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Answer:

The equation of a line that is parallel to x−2y=−4 and passes through the point (0, 0) will be:  \(x-2y=0\)

Step-by-step explanation:

Given the line

\(x-2y=-4\)

\(x+4 = 2y\)

\(y=\left(\frac{1}{2}\right)x+2\)

\(m_1=\frac{1}{2}\)

so, the slope of the line parallel to the given line would have

the same slope as  \(\frac{1}{2}=m\), and passed through the point (0, 0).

Therefore, the equation of the required line is given by

\(y = mx+b\)

\(y=\left(\frac{1}{2}\right)x+0\)

\(y=\left(\frac{1}{2}\right)x\)

\(2y=x\)

\(x-2y=0\)

Therefore,  the equation of a line that is parallel to x−2y=−4 and passes through the point (0, 0) will be:  \(x-2y=0\)

The equation of the circle with a radius of 111 and a center at (9, 5) is:

To determine the equation of a circle, we use the standard form equation:

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

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

In this case, the center of the circle is (9, 5), and the radius is 111. Plugging these values into the equation, we have:

(x - 9)^2 + (y - 5)^2 = 111^2

Expanding and simplifying further:

\((x - 9)^2 + (y - 5)^2 = 12321\)

Therefore, the equation of the circle with a radius of 111 and a center at (9, 5) is:

(x - 9)^2 + (y - 5)^2 = 12321

This equation represents all the points (x, y) that are equidistant from the center (9, 5) by a distance of 111 units, forming a circle shape.

To graphically represent the circle, plot the center point (9, 5) on a coordinate plane and then draw the circle with a radius of 111 units around it. Any point on the graph that satisfies the equation will lie on the circle, while points outside the circle will not satisfy the equation.

It's important to note that the equation of a circle can also be expressed in other forms, such as the general form or parametric form. However, the standard form equation provided above is commonly used for representing circles.

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Answer:

Y=3

Step-by-step explanation:

Multiply 4x3 to get 12. 12-7=5.

Hope it helps!

Answer:

3

Step-by-step explanation:

4y=5+7

4y=12

y=12/4

y=3

The first blank is 32, the second is.... -64 i think.

Working out- plus 32 to each x linear relationship.

The vertical distance between yi and ybi is the length

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

yi and ybi

A vertical distance is the distance between two points or objects measured along a vertical line or in the vertical direction. It is the difference between the vertical coordinates (heights or elevations) of the two points or objects.

In this case, the vertical distance  is the length

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The two figures are not similar and hence will not exactly map to each other

In math, two polygons qualify as similar only under the following condition:

In the polygon the ratio of the sides are not proportional. the sides are

Red: 3 units x 3 units

Blue: 1.5 units x 4 units

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Answer: 10 ft

Step-by-step explanation:

diameter = 2r

diameter = 2(5)

diameter = 10 ft

Answer:

10 ft

Explanation:

When you have the radius, and you're trying to find the diameter, just multiply the radius by 2:

Diameter = Radius × 2

                = 5 × 2

                = 10 ft

Therefore, the radius is 10 ft.

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer:

(1, 3 )

Step-by-step explanation:

Choose any value of x, substitute into the equation for y

Choose x = 1 , then

y = 2(1) + 1 = 2 + 1 = 3

Then (1, 3 ) is an ordered pair on the line

The speed of both printers operating together is 1.333 hours which was found using the given data.

The formula used to explain the connection between speed, distance, and time is speed = distance/time.

Given: Newspapers can be printed twice as quickly on a modern printing press as they can on an old one. The old one takes four hours to publish the afternoon edition.

Let,

a = Speed of New printing press

b = Speed of Old printing press

x = Speed of both printers operating together

We know that,

(1/a)+(1/b)=(1/x)

(1/2)+(1/4)=(1/x)

(4/8)+(2/8)=(1/x)

6/8=1/x

x=8/6

x=1.333

Therefore, the speed of both printers operating together is 1.333 hours which was found using the given data.

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Answer:

Step-by-step explanation:

4. x=50 because 28+17=45, 180-85-45

y=130 becaue 180-50

z=5 because 180-130-45

5. z=59 because 40+24 =64, 180-64-57

y=121 becayse 180-59

x=5 because 180-121-64

The probability of picking a male from the population whose weight will be greater than 251 lbs is 0.13%.

In order to calculate the probability we need to use the formula of z-score

z = (x -μ)/ σ

here,

x = value of interest

μ = population mean

σ = population standard deviation

now adding the values into the given formula

z = ( 251 -182)/23

z =  69/23

z = 3

now after using the standard distribution table the probability of a z-score greater than 3 is 0.13%

The probability of picking a male from the population whose weight will be greater than 251 lbs is 0.13%.

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The differentials of the given functions are:

dy/dt = (1/2)√(3t) sec^2(√(3t)) dt

dy/dv = -v/2 + v

To find the differential of the function y = tan(sqrt(3t)), we can use the chain rule. Let u = sqrt(3t). Applying the chain rule, we have dy/dt = dy/du * du/dt.

First, we find dy/du by taking the derivative of tan(u), which is sec^2(u). Then, we find du/dt by taking the derivative of sqrt(3t), which is (1/2)√(3t). Multiplying these two derivatives together, we get dy/dt = (1/2)√(3t) sec^2(√(3t)) dt.

To find the differential of the function y = 4 - v^2/4 + v^2, we need to take the derivative with respect to v. The first term, 4, does not depend on v, so its derivative is 0.

For the second term, -(v^2/4), we use the power rule for differentiation. The derivative of v^2 is 2v, and dividing by 4 gives -(v/2).

For the third term, v^2, the derivative is 2v.

Combining these derivatives, we get dy/dv = -v/2 + v.

The differentials of the given functions have been calculated as dy/dt = (1/2)√(3t) sec^2(√(3t)) dt and dy/dv = -v/2 + v. These differentials represent the rate of change of the functions with respect to the respective variables.

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The differential of y = tan(sqrt(3t)) is dy/dt = (1/2)(3t)^(-1/2)(3)(sec^2(sqrt(3t))). The differential of y = 4 - v^2/4 + v^2 is dy/dv = 3v/2.

To find the differential of each function, we will differentiate them with respect to the independent variable.

Let's use the chain rule to differentiate this function.

Therefore, the differential of y = tan(sqrt(3t)) is dy/dt = (1/2)(3t)^(-1/2)(3)(sec^2(sqrt(3t))).

Let's differentiate this function using the power rule and the sum/difference rule for derivatives.

Therefore, the differential of y = 4 - v^2/4 + v^2 is dy/dv = 0 - v/2 + 2v = 3v/2.

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let convert to decimal

From the smallest ot the largest

If the average salary of several of the groups was close to $51,000 then least likely to be the average salary of another one of the groups are equal to $41,000.

Random groups of teachers are = 30

If the average salary of several of the groups was close to equal to = $51,000

The mean, or average, salary is the amount derived by adding two or more salary values and dividing the sum by the number of values.

So we can write,

The average wage is known to be close to $41,000

$41,000 < $51,000

Therefore,

The average salary of another one of the groups are equal to $41,000.

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Answer:

The opposite of -4:  4

The opposite of 5:  -5

The opposite of the opposite of -6:  -6

Answer:

It falls in the integer category. The attached picture is a chart if you want to specify a number in a category.

Hope this helps :)

Rounded to 1 decimal place, the wholesaler's in-stock probability during a normal week is approximately 89.2%.

To calculate the wholesaler's in-stock probability during a normal week, we need to consider the number of items that are available for the entire week and divide it by the total demand.

Total demand = 4,800 items

Items not available for the entire week = 250 items

Items available for only part of the week = 270 items

Therefore, the number of items available for the entire week can be calculated as follows:

Items available for the entire week = Total demand - Items not available for the entire week - Items available for only part of the week

                                = 4,800 - 250 - 270

                                = 4,280 items

The in-stock probability can be calculated by dividing the number of items available for the entire week by the total demand and then multiplying by 100 to convert it to a percentage:

In-stock probability = (Items available for the entire week / Total demand) * 100

                   = (4,280 / 4,800) * 100

                   = 89.1666...

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The probability of obtaining a sample mean as large or larger is 0.0228.

option B.

The probability of obtaining a sample mean as large or larger is calculated as follows;

The given parameters;

The standard error (SE) of the sampling distribution is calculated as;

SE = σ / √n

SE = 0.8 / √64

SE = 0.8 / 8

SE = 0.1

The z-score of the sample mean is calculated as follows;

z = (x - μ) / SE

z = (3.4 - 3.2) / 0.1

z = 0.2 / 0.1

z = 2

Using a z-score calculator;

P (X > Z) = 0.0228

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The probability of obtaining a sample mean as large or larger than 3.4 pounds is 0.0228.

The correct answer is: b. 0.0228

Given data:

Population mean (μ) = 3.2 pounds

Population standard deviation (σ) = 0.8 pound

Sample size (n) = 64

Sample mean (x) = 3.4 pounds

We have to standardize the sample mean using the z-score formula and then find the corresponding area under the standard normal distribution curve.

The formula for calculating the z-score is:

z = (x - μ) / (σ / √n)

substituting the values:

z = (3.4 - 3.2) / (0.8 / √64)

z = 0.2 / (0.8 / 8)

z = 0.2 / 0.1

z = 2

Using a calculator, the area to the right of z = 2 is the probability 0.0228.

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Answer: 1 guppy = 3 goldfish

1 goldfish = 2 betta fish.....so 3 goldfish = (3 * 2) = 6 betta fish

1 betta fish = 2 angel fish....so 6 beta fish = (6 * 2) = 12 angel fish

so the number of angelfish that can be formed by 1 guppy is 12 angelfish

The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

Therefore, the missing number in the sequence is 21.

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Answer:

80% of HCl used is 0.75 of a liter

40% or HCl used is 0.25 of a liter.

Step-by-step explanation:

Comment

You need a total of 1 liter which has a concentration of 70%.

Let x be the concentration of the 80%  HCl

Let 1-x be the concentration of the 40% HCl

Solution

(1 - x)*40/100 + x*80/100 = 70/100 * 1           Multiply by 100

40*(1-x) + 80x = 70                                         Remove the brackets (left)

40 - 40x + 80x = 70                                       Combine

40 + 40x = 70                                                 Subtract 40  from both sides

40-40 + 40x = 70 - 40                                    Combine

40x = 30                                                          Divide by 30

x = 30/40

Answer

x = 0.75 of a liter

1-x = 0.25 of a liter.

If a sample includes three individuals with scores of 4, 6, and 8, the estimated population variance is (4 + 0 + 4) / 2 - 4. So, correct option is 4.

The estimated population variance formula is the sum of squared deviations from the mean divided by the degrees of freedom. In this case, the degrees of freedom would be n-1, where n is the sample size.

Using the given sample of 4, 6, and 8, we can calculate the sample mean as (4+6+8)/3 = 6.

Then, we calculate the deviations from the mean for each score:

4 - 6 = -2

6 - 6 = 0

8 - 6 = 2

We square each deviation to get 4, 0, and 4. Then, we sum the squared deviations: 4 + 0 + 4 = 8.

Since there are three scores in the sample, the degrees of freedom is 3 - 1 = 2.

Finally, we divide the sum of squared deviations by the degrees of freedom to get the estimated population variance: 8/2 = 4.

Therefore, option 4) (4 + 0 + 4) / 2 = 4 is the correct answer.

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Answer:

17 is b

18 is b

19 is d

20 is a

Step-by-step explanation:

Answer:

17. B

18. C

19. D

20. A

Step-by-step explanation:

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

1. x + 191 ≥ 214

2. x - 214 ≤ -23

1. To solve this inequality, we add 23 to both sides of the equation: x - 23 = 191.

x + 191 ≥ 214

2. To solve this inequality, we subtract 191 from both sides of the equation: x - 23 = 191.

x - 214 ≤ -23

1. x + 191 ≥ 214

This inequality can be expanded to x + 191 ≥ 214, which means that any value of x that is greater than or equal to 214 satisfies the inequality.

2. x - 214 ≤ -23

This inequality can be expanded to x - 214 ≤ -23, which means that any value of x that is less than or equal to -23 satisfies the inequality.

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x= 6 is the answer

Step-by-step explanation:

hope it helps

Answer:

 -x • (x2 - 5x + 1) • (3x - 4)

Step-by-step explanation:

STEP

1: Equation at the end of step 1

 (((x2) -  5x) +  1) • (4x -  3x2)

STEP2:STEP

2:Pulling out like terms

 Pull out like factors :

4x - 3x2  =   -x • (3x - 4)

Trying to factor by splitting the middle term

 Factoring  x2 - 5x + 1

The first term is,  x2  its coefficient is  1 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  +1

Step-1 : Multiply the coefficient of the first term by the constant   1 • 1 = 1

Step-2 : Find two factors of  1  whose sum equals the coefficient of the middle term, which is   -5 .

     -1    +    -1    =    -2

     1    +    1    =    2

Observation : No two such factors can be found !!

Answer:

k = +10 or -10

Step-by-step explanation:

It's given in the question that the roots of the eqn. are real and equal. So , the discriminant of the eqn. should be equal to 0.

\( = > {b}^{2} - 4ac = 0\)

\( = > {( - 2k)}^{2} - 4 \times 5 \times 20 = 0\)

\( = > 4 {k}^{2} - 400 = 0\)

\( = > 4( {k}^{2} - 100) = 0\)

\( = > {k}^{2} - 100 = 0\)

\( = > k = \sqrt{100} = + 10 \: or \: - 10\)

Step-by-step explanation:

Given Equation

5x-2kx+20=0

\(\boxed{\sf \longrightarrow D=0 }\)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow b^2-4ac=0 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow (-2k)^2-4\times 5\times 20=0 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-20\times 20=0 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-400=0\)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2=400 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=\dfrac {400}{4}\)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=100 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=\sqrt{100}\)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=10 \)

\(\therefore\sf k=10 \)

This is because the Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Pythagorean Theorem is an essential mathematical principle that has been used for centuries. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras. Using this theorem, one can calculate the length of any side of a right triangle if the lengths of the other two sides are known.

This relationship between the side lengths and the angle measures can be used to calculate the exact angle measures when all three side lengths are known.

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