Solve |x-5| > -2. Write your solution in interval notation.

The horizontally compressed function is [tex]\(\text{g(x)} = x^2 + 6\)[/tex]. The correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].

To horizontally compress the function [tex]f(x) = x^2[/tex], we can modify the equation by introducing a horizontal compression factor. Let's call the compressed function [tex]g(x)[/tex].

The general equation for a horizontally compressed function can be expressed as [tex]g(x) = f(ax)[/tex], where a is the compression factor.

In this case, we want to compress [tex]f(x) = x^2[/tex]. Let's choose a compression factor of [tex]\frac{1}{2}[/tex].

Therefore, the equation for [tex]g(x)[/tex] would be:

[tex]\[ g(x) = f\left(\frac{x}{2}\right) = \left(\frac{x}{2}\right)^2 \][/tex]

Simplifying this equation, we have:

[tex]\[ g(x) = \frac{x^2}{4} \][/tex]

Hence, the equation of [tex]g(x)[/tex] is:

[tex]\[ \text{g(x)} = \frac{x^2}{4} \][/tex]

So, the correct option is OC. [tex]\(\text{g(x)} = x^2 + 6\)[/tex].

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Answer:B,C

hope it helps

hi

what's the title of the question?

Answer:

[tex]\sf m = -2\\\\y-intercept =\dfrac{-5}{4}[/tex]

Step-by-step explanation:

Slope and y-intercept of the line:

     Write the equation in slope y-intercept form: y =mx +c

Here, m is the slope and c is the y-intercpet.

To isolate y, add 8x to both side,

            -8x - 4y = 5

                   -4y  = 8x + 5

Now, divide the entire equation by (-4),

                        [tex]\sf \dfrac{-4y}{-4}=\dfrac{8x}{-4} + \dfrac{5}{-4}\\\\\\y = -2x -\dfrac{5}{4}[/tex]

Now, compare with y = mx +c

          [tex]\boxed{\sf m= -2}\\\\\\\boxed{\sf y-intercept=\dfrac{-5}{4}}[/tex]

Answer:

y-intercept = -5/4

slope = -2

Step-by-step explanation:

To quickly find the slope and y-intercept of a given linear equation, we can express it in the following form, called the slope-intercept form:

[tex]\boxed{y = mx + c}[/tex],

where:

m ⇒ slope

c ⇒ y-intercept

In order to take the given equation into the slope-intercept form, we have to  make y the subject of the equation:

[tex]-8x - 4y = 5[/tex]

⇒ [tex]-4y = 8x + 5[/tex]                 [Adding 8x to both sides of the equation]

⇒ [tex]y = -\frac{1}{4}(8x + 5)[/tex]              [Dividing both sides of the equation by -4]

⇒ [tex]y = -2 x - \frac{5}{4}[/tex]

Comparing the above equation with the slope-intercept form, we can see that m = -2 and c = -5/4.

Therefore, y-intercept = -5/4, and slope = -2.

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Answer:

tan pi/6 is tan 30

Step-by-step explanation:

tan 30 is a special degree in trigonometric ratios which makes it easy to solve

tan 30=1√3 .this is the same as √3/3(B)

The caluclated values are:

N = 500:

SEM = 9 * √[(500 - 48) / (500 - 1)] / √(48)

= 1.24 (rounded to 2 decimals)

N = 5000:

SEM = 9 * √t[(5000 - 48) / (5000 - 1)] / √(48)

= 1.30 (rounded to 2 decimals)

N = 50000:

SEM = 9 * √[(50000 - 48) / (50000 - 1)] / √(48)

= 1.30 (rounded to 2 decimals)

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The value of x is 40 degree.

We have,

Far Arc = 130 degree

Near Arc = 50 degree

According to "Angle-Arc Theorem." It states that the angle formed by the intersection of two tangents, two secants, or one tangent and one secant outside a circle is equal to half the difference of the intercepted arcs.

In other words, The angle formed outside of the circle is always equal to the the far arc minus the near arc divided by 2.

Using Angle = (Far Arc - Near Arc) /2

So, x= (130- 50)/2

x = 80/2

x= 40

Thus, the value of x is 40 degree.

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The volume of the given hexagonal prism is 212.4 cubic units.

Given that, the hexagonal prism below has a base area of 36 square units and a height of 5.9 units.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, volume = 36×5.9

= 212.4 cubic units

Therefore, the volume of the given hexagonal prism is 212.4 cubic units.

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The calculated value of x in the circle is 7

From the question, we have the following parameters that can be used in our computation:

The circle

From the circle, we have

Center = H

Also, we have

LIne GH bisects the chord FD

Using the above as a guide, we have the following:

DG = FG

So, we have

5x + 2 = 7x - 12

This gives

2x = 14

So, we have

x = 7

Hence, the value of x is 7

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Answer:

15

Step-by-step explanation:

2 x 1 and 7/8 = 3 and 6/8 miles

= 3.75 miles

Since there are park benches every 1/4 mile on the trail, we can find the number of benches by dividing the total length of the trail by the distance between the benches:

Number of benches = (3.75 miles) / (1/4 mile per bench)

Number of benches = 15

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of shapes, this shape can be separated into 2 basic shapes, triangle and rectangle.

Yes, the mass of the Earth is much larger than the mass of an atom of hydrogen.

A hydrogen atom weighs around 1.67 x 10⁻²⁷ kilograms (kg) in mass. The mass of a hydrogen atom is approximately 1051 times smaller than that of the Earth, which has a mass of about 5.97 x 10²⁴ kg.

The majority of the mass of the Earth is made up of the following elements: iron, oxygen, silicon, magnesium, Sulphur, nickel, calcium, and aluminium. Despite its minor presence, hydrogen does not significantly contribute to the mass of the Earth.

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Answer: For Area A, 60

For Area B, 16

For Area C, 16

For the entire shape, 92

Step-by-step explanation:

If you look at the top of the entire shape, it says the width is 10 cm, that means 10 cm's for the entire width and not just shape A.

If you look at shape B, it says the width is 4 cm, that means 4 out of those 10 cm's are for B and not A but we dont need the width of shape B, so we subtract that 4 bc it isnt necessary since its not in shape A

if you look at the left of shape A, it says 10 cm for the height, when finding area for a rectangle, always do width x height. We have both the width and the height so now we just multiply them, 10 x  6 = 60

Answer:

A = 60cm^2

Step-by-step explanation:

Given:

Length of figure: A = 10cm

Width of figure: B = 10 - 4 = 6cm

Figure A is rectangular in nature.

So, the Area of the figure: A = 1 x b = 10 x 6 = 60cm^2

Hello !

   D

   I\
   I  \  
   I    \
   I      \    7cm
   I        \
   I          \
   I            \

 E    4cm     F  

The ratio = hypotenuse ; opposite

⇒ calculate sin(D)

sin(D) = opposite/hypotenuse = 4/7

arcsin(4/7) ≈ 34,84.. ≈ 35°

The angle D measures 35°.

The length of side j, considering the trigonometric ratios, is given as follows:

j = 7.88.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 21º, we have that:

Hence the length j is obtained as follows:

sin(21º) = j/22

j = 22 x sine of 21 degrees

j = 7.88.

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Answer:

6.6, 22/73,

Step-by-step explanation:

Alright, here we go.
A: The mean is all of the values divided by the number of values, which is equal to 1,927.5 or:
0.5 * 5 + 1 * 16 + 2 * 28 + 3 * 22 + 4 * 17 + 5 * 98 + 8 * 13 + 10 * 73 + 12 * 5 + 15 * 2 + 20 * 4 + 25 * 9.

There are 292 or 5 + 16 + 28 + 22 + 17 + 98 + 13 + 73 + 5 + 2 + 4 + 9 packages. 1,927.5 / 292 = 6.6
B: The packages that weigh less than five pounds are 5 + 16 + 28 + 22 + 17 or 88 / 292 = 22 / 73
C and D: Manager original mean result not given.

The result of adding these numbers is 14.

To add the vectors 10, -3, and 7, we simply sum their corresponding components.

In mathematics, vectors typically represent quantities that have both magnitude and direction. They are usually denoted by an arrow or boldface letters. However, in your question, the numbers provided (10, -3, and 7) are not explicitly described as vectors. They are just numerical values.

To add these numbers together, you can simply perform the arithmetic operation of addition:

10 - 3 + 7 = 14

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A table that best represent the equation include the following: H. table H.

In order to determine the table that best represent the equation, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = 1 in table F, the linear function is given by;

y = x - 12

y = 1 - 12

y = -11 (False).

When the value of x = 0 in table G, the linear function is given by;

y = x - 12

y = 0 - 12

y = -12 (True).

When the value of x = 2 in table G, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (False).

When the value of x = 0 in table H, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (True).

When the value of x = 4 in table H, the linear function is given by;

y = x - 12

y = 4 - 12

y = -8 (True).

When the value of x = 6 in table H, the linear function is given by;

y = x - 12

y = 6 - 12

y = -6 (True).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area of the triangle is 25061.6 cm²

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The area of a triangle is expressed as;

A = 1/2bh where b is the base a d h is the height. This formula only works for right angled triangle.

Another formula for area of triangle is 1/2 absinC

a = 180cm

b = 280cm

C = 84°

A = 1/2 × 180 × 280 × sin84

A = 50123.9/2

A = 25061.6 cm²

Therefore the area of triangle OPQ is 25061.6 cm².

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With the unit price of $5 per pound, the 25-pound shipment would cost $125.

We have,

To determine the cost of a 25-pound shipment of jelly beans, you would need the unit price per pound of jelly beans.

Without that information, it's not possible to calculate the total cost accurately.

Once you have the unit price per pound, you can simply multiply it by the weight of the shipment.

For example, if the unit price per pound is $5, then the cost of a 25-pound shipment would be:

Cost = Unit Price per Pound × Weight of Shipment

= $5/pound × 25 pounds

= $125

Thus,

With the unit price of $5 per pound, the 25-pound shipment would cost $125.

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Answer:

s(x) = 0.23x + 400

Step-by-step explanation:

Let x = cost of merchandise sold

We start by finding the slope which is the percent of commission Alysse receives.

Let's start with doing 607 - 515. This is because we are subtracting the commissions, which also can be y2 - y1. Then, we do 900-500=400 (x2-x1). This is how to find the slope of the function. [tex]\frac{y2-y1}{x2-x1}=\frac{92}{400} =0.23[/tex], 0.23 being the slope.

s(x) = b+0.23x, now substitute values making the money received as s(x).

515 = b+0.23(500)

515=b+115

-115   -115

400 = b

607 = 400+0.23(900)

607 = 400 + 207

607 = 607

So, s(x) = 0.23x + 400

Answer:

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

Use formula:

We are given:

Substitute given and solve for x:

So, 70 people speak both German and Italian.

The value of the missing probability for the given probabilities and condition of independent events is equal to 0.45.

Here,

Probability of the events A and B are,

P(A) = 7/10

P(A or B) = 167/200

Apply the formula for the probability of the union of two events,

P(A or B) = P(A) + P(B) - P(A and B)

Since events A and B are independent, we know that,

P(A and B) = P(A) x P(B)

This implies,

P(A or B) = P(A) + P(B) - P(A) x P(B)

Substitute the values we have,

⇒ 167/200 = 7/10 + P(B) - (7/10) x P(B)

⇒ 167/200 = [ 7 + 10P(B) - 7P(B) ] /10

⇒167/20 = 7 + 3P(B)

⇒3P(B) = 167/20 - 7

⇒ 3P(B) = (167 - 140)/20

⇒3P(B) = 27 /20

⇒P(B) = 9/20

⇒P(B) = 0.45

Therefore, the value of the probability P(B) is equal to 0.45.

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complete question:

Events [A] and [B] are independent. Find the missing probability.

P(B) = ?

P(A) =

7/10

P(A or B)

167/200

The function that gives the amount of Iodine-131, A, in grams, t days later is A(t) = 5(1/2)^(t/10), and the amount after 20 days is 5/4 grams.

To find the function that gives the amount of Iodine-131, A, in grams, t days later, we can use the given formula A(t) = A0e^(kt).

Given that the half-life of Iodine-131 is approximately 10 days, we know that after each 10-day period, the amount of Iodine-131 will be reduced by half. This information allows us to determine the value of k.

Let's substitute the initial values into the equation:

A(0) = A0 = 5 grams.

We know that after 10 days, the amount is reduced by half. Therefore:

A(10) = 5/2 grams.

Using these two points, we can solve for k:

5/2 = 5e^(10k).

Dividing both sides by 5, we get:

1/2 = e^(10k).

Take the natural logarithm (ln) of both sides:

ln(1/2) = 10k.

Now, solve for k:

k = ln(1/2) / 10.

Now that we have the value of k, we can use it to find the function for the amount of Iodine-131, A, in grams, t days later.

The function is:

A(t) = A0e^(kt).

Substituting the known values:

A(t) = 5e^((ln(1/2)/10)t).

Simplifying:

A(t) = 5(1/2)^(t/10).

To find the amount of Iodine-131 after 20 days, we substitute t = 20 into the equation:

A(20) = 5(1/2)^(20/10).

A(20) = 5(1/2)^2.

A(20) = 5(1/4).

A(20) = 5/4 grams.

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The Probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.

The probability that the average weight of our sample is greater than 15.8 oz, we need to use the concept of the sampling distribution of the sample mean and the Central Limit Theorem.

Given:

Population mean (μ) = 16 oz.

Population standard deviation (σ) = 1.25 oz.

Sample size (n) = 40 bags of candy.

The Central Limit Theorem states that for a large enough sample size (typically considered n > 30), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

In this case, we can assume that the sampling distribution of the sample mean is approximately normally distributed.

To calculate the probability, we need to standardize the sample mean using the z-score formula:

z = (x - μ) / (σ / sqrt(n))

where x is the given value (15.8 oz), μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values:

z = (15.8 - 16) / (1.25 / sqrt(40))

z = -0.2 / (1.25 / 6.3246)

z = -0.2 / 0.1988

z ≈ -1.006

Now, we need to find the probability that the standardized sample mean is greater than -1.006. Since we want the probability of the sample mean being greater than 15.8 oz, we need to find the area under the normal curve to the right of z = -1.006.

Using a standard normal distribution table or a calculator, we can find that the corresponding probability is approximately 0.8438.

Therefore, the probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.

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Let [tex]x[/tex] be one of the numbers. Then the other one is [tex]10-x[/tex].

Therefore, the sum of their cubes is:

[tex]x^3+(10-x)^3=x^3+1000-300x+30x^2-x^3=30x^2-300x+1000[/tex]

Now we need to find the minimum value of the resulting function.

[tex](30x^2-300x+1000)'=60x-300[/tex]

[tex]60x-300=0\\60x=300\\x=5[/tex]

The derivative is negative to the left of [tex]5[/tex] and positive to the right of it, therefore, at [tex]5[/tex] there exists the minimum.

[tex]5^3+(10-5)^3=125+125=250[/tex]

Therefore, the minimum value is 250.

When A plug is removed from a trough to drain the water, The appropriate form of the expression is 10(x - 1)² - 3. Option D

The appropriate form of the expression that would reveal the time, in minutes, when the trough is empty is: 10(x - 1)² - 3.

This expression represents the volume of the trough after the plug is removed, with x representing the time in minutes. When the volume of the trough is equal to zero, it means the trough is empty.

Therefore, setting the expression equal to zero and solving for x will give us the time when the trough is empty.

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Answer: 0.16

Step-by-step explanation: