Find the formula for an exponential function that passes through the 2 points given

Okay, here we have this:

Considering the provided information. we are going to calculate the slope, and y-intercept of the line, so we obtain the following:

First we will calculate the slope using the following formula:

m=(y2-y1)/(x2-x1)

m=(80000-40000)/(10-5)

m=40000/5

m=8000

y-intercept:

y=mx+b

40000=(8000)5+b

40000=40000+b

b=0

Finally we obtain that the equation of the line is: y=8000x.

Let's graph the equation:

The witch can make her special brew 6 times with the amount of water present in the small frog pond.

Given that:-

Total amount of water present in the small frog pond = 7 and 1/2 cups = 15/2 cups

Amount of water the witch needs to make her special brew = 1 and 1/4 cups = 5/4 cups

We have to find the number of times Wendy the witch can make her special brew with the amount of water present in the small frog pond.

We know that,

Number of times the witch can make the brew = Total amount of water/Water needed for brew

Hence, by simple division, we can write,

Number of times the witch can make the brew = (15/2) ÷ (5/4) = (15/2)*(4/5) = 6 times.

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therefore, the answer is 70.08

Explanation

Step 1

first multiply as if there is no decimal

Step 2

count the number of digits after the decimal in each factor.

Step 3

Put the same number of digits behind the decimal in the product

therefore, the answer is 70.08

I hope this helps you

With each additional tree , the estimated time increases by 10 minutes .

in the question ,

a table with number of trees and time required to plant them is given .

For planting 1 tree 30 minutes is required to plant them .

for planting 2 trees 40 minutes is required to plant them .

increase in number of tree = 2 tree - 1 tree = 1 tree

change in time required = 40 min - 30 min = 10 min

for planting 3 trees , 50 minutes is required to plant them .

increase in number of tree = 3 trees - 2 trees = 1 tree

change in time required = 50 min - 40 min = 10 min

So, we can see that for every additional tree planted the time increases by 10 minutes .

Therefore , with each additional tree , the estimated time increases by 10 minutes .

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The formula for the nth term is expressed as

an = (an - 1)^2 - 3

This is a recursive formula

This means that the second term, a2 is

a2 = (a2 - 1)^2 - 3

a2 = (a1)^2 - 3

a2 = 4^2 - 3 = 16 - 3 = 13

a3 = (a3 - 1)^2 - 3

a3 = (a2)^2 - 3

a3 = 13^2 - 3 = 169 - 3 = 166

a4 = (a4 - 1)^2 - 3

a4 = (a3)^2 - 3

a4 = 166^2 - 3 = 27556 - 3 = 27553

Thus,

a4 = 27553

Given the word problem, we can deduce the following information:

1. Liz collected 16 cans, which is 20% of her goal.

To determine the number of cans that Liz needs to collect to reach her goal, we use below equation:

where:

x= total number of cans that Liz needs to collect

So,

Hence, the total number of cans is 80.

A.

To complete the double number line, we must determine first the other percent values. It the goal is 100%, we must subtract 20% from 100% and divide it by 4 to get the remaining percent values. So,

So the other percent values are:

0%

20%

20%+20%=40%

40%+20%=60%

60%+20%=80%

80%+20%=100%

To determine the amount of cans for each percent value,the process is shown below:

Therefore, the answer for double number line is:

Cans : 0 16 32 48 64 80

Percent : 0% 20% 40% 60% 80% 100%

B.

Based on the information gathered from A, for every 16 cans Liz collects, she adds 20% toward her goal. She will have 32 cans if she reaches 40% of her goal. Liz must collect 80 cans to reach her goal.

14)

Given data:

The given triangle.

As all the sides of the triangle are equal, it means all the angles are equal. The expression for the angle sum property of the triiangle is,

In the given triangle each angle is 60 degree, so it is an acute angle triangle.

Thus, the given triangle is an acute angle triangle, so first option is correct.

15)

The all sides and all angles of the triangle are equal.

Thus, the given triange is an equilateral triangle, so third option is correct.

The slope intercept form of equation is given as

(y - y1) = m(x - x1)

Where m = slope

From the equation: y + 5 = 2(x + 8)

Equate y + 5 = 0 and x + 8 = 0

y + 5 = 0

y = 0- 5

y = -5

For x + 8 = 0

x + 8 = 0

x = 0 - 8

x = -8

Hence, the point is (-8, -5)

The answer is (-8, -5)

Answer: ∠ABD = 19°

Step-by-step explanation:

The angle formed by ABC is a complementary angle. This means the sum of both angles adds up to 90 degrees.

Since angle DBC is 71 degrees, 90 - 71 equals ∠ABD

90 - 71 = 19

Therefore ∠ABD = 19°

Answer:

m∠ABD = 19°

Step-by-step explanation:

Hello!

Recall that all angles of a rectangle are 90° in measure.

Angle B is 90°, and is made up of angles ABD and DBC.

We know the measure of angle DBC, it's given as 71°. We can find the measure of ABD by subtracting 71° from 90°.

So the measure of angle ABD is 19°.

Answer:

32.50x + 7.50 < 235

Step-by-step explanation:

All the cost have to be less than 325.  x stands for the number of people buying tickets.

Answer:

5 complete cups and 7/8 of a cup

Answer:

23.4%

Step-by-step explanation:

[tex]\frac{18}{77} =\frac{x}{100}[/tex]

$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4

Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)

.

The coodinates of A(3,0) and after reflection A'(-3,0)

The coordinates B(1,4) and after reflection B'(-1,0)

The coordinates C(5,3) and after reflection C'(-5,3)

Plot the image on the graph

According to the given diagram, we have 4 shirts in total, where there's only one short-sleeve white shirt, so we just have to divide 1/4

Then, we multiply by 100 to express it in percentage

The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).

If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.

Then, we can write:

With the value of x, we can replace it in the fraction and know the value of it:

Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.

Given:

Quantum Logic recently expanded its operations at a cost of $450,000.

So, P = 450,000

The rate of growth = r = 8% = 0.08

compounded quarterly, n = 4

We will find the future value of the investment (A) after t = 5 years

We will use the following formula:

Substitute with the given values:

So, the answer will be:

The future investment = $668,676.33

Given:

Point (3,3)

The equation of the line,

To find the equation of the line that passes through (3,3) and is perpendicular to the line:

The perpendicular slope is,

Using the point-slope formula,

Hence, the equation of the line is,

Let us find the intercepts.

When x=0, we get y=8

So, the y-intercept is (0,8).

When y=0, we get

So, the x-intercept is (4.8,0).

Hence, the correct option which satisfies the equation of the line is D (last option).

Answer:

Step-by-step explanation:

The answer is C

Answer:All three 1. to compare groups, not individuals2. to lessen the influence of outliers3. to clearly see trends

Explanation:edge 2022

To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).

A skier travels for 4 seconds and covers 72 meters.

Constant Rate (Speed):

Determining the distance covered in 2 minutes:

Step 1: Convert the time in minutes into seconds.

Step 2: Multiply the time by the constant rate (speed) of the skier.

Therefore, in 2 minutes, the skier travels 2,160 meters.

-4

Explanation:

6+[(-9)+(-1)]

Open the bracket:

6 + (-9) + (-1)

Note: Multiplication of opposite signs give a negative number.

6 - 9 - 1

= 6 - 10

= -4

The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives

Then, the answer is the last option: 120

Total number of student 20.

Total number of fruits are 4.

The theoretical probability that a student will choose a banana is 0.25

The experimental probability is 1/20=0.05.

Thus there is a huge difference in the theoritical probability and experimental probability.

Thus the experimental probability get closer to the theoretical probability is:

A. only give two choices of fruit.

Given:

The function f(x) = 3cos(x) - 2.

Required:

What are the minimum and maximum value of function?

Explanation:

To check maximum and minimum value of function.

First derivate the original function.

After putting first derivative equal to zero, critical points can be found.

Then, do second deritvative to check points of maxima and minima.

The critical points at which second derivative greater than zero. Point will be of minima.

The critical points at which second derivative less than zero. Point will be of maxima.

So,

Now, do second derivative test for maximum and minimum points

Answer:

We have the following:

We can know when they are congruent, since being congruent they are equal sides.

By notation we know that " ' " means that they are the same, therefore

And the parallel lines are:

Therefore, the answer is B.

In quadrilateral ABCD, AB is congruent to CD and AB is parallel to CD. show that ABCD is a parallelogram

Problem

-1.1x + 6.4 > - 1.3

Concept

Solve for x by collecting like terms.

There is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Given,

A data set includes weights of garbage discarded in one week from 62 different households.

significance level of α=0.05.

Now, According to the question:

The correlation​ matrix provided is:

Variables    Paper     Glass

 Paper           1         0.1853

Glass        0.1853         1

The hypothesis for the test is:

H₀: ρ = 0 vs. H₀: ρ ≠ 0

The test statistic is:

r = 0.1983 ≈ 0.198

As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.

The critical value for the two-tailed test is:

[tex]r_{alpha}/2, (n -2) = r_{0.005}/2 ,(62-2) = 0.250[/tex]

The conclusion is:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

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Answer

She burnt 181 calories in that first 10 minutes of the 5,000 meter race.

Explanation

Bella wrote the equation that relates her calories burnt (c) to number of minutes (m) she has run as

c = 18.1m

The question then asks us to find how much calories she burnt in the first 10 minutes of the 5,000 meter race.

That is, find c when m = 10 minutes

Recall,

c = 18.1m

c = 18.1 (10)

c = 181 calories.

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Answer

x = 2, and y = 3

Explanation:

given the following linear equation

7x - 6y = -4------------- equation 1

14x + 5y = 43 ---------- equation 2

This equation can be solve simultaneously by using elimination method

Step 1 : eliminate x

To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1

7x * 2 - 6y * 2 = -4 * 2

14x * 1 + 5y * 1 = 43 * 1

14x - 12y = -8 ----------------- equation 3

14x + 5y = 43------------------ equation 4

Substract equation 4 from3

(14x - 14x) - 12 - 5y = -8 - 43

0 - 17y = -51

-17y = -51

Divide both sides by -17

-17y/-17 = -51/-17

y = 51/17

y = 3

To find x, put the value of y into equation 1

7x - 6y = -4

7x - 6(3) = -4

7x - 18 = -4

Collect the like terms

7x = -4 + 18

7x = 14

Divide both sides by 7

7x/7 = 14/7

x = 2

Therefore, x = 2 and y = 3

From the diagram,

CD is corresponding to WR

VW is corresponding to BC

RS is corresponding to DE

ST is corresponding to EF

TU is corresponding to FA

Final answer