Rick's **deposit** in first 3 weeks is $39

1. Rick's **deposit** in the second week = 3 times($3)

= 3(3)

= 9

= [tex]3^{2}[/tex]

The **exponential expression** for Rick's 2nd week deposit = [tex]3^{2}[/tex]

Where, Base = 3

Exponent = 2

2. Rick's deposit in 1st week = $3

Rick's deposit in 2nd week = 3 (3) = $9

Rick's deposit in 3rd week = 3 (9) = $27

Rick's deposit in first 3 weeks = 3+9+27

= $39

Rick's deposit in all in the first 3 weeks is $39

3. Rick's deposit for 15 weeks = [tex]3^{15}[/tex]

= $1,43,48,907.

We know, no. of weeks in a year = 52

Rick's deposit for 52 weeks ( 1 year ) = 52 times of 3

[tex]=3^{52}\\= 6.4610819e+24[/tex]

Since this is a huge number , Rick cannot keep up this savings plan for a year.

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Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.

What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.

The 95% confidence interval for this population **proportion **is (0.10, 0.23).

A **confidence **interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The **proportion **of likelihood, or certainty, that the confidence **interval **would include the real population parameter when a random sample is drawn several times is referred to as the **confidence **level.

**Sample **size n = 125

number of people who planned to take an **extended** vacation = 21

sample **proportion **p = 21/125 = 0.168

**Confidence **level = 0.95

**significance **level α = 1-0.95 = 0.05

Z score =[tex]Z_{\alpha 2}[/tex] = Z(0.05) = 1.96, from Z table.

The confidence interval for **population** proportion is-

p±[tex]Z_{\alpha 2}[/tex] x √{p(1-p)}/n =0.168±1.96 x 0.168 x √{(1-0.168)}/125

=0.168±1.96 x 0.0334

=0.168±0.0655

=(0.1025, 0.2335)

=(0.10, 0.23)

Therefore, the **confidence **interval is (0.10, 0.23).

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Match each step on the left with the procedure at that step on the right.

Step 1 a. calculate p-value

Step 2 b. write claim symbolically

Step 3 c. compare p-value to alpha

Step 4 d. reject or fail to reject null

Step 5 e. write null and alternative hypotheses

Step 6 f. write conclusion

Step 7 g. calculate test statistic

Step 8 h. identify test type and relevant statistic

the test type and** relevant statistic,** which will depend on the data and the **hypothesis being tested.**

Step 1 - g. calculate test statistic

Step 2 - b. write claim symbolically

Step 3 - c. compare p-value to alpha

Step 4 - d. reject or fail to reject null

Step 5 - e. write null and alternative hypotheses

Step 6 - f. write conclusion

Step 7 - a. calculate p-value

Step 8 - h. identify test type and relevant statistic

Step 1: Calculate the test statistic, which is a numerical measure of how likely the data is under the null hypothesis.

Step 2: Write the claim symbolically, which is a statement of what you are attempting to prove.

Step 3: Compare the p-value to the alpha level, which is the significance level of the test.

Step 4: Reject or fail to reject the null hypothesis, depending on whether or not the p-value is less than the alpha level.

Step 5: Write the null and alternative hypotheses, which are statements that describe the data and are used to test a hypothesis.

Step 6: Write a conclusion, which is a statement about the data based on the results of the test.

Step 7: Calculate the **p-value**, which is the **probability of obtaining **a result as extreme or more extreme than what was observed in the data, given that the null hypothesis is true.

Step 8: Identify the test type and **relevant statistic**, which will depend on the data and the **hypothesis **being tested.

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125x ^ 3 - 27 = 0

Solve this by grouping

The solution to the **equation** 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical **expression** that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the **equation** 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of **cubes** can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

**Polynomial** 25x^ 2 +15x+9 is not **factored** since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Why did he write (x+4), even though the root

is at negative 4?

The **reason **behind this is that when the **negative **root goes from the RHS to LHS, its sign gets converted, and it appears like (x + 4).

A 2nd equation in x is known as a **quadratic **function. Ax2 + bx + c = 0 is the quadratic **equations **in standard form, wherein there a and b are the coefficient, x is the constant, and c is the **constant**.

The **presence **of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.

As per the given information in the question,

The root obtained is -4 or,

We can also write this thing as,

x = -4

So, when -4 will come to the **LHS **the sign will be converted to **positive**, and then it can be written as (x + 4).

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A recent survey found that about 73.2% of all gasoline purchases at a certain service station chain are paid with a credit or debit card. If 250 gasoline purchases completed at this chain are randomly selected, find the probability that at most 195 of those purchases are paid with a credit or debit card. • Use Excel to find the probability, rounding your answer to four decimal places.

The **probability** that **at most** 195 of those purchases are paid with a credit or debit card i.e P(X ≤ 195 ) is 0.9625..

We have given that,

**Sample size** , n=250

Sample proportion, p= 73.2% = 0.732

np = 183

n(1-p) = 67

both np & n(1-p) values are **greater than** 5, So **normal approximation** is applicable

mean, µ = np = 183

**std.**** dev,** σ = √np(1-p) =√250×0.732 ×(1-0.732) =7.0031

we have to calculate probability that at most 195 of those purchases are paid with a credit or debit card i.e **P(X ≤ 195 ) **

= P( X < 195.5 )

= P((x - µ) / σ < (195.5 -183)/ 7.0031)

= P( Z < 1.78 )

= 0.9625

Required probability using **Excel ****function **,

Excel command: **=NORM.S.DIST(z,1)**

= Norm.S.DIST(1.78,1)

= 0.9625

Hence, required probability is 0.9625..

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Digits a, b, and c can be chosen to make the following

multiplication work. What is the 3-digit number abc.

a b c

� 2 4

1 c b a 2

**Answer:**

1

**Step-by-step explanation:**

Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results:

9. The conditional distribution for preferred cookie brand among males (in percents) is given by which of the following?

A. A: 27%; B: 19%; C: 25%; D: 29%

B. A: 4%; B: 6%; C: 13%; D: 15%

C. A: 11%; B: 16%; C: 34%; D: 39%

D. A: 23%; B: 13%; C: 11%; D: 14%

E. A: 38%; B: 21%; C: 19%; D: 22%

They **like **best brand C) A: 11%; B: 16%; C: 34%; D: 39%.

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an **event**, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Have given ,

Ida made four brands A , B , C and D

Mostly students like A brand 11% , B brand 16% , C brand 34% and D brand 39%

So this is best brand like by students male and female

They **like **best brand C) A: 11%; B: 16%; C: 34%; D: 39%.

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Solve for x using the quadratic formula: x² - 6x + 9 = 0

X=

-b± √b²-4ac

2a

Ox=6

Ox=3

Ox=1

Ox=0

**Answer:**

[tex] \huge{ \boxed{x = 3}}[/tex]

**Step-by-step explanation:**

[tex] {x}^{2} - 6x + 9 = 0[/tex]

Using the quadratic formula that's,

[tex] \bold{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}} \\ [/tex]

Comparing the equation to the general form of a quadratic equation **( ax² + bx + c)****,**** **we have.

[tex]a = 1 \\ b = - 6 \\ c = 9[/tex]

Substituting the values into the formula we have.

[tex]x = \frac{- ( -6) \pm \sqrt{( - {6})^{2} - 4(1)(9) } }{2(1)} \\ x = \frac{6 \pm \sqrt{36 - 36} }{2} \\ x = \frac{ 6 \pm\sqrt{0} }{2} \\ x = \frac{6}{2} \: \: \: \: \: \\ \\ x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

x = 3QUESTION ISDOWN BELOW

The **Answers **to the Question are solved below.

A number's **cube **root is the factor that we **multiply three times **to get that number.

The **symbol **for cube root is 3 cube root of, end cube root(∛) .

Given:

1. [tex]5^{-2[/tex]

Using **Exponents**

[tex]a^{-m[/tex] = 1 / [tex]a^m[/tex]

So, [tex]5^{-2[/tex] = 1/5² = 1/25.

2. z+ 5= 12

z= 12-5

z= 7

3. Pythagorean triplet: m²-1, 2m, m²+1

2m= 6

m=3

and, m²-1 = 9-1= 8

and, m²+1 = 9+1= 10

3. **Cube root **of 64 = ∛64= ∛(4 x 4 x 4)= 4

4. 4z+ 3= 6+ 2z

2z = 3

z= 3/2

5. a- b+ ab, b- c + bc, c- a +ac

**Adding**: (a- b+ ab) + (b- c + bc) + (c- a +ac)

= ab+ bc+ ac

6. -1 x -2/5

= 2/5

The **Multiplicative inverse **= -5/2

7. y+3 = 10

y=7

8. 10³= 10 x 10 x 10= 1000

9. [tex]3^{-2[/tex]

= 1/3²

= 1/9

10. **Volume **= Base Area x height

900 = 180 h

h= 900/180

h = 5

11. 16 as sum of 4 add number

= 1 + 3 + 5 + 7

12. 78 x 82

(80- 2)(80+ 2)

= 80² - 2²

= 6400 - 4

= 6396

13. 2/3 x 100

= 200/3 %

14. (ab- bc)+ (bc - ca) + (ca- ab)

= [tex](-4)^5[/tex] ÷ [tex](-4)^8[/tex]

= [tex](-4)^{5-8}[/tex]

= [tex](-4)^{-3[/tex]

15. 4p² - 9q²

= (2p)² - (3q)²

= (2p - 3q) (2p + 3q)

16. 2y-1 = 14- y

3y= 15

y= 5

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Expand the polynomial (x + y)7 and write the coefficients of the terms.

**Answer:**

7x+7y siuuuuuuuuuuuuuuuuu

How do I solve this?

**Answer:**

Area = 5π/2 in^2

Perimeter = 3π + 2 in

**Step-by-step explanation:**

A=area of a circle. P=Perimeter of a circle

F=Area of first semi-circle

T=Area of Figure

Solve for Area:

A=πr^2

F=A/2

A=π(2)^2 ==> solve for A

A=4π

F=(4π)/2

F=2π ==> this is for the first semi-circle

S=Area of second semi-circle

S=(πr^2)/2

S=(π(2/2)^2)/2 ==> the radius is half the diameter, and the diameter is 2 in

S=(π(1)^2)/2

S=π/2

T=F+S ==> The total area is the area of both semi-circles

T=2π + π/2 ==> plugin 2π for F and π/2 for S

T = 4π/2 + π/2 ==> common denominators

**T = 5π/2 in^2**

Now solve for perimeter

P = 2πr.

q = perimeter of first semi-circle

q = P/2

q = 2πr/2

q = 2π(2)/2 ==> plugin 2 for r

q = 2π

R = Perimeter of second semi-circle

R = 2π(1)/2 ==> we calculated that the radius of the semi-circle is half of the

radius of the first semi-circle

R = 2π/2 ==> simplify

R = π

Also, add in side length DC into the perimeter as it is part of the perimeter.

E = Entire perimeter of figure

E = q + R + DC

E = 2π + π + 2

**E = 3π + 2 in**

on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?

**Theresa** should take her **7th dose **at 9:00 AM on **Friday**.

**What are arithmetic operations?**

**Arithmetic** **operations** is a branch of mathematics that studies **numbers** and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like **addition**, **subtraction**, **multiplication**, and **division**.

we have,

The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.

If Theresa took her first dose at 9:00 AM on Monday,

Simply add 12 hours every time up to the 7th dose,

First dose ----> 9:00 AM on Monday,

Second dose ----> 9:00 PM on Monday,

Third dose ----> 9:00 AM on Tuesday,

Fourth dose ----> 9:00 PM on Tuesday,

Fifth dose ----> 9:00 AM on Thursday,

Sixth dose ----> 9:00 PM on Thursday,

Seventh dose ----> 9:00 AM on Friday,

Hence, **Theresa** should take her **7th dose **at 9:00 AM on **Friday**.

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A real estate agent would like to develop a model for predicting sale price of homes in a suburban area. One variable that can be useful for predicting home value is home interior size, which is measured in square feet. Using 13 homes sold recently in the area, the real estate agent uses software to find a least-square line to summarize the relationship. The resulting equation is sale price hat = 0.152 (size) minus 32.84. A graph titled home price versus home size (square feet) has home size (Square feet) on the x-axis, and home price (thousands of dollars) on the y-axis. Points increase in a line with positive slope. A graph titled residuals versus home size (square feet) has home size (square feet) on the x-axis, and residual on the y-axis. Points are scattered throughout the graph. Based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship? A linear model is appropriate because the residual plot shows no pattern. A linear model is appropriate because the mean of the residuals appears close to zero. A linear model is not appropriate because there are potential outliers in the residual plot. A linear model is not appropriate because of the random scatter of points in the residual plot.

Based on the information provided, a linear model is not appropriate for summarizing the relationship between home size and sale price because of the random scatter of points in the residual plot. In a linear model, the residuals should be randomly distributed around a mean of zero, without any discernible pattern. However, the residual plot shown in the question indicates that the residuals are randomly scattered throughout the graph, which suggests that a linear model may not be the best way to summarize the relationship between the variables. Therefore, a linear model is not appropriate for this data.

**Answer:**

Not Appropriate

**Step-by-step explanation:**

Based on the information provided in the problem, it appears that a linear model is not appropriate for summarizing the relationship between home size and sale price. This is because the residual plot shows a random scatter of points, which suggests that there is not a strong linear relationship between these variables. Furthermore, the scatterplot of home price versus home size shows a line with a positive slope, which indicates that there is some relationship between these variables, but it is not necessarily a linear relationship. In this situation, it would be more appropriate to use a non-linear model to summarize the relationship between home size and sale price.

Three students that share a townhouse find that their electric bill for October is $2.23 less than the September bill. The

total of both bills is $292.43, and each bill is split evenly among the roommates. How much did each owe in September?

**Answer:**

$47.48

**Step-by-step explanation:**

Let x = the amount owed Sept.

x + x - 2.23 = 292.43 Combine like terms

2x -2.23 = 292.43 Add 2.23 to both sides

2x - 2.23 + 2.23 = 292.43 + 2.23

2x = 294.66 Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{294.66}{2}[/tex]

x = 147.33 this is the bill for September

Oct. 147.33 -2.23 = 145.10 This is the Bill for Oct.

Total:

147.33 + 145.10 = 292.43

292.43 ÷ 3 = 97.48 This is what each will owe rounded to the nearest penny.

2x - y = 20

2x + y = 48

**Answer:**

Below

**Step-by-step explanation:**

2x-y = 20

2x + y = 48 add the two equations to get

4x = 68

x = 17 <==== use this value in either equation to calculate y = 14

DUE SOON! PLEASE SHOW HOW YOU KNOW! THIS IS A SSA SITUATION BUT NOT SURE HOW TO FIND OUT HOW MANY TRIANGLES ARE POSSIBLE!

This is a **SAS situation**, only **one **triangle is **possible**. Then the **correct **option is C.

The polygonal **shape **of a triangle has a number of **sides **and three independent **variables**. **Angles **in the triangle add up to 180 °.

In triangle ΔABC, the **angle **∠A is 22°. And the measure of the **side **BC is 18.9 cm and the **measure **of the side AC is 15.1 cm.

To **fix **a triangle, the known dimensions of the triangle should be **three **which **one **must be a **side**.

This is a **SAS circumstance**, just a **single **triangle is conceivable. Then the **right choice **is C.

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In 1950, a U.S. population

model

was y = 151. (1.013)^t-1950 million

people, where t is the year. What did

the model predict the U.S. population

would be in the year 2000?

In a case whereby In 1950, a U.S. population **model** was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be **288 million** in the year 2000.

**Population models **are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The** model** was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = **288 million**

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Solve Please and Thank U

The **solution **to the **systems **are (1, 1), (-3, -1), (1, -2), (2, -1), (7, -1) and (-2, 2)

System 1

In this case, the system of equations is given as

y = -3x + 4

y = 3x - 2

Next, we plot the **graph **of the system of equations

In this case, the point of **intersection** of the equations represent the solution to the **system**

From the graph, the lines **intersect **at (1, 1)

So, the solution is (1, 1)

System 2

In this case, the system of equations is given as

y = x + 2

x = -3

Next, we plot the **graph **of the system of equations

In this case, the point of **intersection** of the equations represent the solution to the **system**

From the graph, the lines **intersect **at (-3, -1)

So, the solution is (-3, -1)

System 3

In this case, the system of equations is given as

4x + y = 2

x - y = 3

Next, we plot the **graph **of the system of equations

In this case, the point of **intersection** of the equations represent the solution to the **system**

From the graph, the lines **intersect **at (1, -2)

So, the solution is (1, -2)

System 4

We have

y = 4x - 9

y = x - 3

Substitute y = 4x - 9 in y = x - 3

4x - 9 = x - 3

Evaluate the **like terms**

3x = 6

So, we have

x = 2

Recall that:

y = x - 3

So, we have

y = 2 - 3

y = -1

So, the solution is (2, -1)

System 5

We have

x + 7y = 0

2x - 8y = 22

Make x the subject in x + 7y = 0

x = -7y

Substitute x = -7y in 2x - 8y = 22

-14y - 8y = 22

Evaluate the **like terms**

-22y = 22

So, we have

y = -1

Recall that:

x = -7y

So, we have

x = -7(-1)

x = 7

So, the solution is (7, -1)

System 6

We have

-7x + 2y = 18

6x + 6y = 0

Make x the subject in 6x + 6y = 0

x = -y

Substitute x = -y in -7x + 2y = 18

7y + 2y = 18

Evaluate the **like terms**

9y = 18

So, we have

y = 2

Recall that:

x = -y

So, we have

x = -2

So, the solution is (-2, 2)

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Sami asked 50 people which drinks they liked from tea, coffee and milk.

All 50 people like at least one of the drinks

19 people like all three drinks.

16 people like tea and coffee but do not like milk. 21 people like coffee and milk.

24 people like tea and milk.

40 people like coffee.

1 person likes only milk.

Sami selects at random one of the 50 people. Work out the probability that this person likes tea.

**Answer:**

30

**Step-by-step explanation:**

not sure might be wrong lol soz

How is 25 to 5 and 10 to 2 equivalent ratios

**Answer:**

They are equivalent ratios because if you multiply 10 to 2 by 2.5 you get 25 to five

**Answer:**

equals 25

**Step-by-step explanation:**

the surface area of a sphere is 320 square centimeters what is the radius of the square

The **radius **of the sphere of **surface area** 320 cm² is **5.04 cm.**

A **radius **is defined as half of a diameter. The unit of **radius **is meter.

To calculate the **radius **of the sphere, we use the formula below.

Formula:

r = √(A/4π)....................... Equation 1Where:

r =From the question,

Given:

A = 320 cm²π = 3.14Substitute these values into equation 1

r = √[320/(3.14×4)]r = √(25.48)r = 5.04 cmHence, the **radius **of the **sphere** is **5.04 cm.**

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HELP ASAP!!!

1. Give the equation of the least-squares regression line. Define any variables you use.

2. Use the model from part (a) to predict the area covered by detergent at 5.5 seconds.

3. Based on the residual plot, do you expect the prediction you made in part (b) to underestimate or

overestimate the area covered by detergent? Justify your answer.

4. Is the least-squares regression line an appropriate model for these data? Justify your answer.

**Answer:**

When you run a regression, calculating and plotting residuals help you understand and improve your regression model. In this post, we describe the fitted vs residuals plot, which allows us to detect several types of violations in the linear regression assumptions. You may also be interested in qq plots, scale location plots, or the residuals vs leverage plot.

**Step-by-step explanation:**

NO LINKS!!

A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes ) and T is the temperature (in degrees Celsius).

t T

0 81

5 69

10 60.5

15 54.2

20 49.3

25 45.4

30 42.6

a. Subtract the room temp. from each of the temp. in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T-24). An exponential model for the data (t, T-24) is T-24 = 54.4(0.964)^t. Solve for T.

T=

Graph the model. Compare the result with the plot of the original data.

b. Use a graphing utility to plot the points (t, ln(T-24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T-24) = at + b, which is equivalent to e^(ln(T-24)) = e^(at+b). Solve for T, and verify that the result is equivalent to the model in part (b). Round all numerical values to 3 decimal places).

T=

c. Fit a rational model to the data. Take the reciprocals of the y-coordinates of the revised data points to generate the points. (t, 1/(T-24))

Use a graphing utility to graph these points and observe that they appear to be linear. Use the regression feature of a graphing utility to fit a line to these data. The resulting line has the form 1/(T - 24) = at + b.

Solve for T. (Round all numerical values to 4 decimal places). Use a graphing utility the rational function and the original data points.

T=

Part (a)

Given data table.

[tex]\begin{array}{|c|c|} \cline{1-2}t & T\\\cline{1-2}0 & 81\\\cline{1-2}5 & 69\\\cline{1-2}10 & 60.5\\\cline{1-2}15 & 54.2\\\cline{1-2}20 & 49.3\\\cline{1-2}25 & 45.4\\\cline{1-2}30 & 42.6\\\cline{1-2}\end{array}[/tex]

where,

t = time in minutesT = temperature in CelsiusIt's unfortunate that T is used twice for these variables. It might cause some confusion.

This is what happens when we subtract 24 from each temperature.

[tex]\begin{array}{|c|c|} \cline{1-2}t & T-24\\\cline{1-2}0 & 57\\\cline{1-2}5 & 45\\\cline{1-2}10 & 36.5\\\cline{1-2}15 & 30.2\\\cline{1-2}20 & 25.3\\\cline{1-2}25 & 21.4\\\cline{1-2}30 & 18.6\\\cline{1-2}\end{array}[/tex]

The graph of each set of points is shown in figure A. I used GeoGebra to make the graph.

The first set of data points are in red. The second set in blue. Notice the set of blue points is the result of shifting the red points 24 units down.

The green exponential model is also shown as the curve through the set of red points.

The green regression exponential model doesn't go through each point perfectly. Rather it tries to get as close as possible.

To go from

T-24 = 54.4(0.964)^t

to

T = 54.4(0.964)^t + 24

we simply add 24 to both sides. This means there isn't much to show in terms of steps when solving for T.

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

Part (b)

Use spreadsheet technology or something like GeoGebra to generate this data table.

[tex]\begin{array}{|c|c|} \cline{1-2}t & ln(T-24)\\\cline{1-2}0 & 4.043051\\\cline{1-2}5 & 3.806662\\\cline{1-2}10 & 3.597312\\\cline{1-2}15 & 3.407842\\\cline{1-2}20 & 3.230804\\\cline{1-2}25 & 3.063391\\\cline{1-2}30 & 2.923162\\\cline{1-2}\end{array}[/tex]

The values in the 2nd column are approximate.

Then plot each of those points on the same xy grid. Use technology of your choice to determine the regression line is roughly

y = -0.03723x + 3.99739

So we can say

ln(T-24) = -0.03723t + 3.99739

the right hand side fits the format at + b where

a = -0.03723b = 3.99739both of which are approximate.

Then,

e^(ln(T-24)) = e^(at+b)

T-24 = e^(at+b)

T-24 = e^(-0.03723t + 3.99739)

T-24 = e^(-0.03723t)*e^(3.99739)

T-24 = e^(-0.03723t)*54.45583

T-24 = 54.45583*e^(-0.03723t)

T = 54.45583*e^(-0.03723t) + 24

T = 54.456*e^(-0.037t) + 24

Let's verify that this is equivalent to the model found in part (a).

T = 54.456*e^(-0.037t) + 24

T = 54.456*(e^(-0.037))^t + 24

T = 54.456*(0.963676)^t + 24

T = 54.5*(0.964)^t + 24

which is very close to the model mentioned in part (a). There's some slight rounding error. That's to be expected in problems like this.

-----------------------------

Answer: **T = 54.456*e^(-0.037t) + 24**

See figure B for the graph. Like with the other regression curve, this straight line doesn't go through all of the points. It tries to get as close as possible.

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

Part (c)

Refer to the 2nd table mentioned in part (a).

We'll apply the reciprocal to each item in the column labeled T-24.

For instance, the item 57 becomes 1/57 = 0.017544 approximately.

This is what the data table looks like:

[tex]\begin{array}{|c|c|} \cline{1-2}t & 1/(T-24)\\\cline{1-2}0 & 0.017544\\\cline{1-2}5 & 0.022222\\\cline{1-2}10 & 0.027397\\\cline{1-2}15 & 0.033113\\\cline{1-2}20 & 0.039526\\\cline{1-2}25 & 0.046729\\\cline{1-2}30 & 0.053763\\\cline{1-2}\end{array}[/tex]

The values in the 2nd column are approximate.

The set of points and regression line are shown in figure C1. This line does not go through all of the points. Like with the others, it tries to get as close as possible to each point.

Use technology to determine the equation of the regression line is approximately:

y = 0.00121x + 0.01613

Which tells us that

1/(T-24) = 0.00121t + 0.01613

Let's solve for uppercase T.

1/(T-24) = 0.00121t + 0.01613

T-24 = 1/(0.00121t + 0.01613)

T = 1/(0.00121t + 0.01613) + 24

**T = 1/(0.0012t + 0.0161) + 24**

**which is the approximate final answer.**

Figure C2 shown below represents the original data points (t, T) in red. The blue curve is y = 1/(0.0012x+0.0161)+24, which is the rational regression curve we just found. This curve tries its best to get as close as possible to each red point.

Compare the regression curves of figure A and figure C2. We have a very close tie in terms of which curve does a better job of fitting the original data.

If tan x = 3/4 find sin x and cos x.

**Step-by-step explanation:**

tan(x) = sin(x)/cos(x) = 3/4

in the trigonometric triangle sin(x) and cos(x) are the legs, and the radius is the Hypotenuse, the baseline (opposite of the 90° angle).

so, we can use Pythagoras to find the radius.

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

let's stay integer.

if sin(x) is equivalent to 3, and cos(x) to 4, then what is the radius ?

3² + 4² = c²

9 + 16 = c²

25 = c²

c = radius = 5

so,

3 = sin(x) × 5

4 = cos(x) × 5

sin(x) = 3/5 = 0.6

cos(x) = 4/5 = 0.8

The **value** of sin x is 3/5 and the value of cos x is 4/5.

**What are trigonometry ratios?**

The **trigonometric functions** in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Given that tan x = 3/4.

The tangent of an angle is the ratio of height to the base of the right triangle.

Here the height of the triangle is 3 and the base is 4.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the base and height.

Thus,

hypotenuse = √(3² + 4²)

hypotenuse = 5.

The sine of an angle is the ratio of** height** to the **hypotenuse**.

Sin x = Height/ hypotenuse

sin x = 3/5

The cosine of an angle is the ratio of the base to the hypotenuse.

cos x = base/ hypotenuse

cos x = 4/5

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the following is a listing of the amount of sugar in six popular snacks found on a high school campus: 35g 35g 43g 49g 52g 53g what is the median?

The median is 43 g. By using median formula and by simple **observation** method we can find median of the given data.Hence median is 43 g.

The **middle** number ,by ordering all data points and picking out the one in the middle.Arrange the all values from lowest to highest.Then we can find easily.Median is also type of average which is used to find centre value.

There are the following formula we use to find median.

Median= (n+1)th/2 terms (if n is odd)

Where n is the number of observations.

So,if n is even then we use

Median= (n/2)th terms

if number of term is even,then the median is the simple average of the middle two numbers.

So we can find median by two methods

median= n/2 -th term

median =6/2 -th term

median = 3-th term

Hence our third term is 43 g so our median will be 43 g.

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A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings￼?

**Answer:**

a = 8

b = 2

c = 48

Step-by-step explanation:

3 cups of flour is needed to make 24 servings.

3:24

Simplify. First, divide 3 from both sides of the ratio.

(3)/3 : (24)/3

1:8

Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1

1 x 2 = b = 2

Finally, multiply 8 to 6 to get c.

8 x 6 = c = 48

~

Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon? A. 0.2 B 1/0.2 C. 0.2^8 D 0.2 (0.8)^7

E. 0.8 (0.2)^7

The **probability **of needing to catch 8 **fish **to get the first **salmon **is D) 0.2 (0.8)^7.

**How to calculate probability of needing to catch 8 fish to get the first salmon?**

Given that he **probability **of fishing a salmon in a certain **river **is 20% i.e. 0.2. Now, the probability of not getting a salmon will be

1 - probability of not getting salmon = 1 - 0.2 = 0.8.

So, the first fish should be salmon and the others should not be salmon. So, the required probability of independent events can be calculated as,

P =0.2×0.8×0.8×0.8×0.8×0.8×0.8×0.8×0.8

P = 0.2× (0.8)^7

Hence,the probability of needing to catch 8 fish to get the first salmon is 0.2 (0.8)^7.

The probability of needing to catch 8 fish to get the first salmon is D) 0.2 (0.8)^7.

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I need help asap i don’t get it

∠SWV is **congruent** to ∠TWU because vertically opposite angle.

If one of the geometric figures can be superimposed on the other so that their entire surface coincides, then the two are said to be **congruent**, or to be in the relation of congruence. Two triangles are said to be congruent if their two sides and their included angle are the same in both of them. Congruence appears to be based on the concept of a "rigid body," which may be transported from one location to another without affecting the internal relationships between its components.

Given

∠SWV ≅ ∠TWU

**Vertically opposite angle**

∠SWV is **congruent** to ∠TWU because vertically opposite angle.

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Suppose that the function h is defined, for all real numbers, as follows.

=hx +−12x24 ≠if x2

−2 =if x2

Find h−3, h2, and h4.

The **function **h is defined, for all **real numbers** h(-3) = -1/2 , h(2) = -2 and h(4) = -4.

**What is a function ?**

When it comes to arithmetic, a **function **is represented as a rule that produces a different result for each input x. Mathematicians refer to functions as mapping or transformations.

The given** function**,

h(x) = -1/2 x^2 + 4 if x≠ 2

-2 if x=2

So, h(-3) = -1/2 (-3)^2 + 4

= - 9/2 + 4

= -1/2

h(2) = -2 ( given )

h(4) = -1/2 (4)^2 + 4

= -8 + 4

= -4 .

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PLS HELP ASAP pic attached

The** slope and y-intercept, **or the points, should be used to graph the line. Slope: 3 y-intercept: (0, 1 )

**g ( x ) = − 3 x − 1**

Create an equation using the function.

y = − 3 x − 1

Calculate the slope and y-intercept using the** slope-intercept form.**

Less steps by tapping...

In the slope-intercept form, y = m x + b denotes the slope and the y-intercept, respectively.

y = m x + b

With the use of the formula y = m x + b, determine the values of m and b.

m = − 3 b = − 1

m is the line's slope, and is the value of the y-intercept.

B. Slope: 3 Y-intercept: (0, 1 )

Two points are all that are required to graph any line. To determine the associated y values, enter two x values into the equation.

Less steps by tapping...

Assign the x and y values to a table.

x y

0 − 1

1 − 4

The slope and y-intercept, or the points, should be used to graph the line.

Slope: 3 y-intercept: (0, 1 )

x y

0 1

1 4.

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