Use the following two points to answer parts a -c . (2, 3) , (- 1, - 6) a. Find the slope of the line passing through the two pointsb . Write an equation of a line passing through the two points in point slope form . c . Rewrite the equation of the line in slope -intercept form .

Answer:

The amount invested at 8% was $11,000

The amount invested at 9% was $19,000

Step-by-step explanation:

Let the variable x represent the amount in $ invested at 8% and let y be the amount in $  invested at 9%

Total amount invested:
x + y = 30000   [1]

8% = 8/100 = 0.08

9% = 9/100 = 0.09

Interest at 8% on $x = 0.08x

Interest at 9% on $x = 0.09x

Total Interest :

0.08x + 0.09y = 2590  [2]

Using equations [1] and [2] we can solve for x and y

We have

x + y = 30000   [1]
0.08x + 0.09y = 2590  [2]

Multiply equation 1 by 0.08 to get
0.08x + 0.08y = 0.08(30,000)

0.08x + 0.08y = 2,400  [3]

Subtract [3] from [2] :

0.08x + 0.09y = 2590  
-
0.08x + 0.08y = 2400  
----------------------------------
       0x + 0.01y = 190

Divide both sides by 0.01
0.01y/0.01 = 190/0.01

y = = 19,000

Use [1] to get value of x

x + y = 30,000

x + 19,000 = 30,000

x = 30,000 - 19,000

x = 11,000

The p-value of the test corresponding to study a was found to be 0. 40. and the p-value for study b is 0.80

The entire area under the crucial range of values on both sides of the curve in a two-tailed test represents the likelihood of occurrence (negative side and positive side)

As a result, the connection below provides the probability values for a two-tailed test when compared to a one-tailed test.

Here

By replacing the supplied value in the previous equation, we obtain -

values of the probabilities for a two-tailed test

p-value = P (alpha/2) +  P (alpha/2)

p-value = 0.40 + 0.40

            =0.8

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1) Area of patio = 1/2 base x height

Height = 3.1ft

base = 7 + 10 =17 ft

Area = 1/2 x 3.1 x 17

Area of patio = 26.35 square ft

1 yard = 3 ft

1 square yard = 9 square ft

so the area of the patio in yard is

26.35/9 = 2.927777778 square yard

2) Cost of concrete = $10/square yard poured 1/9 yard deep+ $60 delivery fee

for 2.9277777778 square yard it will cost 1/9($10 x 2.9277777778) + $60 =$

3)

Type 1 error is the error occurs when a test indicates a significate  difference between two or more populations.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes. The significance level you select (alpha or ) determines the likelihood that you will make this mistake.

Data cleansing—also known as data cleaning, data scrubbing, or data rectification—is the process of correcting inaccurate, insufficient, duplicate, or other wrong data in a data set. It entails locating data mistakes and then correcting them by modifying, updating, or eliminating data.

Using independent samples from two independent groups, the two-sample (independent groups) t-test is used to assess whether the unknown means of two populations are different from one another.  

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√12

Explanation:

though it may not be a simplification,

2√3

can be shown as

√12

.

2=√4

Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below

The statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.

In the given statements

There are no outliers in this distribution.

The shape of the boxplot is fairly symmetric.

The range of the distribution is around 60 cm.

The center of the distribution is around 180 cm.

The statement "The range of the distribution is around 60 cm" is true.

The range is the spread of your data from the lowest to the highest value in the distribution.

In the given graph

Range=200-140

=60

So it is true.

The center of the distribution is around 180 cm is also true.

Hence the statements The range of the distribution is around 60 cm and

the center of the distribution is around 180 cm are true.

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Given:

Principal (p) =$3,000

Time (T) = 48 months = 4 years

Interest rate = 4.5%

Required :

Ending balance = ?

The simple interest :

Ending balance :

Ending balance = $ 3540

There are 264 red marbles in a bag.

What is Marbles?

A marble is a tiny, sphere-shaped object that is frequently fashioned of agate, glass, clay, steel, or plastic. They come in a variety of sizes, but the most have a diameter of about 13 mm (12 in). These toys can be made into works of art or utilized in a variety of marble-based activities. They can also be used in races or runs. They are frequently collected for their pleasing colors and nostalgic appeal.

Let x = Number of red marbles

y = Number of black marbles.

A bag contains 275 marbles.

So, x + y = 275             ..(1)

There are 24 red marbles for every black marble.

x = 24y       ..(2)

Plug value of x in equation (1).

24y + y = 275

25y = 275

y = 11

Put y = 11 in equation (2),

x = 24(11)

x = 264

Hence, there are 264 red marbles in the bag.

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Answer:

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

[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]                                              Given

[tex]3(ax+b)=4(x+c)[/tex]                                     Cross-multiply

[tex]3ax + 3b=4x+4c[/tex]                                       Distribute

[tex]3ax-4x=4c-3b[/tex]                                       Collect terms with x

[tex]x(3a-4)=4c-3b[/tex]                                       Factor out x

[tex]x=\cfrac{4c-3b}{3a-4}[/tex]                                                   Divide both sides by 3a - 4

We can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.

So, according to the given image, we can easily say that Germany has a negative correlation.

We can observe that the slope of the regression equation is negative.

Therefore, we can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.

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Answer:

plan b

Step-by-step explanation:

unless your making 120 calls or more plan B is better

24-18=6

6/0.05

=120

The average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².

Given in the question is:

Since the ball started from rest

Initial velocity; u= 0m/s

Final velocity; v = 14.7 m/s

Time taken for the golf ball to hit the sidewalk; t = 1.5 s

Average Acceleration; g =?

To determine the average acceleration of the golf ball, we use the First Equation of Motion:

v = u + at

The Equation will be :

v = u + gt

Plug the all values in above equation:

14.7m/s = 0 + g x 1.5 s

g =  14.7 / 1.5

g = 9.8m/[tex]s^2[/tex]

Therefore, the average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².

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The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)

Linear equation can be represented in different form such as point slope form, slope intercept form  and standard form.

Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.

Hence,

y - y₁ = m(x - x₁)

where

Therefore,

m = slope = -1

using (-12, 15)

Hence,

y - 15 = - 1(x - (-12))

Therefore,

y - 15 = - 1(x + 12)

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the answer is 5896. . . . . . ... . . . . . ......................

Hello!

When multiplying 67 x 88, the correct answer would be 5896.

Hope this helped!

Based on the amount you have received in grants, and the amount the boss wants to increase it to, the increase the new amount represents over the previous amount is $15,000 or 33.3%.

Your boss wants to increase the grants to $60,000 from the current amount of $45,000.

This means that the new amount will represent an increase over the previous amount by:
= 60,000 - 45,000

= $15,000

In percentage terms this is:
= Increase over previous amount / Previous amount x 100%

= 15,000 / 45,000 x 100%

= 33.3%

In conclusion, the difference between the grants applied for in the past 5 years and the amount the boss is asking for, gives the increase of $15,000.

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The original equation is:

5 x^2 + (10 x^2 + 10) = 3 x^2 - 5

The first step the person did was:

15 x^2 + 10 = 3 x^2 - 5

so in this first step the person used the associative property of addition by associating 5 x^2 with 10 x^2 and combining them to give 15 x^2.

Please check if there is an option that states such among your options.

Answer:

3

Step-by-step explanation:

the size of the wedge for aqua pencils is 43°

Given:

A table showing the pencil collection

To find:

the portion that represents the aqua pencils in degree

The total number of pencils = 23 + 106 + 62 + 47 + 32

The total number of pencils = 270

In degrees:

Total angle in a circle = 360°

Size of the wedge for aqua = number of aqua pencils/total pencils × 360°

To the nearest degree, the size of the wedge for aqua pencils is 43°

There are 54% of the participants are female.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage

Given:
There are 104 males and 121 females

participating in a marathon.

So, the total number of participants are,

104 + 121 = 225.

There are 225 total number of participants.

So, the percent of the female are,

[tex]\frac{121}{225} (100) = 53.78[/tex]

Therefore, the percent of the participants of female are 54%.

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Note that a line whose equation is in the form :

has a slope of m

and a y-intercept of b

Slope is also equal to rise/run :

where rise is the number of vertical units between two points and run is the number of horizontal units between two points.

Note also that upward and right movement is positive, downward and left movement is negative.

From the figure, the vertical units between two given points is 3 units upward, so this is positive.

The horizontal units between them is 2 units to the right which is also positive.

The slope will be :

Next is to solve for b (y intercept).

y-intercept is the point where the line intersects the y-axis.

From the graph, the lines intersects at point (0, 2) on the y-axis

Therefore, the value of b is 2

Rewriting the equation, the answer is :

Answer:

249.40

Step-by-step explanation:

The transformation on a line such that a line is obtained which is pependicular to previous line is possible only when it is reflected through y = x axis. This can be understood as,

When line is reflected about x-axis, the x coordinate remain same where as y-coordinate changes in opposite sign with same magnitude. So reflection of line x = 3 about x axis remain same.

Simillarly reflection of line x = 3 about x = 1 remain same as x = 3.

The reflection of line x = 3 about y-axis results n a parallel line passing through x = -3.

So answer is reflection across y = x.

Answer:

[tex]m[/tex]perpendicular = 6

Step-by-step explanation:

Hope this helps! :))

Two triangles are similar if the ratio of their corresponding side equal'

Triangle

Because

Corresponding sides are

Therefore,

Triangle

Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.

As given in the question,

Given equation :

|x – 55| = 4.2

To determine the maximum and minimum speed in miles per hour from the given equation we have,

x-55 = 4.2 or x-55 =-4.2

Add 55 both the side of the equation,

x-55 +55 =4.2+55  or x-55+55 = -4.2 +55

x =59.2 or x = 50.8

Maximum speed is 59.2 determine by equation x-55 = 4.2

Minimum speed is 50.8 determine by equation x-55 = -4.2

Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to

x -55 =4.2.

The complete question is:

On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?

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Answer:

3.44571

Step by step explanation:

3.44570830811

8 is the number next to the place value of hundred-thousandth, so we round it up to 1 and add it to 0

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The negative sign means that temperature decreases of fell.

Deteremine the change in temperature for 5 hours.

So temperatute fell 4 degrees. Option C is correct.

(1) The graph is attached with the answer below.

(2)The equation of the line is y = x + 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The points are ( 3, 0 ) and ( 0, 3). The slope of the line will be calculated as:-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 3 - 0 ) ( 0 - 3 )

Slope = 1

Calculate the y-intercept,

y = mx + c

3 = 0 + c

c = 3

The equation of the line will be:-

y = x + 3

Therefore, the graph is attached with the answer below the equation of the line is y = x + 3.

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