Solve the system of equations. ​ 2y+7x=−5 5y−7x=12 ​

Answers

Answer 1

[tex]\text{Solve the systems of equations:}\\\\2y+7x=-5\\5y-7x=12\\\\\text{Solve by adding and subtracting}\\\\7y=7\\\\\text{Divide}\\\\y=1\\\\\text{To find x, plug 1 into y in one of the equations and solve:}\\\\2(1)+7x=-5\\\\2+7x=-5\\\\\text{Subtract 2 from both sides}\\\\7x=-7\\\\\text{Divide by 7}\\\\x=-1\\\\\boxed{y=1\,\,and\,\,x=-1}[/tex]


Related Questions

In accounting, a company's gross profit rate measures how well the company controls cost of goods sold to maximize gross profit. The gross profit rate, PPP, is calculated using the formula P = \dfrac{S - C}{S}P= S S−C ​ P, equals, start fraction, S, minus, C, divided by, S, end fraction, where SSS is the net sales and CCC is the cost of goods sold. Rearrange the formula to solve for the cost of goods sold (C)(C)left parenthesis, C, right parenthesis. C=C=C, equals What is the cost of goods sold if the net sales is \$1{,}200{,}000$1,200,000dollar sign, 1, comma, 200, comma, 000 and the gross profit ratio is 0.20.20, point, 2? Round your answer, if necessary, to the nearest dollar. C=C=C, equals dollars

Answers

Answer:

$960,000

Step-by-step explanation:

The gross profit rate of the company is expressed as [tex]P = \dfrac{S - C}{S}[/tex] where C is the cost of goods sold and S is the net sales. If the net sales S = $1,200,000, and gross profit ratio is 0.20, the cost of goods sold will be expressed as shown;

Making C the subject of the formula from the expression given.

[tex]P = \dfrac{S - C}{S}\\\\cross \ multiply\\\\SP = S-C\\\-C = SP-S\\\\C = S -SP\\[/tex]

Substituting P = 0.20 and S = $1,200,000 into the resulting equation, we will have;

[tex]C = $1,2000,000 - 0.2($1,2000,000)\\C = $1,2000,000- 240,000\\ C = 960,000[/tex]

Hence the cost of goods sold is $960,000

a lottery offers one $1000 prize one $500 and two $50 prizes. one thousand tickets are sold at $2.50. what is the expectived profit

Answers

Answer:

 $900

Step-by-step explanation:

To begin with let us estimate the total cash value of the prices

$1000 x 1= 1000

$500 x 1=  500

$50 x 2= 100

Total = $1600

Now let us calculate the total cost of tickets sold at $2.50 per tickets for 1000 tickets

2.5*1000= $2,500

Assuming worse case that the lottery had winners in all three categories and i.e the total prices given out is $1600

Then the expected profit is = $2,500-$1600= $900

Suppose 65% of people in Georgia support a special transportation tax. Alejandro is not confident that this claim is correct. To investigate the claim, he surveys 150 people in his community and discovers that 78 people support a special transportation tax.
A. calculate sample proportion.
B. calculate standard error of the sample proportion, (SE). Give answer to three decimal places
C. Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.

Answers

Answer:

C

Step-by-step explanation:

Calculate the standard error of the sample proportion estimate. (SEest.) Give your answer to three decimal places.

A. The sample proportion is 0.52.

B. The standard error of the sample proportion is approximately 0.041.

C. The standard error of the sample proportion estimate is approximately 0.041.

A. To calculate the sample proportion, we divide the number of people who support the special transportation tax (78) by the total number of people surveyed (150):

Sample proportion = 78 / 150 = 0.52

B. To calculate the standard error of the sample proportion (SE), we use the formula:

[tex]SE = \sqrt{(p * (1 - p)) / n}[/tex]

where p is the sample proportion and n is the sample size. Substituting the values into the formula:

[tex]SE = \sqrt{(0.52 * (1 - 0.52)) / 150}\\\\SE = \sqrt{0.2496 / 150}\\\\SE = \sqrt{0.001664}\\\\SE = 0.0407[/tex]

Therefore, the standard error of the sample proportion is approximately 0.041 (rounded to three decimal places).

C. The standard error of the sample proportion estimate (SEest) is the same as the standard error of the sample proportion (SE) calculated in part B. Hence, the standard error of the sample proportion estimate is also approximately 0.041 (rounded to three decimal places).

To know more about proportion, refer here:

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#SPJ2

is -2.75 an integer?

Answers

Answer:

yes

Step-by-step explanation:

every negative any positive number is an integer

Answer:

Step-by-step explanation:

No.  Integers do not have fractions in them.

-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer

A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with a mean 0.499 in. and standard deviation 0.002 in. What percentage of bearings will now not be acceptable

Answers

Answer:

the percentage of  bearings   that will  not be acceptable = 7.3%

Step-by-step explanation:

Given that:

Mean = 0.499

standard deviation = 0.002

if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.

Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )

= ( 0.496 , 0.504)

If x represents the diameter of the bearing , then the probability for the  z value for the random variable x with a mean and standard deviation can be computed as follows:

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]

[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]

[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]

From the standard normal tables

[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]

[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]

By applying the concept of probability of a  complement , the percentage of bearings will now not be acceptable

P(not be acceptable)  = 1 - P(acceptable)

P(not be acceptable)  = 1 - 0.927

P(not be acceptable)  = 0.073

Thus, the percentage of  bearings   that will  not be acceptable = 7.3%

17. In figure, BAC -859, CA = CB and BD - CD. Find the measure of ZX, Zy and Zz. Give
reasons to support your answer.
A
85°
ب
B
H
V​

Answers

Answer:

x = 10°, y = 10° and z = 160°

Step-by-step explanation:

Given : m∠BAC = 85°

            CA ≅ CB and BD ≅ CD

In the given ΔABC,

Since, CA ≅ CB

Angles opposite to these equal sides will be equal in measure.

m∠BAC ≅ m∠ABC ≅ 85°

Since, sum of interior angles of a triangle = 180°

m∠BAC + m∠ABC + m∠BCA = 180°

85° + 85° + m∠BCA = 180°

m∠BCA = 180° - 170°

m∠BCA = 10°

x = 10°

In ΔBDC,

Since, BD ≅ DC [Given]

Opposite angles to these equal sides will be equal in measure.

Therefore, x° = z° = 10°

Since, x° + y° + z° = 180°

10° + y° + 10° = 180°

y = 180 - 20°

y = 160°

We have to accept or reject a large shipment of items. For quality control purposes, we collect a sample of 200 items and find 24 defective items. Construct a 95% percent confidence interval for the proportion of defective items in the whole shipment.

Answers

Answer:

A 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                             P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of defective items = [tex]\frac{24}{200}[/tex] = 0.12

            n = sample of items = 200

            p = population proportion  of defective items

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                      of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95

95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

  = [ [tex]0.12-1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] , [tex]0.12+1.96 \times {\sqrt{\frac{0.12(1-0.12)}{200} } }[/tex] ]

 = [0.075, 0.165]

Therefore, a 95% confidence for the population proportion of defective items in the whole shipment is [0.075, 0.165] .

I will rate you brainliest!

Answers

Answer:

B

Step-by-step explanation:

X must not be equal to -6, -1, 1 or 3

Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25

x y
1 5
2 20
3 45
4 80
5 125

x y
1 5
2 25
3 125
4 625
5 3125

x y
1 2
2 4
3 7
4 16
5 32​

Answers

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

Linear function

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

At x = 1, y = 5 and;

Slope = 5/1 = 5

At x = 2; y = 10 and;

Slope = 10/2 = 5

At x = 3, y = 15 and;

Slope = 15/3 = 5

At x = 4, y = 20 and;

Slope = 20/4 = 5

At x = 5, y = 25 and;

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

Read more about Linear function at; https://brainly.com/question/15602982

1. What is the difference between an exponential growth and exponential decay? 2. What is an example equation for expoential growth and an example equation for exponential decay?

Answers

Answer: see below

Step-by-step explanation:

The standard form of an exponential equation is: y = a(b)ˣ    where

a is the initial valueb is the rate

Growth:

Exponential growth is where the final value (y) is greater than the initial value (a).

An example would be the spreading of a rumor:  

You tell 1 person (a = 1) who then tells 2 people each minute (b = 2).  How many people will they have spread the rumor to after 5 minutes (x = 5)?

y = 1(2)⁵

  = 32

Decay:

Exponential decay is where the final value (y) is less than the initial value (a).

An example would be the decrease of bacteria in a person:

A person has 100 bacteria (a = 1) who takes a pill that is supposed to cut in half the number of bacteria each hour (b = 1/2).  How many bacteria will the person have after 2 hours (x = 2)?

[tex]y=100\bigg(\dfrac{1}{2}\bigg)^2\\\\\\.\quad =100\bigg(\dfrac{1}{4}\bigg)\\\\\\.\quad = 25[/tex]

A recipe calls for 2 tablespoons of sugar for every 7 tablespoons of flour. If you plan on tripling the recipe what is the ratio of
sugar to flour?
-0)
A)
2 to 7
B)
2 to 21
5 to 10
DY
5 to 7

Answers

Answer:

It is still 2 to 7

Step-by-step explanation:

It is still 2 to 7 because if you triple the recipe, it will become 6 to 21 which still simplifies to 2 to 7.

8) The perimeter of a rectangle is 20x2 + xy - 7y2 and one of it's sides is
7x2 - xy. Find the other side.

Answers

Answer:

3x^2 + 3xy/2 - 7xy^2/2

Step-by-step explanation:

So we know the perimeter is 20x^2 + xy - 7y^2,

To find any perimeter you need 2l + 2w = P so,

One of the sides is 7x^2 - xy

First plug in the values,

2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2

Multiply,

14x^2-2xy + 2w = 20x^2 + xy - 7y^2

Subtract,

14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy

2w = 6x^2 + 3xy - 7y^2

w = 3x^2 + 3xy/2 - 7xy^2/2

The top speed of this coaster is
128 mph. What is the tallest peak
of this coaster?
** Hint... convert mph into m/s.*​

Answers

To convert miles per hour to meters per second divide by 2.237

128 miles per hour / 2.237 = 57.22 meters per second.

Using the first equation:

57.22 = sqrt(2 x 9.81 x h)

Remove the sqrt by raising both sides to the second power:

57.22^2 = (2 x 9.81 x h)

Simplify Both sides:

3274.1284 = 19.62h

Divide both sides by 19.62:

H = 3274.1284/ 19.62

H = 166.88 meters

PLEASE HELP ME ASAP On a test, the average score of 25 boys and 15 girls is 68 points. The average test score of the boys is 62 points. What is the average score of the girls? SHOW YOUR WORK

Answers

Answer:

74

Step-by-step explanation:

The average score of boys and girls is 68 and boys is 62

Think of it as an equation (62 + x)/2 = 68, where x is the average score of girls

First multiply each side by 2 making the equation 62 + x = 136

Now subtract each side by 62, which will make the average score for girls 74

(x = 74)

The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line?

Answers

Answer:

-4

Step-by-step explanation:

Hey there!

Well the slopes of 2 parallel lines have the same slope,

meaning if the green line has a slope of -4 then the slope of the red line has a slope of -4.

Hope this helps :)

If a person earns $8.74 per hour, estimate how much the person would earn per year. Assume a person works 40 hours per week and 50 weeks per year.


Answers

Answer:

$17,480 per year.

Step-by-step explanation:

Amount earned per hour = $8.74

If a person works for 40 hours every week for 50 weeks in a year, number of hours worked in a year = [tex] 40hrs*50weeks = 2000 hrs [/tex]

Estimated amount earned per year by the person = [tex] 2000hrs * 8.74 dollars [/tex]

= $17,480 per year.

The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend

Answers

Answer:

The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].

Step-by-step explanation:

The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:

[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]

[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]

[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]

[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]

The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].

Answer:

A

Step-by-step explanation:

1 liter of ink can print 5000 pages of text. If you had 100 gallons of ink then how many pages
could you print?

Answers

100 gallon / 0.264 = 378.541 liter
378.541 * 5000 = 1892705 pages

Will mark the brainliest i havent chosen an answer but I pressed accidentally

Answers

The full answer is 20.125 but it says to round so the answer is C. 20.13

Answer:

The full answer is 4.40625 but rounded it would be 4.41

How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9?

Answers

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.

For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.

Answers

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

During the school year, there were 315 total points scored between basketball, soccer, baseball, and football. The baseball team scored 55 points. The soccer team scored twice as much as the baseball team. The football team scored 0.5 more than 1.5 times as much as the baseball team. How many points did the basketball team score?

Answers

Answer:

67.5p.

Step-by-step explanation:

315p in total.

- Baseball has 55p.

- Soccer teams points = 55x2 = 110p.

-  Football team points = 110 x 0.5 = 55 x 1.5 = 82.5p.

So then you just do 315p - 82.5p - 55p - 110p = 67.5p

The perpendicular bisectors of ΔKLM intersect at point A. If AK = 25 and AM = 3n - 2, then what is the value of n?

Answers

Answer:

n = 9 is the answer.

Step-by-step explanation:

Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.

AK = 25 units and

AM = 3n -2

To find:

Value of n = ?

Solution:

First of all, let us learn about perpendicular bisectors and their intersection points.

Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.

And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.

We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.

i.e.

Circumcenter of a triangle is equidistant from all the three vertices of the triangle.

In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].

Please refer to the attached image for the given triangle and sides.

The distance of A from all the three vertices will be same.

i.e. AK = AM

[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]

Therefore, n = 9 is the answer.

It keeps saying my answer is wrong after i identified the GCF as 3 but maybe I typed it wrong.

Answers

Answer:

3(9t^5-7p^4)(9t^5+7p^4)

Step-by-step explanation:

243 t^10 - 147 p^8

3 ( 81 t^10-49 p^8 )

Then we need to factor what is in the parentheses

3 ( ( 9t^5) ^2 - ( 7p^4) ^2)

This is the difference of squares  ( a^2 -b^2) = ( a-b) (a+b)

3(9t^5-7p^4)(9t^5+7p^4)

Finding the perimeter or area of a rectangle given one of th
The length of a rectangle six times its width.
If the area of the rectangle is 150 cm”, find its perimeter.

Answers

Answer:

The answer is 70cm

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

The length of a rectangle six times its width which is written as

l = 6w

Area = 150cm²

Substitute these values into the formula for finding the area

That's

150 = 6w²

Divide both sides by 6

w² = 25

Find the square root of both sides

width = 5cm

Substitute this value into l = 6w

That's

l = 6(5)

length = 30cm

So the perimeter of the rectangle is

2(30) + 2(5)

= 60 + 10

= 70cm

Hope this helps you

If Tristan wants to stretch the spring by 9 inches, how many kilograms of weight must he apply to it? I need help with it please.

Answers

Answer:

9/3 = 3x/3

3 = x

The spring stretches 9 inches with 3 kilograms of weight attached to it

Step-by-step explanation:

Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:

y = 3x

9 = 3x.

Divide both sides of the equation by 3

Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.

Step-by-step explanation:

Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:

y = 3x

9 = 3x.

Divide both sides of the equation by 3:

   

The spring stretches 9 inches with 3 kilograms of weight attached to it.

What is the approximate value of x in –2 ln (x + 1) − 3 = 7?

Answers

Answer:

x = 1/e^-5 - 1

Step-by-step explanation:

–2 ln (x + 1) − 3 = 7

–2 ln (x + 1) = 10

ln (x + 1) = –5

x + 1 = e^-5

x = e^-5 - 1

x = 1/e^-5 - 1

the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:

1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.

2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.

3. Simplify: -2 ln(x + 1) = 10.

4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.

5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.

6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.

7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.

8. Simplify: x ≈ -0.9933.

Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

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In the game plan for model building on your multiple regression project, which of the following is true about the test that determines whether the interaction term(s) is/are significant in predicting y?
A. It will definitely be a t-test
B. It will either be a t-test or a best subset for partial) F-test depending on whether we kept or dropped the quadratic terms
C. It will definitely be a partial F-test
D. It will definitely be a global

Answers

Answer:

A. It will definitely be a t-test

Step-by-step explanation:

T-test is a type of inferential statistic test which used to determine whether there is a significant difference between mean of two group sets or variables.The t-test technique is widely used in hypothesis testing in statistics.  When the model building for game play is determine through regression analysis, it will require t-test to be conducted to reach a conclusion.

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A standard I.Q. test produces normally distributed results with a mean of 100 and a standard deviation of 15 for the city of New York. Out of approximately 8,400,000 citizens, how many of these people would have I.Q.s below 67?

Answers

Answer:

approx  193200

Step-by-step explanation:

As known for normal distribution is correct the rule 95.4% of the results are situation within mean+-2*s  ( where s is a standard deviation)

So the border is 100+-2*15=70 and that is approx=67.

95.4% of 84000000 citizens are= 8 400 000*0.954=8013600 persons

So the residual number of the citizens =8400000-8013600=386400 citizens

Because of the simmetry of normal distribution to find the number of the citizens that have IQ below 67 we have to divide 386400 by 2.

N=386000/2=193200

A slope triangle for line l is shown on the graph below. If the
slope of the line is 4/3 what is the value of w?

Answers

Answer:

9

Step-by-step explanation:

What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.

We can now use a proportion to find the value of w.

[tex]\frac{4}{3} = \frac{12}{x}[/tex]

Cross multiply:

[tex]12\cdot36 = 36\\\\36\div4=9[/tex]

Hope this helped!

Answer: 9

Step-by-step explanation:

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