Round each decimal to the nearest tenth
4. 13.392
5. 27.149
6.8.84858
Help!!

Answer:

c

Step-by-step explanation:

ax - ay - bx + by ( factor a out of the 1st 2 terms and - b out of the last 2 terms )

= a(x - y) - b(x - y) ← factor out (x - y) from each term

= (a - b)(x - y)

Answer:

(3/2)x - 2 < 11/2

(3/2)x < 15/2

x < 5

number line with a closed circle at 5 and the arrow going to the left

2x - 2 > 8

2x > 10

x > 5

number line with a closed circle at 5 and the arrow going to the right

4x - 7 > 13

4x > 20

x > 5

number line with an open circle at 5 and the arrow going to the right

3x + 4 < 19

3x < 15

x < 5

number line with an open circle at 5 and the arrow going to the left

Answer:

$1.129

Step-by-step explanation:

As number is rounded off to 30,000, the correct option is A i.e, it is closer to 30,000 than 29,000.

We look at the last three digits and round to the closest thousand. If these digits total 500 or more, the thousands digit is rounded up; if they total less than 500, the thousands digit is rounded down while remaining the same.

For example, to solve this question we have to check whether 16796 is closer to 16000 or 17000 in the counting. In this case, 16796 is closer to 16000, hence 17000 is the round figure of 16796.

In this problem, as the number is said to be rounded off to the nearest thousand is 30,000, this means that, the number is closer to 30,000 than 29,000.

The question is incomplete. The picture of number line is missing. It is placed in the attachment below.

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The correct statement are:

Based on the given information, we can make the following conclusions:

A. The interquartile range for high school students is smaller than college students.

The statement is False

B. The mean for high school students is smaller than college students.

The statement is False because the mean of College is 25.28 and mean for High school is 30.4.

C. The range for high school students is larger than college students.

The statement is True .

D. The college median is equal to the high school median.

The statement is True because the median for both is 24..

E. The mean absolute deviation is larger for college students than high school students.

The statement is False.

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Answer:

Therefore, the elevation of the car on the stretch of road, rounded to the nearest tenth, is approximately 29.7 meters.

Step-by-step explanation:

To find the elevation of the car on a stretch of road that extends horizontally 125 meters, we can use trigonometry.

Given:

Angle of the road = 13°

Horizontal distance = 125 meters

We can use the tangent function to calculate the elevation:

tan(angle) = opposite / adjacent

In this case, the opposite side represents the elevation, and the adjacent side represents the horizontal distance.

Let's denote the elevation as "e". The equation becomes:

tan(13°) = e / 125

To solve for "e", we can rearrange the equation:

e = 125 * tan(13°)

Using a calculator, we can evaluate this expression:

e ≈ 125 * tan(13°) ≈ 29.7

The total cookies she baked altogether is 28 cookies

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.

Therefore the total cookies put on the plate is 6+4+4= 14cookies

half of all the cookies were put in the plate,

therefore the total cookies made is 14×2= 28cookies.

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Answer:

you add then you multiply the number that you have and then whatever you get thats your answer

Step-by-step explanation:

hopes this help :)

Answer:

145

Step-by-step explanation:

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Answer:

0.097%

Step-by-step explanation:

Since this is a series of events probability question, in order to calculate the probability you need to first find the probability of getting each individual answer right and then multiplying those probabilities together. This will give you the probability of getting 100% on the entire test. Since the questions are multiple-choice with 4 choices and only 1 correct choice then the probability of getting one right is 1/4 or 25%. Now that we have that probability we simply need to multiply it 5 times for each individual question.

1/4 * 1/4 * 1/4 * 1/4 * 1/4 = 1/1024 or 0.0009765 or 0.097%

The minimum surface area of a rectangular prism with a volume of 300 units must lie somewhere between 0 and ∞.

Let's say that the rectangular prism has a length of "l" units, width of "w" units, and height of "h" units. The volume of the rectangular prism is given by the formula V = l × w × h, and we know that V = 300 units.

To find the smallest surface area possible, we need to minimize the sum of the areas of all six faces. The surface area (SA) of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh.

Using the formula for volume, we can solve for one of the variables in terms of the other two. For example, we can solve for "h" as follows:

V = l × w × h

300 = l × w × h

h = 300 / (l × w)

Substituting this expression for "h" into the formula for surface area, we get:

SA = 2lw + 2l(300 / lw) + 2w(300 / lw)

SA = 2lw + 600 / w + 600 / l

Now we need to find the minimum value of SA. To do this, we can take the derivative of SA with respect to either "l" or "w", set it equal to zero, and solve for the corresponding variable. Since the derivative is the same regardless of which variable we choose, we can take the derivative with respect to "l":

dSA/dl = 2w - 600 / l² = 0

l² = 300 / w

Substituting this expression for "l²" back into the formula for surface area, we get:

SA = 2lw + 600 / w + 600w / 300 / w

SA = 2lw + 600 / w + 2w²

Now we can take the derivative of SA with respect to "w" and set it equal to zero:

dSA/dw = 2l - 600 / w² + 4w = 0

w³ - 150lw + 150 = 0

Taking the limit as "w" approaches infinity, we get:

lim SA as w → ∞ = 2lw + 600 / ∞ + 2∞²

lim SA as w → ∞ = 2lw + 0 + ∞

This limit is also undefined, which means that there is no rectangular prism with a volume of 300 units and infinite surface area.

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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

39.50 + -51.25 is the expression

Step-by-step explanation:

I got it correct on I-ready!

Answer:

39.50+(-51.25)

Explanation:

Hope this helps 'cause it's correct! :)

Answer:

x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Step-by-step explanation:

Solve for x:

y = -x^2 - 4 x + 7

y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:

-x^2 - 4 x + 7 = y

Multiply both sides by -1:

x^2 + 4 x - 7 = -y

Add 7 to both sides:

x^2 + 4 x = 7 - y

Add 4 to both sides:

x^2 + 4 x + 4 = 11 - y

Write the left hand side as a square:

(x + 2)^2 = 11 - y

Take the square root of both sides:

x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer:

I think is -x + 105/42y

Step-by-step explanation:

2(3/10)x - 5/7y - 4(5/6)y - 2(4/5)x

6/10x - 5/7y - 20/6y - 8/5x

6/10x - 8/5x - 5/7y - 20/6y

6-16/10x - 35+140/42y

-10/10x + 105/42y

-x + 105/42y

Answer:

see explanation

Step-by-step explanation:

Calculate the distance between (x, y) and the 2 given points and equate them.

Using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (x, y) and (x₂, y₂ ) = P(- 3, 4)

d = \(\sqrt{(-3-x)^2+(4-y)^2}\)

Repeat with (x₁, y₁ ) = (x, y) and (x₂, y₂ ) = Q(2, - 1)

d = \(\sqrt{(2-x)^2+(- 1- y)^2}\)

Equating both distances

\(\sqrt{(2-x)^2+(-1-y)^2}\) = \(\sqrt{(-3-x)^2+(4-y)^2}\)

Square both sides

(2 - x)² + (- 1- y)² = (- 3 - x)² + (4 - y)² ← expand and simplify both sides

4 - 4x + x² + 1 + 2y + y² = 9 + 6x + x² + 16 - 8y + y²

subtract x² + y² from both sides

5 - 4x + 2y = 25 + 6x - 8y ( add 8y to both sides )

5 - 4x + 10y = 25 + 6x ( subtract 5 from both sides )

- 4x + 10y = 20 + 6x ( add 4x to both sides )

10y = 10x + 20 ( divide all terms by 10 )

y = x + 2 ← as required

The probability that the average number of months since the last examination in a sample of 150 patients is 14 or larger is practically 0, which means it is highly unlikely to occur by chance.

Now that we know the mean and standard deviation of the distribution of the sample mean, we can standardize the variable using the standard normal distribution formula:

Z = (x - μ) / (σ/√n)

where Z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values we obtained, we get:

Z = (14 - 12) / (0.237)

Z = 8.43

To find the probability that the sample mean is 14 or larger, we need to find the area under the standard normal distribution curve to the right of Z = 8.43.

This can be done using a standard normal distribution table or a calculator. The probability turns out to be practically 0.

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The equation of the circle with the center at the origin and a radius of 4 is \(x^2 + y^2 = 16\).

To write the circle equation with the center at the origin (0, 0) and a radius of 4, we can use the general equation for a circle:

\((x - h)^2 + (y - k)^2 = r^2\)

Where (h, k) represents the coordinates of the center and r is the radius.

In this case, the center is at (0, 0), and the radius is 4.

Substituting these values into the equation, we get:

\((x - 0)^2 + (y - 0)^2 = 4^2\)

Simplifying:

\(x^2 + y^2 = 16\)

Therefore, the equation of the circle with the center at the origin and a radius of 4 is \(x^2 + y^2 = 16\).

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Yes, f/x )= x² is a one to one function

One-to-one functions are those where each element in the domain has a unique and different element in the range. In other words, a one-to-one function has no repeating elements in its range.

To determine if f(x) = x² is a one-to-one function, we can look at the range of the equation. The range of f(x) = x² is all positive real numbers, and since all elements in the range are unique and different, we can conclude that f(x) = x² is a one-to-one function.

A one to one function is a function in which each element in the range is associated with exactly one element in the domain.

In the case of f/x )= x², each element in the range has exactly one associated element in the domain, which means it is a one to one function.

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The frequency table is:-

Data        Frequency

10             1

11              2

12             2

13             4

14             6

15             5

The frequency table determines the frequency of the data. In other words, it tells us how many times the same data is repeated.

The given data set is, 13, 14, 12, 15, 15, 14, 15, 11, 13, 14, 11, 13, 15, 12, 14, 14, 10, 14, 13, 15

The frequency table can be written as:-

Data        Frequency

10             1

11              2

12             2

13             4

14             6

15             5

The distribution's shape for the next data set you provided is left- or negatively skewed. This is due to the fact that as a number's value increases, so does its frequency.

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Answer:

$ 94.28

Step-by-step explanation:

75 x 1.18 = 88.50

75 x .077 = 5.78

88.50+5.78= 94.28

The equation given by Jill and Joel both are correct. Option C .

The line passing through the points (2, -1) and (-1, 14).

The equation of a line passing through a point \((x_1, y_1)\) is \(y-y_1=m (x-x_1)\) where m is the slope.

To find the slope m, using slope formula.

\(m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{14-(-1)}{-1-3} \\m=-5\)

Further simplify,

Substitute the values in the given formula.

\(y-y_1=m(x-x_1)\\y-(-1)=-5(x-2)\\y+1=-5(x-2)\)

Further simplify,

5x+y=9

Both the equations are correct.

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Answer:

13

Step-by-step explanation:

Answer:

-125

Step-by-step explanation:

sea level is zero so cant be above that and the answer has to be below -100 and the only option is -125

Answer:

A -125

Step-by-step explanation:

because they went over 100ft below sea level

and if sea level is exactly 0 and they went under it over 100 the only option over 100 with a negative sign to show they went below sea level would be -125

Answer:

5

Step-by-step explanation:

Based on the given conditions, formulate

Evaluate the expression:

Calculate the power:

Calculate the first two terms:

Answer: