the price of a discount airline ticket starts at $150 and increases $30 each week.write and algebraic expression that molds this situation?

Answer:

\((a)\ Area = 3765.32\)

\((b)\ Area = 4773\)

Step-by-step explanation:

Given

\(A_1 = 169in^2\) --- area of each square

\(Shade = 4in\)

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

\(L^2 = A_1\)

\(L^2 = 169\)

\(L = \sqrt{169\)

\(L=13\)

The length of two squares make up the radius of the semicircle.

So:

\(r = 2 * L\)

\(r = 2*13\)

\(r = 26\)

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

\(A_2 = 16 * 169\)

\(A_2 = 2704\)

The area of the semicircle is:

\(A_3 = \frac{\pi r^2}{2}\)

\(A_3 = \frac{3.14 * 26^2}{2}\)

\(A_3 = 1061.32\)

So, the area of the window is:

\(Area = A_2 + A_3\)

\(Area = 2704 + 1061.32\)

\(Area = 3765.32\)

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

\(Length = 4 * 13 + 8\)

\(Length = 60\)

\(Height = 4*13 + 4\)

\(Height = 56\)

The area is:

\(A_1 = 60 * 56 = 3360\)

The radius of the semicircle becomes initial radius + 4

\(r = 26 + 4 = 30\)

The area is:

\(A_2 = \frac{3.14 * 30^2}{2} = 1413\)

The area of the shade is:

\(Area = A_1 + A_2\)

\(Area = 3360 + 1413\)

\(Area = 4773\)

Answer:

change in temperature = final - temperature

= -9°-15° = -24°C

Answer:

√28 = 2√7 or roughly 5.29

Step-by-step explanation:

work backwards! sqr of 28 = x^2 that equals 28

√28 = 2√7 or roughly 5.29

Answer:

2

√

7

Step-by-step explanation:

Answer:

a9

Step-by-step explanation:

5+4= 9 and its the same variable.

Answer:

I think 31° is the answer

In the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

The domain refers to the set of possible inputs or variables in a given context. In this case, the scatterplot is being created based on the relationship between the time students spent studying and their corresponding test grades. Therefore, the domain in this context would be the number of minutes the students studied (option D).

The domain represents the independent variable, which is the variable that is controlled or manipulated in the analysis. In this scenario, the math teacher wants to analyze the relationship between studying time and test grades, so the number of minutes studied would be the independent variable. The teacher surveys the students to collect data on the time spent studying, and this variable becomes the domain of the scatterplot.

The range, on the other hand, represents the dependent variable, which is the variable that is measured or observed as an outcome or response. In this case, the dependent variable would be the students' test grades. The scatterplot will show how the test grades correspond to the amount of time students studied.

To summarize, in the context of analyzing the relationship between studying time and test grades, the domain of the scatterplot would be the number of minutes the students studied (option D).

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Answer: 2 + 6x

Step-by-step explanation:

i cannot do the graph here but you just have to put the amount deposited in this instance as the variable and you got your answer

Answer:

2+6

Step-by-step explanation:

The probability of the principal drawing a student's name from the Voyagers team on the second try, we need to consider the total number of students in the school after the first selection.the probability is: Probability = 82 / 399 ≈ 0.205

Initially, there are a total of 400 students in the school. Since the principal selects a student from the Voyagers team on the first try, one student is removed from the pool of possible candidates. Therefore, there are now 399 students remaining in the school.

Out of these 399 students, the number of students in the Voyagers team is 82. So, the probability of the principal drawing a student from the Voyagers team on the second try can be calculated as:

Probability = Number of favorable outcomes / Total number of outcomes

Number of favorable outcomes = Number of students in the Voyagers team after the first draw = 82

Total number of outcomes = Total number of remaining students in the school after the first draw = 399

Therefore, the probability is:

Probability = 82 / 399 ≈ 0.205

So, there is approximately a 20.5% chance that the principal will draw the name of a student from the Voyagers team on the second try.

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Answer:

1. D. 150%

2. C. 37.19

Step-by-step explanation:

hope this helps!

To find the force constant of the spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Hooke's Law can be written as:

F = kx

where F is the force applied, k is the force constant (also known as the spring constant), and x is the displacement from the equilibrium position.

In this case, we have two situations:

Situation 1:

Length of the spring (equilibrium position) = 0.333 m

Mass hanging from the spring = 0.300 kg

Situation 2:

Length of the spring (equilibrium position) = 0.750 m

Mass hanging from the spring = 3.22 kg

Using the information provided, we can calculate the displacement in each situation:

Displacement in Situation 1:

x1 = 0.750 m - 0.333 m = 0.417 m

Displacement in Situation 2:

x2 = 0.333 m - 0.750 m = -0.417 m (negative sign indicates the opposite direction)

Now, we can use Hooke's Law to set up two equations:

For Situation 1:

F1 = kx1

For Situation 2:

F2 = kx2

The gravitational force acting on an object can be calculated as:

F = mg

where m is the mass and g is the acceleration due to gravity.

For Situation 1:

F1 = (0.300 kg) * (9.8 m/s^2) = 2.94 N

For Situation 2:

F2 = (3.22 kg) * (9.8 m/s^2) = 31.556 N

Substituting the forces and displacements into the equations:

2.94 N = k * 0.417 m (Equation 1)

31.556 N = k * (-0.417 m) (Equation 2)

Solving Equation 1 for k:

k = 2.94 N / 0.417 m ≈ 7.038 N/m

Thus, the force constant (spring constant) of the spring is approximately 7.038 N/m.

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Answer:

The confidence interval is (657.18, 661.02)

or , CI = 659.1 ± 1.922

Step-by-step explanation:

We have to ind the 95% confidence interval,

Mean = Y = 659.1

Standard Deviation = s(Y) = 19.9

Confidence level = 95%

Alpha value = (1 - 0.95)/2

Alpha value = 0.025

So,

This gives a z value of,

z = - 1.96

Now, there are 412 districts so, n = 412

so,

The upper limit is,

Upper limit =  UL = Y + z(s(Y))/sqrt(n)

\(UL = Upper limit = Y + z(s(Y))/\sqrt{n}\\UL = 659.1 + (1.96)(19.9)/|sqrt(412)\\UL = 661.02\)

Lower limit is,

LL = Y - z(s(Y))/sqrt(n)

\(LL = 659.1 - (1.96)(19.9)/\sqrt{412}\\LL = 657.18\)

Hence the confidence interval is (657.18, 661.02)

Step-by-step explanation:

\(perimeter = 10 + 10 + 10 \\ = 30\)

Answer:

I believe 34.

Step-by-step explanation:

12+12+10= 34

Answer:4

Step-by-step explanation:

Answer:

\((x - 8) + (x + 8) + x + (2x + 7) + (3x - 11)\\ 2x + x + 2x + 7 + 3x - 11 \\ 8x - 4 \\ 8x = 4 \\ x = \frac{1}{2} \)

Answer: 27

Step-by-step explanation:

If 2 scoops of ice cream cost $6, then 1 scoop of ice cream costs $6/2 = $3.

So, 9 scoops of ice cream would cost 9 x $3 = $27.

Answer:

27$

Step-by-step explanation:

If two wcoops of ice crewm cost 6$ them one scoop would cost 3$ because 6/2 =3. If one scoop costs 3$ then 9 scoops would cost 9x3 so 27$

Answer:

Step-by-step explanation:

11

Answer:

a. +34 b. +46 c. +45 d. +31

Step-by-step explanation: use a number line

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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Answer:

Please check the explanation below.

Step-by-step explanation:

Note: As you forgot to mention the graphs of a linear function. But, let me clear your concept with an example of a linear function.

We know that linear function is of the form

y = mx+b

where

We know that the graph of a linear function is a straight line because the highest power of the exponent of the x variable is 1.

Thus, y = mx+b represents a straight line.

For example,

Let the linear function

y = 2x+3

comparing with the linear function of the form y = mx+b

As the highest power of the exponent of a variable is 1, therefore y = 2x+3 represents a straight line.

The graph of the linear function y = 2x+3 is also attached below.

Answer:

Step-by-step explanation:

\(f(x) = - 4 {x}^{2} - 7x + 4\)

To find f(-7) , substitute the value of x that's - 7 into f(x). That is for every x in f(x) replace it with - 7

We have

\(f( - 7) = - 4 ({ - 7})^{2} - 7( -7 ) + 4 \\ = 4(49) + 49 + 4 \\ = 196 + 53 \: \: \: \: \: \: \: \: \: \: \: \)

We have the final answer as

Hope this helps you

Answer:

B=28

Step-by-step explanation:

Answer:

Choice C

Step-by-step explanation:

Point D is in the 4th quadrant where we generally have points in the form (x, -y).

To reflect about the y-axis from quadrant 4, (x,-y) becomes (-x-y). This both coordinates become negative. See it?

So, D becomes (-4, -1).

To reflect about the y-axis from quadrant 1, (x, y) becomes (-x, y).

So, points E and F become (-5, 2) and (-1, 2), respectively.

In other words, the x-coordinate becomes negative. See it?

Answer: Choice C

Answer:

3-[1]

3-1

2

Step-by-step explanation:

=//7777/))_+++++++4

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Represent the first statement

Let the number be n

twice a number is given as:

difference between twenty and twice the number is given as:

Hence, the answer is 20-2n

The amount will be equal to $1348.07. The correct option is A.

Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-

\(\rm A = P(1+\dfrac{r}{n})^{nt}\)

Compound Interest Formula:

A = Account Balance

P = Principle/Initial Amount

r = Rate of Interest (decimal)

n = Number of times compounded (per year)

t = Number of Years

Given Information

Account Balance = ?

It is given that the balance after 15 years in a savings account earns 2% interest compounded bi-monthly when the initial deposit is 1000.

This is because we are gaining money, so the multiplier should be greater than 1. We already added 1, which is 100% so you simply add the 0.02 for the extra 2%.

Number of times compounded per year = 6

This is because it is being compounded bi-monthly, or once every 2 months. 12 months divided by 2 months is 6 months, so 6 times a year.

Number of years = 15

Solve by plugging the given values into the formula.

\(\rm A = P(1+\dfrac{r}{n})^{nt}\)

\(\rm A = 1000(1+\dfrac{0.02}{6})^{6 \times 15}\)

A = 1000 x (1.14)

A = $1348.07.

Therefore, the amount will be equal to $1348.07. The correct option is A.

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Answer:

120°

Step-by-step explanation:

m<ABD+m<DBC=m<ABC

61°+59°=120°

hope this helped!

Answer:

We conclude that the value of m∠ABC = 120°

Step-by-step explanation:

Given

m∠ABD = 61°

m ∠DBC = 59°

To Determine

m∠ABC = ?

It is clear that the value of m∠ABC can be determined by adding m∠ABD and m∠DBC because m∠ABC the segment BD divides the angle m∠ABC into two adjacent angles m∠ABD and ∠DBC.

Therefore,

m∠ABC = m∠ABD + m∠DBC

             = 61° + 59°            ∵ m∠ABD = 61°, m ∠DBC = 59°

             = 120°

Therefore, we conclude that the value of m∠ABC = 120°

The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose.

The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose. This angle varies depending on the properties of the granular material such as size, shape, and degree of consolidation. The angle of repose is a critical factor in many fields such as engineering, geology, and agriculture. For example, in civil engineering, the angle of repose is essential in designing stable slopes and retaining walls. In agriculture, it is crucial for understanding the flow and distribution of granular materials such as seeds, fertilizers, and grains. In general, the angle of repose for unconsolidated granular materials ranges from 25 to 45 degrees, but it can be higher for certain materials such as sand, or smaller for cohesive soils.
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The number which best completes the sequence is option c) 72.

The sequence seems to be alternating between multiplying by 3 and dividing by 2.
Starting with 10, we have:
10 x 3 = 30
30 ÷ 2 = 15
15 + 1 = 16
16 x 3 = 48
48 ÷ 2 = 24
24 + 1 = 25

So, the next number in the sequence should be:
25 x 3 = 75
75 ÷ 2 = 37.5

However, none of the answer options match 37.5. Therefore, we need to look for a pattern that matches one of the answer options.

If we multiply 25 by 3 and then divide by 2, we get 37.5. However, if we continue with this pattern, we get:
37.5 x 3 = 112.5
112.5 ÷ 2 = 56.25

Again, none of the answer options match 56.25.

Let's try multiplying 24 by 3 and then dividing by 2:
24 x 3 = 72
72 ÷ 2 = 36

Since 36 is not in the sequence, we can eliminate option b) 75.

Therefore, the number which best completes the sequence is option c) 72.
The number which best completes the sequence 10, 30, 15, 16, 48, 24, 25 is:

c) 72

The sequence can be described as alternating between multiplying by 3 and dividing by 2, then adding 1.

10 x 3 = 30
30 / 2 = 15
15 + 1 = 16
16 x 3 = 48
48 / 2 = 24
24 + 1 = 25
25 x 3 = 75

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The fraction shows that D. Maddy made 4 bows from the piece of ribbon and had enough left for of a bow.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case the fraction divided will be:

= 3 1/2 ÷ 3/4.

= 7/2 ÷ 3/4

= 7/2 × 4/3

= 28/6

= 14 / 3

= 4 2/3

Therefore, the correct option is D.

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