A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?
O y=-3x+1
O y=zx+7
y=-2x - 8
y = 2x + 16

Answer:

\( \sf \: f(5) = - 12\)

Step-by-step explanation:

Given function,

→ f(x) = -2(x + 1)

Now we have to,

→ Find the required value of f(5).

Then the value of f(5) will be,

→ f(x) = -2(x + 1)

→ f(5) = -2(5 + 1)

→ f(5) = -2(6)

→ [ f(5) = -12 ]

Hence, the value of f(5) is -12.

Answer:

a) 9/25

b) 27/100

c) 3/19

d) 1/4

Step-by-step explanation:

a) 72/200 = 9/25

b) 54/200 = 27/100

c) 18/114 = 3/19

d) 32/128 = 1/4

Answer:

-40%

Step-by-step explanation:

NV = new value

OV = old value

percent change = (NV - OV)/(OV) × 100%

percent change = (30 - 50)/(50) × 100%

percent change = -20/50 × 100%

percent change = -40%

(a) No, the lifetime of the light bulbs cannot have an exponential distribution. The exponential distribution is a continuous probability distribution that is typically used to model the time between events in a Poisson process. It assumes a constant hazard rate, which means that the probability of an event occurring is independent of the time that has elapsed since the last event. In the case of light bulbs, the lifetime is not expected to follow an exponential distribution because the mean and standard deviation have been provided, indicating that the distribution is right-skewed and likely not exponential.

(b) The sampling distribution of the sample means (denoted by "i") for random samples of size 60 can be approximated by a normal distribution. This is known as the Central Limit Theorem, which states that for a sufficiently large sample size, the distribution of the sample means will be approximately normal, regardless of the shape of the population distribution. The parameters of this sampling distribution are the mean and the standard error. The mean of the sampling distribution is equal to the mean of the population, which is 600 hours in this case. The standard error can be calculated by dividing the standard deviation of the population by the square root of the sample size (160 / √60).

To estimate the probability that the average lifetime of 60 randomly selected bulbs will be between 580 and 630 hours, we can use the normal distribution approximation. We standardize the values by subtracting the population mean from each value and dividing by the standard error. Then we look up the corresponding z-scores in the standard normal distribution table or use a statistical software/tool to calculate the probabilities. The probability can be estimated as the difference between the cumulative probabilities associated with the standardized values for 580 hours and 630 hours.

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Answer:

What he did wrong is that he did not flip all of the points. since S is 1 point up, it would then reflect 1 point down. point P is 3 up and the reflection should be 3 down. Q should be 3 down as well and R is 1 down below the x axis. The Y does not move for all of the points.

Step-by-step explanation:

I hope this helps!

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

289819

Step-by-step explanation:

The charge q is ±7.46 × 10⁻⁷C.

Give:

Take a look at the charge on the left. The following forces are at work in response to this charge:

(Refer to the diagram below)

Because the charge is in equilibrium, the charge's vertical and horizontal forces must be zero.

We have the following in the vertical direction:

\(\begin{aligned}T \cos 20^{\circ} &=W \\\Rightarrow T &=\frac{m g}{\cos 20^{\circ}} \\&=\frac{3.0 \times 10^{-3} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2}{\cos 20^{\circ}} \\&=3.13 \times 10^{-2} \mathrm{~N}\end{aligned}\)

Coulomb's Law states that the electrostatic force between two point charges, q₁, and q₂, separated by r is given by the equation:

\(\begin{aligned}F &=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2} \\&=\frac{K q_1 q_2}{r^2}\end{aligned}\)

Here,

Using trigonometric personalities, the distance between any two charges is:

\(\begin{aligned}r &=2 l \sin 20^{\circ} \\&=2 \times 1.0 \mathrm{~m} \times 0.342 \\&=0.684 \mathrm{~m}\end{aligned}\)

We have the following in the vertical direction:

\(\begin{aligned}F_e &=T \sin 20^{\circ} \\\Rightarrow \frac{K q_1 q_2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow \frac{K q^2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow q^2 &=\frac{r^2 T \sin 20^{\circ}}{K} \\&=\frac{(0.684 \mathrm{~m})^2 \times 3.13 \times 10^{-2} \mathrm{~N} \times \sin 20^{\circ}}{9 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2} \\&=55.65 \times 10^{-14} \mathrm{C}^2 \\\Rightarrow q &=\pm 7.46 \times 10^{-7} \mathrm{C}\end{aligned}\)

Therefore, the charge q is ±7.46 × 10⁻⁷C.

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The correct question is given below:
Two 3.0g point charges on 1.0m - long threads repel each other after being equally charged, as shown in the figure. What is the charge q?

There are 10,000 possible combinations if there are no restrictions on the number of times talula can use each number.

since the lock has four number positions and each position can have any number from 0 to 9, we can use the multiplication    principle   to determine the total number of possible combinations:

10 options for the first position x 10 options for the second position x 10 options for the third position x 10 options for the fourth position

this gives us:

10 x 10 x 10 x 10 = 10,000

biking talula got a new bicycle lock that has a four-number combination. each number in the combination is from 0 to 9. a. how many combinations are possible

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Answer:

b

Step-by-step explanation:

Answer:

B=28

Step-by-step explanation:

Answer:

a = -0.5

Step-by-step explanation:

\( \rm Solve \: for \: a: \\ \rm \longrightarrow - \dfrac{1}{4}a - 4 = \dfrac{7}{4}a - 3 \\ \\ \rm Put \: each \: term \: in \: - \dfrac{1}{4}a - 4 \: over \: the \\ \rm common \: denominator \: 4: \\ \rm - \dfrac{a}{4} - 4 = - \dfrac{a}{4} - \dfrac{16}{4} : \\ \rm \longrightarrow - \dfrac{a}{4} - \dfrac{16}{4} = \dfrac{7}{4}a - 3 \\ \\ \rm - \dfrac{a}{4} - \dfrac{16}{4} = \dfrac{ - a - 16}{4} : \\ \rm \longrightarrow \dfrac{ - a - 16}{4} = \dfrac{7}{4}a - 3 \\ \\ \rm Put \: each \: term \: in \: \dfrac{7}{4}a - 3 \: over \: the \\ \rm common \: denominator \: 4: \\ \rm \dfrac{7a}{4} - 3 = \dfrac{7a}{4} - \dfrac{12}{4} : \\ \rm \longrightarrow \dfrac{ - a - 16}{4} = \dfrac{7a}{4} - \dfrac{12}{4} \\ \\ \rm \dfrac{7a}{4} - \dfrac{12}{4} = \frac{7a - 12}{4} : \\ \rm \longrightarrow \dfrac{ - a - 16}{4} = \dfrac{7a - 12}{4} \\ \\ \rm Multiply \: both \: sides \: by \: 4: \\ \rm \longrightarrow \dfrac{ - a - 16}{ \cancel{4}} \times \cancel{4}= \dfrac{7a - 12}{ \cancel{4}} \times \cancel{4} \\ \\ \rm \longrightarrow -a - 16 = 7 a - 12 \\ \\ \rm Subtract \: 7 a \: from \: both \: sides: \\ \rm \longrightarrow (-a - 7 a) - 16 = (7 a - 7 a) - 12 \\ \\ \rm -a - 7 a = -8 a: \\ \rm \longrightarrow -8 a - 16 = (7 a - 7 a) - 12 \\ \\ \rm 7 a - 7 a = 0: \\ \rm \longrightarrow -8 a - 16 = -12 \\ \\ \rm Add \: 16 \: to \: both \: sides: \\ \rm \longrightarrow (16 - 16) - 8 a = 16 - 12 \\ \\ \rm 16 - 16 = 0: \\ \rm \longrightarrow -8 a = 16 - 12 \\ \\ \rm 16 - 12 = 4: \\ \rm \longrightarrow -8 a = 4 \\ \\ \rm Divide \: both \: sides \: of \: -8 a = 4 \: by \: -8: \\ \rm \longrightarrow

\dfrac{ - 8a}{ - 8} = \dfrac{4}{ - 8} \\ \\ \rm \dfrac{ - 8}{ - 8} = 1: \\ \rm \longrightarrow a = - \dfrac{4}{ 8} \\ \\ \rm - \dfrac{4}{ 8} = - \dfrac{1}{2} : \\ \rm \longrightarrow a = - \dfrac{1}{2} \\ \\ \rm \longrightarrow a = - 0.5\)

Answer: (2, -2)

x=2, y=-2

Answer:

(2, -2)

Step-by-step explanation:

4x + y = 6

x - 2y = 6

x = 2y + 6

4(2y + 6) + y = 6

8y + 24 + y = 6

9y + 24 = 6

9y = 6 - 24

9y = -18

y = -18 ÷ 9

y = -2

4x + (-2) = 6

4x - 2 = 6

4x = 6 + 2

4x = 8

x = 8 ÷ 4

x = 2

Confirm:

4x + y = 6

4(2) - 2 = 6

8 - 2 = 6

6 = 6 (Correct)

(2, -2)

Answer:

-12

Step-by-step explanation:

4y=4*(-3) 4*(-3)=-12

Answer:

It’s -12

Step-by-step explanation:

The end behavior of the graph of f(x) is,

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.

A data set is a collection of organized data. Data is a collection of information that has been obtained by observations, measurements, study, or analysis, as we are all aware. It could contain names, numbers, facts, and even straightforward descriptions of items. For our study, data can be arranged in the form of graphs, charts, or tables.

Given the data,

x           -5     -4     -3     -2      -1       0      1         2         3

f(x)         -6     -2     0       4      4       0     -2      -6      -10

the graph moves towards the negative side for negative values of x,

so from the data, we observed that,

if x tends to -∞ then f(x) will be -∞,

and the value of f(x) again moves towards the negative side for all positive values of x.

so  x tends to ∞ then f(x)  will again -∞.

Hence option D is correct.

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According to the given statement by the height of the kite was 30 feet off the ground by using the Pythagorean theorem,

To find the height of the kite, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the string of the kite, which is 50 feet, and one of the other sides is the distance from the child to the stop sign, which is 40 feet.

Using the Pythagorean theorem, we can set up the equation as follows:

Hypotenuse² = Side1² + Side2²
50² = 40² + Side2²

Simplifying the equation:
2500 = 1600 + Side2²

Subtracting 1600 from both sides:
Side2² = 2500 - 1600
Side2² = 900

Taking the square root of both sides:
Side2 = √(900)
Side2 = 30

So, the height of the kite is 30 feet off the ground.

Therefore, the height of the kite was 30 feet off the ground.

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By using the Pythagorean theorem and the given information of the distance between the child and the stop sign, as well as the length of the string, we can calculate that the height of the kite is 30 feet off the ground.

To determine the height of the kite, we can use the concept of similar triangles. Let's consider the child, the kite, and the stop sign as the three vertices of a triangle.

Since the child is 40 feet away from the stop sign and the string is 50 feet long, we have a right triangle. The height of the kite will be the missing side, which we can call 'x.'

Using the Pythagorean theorem, we can find the length of the missing side:

x^2 + 40^2 = 50^2

Simplifying the equation, we get:

x^2 + 1600 = 2500

Subtracting 1600 from both sides, we have:

x^2 = 900

Taking the square root of both sides, we find:

x = 30

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Answer:

D

Step-by-step explanation:

==========================================================

Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

Solution

Using BODMAS to solve the fraction

Therefore the answer = -3/4

Answer:

49 is the answer

thank you

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Step-by-step explanation:

14x + 5 = 12

14x = 12 - 5

14x = 7

x = 7/14

x = 1/2

Answer:

(2x/5)-7

Hope you got it!

The correlation between the number of wins and each of the four baseball statistics would be an example of bivariate correlation analysis, which measures the strength and direction of the relationship between two variables.

The correlation between number of wins and each of the four baseball statistics would be an example of a bivariate correlation, which measures the strength and direction of the linear relationship between two variables. In this case, the two variables would be the number of wins and each of the four baseball statistics. The correlation coefficient would provide a numerical value that represents the degree of association between the two variables

A positive correlation coefficient would indicate that as one variable increases, so does the other, while a negative correlation coefficient would indicate that as one variable increases, the other decreases.

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If all these statistics were analyzed at the end of the season, the correlation between the number of wins and each of

the four baseball statistics would be an example of bivariate analysis.

Bivariate analysis involves analyzing the relationship between two variables to determine if there is any correlation or

association between them.

In this case, the two variables are the number of wins and each of the four baseball statistics.

By conducting a bivariate analysis, you can identify if there is any significant relationship between these variables and

potentially draw conclusions about their impact on team performance.

If all these statistics were analyzed at the end of the season, the correlation between the number of wins and each of

the four baseball statistics would be an example of bivariate analysis.

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Answer:

hope this help you

of my handwriting is bad then sorry.

Answer:

have a great day

may god bless you a lot