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What two numbers on the number line have an absolute value of 3?



Question 1 options:

2 and -2


1 and -1


3 and -3


5 and -5

9514 1404 393

Answer:

  13 1/3 cups

Step-by-step explanation:

We assume flour is proportional to cookies, so we have ...

  cups/dozens = x/10 = 4/3

Multiplying by 10 gives ...

  x = 40/3 = 13 1/3

13 1/3 cups of flour are needed for 10 dozen cookies.

Answer:

13 1/2 cups of flour.

Step-by-step explanation:

If the new copier costs $800 per month plus $0.25 for each copy, then the total cost for 6000 copies a month is $2300.

The total cost of leasing a copier from the Shelly group depends on the number of copies made each month.

We have to find the cost for making 6000 copies a month,

The equation to represent the total cost is represented as :

⇒ Total cost = (Monthly lease cost) + (Cost per copy × Number of copies),

⇒ Monthly lease cost = $800

⇒ Cost per copy = $0.25

⇒ Number of copies = 6000,

Substituting the values,

We get,

⇒ Total cost = $800 + ($0.25×6000)

⇒ $800 + $1500

⇒ $2300

Therefore, the total monthly cost is $2300.

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Answer:

Below in bold,

Step-by-step explanation:

a. There's is only one card that fits this description so

Probability = 1/52.

b. There are 2 black Kings so

Probability = 2/52 = 1/26.

c. There are 2 of these - 7 of diamonds and 7 of hearts

so

Probability = 2/52 = 1/26.

d.  There 13 diamonds and 13 hearts so

Probability = 26/52 = 1/2.

e.  There  26 black cards

Probability = 26/52 = 1/2.

Answer:

The overall change in temperature over the time period ∆T = -12.6°F

Step-by-step explanation:

Rate of change of temperature r = -2.8°F per hour

Time t = 4.5 hours

The overall change in temperature ∆T = Rate of change of temperature × time period

∆T = r × t

∆T = -2.8°F per hour × 4.5 hours

∆T = -12.6°F

The overall change in temperature over the time period is -12.6°F

Answer: -12.6

Step-by-step explanation:

Answer:

The second one. The -2y should have been +2y

Step-by-step explanation:

a negative multiplied by a negative gives you a positive

Answer:

it should be the second answer

Step-by-step explanation:

hope this helps

Answer:

5/24.

Step-by-step explanation:

2/6 of 5/8 were beginners and girls

= 1/3 * 5/8

= 5/24.

Answer: x=4

Step-by-step explanation: 3x+6= 54-9x

6= 54 -12x

-48=-12x

x=4

Angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts.

Given that lines AB and BC are parallel. Angles ABD and CBD are bisected by the dashed rays. Angle EBF is measured at 45 degrees because angle ABC is 90 degrees, line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.

As a result, the angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.

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The limit of the function is 1 and it does exist .

Given,

\(\lim_{x \to \ -5} 5 - |x| / 5 + x\)

|x| : modulus function, also known as the absolute value function, is a function that takes any real number as input and returns its distance from zero on the number line.

In mathematical notation, the modulus function can be represented as |x|, where x is the input.

For example, if x = -3, then |x| = 3, and if x = 5, then |x| = 5.

Solving the limits further,

\(\lim_{x \to \ -5} 5 - |x| / 5 + x \\ \lim_{x \to \ -5} 5 - (-x) /5 + x\\ \lim_{x \to \ -5} 5 + x/ 5 + x\\\)

\(\lim_{x \to \ -5} 1\) = 1

Thus the limit exist and it is equal t o 1 .

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After using the triangle inequality theorem, the possible values of the unknown side of the triangle is 15 < n < 25.

In this case, we are given that:

The lengths of the sides of a triangle are 20, 5, and n centimeters.

The theorem of triangle inequality stated that the lengths of any two of a triangle's sides added together must be bigger than the length of the third side. Given two sides, x and y, we can use the triangle inequality theorem to predict that the length of the third side will be between x + y and x - y.

Therefore,

x - y < n < x + y

20 - 5 < n < 20 + 5

15 < n < 25

As the result, the possible value of the unknow side of the triangle would be 15 < n < 25.

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Answer:

27_5_10/2

27_5_5

22_5

17

A line passes through the two points (-4,6) and (2,-5). 11x +6y - 80 = 0 is the given line equation.

Its slope would be:

\(m = \dfrac{y-q}{x-p}\)

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope m of the line is given as

\(m = \dfrac{y-q}{x-p}\\\\ m = \dfrac{-5-6}{2+4}\\\\ m = \dfrac{-11}{6}\)

The equation of a line is  

\(( y -y_0) = m (x - x_0)\\\\( y -6) = \dfrac{-11}{6} (x+4)\\\\6( y -6) = (-11) (x+4)\\\\6y -36 = (-11x +44)\\\\11x +6y - 80 = 0\)

Hence, the equation is  11x +6y - 80 = 0

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The value of x from the exponential equation is 2.866.

Logarithm:

A logarithm is a power to which a number must be raised to get some other number.

Here we have to find the value of x.

The equation is given:

\(6^{x}\) = 170

Taking logarithms on both sides, we have:

log \(6^{x}\) = log 170

x log 6 = log 170

x = log 170 / log 6

 = 2.230/ 0.778

 = 2.866

Therefore the value of x is 2.866.

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Answer:

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

Piano lessons cost $30 per lesson.

This can be expressed as function:

Evaluate the given ordered pairs:

Answer:

look at the picture i have sent

Answer:

y= 9

Step-by-step explanation:

Please see the attached picture for the full solution.

The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

\(\overline{x} = 1400, n = 64, s = 240\)

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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Answer: x≈3.7

Step-by-step explanation:

7x+4=30

-4 on both sides

30-4=26

7x=26

divide 7 on both sides

x=3.7142...

Answer:

3.7

Step-by-step explanation:

7x+4=30

7x=30-4

7x=26

26/7

3.7

Answer:

All systems have 2 real solutions.

Step-by-step explanation:

there are X and Y unknowns.

Answer:

9

Step-by-step explanation

First you multiply 3 five times, then you multiply 3 seven times and you divide the results of each multiplication

Answer:

0.111111111111111

Step-by-step explanation:

=> 3⁵÷3⁷

Note 3⁵ means multiplying 3 five times

And 3⁷ means multiplying 3 7 times

=> 3×3×3×3×3÷3×3×3×3×3×3×3

multiply the values and then divide

=> 243÷2,187

divide 243 by 2187

=> 0.111111111111111

Answer: 2x+10 is equivalent but id.k if it was a choice bc u didnt put any

Step-by-step explanation: thx for the points

If ten workers are randomly selected, the probability exactly nine of them say that their jobs were sometimes or always stressful is 0.268 or 26.8%

The result of the recent poll is

80% of respondents said that their jobs were sometimes or always stressful

The 10 workers are randomly selected

Then we have to find the probability exactly nine of them say that their jobs were sometimes or always stressful

The equation

P(X) = nCx × P^x × (1-P)^n-x

Here n = 10

r  = 9

P = 0.80

Substitute the values in the equation

P(9) = 10C9 × 0.80^9 × (1-0.80)^(10-9)

= 10 × 0.134 × 0.20

= 0.268

= 26.8%

Therefore, the probability exactly nine of them say that their jobs were sometimes or always stressful is 26.8%

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To construct orthogonal polynomials of degrees 0, 1, and 2 on the interval (0, 1) with respect to the weight function (a) w(x) = log 1/x, we use the Gram-Schmidt process.

First, we start with the constant function 1 as our zeroth degree polynomial. Then, we construct our first degree polynomial by subtracting the projection of 1 onto x*w(x) from x*w(x), where the inner product is defined as:

⟨f, g⟩ = ∫_0^1 f(x)g(x)w(x) dx

Using this inner product, we get:
p_1(x) = x - ⟨x, 1⟩/⟨1, 1⟩ = x - (1/2)

Now, for the second degree polynomial, we subtract the projection of p_1 onto x^2*w(x) and 1*w(x) from x^2*w(x), where the inner product is defined as before.

p_2(x) = x^2 - ⟨x^2, 1⟩/⟨1, 1⟩ - ⟨x^2, x-1/2⟩/⟨x-1/2, x-1/2⟩ * (x-1/2)

p_2(x) simplifies to:
p_2(x) = x^2 - (1/3) - (2/3)(x-1/2)^2

Thus, we have constructed orthogonal polynomials of degrees 0, 1, and 2 on the interval (0, 1) with respect to the weight function w(x) = log 1/x.

For the weight function w(x) = 1/√x, we use the same process.

Our zeroth degree polynomial is 1, and our first degree polynomial is:

p_1(x) = x - ⟨x, 1⟩/⟨1, 1⟩ = x - (2/3)

Our second degree polynomial is:

p_2(x) = x^2 - ⟨x^2, 1⟩/⟨1, 1⟩ - ⟨x^2, x-2/3⟩/⟨x-2/3, x-2/3⟩ * (x-2/3)

p_2(x) simplifies to:

p_2(x) = x^2 - (2/5) - (6/5)(x-2/3)^2

Thus, we have constructed orthogonal polynomials of degrees 0, 1, and 2 on the interval (0, 1) with respect to the weight function w(x) = 1/√x.

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Answer:

1 meter of rise over 3 meters distance

Step-by-step explanation:

Slope is the rise / run ratio

1/3 slope means 1 meter of rise over 3 meters long section (or other unit of length)

Answer:

f(x)=17

Step-by-step explanation:

f(x)=(2)2+4(2)+5

=4+8+5

=17

f(x)=17

Answer:

f(2) = 17

Step-by-step explanation:

f(2) - sub in the number 2 in x

(2)² + 4(2) + 5

4 + 8 + 5

f(2) = 17

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

The probability that the spinner lands on 4​ under the condition that he rolls a 1 is 2/27,

Given that the spinner with 9 equally spaced regions numbered 1 to 9​ and a standard number cube is rolled,

So, the probability of spinning a 4 is = 4/9

The probability of rolling a 1 is = 1/6

The probability of both happening is = 1/6 x 4/9 = 4 / 54 = 2/27

Hence the probability that the spinner lands on 4​ under the condition that he rolls a 1 is 2/27,

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The probability for the given mean and variance is given by ,

P(X ≤ 1.5) ≈ 0.9332

P(X ≤ -1) ≈ 0.1587

PDF of (Y - 1) / 2 is φ(z).

P(-1 ≤ Y ≤ 1) is approximately 0.6826

Mean = 0

Variance = 1

P(X ≤ 1.5),

Calculate the cumulative distribution function (CDF) of the normal distribution.

Use standardization by subtracting the mean and dividing by the standard deviation, evaluated at 1.5.

Z

= (X - mean) / standard deviation

= (X - 0) / 1

= X

Using the Z-score calculator, find the corresponding probability for Z ≤ 1.5, which is approximately 0.9332.

P(X ≤ 1.5) ≈ 0.9332

To find P(X ≤ -1), similarly standardize and find the probability for Z ≤ -1,

Z

= (X - mean) / standard deviation

= (X - 0) / 1

= X

Using the Z-score table or a calculator, we find the probability for Z ≤ -1 to be approximately 0.1587.

P(X ≤ -1) ≈ 0.1587

To find the probability density function (PDF) of (Y - 1) / 2,

Use the properties of linear transformations of random variables.

Let Z = (Y - 1) / 2. To find the PDF of Z,

Compute its mean and variance.

The mean of Z can be found as follows,

E[Z]

= E[(Y - 1) / 2]

= (1/2) × E[Y - 1]

= (1/2) × (E[Y] - E[1])

= (1/2) × (1 - 1)

= 0

The variance of Z can be found as follows,

Var[Z]

= Var[(Y - 1) / 2]

= (1/4) × Var[Y - 1]

= (1/4) × Var[Y]

= (1/4) × 4

= 1

Since Z follows a standard normal distribution mean 0 and variance 1,

the PDF of Z is the standard normal distribution's PDF, denoted as φ(z).

Therefore, the PDF of (Y - 1) / 2 is φ(z).

To find P(-1 ≤ Y ≤ 1), we can use the cumulative distribution function (CDF) of the normal distribution with mean 1 and variance 4.

P(-1 ≤ Y ≤ 1) = P(Y ≤ 1) - P(Y ≤ -1)

To calculate these probabilities, we need to standardize the values,

For Y ≤ 1

Z1

= (1 - mean) / standard deviation

= (1 - 1) / 2

= 0

For Y ≤ -1,

Z2

= (-1 - mean) / standard deviation

= (-1 - 1) / 2

= -1

Using the Z-score calculator, we find,

P(Y ≤ 1) ≈ 0.8413

P(Y ≤ -1) ≈ 0.1587

P(-1 ≤ Y ≤ 1)

= P(Y ≤ 1) - P(Y ≤ -1)

≈ 0.8413 - 0.1587

≈ 0.6826

P(-1 ≤ Y ≤ 1) is approximately 0.6826.

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The area of the square is 1/4inches² in square inches

The area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.

The square has side of length = 6/12

this can be simplified as 1/2

so

area of the square = (1/2 × 1/2) inches ²

area of the square = 1/4inches²

Thus, the area of the square is calculated using area = s × s, as 1/4inches²

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