 20 is 25% (100% - 75%)

15 is the median. Scores less than 15 is 50% (100 - 50%),

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The quotient after the long division of 35/456 is 0.076.

So, after the long division:

Therefore, the quotient after the long division of 35/456 is 0.076.

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Answer:

Question have problem.

Step-by-step explanation:

The formula for circumference when the diameter is given is C = π • d

C = circumference

π = pi

d = diameter

So to find the circumference plug in the number (18 - diameter).

C = π • 18

C = 56.5486677646

If needed to round to nearest ...

tenth = 56.5

hundredth = 56.55

However, if the directions say to use 3.14 for π (pi) then the answer would be different.

C = 3.14 • 18

C = 56.52

Hope this helps :)

It should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.

It should be noted that it's important to understand ratio and use ratio language to describe the relationship between two quantities.

For example, it van be stated that the ratio of wings to beaks in the bird house at the zoo is 2:1, this implies that b for every 2 wings there is 1 beak.

Therefore, it should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.

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Answer: 5/8 + 3/4 = 11/8 = 1 3/8 = 1.375

Step-by-step explanation:5/8+ 3/4= 5/8+ 3 · 2/4 · 2 = 5/8+ 6/8= 5 + 6/8 = 11/8

Answer: Incorect answer

Step-by-step explanation:

5/8X3/4 =11/8 =1 3/8=1.375

If a > b then;

a + -b = a positive number

If b > a then;

a + -b = a negative number

If both addends are positive or if the positive addend has a greater absolute value than the negative addend, the sum will be positive. If both addends are negative or if the negative addend has a greater absolute value than the positive addend, the sum will be negative.

Answer:

5 5/8 pounds

Step-by-step explanation:

I added the fractions and got that

Answer:

[tex]c=\frac{bd}{ad+b}[/tex]

Step-by-step explanation:

By isolating the term c, we are trying to arrive at the equation c= ____.

[tex]a=b(\frac{1}{c}-\frac{1}{d} )[/tex]

Divide both sides by b:

[tex]\frac{a}{b}= \frac{1}{c}-\frac{1}{d}[/tex]

Add [tex]\bf{\frac{1}{d}[/tex] to both sides:

[tex]\frac{1}{c} =\frac{a}{b} +\frac{1}{d}[/tex]

Rewriting the right-hand side as a single fraction:

[tex]\frac{1}{c} =\frac{a(d)}{b(d)} +\frac{1(b)}{d(b)}[/tex]

[tex]\frac{1}{c} =\frac{ad+b}{bd}[/tex]

Find the expression of c:

[tex]1\div\frac{1}{c} =1\div\frac{ad+b}{bd}[/tex]

[tex]\bf{c=\frac{bd}{ad+b}[/tex]

Additional:

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Answer:

[tex]c=\dfrac{bd}{ad+b}[/tex]

Step-by-step explanation:

Given equation:

[tex]a=b\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

Divide both sides by b:

[tex]\implies \dfrac{a}{b}=\dfrac{b}{b}\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

[tex]\implies \dfrac{a}{b}=\dfrac{1}{c}-\dfrac{1}{d}[/tex]

Add 1/d to both sides:

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}-\dfrac{1}{d}+\dfrac{1}{d}[/tex]

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}[/tex]

[tex]\textsf{Simplify the left side by applying the fraction rule} \quad \dfrac{p}{q}+\dfrac{r}{s}=\dfrac{ps+qr}{qs}:[/tex]

[tex]\implies \dfrac{ad+b}{bd}=\dfrac{1}{c}[/tex]

Cross multiply:

[tex]\implies c(ad+b)=bd[/tex]

Divide both sides by (ad + b):

[tex]\implies \dfrac{c(ad+b)}{ad+b}=\dfrac{bd}{ad+b}[/tex]

[tex]\implies c=\dfrac{bd}{ad+b}[/tex]

Answer:

the gcf of 41 and 48 would be 1

Answer: 1

Step-by-step explanation:

41      48

 /\       /\

1 * 41  1 * 48

The required possible side length of the tablecloth is 11ft x 11ft.

A square is for sided regular polygon, where the length of all sides is identical and the angle between the adjacent side is 90°.

Given the following parameters

Area of fabric =121 ft² of fabric.

She wants to make a square tablecloth for her dining room table.\

Area of the square = a²

121 = a²

a = √121

a = 11 ft

Thus, the required possible side length of the tablecloth is 11ft x 11ft.

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Answer: -4/7

Step-by-step explanation:

the formula for the slope is rise/run

or (y-y1)/(x-x1)

we can apply this concept like this:

7-(-7)=7+7=14

-4-4=-8

since -8 is the rise and 14 is the run, the slope is -8/14

simplify to -4/7

Answer:

Conditional Probability

Step-by-step explanation:

Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

Here are the values of the expressions :

a. 3(4) = 12

b.  4 + 11 + (-4)  = 11

c. 3.2(2)  = 6.4

d. | (-2) + (-2) + (-2) | = 6

e. |2 (-7.5) |  = 15

f. 10 1/5(-5) = -51

a. 9(410)  = 3690

b. 6(592) = 3552

Take not of the following rules:

When a term is in bracket, it means that the values should be multiplied : 2 (3) = 2 x 3 = 6

When numbers are between this sings | |, it means that the answer should be an absolute value. e.g. | - 5 - 5 | = 10

When a negative sign is multiplied by a positive sign, the result would be a negative sign. -1 x + 1 = -1

a. 3(4) = 3 x 4 = 12

b.  4 + 11 + (-4)

= 4 + 11 - 4 = 11

c. 3.2(2)  = 3.2 x 2 = 6.4

d. | (-2) + (-2) + (-2) |

|- 2 - 2 - 2| = 6

e. |2 (-7.5) |

|2 x -7.5| = 15

f. 10 1/5(-5)

10 1/5 x - 5

51/5 x - 5 = -51

a. 9(410)

= (9 x 400) + (10 x 9)

3600 + 90 = 3690

b. 6(592)

= (6 x 500) + (92 x 6)

3000 + 552

3552

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Answer:

C(x) = (1/9)x + 242/9

Step-by-step explanation:

Let x = number of pages.

Let y = cost.

We are given two ordered pairs, (x, y):

(100, 38) and (208, 50)

We must find the equation of the line that passes through these two points.

y = mx + b

m = (y_2 - y_1)/(x_2 - x_1) = (50 - 38)/(208 - 100) = 12/108 = 1/9

y = (1/9)x + b

Use point (100, 38) as x and y to find b.

38 = (1/9)(100) + b

38 × 9 = 100 + 9b

9b + 100 = 342

9b = 242

b = 242/9

The equation is:

y = (1/9)x + 242/9

Answer: C(x) = (1/9)x + 242/9

Step-by-step explanation:

use fog

3(1/3x-3)+9

=x

use gof

1/3(3x+9)-3

=x

we can see that both results give us x hence they are inverse

A mathematical model that gives the demand y in terms of the price x in dollars.

y = 1400/ x

This is further explained below.

Generally, The following formula would apply in the situation when there is an inverse link between y and x:

y = k/x

where k is constant.

In a relationship with an inverse connection, one variable will tend to decrease as the other variable grows.

y denotes the amount of demand.

x is equivalent to the cost.

400 = k/3.5

k = 400 * 3.5

k = 1,400

The following is the formula for the mathematical model that calculates the demand y based on the price x in dollars:

y = 1400/ x

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[tex]3 \cdot 3^2 + 8 : 2 - (4+3) =[/tex]

[tex]3 \cdot 3^2 + 4 - 7=[/tex]

[tex]3 \cdot 9 +4 -7=[/tex]

[tex]27 + 4 - 7 = 24[/tex]

==axel134==

Answer:

Step-by-step explanation:

The point that is 1/3rd of the distance from (-4.5,0) to (0,9) is (-3,3).We use a formula similar to the midpoint formula for finding the point.

We have been given two points (-4.5,0) and (0,9), we have to find the point is on the line formed by these two points and is 1/3rd away. We don't need to find the distance between these two points to find the asked point. We have to use a formula that is similar to finding the midpoint of a line. For two points (a,b) and (x,y) the midpoint is ([tex]\frac{a+x}{2} ,\frac{b+y}{2}[/tex]).We used equal parts of the two points to find the midpoint, for 1/3rd we will be using uneven parts of the two points.

[tex]x_{1} =\frac{2}{3} (-4.5)+\frac{1}{3} (0)=-3[/tex]

[tex]y_{1} =\frac{2}{3} (0)+\frac{1}{3} (9)=3[/tex]

Therefore the point that lies 1/3rd of the distance from (-4.5,0) and (0,9) is (-3,3).

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Taking into account the definition of a system of linear equations, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{xa + xb=47} \atop {4xa + 5xb=200}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable xa from the first equation, you obtain:

xa= 47 - xb

Substituting this expression in the second equation you get:

4×(47 -xb) + 5xb= 200

Solving:

4×47 - 4xb + 5xb= 200

188 - 4xb + 5xb= 200

- 4xb + 5xb= 200 - 188

xb= 12

Remembering that xa= 47 - xb. you get: xa=47 - 12 → xa= 35

Finally, the movie theater sold 35 tickets for Movie A and 12 tickets for Movie B.

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Answer:a

a

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer: So that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.

Step-by-step explanation:

Answer:

3.1kg

Step-by-step explanation:

4.7+5.6+6.4+2.8+3.5+4.4+4.5 = 31.9

4.375 x 8 = 35

35 - 31.9 = 3.1

The value of the x in the linear equation of the midpoint is a 3.85.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

Midpoint is the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.

From the given information:

Given K is the midpoint of GH, GK = 5x - 3,and GH = 2x + 24

As the midpoint the both equation are equal to the each other.

Then

GK = GH

5x - 3 = 2x + 24

5x+2x = 24+3

7x = 27

x = 27/7

x = 3.85.

So, The value of the x in the linear equation of the midpoint is a 3.85.

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The scale factor going from the first to the second triangle according to the task content is; 2.

The length of the longest side of.the triangle as required in the task content is; 24.

According to the task content, it follows that the two triangles are similar.

Therefore, the corresponding sides of such triangles must be in proportion.

Therefore the scale factor from the first to the second triangle as required is;

Scale factor = 12/6; since the shortest sides are corresponding sides.

Scale factor = 2.

Hence, since the length of the longest side in the first triangle is 14, the length of the longest side in the second triangle is;

L = 2 × 14

L = 28

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