the only question i need help is number 48 pleaseee

Answer:

1) y = (1/15)x + 18

2) y = (5/144) (x - 16)^2 + 20

Solution:

1) The solution consists in establishing the equations that model the two paths.

2) Let's start with the easiest one. It is the linear path.

You have that the equation is a line that passes through the points (0,18) and (30,20). This equation is found using this formula:

[tex]\dfrac{y-b}{x-a} =\dfrac{d-b}{c-a}[/tex]

where the two points are (a,b) and (c,d)

So, for the two points given:

[tex]\dfrac{y-18}{x-0} =\dfrac{20-18}{30-0} =\dfrac{2}{30}[/tex]

=> [tex](y - 18)\times30 = x\times2[/tex]

=> [tex]30y - 540 = 2x[/tex]

=> [tex]30y = 2x + 540[/tex]

=> [tex]y = 2x \div 30 + 540 \div 30[/tex]

=> y = x/15 + 18 ---------------> this is the first equation of the system.

3) Now, find the equation for the path modeled by the quadratic function.

The vertex form of a quadratic function is: [tex]y = A (x - h)^2 + k[/tex]

where the vertex is (k,h).

Then, so far you can write [tex]y = A (x - 16)^2 + 20[/tex]

Now, replace the coordinates of the point (4,25) to find the value of A:

[tex]25 = A (4 - 16)^2 + 20[/tex]

=> [tex]25 = A (-12)^2 + 20[/tex]

=> [tex]25 = A\times144 + 20[/tex]

=> [tex]144A = 25 - 20[/tex]

=> [tex]144\ A = 5[/tex]

=> [tex]A = 5 \div 144[/tex]

=> y = (5 / 144) (x - 16)^2 + 20 ---------> this is the second equation of the system.

System:

1) [tex]y = (\frac{1}{15} )x + 18[/tex]

2)[tex]y = (\frac{5}{144} )\ (x - 16)^2 + 20[/tex]

Answer:

23,520

Step-by-step explanation:

The population of an island has decreased by 2% when the population was 24000. What we want to do is find out how much of a population is each percentage. We want to divide 24,000 with 100 because 24,000 is 100% of the population 10 years ago.

24,000 ÷ 100 = 240

Now we know 1% of the population is 240, but we want to find out 2% of the population. Now we want to multiply by 2.

240 × 2 = 480

Now we know the population has decreased by 480 over the last 10 years, but we want to know the population of the island now. This is easy, all we got to do is take the original population and subtract how much the population it has decreased over 10 years.

24,000 - 480 = 23,520

The population of the island now is 23,520

Hope this helps : )

Answer:

23,520

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If the island had a population of 24,000 10 years ago, we could solve for the population decrease by using this expression:

Well, if percentages are fractions of 100, this means that 2% is equivalent to [tex]\frac{2}{100}[/tex], which is also equivalent to 0.02.

This means over the past 10 years the population decreased by 480.

Now that we know this, we can subtract that from the total amount to get the population now.

This means that the population of the island now is 23,520.

Therefore, the population of the island now with a 2% decrease is 23,520.

Shop A sells 16 ounces of peanut butter for $3.99 (24.94 cents/oz), but Store B sells 32 ounces for $6.49 (20.28 cents/oz). At 20.28 cents/oz, Shop B is offering a better price.

To save money while shopping, it is important to compare unit pricing of supermarket items. In this analysis, we contrasted the unit costs of peanut butter at two various retailers. Shop A sells 16 ounces for $3.99, which works out to 24.94 cents per ounce; Store B sells 32 ounces for $6.49, which works out to 20.28 cents per ounce. With a cheaper unit price of peanut butter, Shop B is the preferable option. Comparing unit prices makes it simple to identify which retailer is providing the greatest bargain for the item we need to purchase.

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Answer:

We can use the formula distance = speed x time to find the distance traveled by the bullet.

distance = speed x time

distance = 3 mi/s x 3290 s

distance = 9870 miles

Therefore, the target is 9870 miles away.

Step-by-step explanation:

We can deduce from these findings that the actual population mean is variable probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.

In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols.

The first thing I want to say is that it is a widespread misconception that the average body temperature is 98.6 degrees. Although the "normal" or average body temperature is frequently stated as 98.6 degrees Fahrenheit (or 37 degrees Celsius), this value is not true for everyone. The average body temperature may actually be lower than previously thought, hovering around 97.5–97.7 degrees Fahrenheit, according to study.

Here is the SPSS output for the one-sample t-test so that we can get back to the job at hand:

Descriptive Statistics

N       Mean      Std. Deviation   Std. Error Mean

25      97.528    0.694            0.139

One-Sample Test

Test Value = 98.6

t         df        Sig. (2-tailed)   Mean Difference

-5.238    24        .000              -1.072

We can deduce from these findings that the actual population mean is probably lower and reject the null hypothesis that the population mean for body temperature is 98.6o.

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Answer:486

Step-by-step explanation:

V=a*a*a=729

a=9

S=6a*a=6*81=486

Answer:

486

hope this helps

Part a: The amount of leather needed to create both drum heads is 2769.48 cm².

Part b: Total surface area of Iranian cylindrical drum: 4022.34 cm².

A cylinder is just a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface.

Part a: The amount of leather needed to create both drum heads.

Amount of leather = 2 * area of circle

Amount of leather = 2 * πr²

Amount of leather = 2 * 3.14 * 21²

Amount of leather = 2769.48 cm².

Thus, the amount of leather needed to create both drum heads is 2769.48 cm².

Part b: Total surface area of Iranian cylindrical drum:

TSA = 2πr(h + r)

TSA = 2*3.14*21*(21 + 9.5)

TSA =

Thus, the total area of wood used to make the body of the drum 4022.34 cm².

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Answer:

The unit is unit square or we can also find a by replacing pi by 3.1. 4 point so this equals 2 times of 3.14 and this equals 6.28. This is a unit square, and so the exact area of semicircle is 2 pi unit square or in terms of decimals. It is 6.28 unit square.

Answer:

6.28

Step-by-step explanation:

For the value of a = 7, the expression is true.

A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables. Let's examine the writing style of expressions. A number is 6 times larger than the other number, x, by a factor of 2.

Now in the given question,

1/2 a - 5 1/2 = 5 - a

We first simplify the expression as:

a/2 -11/2 = 5 - a

⇒ (a-11)/2 = 5 - a

⇒ a - 11 = 10 - 2a

⇒ a+ 2a = 10 + 11

⇒ 3a = 21

⇒ a = 7.

Therefore, for the value of a = 7 the expression is true.

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The total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.

What is a composite figure?

Composite geometric figures are made from two or more geometric figures. Finding the area of a composite shape can be done using one of two broad approaches.

The given composite figure consists of two right triangles and a rectangle.

The area of the figure is the sum of the areas of the right triangles and the rectangle.

Both the right triangle are the same.

So the area of one triangle = 0.5 * base * height = 0.5 * 6.4 * 12.8

                                                                = 40.96 sq. yards

So the total area of both triangles = 2 * 40.96 = 81.92 sq. yards.

Now the area of the rectangle = length * breadth = 14.9 * 12.8

                                                            = 190.72 sq. yards

The total area of the figure = 190.72+40.96 = 231.68 sq. yards.

Therefore the total area of the given composite figure found using the areas of right triangles and rectangle is 231.68sq. yards.

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Answer:

6 students

Step-by-step explanation:

We know

There are 120 students in the seventh grade.  5% are in the Environmental Club.

How many students are in the Environmental Club?

5% = 0.05

120 x 0.05 = 6 students

So, there are 6 students in the Environmental Club.

Answer:

6

Step-by-step explanation:

To find the answer to this question we have to find 5% of 120, this will give us how many students there are in the Environmental Club.

To do this we have to do...

Then...

This means that 6 of the students in the seventh grade are in the Environmental Club!

Hope this helps, have a lovely day! :)

a. The balances in the accounts after 5 and 20 years is $12,164.77.

b. The percentage of the balance that is interest is 70%.

c. We need to deposit $17,426.93 today to have $25,000 in 8 years in an account with annual compounding and an APR of 5%.

Principal refers to  initial amount of money invested or borrowed. It is  starting point for calculating  interest or return on investment, or amount owed on loan.

96)

a) To compute the balances in the accounts after 5 and 20 years, we can use the formula for compound interest:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

where A is the ending balance, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

For Paula's account:

After 5 years:

A = 4000(1 + 0.048/365[tex])^{(3655)[/tex] = $5,478.71

After 20 years:

A = 4000(1 + 0.048/365[tex])^{(36520)[/tex] = $9,847.15

For Petra's account:

After 5 years:

A = 3600(1 + 0.056/365[tex])^{(3655)[/tex] = $5,029.80

After 20 years:

A = 3600(1 + 0.056/365[tex])^{(36520)[/tex] = $12,164.77

b) To determine the percentage of the balance that is interest, we can subtract the principal from the ending balance, and then divide by the ending balance:

For Paula's account:

After 5 years:

Interest = $5,478.71 - $4,000 = $1,478.71

Percentage of balance that is interest = (Interest / $5,478.71) * 100% = 27%

After 20 years:

Interest = $9,847.15 - $4,000 = $5,847.15

Percentage of balance that is interest = (Interest / $9,847.15) * 100% = 59%

For Petra's account:

After 5 years:

Interest = $5,029.80 - $3,600 = $1,429.80

Percentage of balance that is interest = (Interest / $5,029.80) * 100% = 28%

After 20 years:

Interest = $12,164.77 - $3,600 = $8,564.77

Percentage of balance that is interest = (Interest / $12,164.77) * 100% = 70%

c) The effect of interest rates and patience can be observed in the significant differences between the ending balances and percentage of interest earned by Paula and Petra. Petra's account had a higher interest rate, resulting in a larger ending balance and a higher percentage of interest earned. Additionally, the longer the investment period, the more the interest compounds and the greater the ending balance becomes. Therefore, patience is key in allowing the investment to grow over time.

81) An account with annual compounding and an APR of 5%

P = 25,000 / (1 + 0.05/[tex]1)^{(1\cdot 8)[/tex] = $17,426.93

Therefore, we need to deposit $17,426.93 today to have $25,000 in 8 years in an account with annual compounding and an APR of 5%.

82) An account with quarterly compounding and an APR of 4.5%

P = 25,000 / (1 + 0.045/4[tex])^{(4 \cdot 8)[/tex] = $17,721.15

Therefore, we need to deposit $17,721.15 today to have $25,000 in 8 years in an account with quarterly compounding and an APR of 4.5%.

87)  An APR of 2.8%, compounded quarterly

First, we need to convert the annual interest rate to a quarterly interest rate by dividing it by 4:

r = 0.028/4 = 0.007

Then, we can use the formula:

P = 120,000 / (1 + 0.007[tex])^{(4\cdot 15)[/tex] = $70,055.47

Therefore, we need to deposit $70,055.47 today in an account with an APR of 2.8%, compounded quarterly, to have a $120,000 college fund in 15 years.

89)  We can use the formula for compound interest to calculate the balance in the accounts after 10 and 30 years:

Balance for Chang: B = [tex]P(1 + r)^t[/tex]

where P = 500, r = 0.035, and t = 10 or 30 years.

Balance for Kio: B = [tex]P(1 + r)^t[/tex]

where P = 500, r = 0.0375, and t = 10 or 30 years.

After 10 years:

Chang's balance: B = [tex]500 (1 + 0.035)^{10[/tex] = $743.22

Kio's balance: B = 500*(1 + 0.0375)^10 = $779.58

After 30 years:

Chang's balance: B = [tex]500 (1 + 0.035)^{30[/tex] = $1,373.63

Kio's balance: B = [tex]500(1 + 0.0375)^{30[/tex] = $1,441.39

As we can see, even though the difference in interest rates is small (0.035 vs 0.0375), it can have a significant impact on the final balance of the account over a long period of time. In this case, after 30 years, Kio's account balance is almost $70 higher than Chang's account balance, even though they both invested the same amount of money.

91)   The formula for calculating the annual percentage yield (APY) is:

APY = [tex](1 + r/n)^n - 1[/tex]

where r is the annual interest rate (in decimal form) and n is the number of compounding periods per year.

For quarterly compounding:

n = 4

APY = (1 + 0.066/4)⁴ - 1 = 0.0677 or 6.77%

For monthly compounding:

n = 12

APY = (1 + 0.066/12)¹² - 1 = 0.0681 or 6.81%

For daily compounding:

n = 365

APY = (1 + 0.066/365[tex])^{365[/tex] - 1 = 0.0682 or 6.82%

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The length of the wire with a radius of 0.236 millimeters is 16.5 cm.

We are given the formula for the radius of a platinum wire in terms of its length L and resistance R:

[tex]r = 0.059L^{(1/2) } \ mm[/tex]

We are also told that the resistance of the wire is 0.1 ohm.

We can use the formula for the resistance of a wire in terms of its length L, cross-sectional area A, and resistivity rho:

R = ρL/A

where;

We can rearrange this formula to solve for the cross-sectional area:

A = ρL/R

Substituting the given values, we have:

A = (10.6 x 10⁻⁸ ohm. m)(L m)/(0.1 ohm)

A = 1.06 x 10⁻⁶ m L

We can also use the formula for the area of a circle in terms of its radius:

A = πr²

Solving for the radius, we have:

r = √(A/π)

Substituting the expression for A, we have:

r = √[(1.06 x 10⁻⁶ m.L )/π]

Substituting the given radius of 0.236 mm, we can solve for the length L:

0.236 x 10⁻³ m = √[(1.06 x  10⁻⁶ m.L)/π]

Squaring both sides, we have:

(0.236 x 10⁻³ m)² = (1.06 x 10⁻⁶ m.L)/π

Solving for L, we have:

L = [(0.236 x 10⁻³ m)² π]/(1.06 x  10⁻⁶ m)

L = 0.165 m = 16.5 cm

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Answer:

Step-by-step explanation:

1 treat bag [tex]=\frac{\$5.20}{2} =\$2.60[/tex]

So 5 treat bags [tex]=5\times \$2.60=\$13.00[/tex]

Dani would have to spend an extra $13 to make 5 more bags.

In response to the supplied query, we may state that 759 is the value decimal entered into the green box.

Both integer and non-integer values are frequently stated in decimal form. Non-integer values are now part of the enlarged Hindu-Arabic numeral system. The process of representing numbers in the decimal system is referred to as decimal notation. A decimal is a number that consists of both a whole and a fractional part. Whole and partially entire quantities are expressed numerically using decimal numbers, which fall between integers. A decimal number's whole number and its fractional component are separated by a decimal point. The decimal point is the dot that separates the full number from the fractions. For instance, 25.5 is a decimal number.  

We may leverage the fact that 0.83 is a decimal representation of a rational number with a finite decimal portion to express 0.83 as a fraction. We may say it this way:

0.83 = 83/100

[tex]8.39 = 8 + 0.39\s= 8 + 39/100\s= 8 + 39/(10^2)\s= 8 + F/(10) (10)[/tex]

Now that the decimal is gone from the right-hand side's numerator, we may multiply both sides by 10:

[tex]10 * 8.39 = 10 * (8 + F/10)\\839 = 80 + F\sF = 839 - 80 = 759[/tex]

So, 8.39 may be expressed as the following fraction:

8.39 = 8 + 0.39 = 8 + 39/100 = 8 + 759/1000

759 is the value entered into the green box.

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The sample proportion should fall between 56.8% and 65.2% of the time for 68% confidence, between 54.6% and 67.4% of the time for 95% confidence, and between 53.4% and 68.6% of the time for almost all of the time.

a. 68%: The sample proportion should fall between 56.8% and 65.2% of the time.

95%: The sample proportion should fall between 54.6% and 67.4% of the time.

Almost all of the time: The sample proportion should fall between 53.4% and 68.6% of the time.

b. Yes, the observed value of 61% is reasonable, based on the answer to part a.

c. For a sample of 400 people, the standardized score corresponding to the 61% response would be 0.5, which would not be considered extreme.

The sample proportion should fall between 56.8% and 65.2% of the time for 68% confidence, between 54.6% and 67.4% of the time for 95% confidence, and between 53.4% and 68.6% of the time for almost all of the time. For a sample of 400 people, the standardized score corresponding to the 61% response would be 0.5, which would not be considered extreme.

The complete question is :

In Case Study 19. 1, we learned that about 56% of American adults actually voted in the presidential election of 1992, whereas about 61% of a random sample claimed that they had voted. The size of the sample was not specified, but suppose it were based on 1600 American adults, a common size for such studies.

a. Into what interval of values should the sample proportion fall 68%, 95%, and almost all of the time?

b. Is the observed value of 61% reasonable, based on your answer to part a?

c. Now suppose the sample had been of only 400 people. Compute a standardized score to correspond to the 61% response and determine if this would be considered extreme.

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A company's break-even point is the level of sales or revenue that the company needs to generate in order to cover all of its expenses and to neither make a profit nor incur a loss.

The amount of sales or revenue that a business must achieve in order to pay all of its costs while not turning a profit or suffering a loss is known as the break-even point. The company's total income and entire costs are equal at the break-even point.

In other words, the firm reaches its break-even point when its entire income matches the sum of its total variable expenses and total fixed costs. Raw materials, labor, and commissions are examples of expenses known as variable costs that fluctuate in response to variations in the volume of production or sales. Rent, salary, and insurance are examples of fixed expenditures that don't fluctuate while output or sales alter.

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Answer:

1.89m

Step-by-step explanation:

The area of the wall is given by:

Area = length x height

Area = 15m x 12m

Area = 180m²

Since the mural is to cover 75% of the area of the wall, the area of the mural is:

Mural area = 75% x Area

Mural area = 0.75 x 180m²

Mural area = 135m²

Let x be the width of the border. Then the dimensions of the mural (including the border) will be:

Length = 15m + 2x

Height = 12m + 2x

The area of the mural (including the border) will be:

Mural area = Length x Height

Mural area = (15m + 2x) x (12m + 2x)

Mural area = 180m² + 54x + 4x²

Since the area of the mural is given by 135m², we can write:

180m² + 54x + 4x² = 135m²

Simplifying and rearranging, we get:

4x² + 54x + 45m² = 0

Solving for x using the quadratic formula, we get:

x = (-54 ± sqrt(54² - 4(4)(45))) / (2(4))

x = (-54 ± sqrt(1536)) / 8

x = (-54 ± 39.12) / 8

We take the positive value for x, since it represents the width of the border:

x = (-54 + 39.12) / 8

x = 1.89m (rounded to the nearest hundredth)

Therefore, the width of the border should be approximately 1.89 metres.

The statement that isn't true is:

B. The median can be different from all of the data values.

The median of a set of data is the middle value when the data is arranged in order from smallest to largest.  

Let's check the given options

A. The median can be the same value as the IQR.

This statement is true, as the IQR is defined as the difference between the third quartile (Q3) and the first quartile (Q1), which are both data values that can include the median.

C. The median can be less than the lower quartile.

This statement is true, as the median is simply the middle value of the dataset when it is arranged in order, whereas the lower quartile (Q1) is the value that separates the bottom 25% of the data from the top 75%.

D. The median can be the same value as the mean.

This statement is true in a symmetric distribution, where the mean and median are equal. However, in skewed distributions, the mean and median can be different values.

B. The median can be different from all of the data values.

The median is a value that divides the dataset into two equal halves. It is always a data value, and it is not possible for the median to be different from all of the data values.  

Therefore,

The statement that isn't true is:

B. The median can be different from all of the data values.

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Answer:

42

Step-by-step explanation:

7 x 6 = 42, making 42 a multiple of seven and less than 45.

Therefore , the solution of the given problem of expressions comes out to be 14x + 70(900 - x) .

Estimates that combine joining, deactivating, but instead random divide should be produced with shifting variables. If they banded together, they could do the following: a mathematical conundrum, some data, and software. A statement of truth contains formulas, components, and arithmetic procedures like adding, subtractions, omissions, and groupings. It is possible to assess and analyse both words and sentences.

Here,

Assume that her vehicle contains x 14-ounce cans.

900 - x = the amount of bottles in her truck (since the total number of cans and bottles is 900.

The cans in her truck carry a total of 14 ounces.

Similar to that, her truck's entire bottle weight is

=>  70(900 - x) ounces.

As a result, the cans and bottles in her truck's entire combined weight (in ounces) can be expressed as follows:

=> 14x + 70(900 - x)

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Step-by-step explanation:

write true if the statement is correct if not write False

The down payment and the amount financed are given as follows:

The down payment and the amount financed are obtained applying the proportions in the context of the problem.

Anna wants to add a $15,280 sunroom to her house. Her bank requires 20% down before lending her any money, hence the down payment is given as follows:

0.2 x 15280 = $3,056.

The amount financed is the part of the price that is not part of the down payment, hence it is given as follows:

15280 - 3056 = $12,224.

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Answer:

242 cm

Step-by-step explanation:

20x12x0.2=242

Answer:

(q²-p)(p²-q), 240

Step-by-step explanation:

Q1     p²q²+pq-q³-p³=(p²q²-q³)+(pq-p³)

                               =q²(p²-q)-(p³-pq)

                               =q²(p²-q)-p(p²-q)

                                =(q²-p)(p²-q)

Q2  If p=4 and q=-4

(4)²(-4)²+(4) x(-4)-(-4)³-4³=256-16+64-64=240

Answer:

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The ratio of x to z is equal to 15 : 42.

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Based on the information provided above, we have the following ratio parameters:

x : y = 5 : 6 ⇒ x/y = 5/6

z : y = 7 : 3 ⇒ z/y = 7/3

Therefore, we can logically deduce the following:

x/z = x/z × y/y

x/z = x/y × y/z

x/z = 5/6 × 3/7

x : z = 15 : 42

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Answer:

x = 18.1

Step-by-step explanation:

1) 12x - 5 + 8x + 3 = 360

2) Subtract 5 from both sides

3) Add 2 on both sides

4) Divide both sides

5) x = 18.1