Use the perpendicular slope 1/2 and the point
(-3,2) to find the equation of the line
y = -2x + 12
y = 1/2x + 1
y = 1/2x + 5
y = 1/2x +3.5

Answer:

x+3

Step-by-step explanation:

1/2 ( 3/5x -8) + 7/4 ( 2/5x +4)

Distribute

3/10 x -4  + 7/10x +7

Combine like terms

10/ 10x +3

x+3

Answer: x+3 Step-by-step explanation:

Step-by-step explanation:

(3x-40) + 7 • (x+10)     10x + 30

—-—-—-———————————————  =  ————————

        10                 10  

Pulling out like terms :  

11.1

Pull out factors like :

10x + 30 = 10 • (x + 3)

Final result :

  x + 3

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

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The required exponential expression is 9⁵ for the numerical expression 9⋅9⋅9⋅9⋅9.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

"9⁵," or "nine to the fifth power is respectable because we have multiplied the number "9" by itself "five times."

Hence, the value is equal to:    

⇒ 9⋅9⋅9⋅9⋅9 is equal to:  " 9⁵ " ;  

that is, "nine to the fifth power"  or "nine to the power of "five" ;

Thus, the required exponential expression is 9⁵ for the numerical expression 9⋅9⋅9⋅9⋅9.

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Answer:

it’s A

Step-by-step explanation:

I graphed it out

Answer:

p = 62

Step-by-step explanation:

(x^25)^2 = x^(25*2) = x^50.  Then we have:

(x^12)(x^50) = x^(12 + 50) = x^62

Therefore, p = 62

The value of BC the nearest hundredth is 15.01 .

From the image , we are able to see that CA = seven and angle A = 65°

Using ,Trigonometric Ratios , we get

Tan A = Perpendicular / Base

Tan 65° = BC / CA

2.144 =BC / 7

2.144 ×7 = BC

15.011 = BC

On rounding off to the closest hundredth , we have a tendency to get BC = 15.01

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The word "LOGARITHMS" is made up of 10 different letters. The following four-letter words can be created from a collection of 10 letters: "=""(10)P (4)=(10xx9xx8xx7)=5040. Consequently, 5040 four-letter words are required to finish the statement.

a)The sum of the number of arrangements in each of the three examples now yields the total number of arrangements for four letters. Thus, there are 2454 possible arrangements for the four letters in the word "mathematics."

b) The likelihood of selecting an A is 1/5 because there is only one A. Picking a vowel has a 2/5 chance due to the two available options. Given that there are three consonants, the likelihood of selecting one is 3/5.

c)Solution, There is a 2/11 chance of selecting the letter "m" from the provided word.

There are four primary categories of probability: classical, empirical, subjective, and axiomatic. Probability is the area of mathematics that deals with the occurrence of a random event.

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You need 500 factors to rank up and come to be Virtuoso in Brainly app.

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Using the service is quite easy because after registering on the Brainly application, we can immediately ask and answer questions.

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a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of each line,

LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,

Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3

Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.

Thus, the solution of the pair of lines has been shown above.

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Main Answer:The correct answer is "equality of three or more population means."

Supporting Question and Answer:

What is the purpose of the one-way analysis of variance (ANOVA) test?

ANOVA helps to assess whether these differences are statistically significant by comparing the variation between the groups to the variation within the groups.

Body of the Solution:The one-way analysis of variance (ANOVA) is used to test for" the equality of three or more population means". ANOVA compares the variation between the groups (due to differences in means) to the variation within the groups (due to individual differences within each group) to assess whether the observed differences in means are statistically significant. Therefore, the correct answer is:

"equality of three or more population means."

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There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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Answer:

9 7/8

Step-by-step explanation:

Answer: 55mph

Step-by-step explanation:

660/12=55 simple math don't be scared of word problems

Answer:

55 miles per hour

Step-by-step explanation:

Speed =Distance divided by time

Answer:

Part A: (C) 16 square inches

Part B: (C) 36 square inches

Answer:D

Step-by-step explanation:Hope that helped

The solution of the differential equation with initial conditions is y(x)= (1/4)xe2x + 1/4x2e2x + 1/4xe2x + 1/16e2x + x2/4e2x ...

The characteristic equation is given by

m2-4m+4=0(m-2)2=0

So, the complementary function is

\(y_c\)(x)=(c1+c2x)e2x Where c1 and c2 are constants.

Taking yp(x)= A+Bx+Cx2+Dx2e2x+Ex2e2xAs the given function e2x is a part of complementary function and y=Ax2+Bx+Cx2e2x is also a part of complementary function. So, the product of these two will also be a part of complementary function. So, assume that,

yp(x)=Dx2e2x

Now, y′p(x)=2Dxe2x+2Dx2e2x

And, y′′p(x)=4De2x+4Dxe2x+4Dx2e2x

Substituting the values of y′′p(x) and y′p(x) in the differential equation,

4De2x+4Dxe2x+4Dx2e2x-4(2Dxe2x+2Dx2e2x)+4(Dx2e2x)=49+x2e2x

Or, 4De2x=49+x2e2xOr, D=1/4 + x2/4e-2x

Now, the particular solution is given by,

yp(x)=1/4x2e2x + 1/4xe2x + 1/16e2x + x2/4e2x

Using principle of superposition, the general solution of the differential equation is

y(x)=\(y_c(x)+y_p(x)\) = (c1+c2x)e2x + 1/4x2e2x + 1/4xe2x + 1/16e2x + x2/4e2x ... equation (1)

Next, find the values of c1 and c2 using the initial conditions given:

y(0)=0 So, from equation (1), putting x=0y(0)=c1=0 So, the solution of the differential equation is

y(x)= c2xe2x + 1/4x2e2x + 1/4xe2x + 1/16e2x + x2/4e2x ... equation (2)

Now, find the value of c2: y′(0)=3 Substituting x=0 in y'(x),

y'(0)=2c2+1/2So, 2c2+1/2=3 or c2=1/4

Therefore, the solution of the differential equation with initial conditions is y(x)= (1/4)xe2x + 1/4x2e2x + 1/4xe2x + 1/16e2x + x2/4e2x ...

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Answer:

4.3

Step-by-step explanation:

78= -16t²+37t+211

0= -16t²+37t+133

Using the quadratic formula,

(-37±√(37²-4*-16*133))/(2*-16)

(-37±√9881)/(-32)

(-37-√9881)/ -32 = 4.2626= 4.3

While -1.95 is a solution to the quadratic formula, a negative value doesn't make sense in this context.

Answer:

E. 4.3

Step-by-step explanation:

We have the equation S = -16t^2 + 37t + 211

Given S = 78, then

78 = -16t^2 + 37t + 211

-16t^2 + 37t + 211 - 78 = 0

-16t^2 + 37t + 133 = 0

Using quadratic equation ax^2 + bx + c = 0

x = [-b ± √(b^2 - 4ac)] / (2a)

t = [-37 ± √(37^2 - 4(-16)(133)] / 2(-16)

t = [-37 ± √(1369 - (-8512)] / (-32)

t = [-37 ± √(9881)] / (-32)

a. t = [-37 + √(9881)] / (-32)

t = (-37 + 99.403) / (-32)

t = -1.95

b. t = [-37 - √(9881)] / (-32)

t = (-37 - 99.403) / (-32) = 4.26

Since t can't be a negative number, we have t = 4.26 or 4.3

Please double check my calculation. Hope this helps.

If population grew by 5% from 2010 to 2015 and fell by 3% from 2015 to 2020 , then the population decrease from 2015 to 2020 is 6678    .

Let the population of the city in 2015 be = "p".

To find the population in year "2015" , we first find the growth from 2010 to 2015  ;

⇒ p = 212000×(1 + 0.05) = 212000 × 1.05 = 222600 ;

So, the population in 2015 was 222600 .

Next, we find the population in 2020 by applying the decrease of 3%:

⇒ p = 222600×(1 - 0.03) = 222600×0.97 = 215922

So, the population in 2020 was 215922.

To , find the decrease from 2015 to 2020, we subtract the population in 2020 from the population in 2015 ;

⇒ 215922 - 222600 = -6678

Therefore , the population of the city decreased by 6678 people from 2015 to 2020.

The given question is incomplete , the complete question is

In 2010, the population of a city was 212000. From 2010 to 2015, the population grew by 5%. From 2015 to 2020, it fell by 3%. How much did the population decrease from 2015 to 2020, to the nearest 100 people ?

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This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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Answer:

C. 12,000≤715m+645

Step-by-step explanation:

You want to have either equal to or more than 12,000

Answecr:

C

Step-by-step explanation:

According to the question, the line is through the points \((0,5)\) and \((-2,11)\)

To calculate the slope using standard formula that is :

\(m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(11-5)}{(-2-0)} =\frac{6}{-2} = -3\)

Now the slope equation will be: \(m(x(2)-x(1)) = (y(2)-y(1))\)

\(y-5 =(-3)(x-0) = y = -3(x)+5\)

The slope-intercept form is:\(y = -3x+5\)

What is the equation of the line?

To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.

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Answer:

x^2+x+1

Step-by-step explanation:

(3x^2+4x−1)+(−2x^2−3x+2)

Combine like terms

3x^2-2x^2+4x-3x-1+2

x^2+x+1

As per the volume, we need to to purchase 4 containers of punch.

To calculate the amount of punch required, we need to find the total volume of punch needed, which can be calculated as follows:

Total volume of punch = number of students * volume of punch per student

= 25 * 8 fluid ounces

= 200 fluid ounces

Now, we know that the punch is sold in half-gallon containers. One gallon is equal to 128 fluid ounces. Therefore, a half-gallon container is equal to 64 fluid ounces. We can use this information to find out how many containers of punch are needed:

Number of containers of punch = Total volume of punch / Volume of punch per container

= 200 / 64

= 3.125

Since we cannot purchase a fractional number of containers, we need to round up to the nearest whole number. Therefore, we need to purchase 4 containers of punch.

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The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

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The Statement which is true is (c) the smaller the standard deviation, the more concentrated the data will be.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.

The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same

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Answer:

the answer is c hope it help

Answer: D

Step-by-step explanation:

1. movethe constanat to the right

2. Calculate

3.The statement is false

Answer:

CB : HF

CA : HG

CD : HE

DA : EG

DB : EF

AB : GF

If the Triangle BCD is similar to triangle FHE. The three equivalent ratios based on the diagram will be CB: HF, CA: HG, and CD: HE.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

The similarity law for triangles is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

The equivalent ratios are based on the diagram will be,

CB: HF

CA: HG

CD: HE

DA: EG

DB: EF

AB: GF

Thus, if the Triangle BCD is similar to triangle FHE. The three equivalent ratios based on the diagram will be CB: HF, CA: HG, and CD: HE.

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