make a number line a ns mark all the points that represent the following values of x.

x≤-2 and x<-5

The percentages of people taking the test who scores between 421 and 645 is: 68 %

The empirical rule, also referred to as the three-sigma rule or the 68-95-99.7 rule, is defined as a statistical rule which states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

We are given:

Sample mean: x' = 553

standard deviation; s = 112

Thus:

x' - ns = 421

x' + ns = 645

Where n is the number of standard deviations from the mean. Thus:

553 - 112s = 421

112s = 553 - 421

112s = 132

s = 132/112

s ≈ 1

So 1 standard deviation from the means indicates a percentage of 68%

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The formula that will be useful in finding the area of the triangle is: Pythagoras theorem

The formula to find the area of the triangle is expressed by the formula:

A = ¹/₂bh

Where:

b is base

h is height

Now, we have the base but we don't have the height.

Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.

The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

where c is the hypotenuse

Thus, to find the height of the triangle, we will use Pythagoras theorem to get:

h = √(6² - 4²)

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The value of x is given as follows:

B. 6.

The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:

4(x + 4) = 5(5 + 3)

(we add the two parts), with the outer part being the multipler.

Expanding the operations, the value of x is obtained as follows:

4x + 16 = 40

4x = 24

x = 6.

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The probabilities for this problem are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The number of cars with purchase prices less than $20,000 is given as follows:

86 + 67 + 35 = 188.

Of those 188 cars, 86 had repair costs less than $10,000, hence the probability is given as follows:

p = 86/188

p = 0.4574.

The number of cars with repair costs less than $10,000 is given as follows:

86 + 71 + 40 = 197.

Of those, 40 had a purchase price of more than $40,000, hence the probability is given as follows:

p = 40/197

p = 0.203.

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The equation to represent the relationship is a = [tex]\frac{3}{4}[/tex] b.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here the given two quantities in proportional relationship . Then,

=> a∝ b

=> a=kb

Where k is constant. Then, put a=-3 and b=-4 rhen,

=> -3=-4k

=> k = 3/4

Then the equation is ,

=> a = [tex]\frac{3}{4}[/tex] b.

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The total number of kilometers that the friends hiked in all would be 2. 02 km.

The total distance that Jordan, Jessica, Eloise, and James hiked in the Austrian Alps, can be found to be :

= Distance on Monday + Distance on Tuesday

= 1. 08 + 0. 94

= 2. 02 km

Using grids, you can represent a single box as 0. 1 km so that for 1. 08 km you will have a grid of 108 cubes. Do the same for Tuesday to get 94 cubes.

Add them up and you will get 202 cubes which would be 2.02 km.

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In a case wherebyMr. Pearson drives a bus for the city of Greenwood and Last month, he kept track of the number of bus riders each day the least number of bus riders is 50.

The least number can be described as the number that serves as the smallest among the given number.

Based on the record that was kept, t can be deduced that the highestnumber is 100 whereby the least of the number is 50 which implies that option A is correct because it is considered to be smallest number hence te least number.

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compete question;

Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day.

Bus riders

50

60

70

80

90

100

What was the least number of bus riders?

The probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

There are 5 Donut Shop pods and Maddy and Charlie each took 2, leaving 3 Donut Shop pods in the green basket.

There are 17 pods left in the basket after Maddy and Charlie's selection (5 Donut Shop, 6 Swiss Miss, and 6 Breakfast Blend), so the probability that Ben will get the Donut Shop pod is 3/17.

Therefore, the probability that Ben will get the Donut Shop pod after Maddy or Charlie's selection is 3/17.

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Answer:

A

Step-by-step explanation:

It is a double angle identity.

sin2x = 2sinxcosx

Answer: 2sinxcosx

Step-by-step explanation:

In the conversion of fractions to decimals, the fraction should be thought of as a division problem.

A fraction represents the division of the numerator (n) by the denominator (d). So, when you have a fraction like n/d, you can convert it to a decimal by dividing n by d.

Answer: False.

Step-by-step explanation:

Squares have to have the same shape and size to be congruent. Therefore, not all squares are congruent, since not all of them are the same size. ... This means that they have the same shape, although not necessarily the same size.

The solution of the equation written by completing square is (x + 1/2)² = 289/4.

In algebra, the process of "completing the square" is used to transform a quadratic expression into a perfect square trinomial. Using this method, a constant term is either added or subtracted from the quadratic expression to produce a perfect square trinomial that may be factored as the square of a binomial. Solving quadratic equations, locating the vertex of a parabola, and simplifying formulas with square roots all involve the completion of the square.

The value of the equation x² + x = 72 can be written as a completer square by taking half of the coefficient of the x-term.

(1/2)² = 1/4

Add this to both sides of the equation:

x² + x + 1/4 = 72 + 1/4

Now, the LHS is:

(x + 1/2)² = 289/4

x = -1/2 ± (17/2)

Hence, the solution of the equation written by completing square is (x + 1/2)² = 289/4.

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The function is never negative.

option D is the correct answer.

A negative function is a function in which the resulting y value is negative.

Also, a negative function is a function that has y values that are less than zero for any x values. In other words, a negative function has a negative sign in front of its output.

From the given graph, the x and y values started from 0 and increases into the positive direction, so we can conclude that the function can never be negative.

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The three sizes of school pictures may feature the same subject, but they are not similar to each other in terms of size and aspect ratio.

The 8 in. by 10 in. size has an aspect ratio of 5:4, which is wider than the 5 in. by 7 in. size that has an aspect ratio of 7:5. The wallet size 2¼ in. by 3¼ in. has an aspect ratio of 9:13, making it even more elongated. This means that the relative proportions of the images are different.

Furthermore, the larger sizes such as 8 in. by 10 in. and 5 in. by 7 in. provide a lot more detail than the wallet size, which is smaller and often used as a miniature version of the larger sizes. The larger sizes also have a higher resolution, making them more suitable for framing and displaying.

Therefore, while the school pictures may depict the same subject, they are not similar in size, aspect ratio, and level of detail.

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Answer:

The probability of choosing a brown egg from the carton is 2/12 or 1/6. This is because there are two brown eggs in the carton and a total of twelve eggs, so the probability of choosing a brown egg is 2/12 or 1/6.

To solve this problem, we can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal amount (the initial deposit), r is the interest rate as a decimal, and t is the time in years.

We want to find how long it will take for the account balance to earn $1,500 in interest, so we can set up the equation:

$1,500 = $5,000 * 0.025 * t

where t is the time in years.

Simplifying this equation, we get:

t = $1,500 / ($5,000 * 0.025)

t = 12 years

Therefore, it will take 12 years for the balance of the account to earn $1,500 in interest

Step-by-step explanation:

so, she drove the 12,000 miles with an SUV that gave her 15 miles per gallon.

that means she used

12000 / 15 = 800 gallons of gasoline.

if she would have used a car that gave her 48 miles per gallon, she wound have needed

12000 / 48 = 250 gallons of gasoline.

so, she would have saved

800 - 250 = 550 gallons of gasoline.

An equation to determine p is 12 = 3p/4.

The total number of players at the baseball game is 16 players.

In order to write a linear equation to describe this situation, we would a assign variable to the total number of players at the baseball game, and then translate the word problem into a linear equation as follows:

Let the variable p represent the the total number of players at the baseball game.

Since the players had the choice of having a bottle of water or a box of juice., and of all of the players, only 12 chose a bottle of water, which was of the total number of players, a linear equation that can be used to model this situation is given by;

12 = 3/4 × p

48 = 3p

p = 48/3

p = 16 players.

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Answer:

No

Step-by-step explanation:

The angles of a triangle must add up to 180. 140+15+15 = 140 +30 = 170. This is not 170, so no. Hope this helps!

Answer:

It is not possible to draw a triangle with these angles because 140 + 15 + 15 = 170, triangle angles must add up to 180 and 180=170 is a false statement.

Step-by-step explanation:

Answer:

1500 pounds Or 0.75 tons

Step-by-step explanation:

To solve this problem, we need to convert all units to the same unit, either tons or pounds. Let's convert 1 ton and 500 pounds to pounds:

1 ton = 2000 pounds

1 ton and 500 pounds = 2000 + 500 = 2500 pounds

Now we can subtract the amount of grain that was unloaded from the total amount:

2 tons = 2 * 2000 = 4000 pounds

4000 pounds - 2500 pounds = 1500 pounds

Therefore, the trucker still has 1 ton and 500 pounds, or 1500 pounds, of grain left on the truck.

To convert 1500 pounds to tons, we can use the conversion factor:

1 ton = 2000 pounds

Dividing both sides by 2000, we get:

1 pound = 1/2000 tons

Multiplying both sides by 1500, we get:

1500 pounds = 1500/2000 tons

Simplifying the fraction, we get:

1500 pounds = 0.75 tons

Therefore, 1500 pounds is equivalent to 0.75 tons.

The probability solutions are given as follows;

- P(CS Major and Not Hired) = 43.6% (Marginal)

- P(Other Major) = 31.5% (Marginal)

- P (Hired + CS Major) = 36.3% (Conditional)

- P (Not Hired + Other Major) = 48.5% (Conditional)

First we need to clarify the meaning of Joint, Marginal, and conditional probability.

Note that the table of values are attached.

So, the calculation is shows as follows:

P(CS Major and Not Hired) = 102/234 = 43.6% (Marginal)

- P(Other Major) = 74/234 = 31.5% (Marginal)

- P (Hired + CS Major) =  58/160 =  36.3% (Conditional)

- P (Not Hired + Other Major) = 36/74 48.5% (Conditional)

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Answer:

Account balance = $6,834.01

Interest accrued = $1,834.01

Step-by-step explanation:

To find the account balance of an initial investment of $5,000 at 6.25% compounded daily for 5 years, use the Compound Interest Formula.

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

As the interest is compounded daily, n = 365.

Therefore, the values to substitute into the formula are:

Substitute the values into the formula and solve for A:

[tex]\implies A=5000\left(1+\dfrac{0.0625}{365}\right)^{365 \cdot 5}[/tex]

[tex]\implies A=5000\left(1.000171232...\right)^{1825}[/tex]

[tex]\implies A=5000\left(1.3668013759...\right)[/tex]

[tex]\implies A=6834.0068795...[/tex]

[tex]\implies A=6834.01\; \sf (2\;d.p.)[/tex]

Therefore, the account balance after 5 years is $6,834.01, and the total amount of interest earned is $1,834.01.

Answer:

A. g(x) = -x^2 - 2

Step-by-step explanation:

Okay so it has the same slope as f(x) which means it's x^2, however, it's negative and going the other way so it's -x^2

Since the y-intercept is -2,

g(x) = -x^2 - 2

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On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.

For selling the machinery,

Revenues = $277,800

Costs = 277,800 × 5% = $13,890

Profit = Revenues - Cost = $277,800 - $13,890 = $263,910

For leasing the machinery,

Revenues = $286,800

Costs = $24,900

Profit = Revenues - Cost = $286,800 - $24,900 = $261,900

Here the profit generated by selling the machinery is greater, which is the better option.

Hence selling the machinery is the better option.

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On the basis of the data presented, it would be advisable to sell the machinery based on the differential analysis.

For selling the machinery,

Revenues = $277,800

Costs = 277,800 × 5% = $13,890

Profit = Revenues - Cost = $277,800 - $13,890 = $263,910

For leasing the machinery,

Revenues = $286,800

Costs = $24,900

Profit = Revenues - Cost = $286,800 - $24,900 = $261,900

Here the profit generated by selling the machinery is greater, which is the better option.

Hence selling the machinery is the better option.

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Answer:

416

Step-by-step explanation:

The front and back are triangles

a = 1/2 bh

a = 1/2(12)(8)

a = 48

We times this by 2 to find the front and the back.

96

Bottom

a = lw

a = 10 x 12

a = 12

120

Right and left sides

a = lw

a = 10 x10 = 100

Multiply this by 2 to find the right and the left sides.

200

Add the numbers together:

96 + 120 + 200 = 416

Helping in the name of Jesus.

To find the surface area of a three-dimensional object, you need to add up the area of all its faces.

This can be done using formulas specific to the shape of the object. For example, the surface area of a rectangular prism (a box) can be found using the formula SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively. Other common three-dimensional shapes include spheres, cones, and cylinders, each with their own unique formulas for finding surface area. So, to answer your question, I would need to know what specific object you are referring to in order to provide an accurate answer about its surface area.

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The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

The height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.

Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.

Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:

h_A = radius + center's height

h_A = 85 + 100

h_A = 185 feet

So, the height of point A off the ground is 185 feet.

To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:

h_A = radius * sin(0)

h_A = 85 * 0

h_A = 0

So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.

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The gain on sale of the laptop which Jack purchased in 2012 for $64,000 with a current book value of $18,000 but sold for $28,000 is $10,000.

The book value of an asset is the difference between the original value or purchase cost and the accumulated depreciation.

Accumulated depreciation represents the depreciation from the purchase date to the current period. It can be determined as the difference between the purchase price and the current value.

The purchase price of the laptop in 2012 = $64,000

Current book value = $18,000

Accumulated depreciation = $46,000 ($64,000 - $18,000)

Sales price = $28,000

Gain on sale = $10,000 ($28,000 - $18,000)

Thus, when the laptop is sold by Jack, he realized a gain of $10,000 because the sales price exceeded the current book value.

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