A right triangle has a base of 8 1/2 inches and a height of 12 1/2. If the height is reduced to 4 inches, how many inches is the new base?

need help I don't know the answer

The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

According to the statement

we have given that the Smith family's sprinkler was 25L per hour and

Stewart family's sprinkler was 30L per hour and The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L.

And we have to find the How long was each sprinkler used.

So, For this purpose,

The given statements in the equation form become:

Let Smith family's sprinkler be x

Let Stewart family's sprinkler be y then

The equation become

x + y = 65 -(1)

25x + 30y = 1750 -(2)

Here we use the elimination method.

So, Multiply (1) by 25 and (2) by 1 then

25x + 25y = 1625

25x + 30y = 1750

Now eliminate x from the equations then

-5y = -125

y = 25

then x value becomes

x + y = 65

x + 25 = 65

x = 40.

So, The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

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Answer:

120 four digit numbers can be created from the gives.

Step-by-step explanation:

Solution

You are given 5 digits in the givens.

1 3 5 7 9

Therefore

5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.

Answer:

Step-by-step explanation:

If they all exist in proportion to one another (READ: ratio) then multiplying each of the angles by the same number (here, some unknown "x" value) will maintain the proportionality. Since all the angles of a quadrilateral have to add up to equal 360, then

2x + 4x + 5x + 7x = 360 and

18x = 360. Divide both sides by 18 to get that

x = 20. That means that

2x = 2(20) = 40 and

4x = 4(20) = 80 and

5x = 5(20) = 100 and

7x = 7(20) = 140. Adding all of those up:

40 + 80 + 100 + 140 = 360

Answer:

40,80,100,140

Step-by-step explanation:

Let the ratio 2:4:5:7 angles be 2x, 4x, 5x, 7x

Now

2x + 4x + 5x + 7x=360 degrees

18x = 360 degrees

x =360/18

x=20

2x=2 *20=40

4x=4 *20=80

5x=5 *20=100

7x=7* 20=140

The price elasticity of demand of the pen will be -0.2.

The demand and supply schedule will be:

Price Qd. Qs

$10. 250. 100

$20. 200. 90

$30. 180. 80

The price elasticity of demand from $1 to $2 will be:

= Percentage change in quantity demanded/percentage change in price

Percentage change in quantity demanded will be:

= (200 - 250)/250 × 100

= -20%

Percentage change in price will be:

= (20 - 10)/10 × 100

= 100%

Therefore, the elasticity of demand will be:

= -20/100

= - 0.2

The value gotten illustrates an inelastic demand.

In order to increase the total revenue, the price can be reduced as it will lead to more sales.

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Complete question:

Choose any product or service. Create the demand and supply schedule.

Calculate just one PED.

Is the demand elastic or inelastic?

What price change would you recommend to increase TR?

The number of license plates is 11232000

The given parameters are:

Characters = 6 i.e. 3 letters and 3 digits

Letters = 3 different letters

Digits = 3 different digits

There are 10 different digits and 26 different letters.

Since each character is different from the other, then we have:

Digits = 10, 9 and 8

Characters = 26, 25 and 24

The number of license plates is then calculated as:

n = 10 * 9 * 8 * 26 * 25 * 24

Evaluate the product

n = 11232000

Hence, the number of license plates is 11232000

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a. The changes in each four-month period are as follows:

Month and       Prices       Absolute      Relative

Year              in Dollars     Change       Change

Apr-20              1.841             n/a                n/a

Aug-20            2.183         $0.342        18.58%

Dec-20            2.195            0.012         0.55%

Apr-21             2.858          0.663         30.21%

Aug-21             3.158          0.300        10.50%

Dec-21            3.307           0.149          4.72%

Apr-22            4.109          0.802        24.25%

b. The change in gas prices has been relatively unstable.

c. Using the inflation calculator, the costs of gas in April 2020 in 2022 dollars terms should be $2.08.

d. The inflation-adjusted cost of gas in April 2020 when compared to April 2022 as absolute and relative changes are as follows:

Absolute change = $2.268 ($4.109 - $1.841)

Relative change = 123.2% ($2.268/$1.841 x 100)

e. The two most drastic rises in gasoline prices in April 2021 and April 2022 can be attributed to spikes in demand relative to supply.

Gasoline prices rise when there is an increased demand relative to supply.

Increasing prices in gasoline prices can also be attributed to cuts in production and supply by the oil cartel.

An absolute change is a dollar change from one period to another.

A relative change is an absolute change expressed in percentages.

The calculations of absolute change and relative change are demonstrated below.

Month and       Prices       Absolute      Relative

Year              in Dollars     Change       Change

Apr-20              1.841             n/a                n/a

Aug-20            2.183         $0.342        18.58% ($0.342/$1.841 x 100)

Dec-20            2.195           0.012         0.55% ($0.12/$2.183 x 100)

Apr-21             2.858          0.663        30.21% ($0.663/$2.195 x 100)

Aug-21             3.158          0.300        10.50% ($0.3/$2.858 x 100)

Dec-21            3.307           0.149          4.72% ($0.149/$3.158 x 100)

Apr-22            4.109          0.802        24.25% ($0.802/$3.307 x 100)

Absolute Change for Aug-20 = $0.342 ($2.183 - $1.841)

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green balls = 83

orange balls = 19

Step-by-step explanation:

green balls = g

orange balls = r

g = 7 + 4r

g + r = 102

7 + 4r + r = 102

5r = 95

r = 19

g + 19 = 102

g = 83

The option that is a proportion is: B. 4/6 = 2/3.

A proportion can be defined as an equation whereby two ratios are set equal to each other, in such a way that the ratio on one side equals the ratio on the other side of the equation when simplified.

First Option is not a proportion because:

5/7 ≠ 10/12 (10/12 can be simplified further as 5/6, which is not equal to 5/7).

Second option is a proportion because:

4/6 = 2/3

8/12 = 2/3

Thus, 4/6 = 8/12.

Third Option is not a proportion because:

14/21 = 2/3

9/12 = 3/4

Therefore, 14/21 ≠ 9/12.

Fourth Option is not a proportion because:

9/15 = 3/5

12/18 = 2/3

Therefore, 9/15 ≠ 12/18.

In conclusion, the option that is a proportion is: B. 4/6 = 2/3.

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Answer:

[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2[/tex]

Step-by-step explanation:

[tex]x^{2}+\frac{1}{2} x=x^{2}+2 \times \frac{1}{4} \times x +(\frac{1}{4})^2 - (\frac{1}{4})^2[/tex]

[tex]=[x^{2}+2 \times \frac{1}{4} \times x +(\frac{1}{4})^2] - (\frac{1}{16})[/tex]

[tex]=[x + \frac{1}{4}]^2 - (\frac{1}{16})[/tex]

____________________

then

[tex]x^{2}+\frac{1}{2} x = [x + \frac{1}{4}]^2 - (\frac{1}{16}) -2 + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{1}{16}) -2] + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x = [(x + \frac{1}{4})^2 - (\frac{33}{16}) ] + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x = (x + \frac{1}{4})^2 - \frac{33}{16} + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= (x + \frac{1}{4})^2 + 2[/tex]

then

[tex]x^{2}+\frac{1}{2} x + \frac{33}{16}= 2 + (x + \frac{1}{4})^2[/tex]

The company's inventory turnover ratio, based on the financial data, equals 10 times.

The inventory turnover ratio measures the number of times the company sells and replaces its inventory over a given period.

The formula for calculating the Inventory Turnover Ratio is the Cost of Goods Sold divided by the Average Inventory.

The Average Inventory is the mean of the beginning and ending inventories.

Sales revenue = $60,000

Cost of goods sold = $20,000

Beginning inventory = $1,600

Ending inventory = $2,400

Average inventory = $2,000 ($1,600 + $2,400)/2

Inventory turnover ratio = 10x ($20,000/$2,000)

Thus, the company sells and replaces its inventory over a period of 10 times.

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The conclusion for p, from the confidence interval, using an absolute value inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

A confidence interval is given by the estimate plus minus the margin of error. As an inequality, we have that the absolute value of the difference between the proportion and the estimate is of at most the margin of error, that is:

[tex]|p - E| \leq M[/tex]

For this problem, the estimate and the margin of error are:

E = 0.27, M = 0.019.

Hence the inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

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Answer:

0

Step-by-step explanation:

We are looking at the change in y over the change is x.  The change is y is always 0 and 0 divided by anything will be zero.

The probability that the person is a man or heavy smoker is 621 / 1124.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the respondent is a man or heavy smoker can be determined by adding the probability that the respondent is a man and the probability that the respondent is a heavy smoker together.

The probability that the person is a man or heavy smoker = (number of men / total number of respondents) + (number of heavy smokers / total number of respondents)

(531 / 1124) + (90 / 1124) = 621 / 1124

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The equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

The given parameter is

constant rate of 20 kilometers per hour.

This means that

Rate = 20km per hour

When Seb bikes for t hours, the distance is

d = rate * t

This gives

d = 20t

Hence, the equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t

This means that

t = 5

So, we have:

d = 20 * 5

Evaluate

d = 100

Hence, Seb will travel 100 kilometers if he bikes at this rate for 5 hours

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Answer:

1. d=20t

2. 50

The rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.

Given the function of the population to be;

n (t) = 24 e^0. 015t

Where;

In 2004, t = 1

Substitute into the formula;

n(1) = 24 e^0. 015t

n(1) = 24 e^(0.015 × 1)

n(1) = 24 e^0. 015

n(1) = 24. 8 millions

In year 2012, t = 8

n(8) = 24 e^(0. 015 × 8)

n(8) = 24e^0. 12

n(8) = 31. 6 millions

Thus, the rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.

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Filling in the frequency table according to the colors observed and expected on the M & M Peanut candies is as follows:

Color                              Brown    Yellow     Red      Green     Orange    Total

Observed Frequency     67           22           51           24           24         188

Expected Frequency     56           38           38           38            18         188    

Observed Frequency   36%         12%       27%         13%          13%

Expected Frequency    30%        20%      20%        20%          10%

A frequency table is a display of the number of occurrences of a particular value or characteristic.

A frequency table makes it easy to display and interpret a distribution of data.

The absolute frequencies shows the absolute values of the observed and expected frequencies, while the relative frequencies shows the percentage values of the observed and expected frequencies.

Color                              Brown    Yellow     Red      Green     Orange    Total

Observed Frequency     67           22           51           24           24         188

Expected Frequency     30%        20%       20%        20%         10%      100%

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Fill in the following table on the frequency of the colors, indicating the absolute and relative frequencies of the distributions.

Using the Fundamental Counting Theorem, it is found that there are 124 three-digit multiples of 5 that have three different digits and at least one prime digit.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Multiples of 5 finish at 0 or 5, hence the parameters to find the number of three-digit multiples of 5, with different digits are:

[tex]n_1 = 9, n_2 = 8, n_3 = 2[/tex]

And the number is:

N = 9 x 8 x 2 = 144.

With no prime digits, 2, 3, 5 and 7 cannot be used, hence the parameters are:

[tex]n_1 = 5, n_2 = 4, n_3 = 1[/tex]

Hence 20 of the numbers have no prime digits, and 144 - 20 = 124 have at least one prime digit.

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Answer:

Length = 52 ft

Width = 40 ft

Step-by-step explanation:

Given information:

Scale

[tex]\implies \sf 3 \: in : 8 \: ft[/tex]

[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]

To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:

[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]

[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]

Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.

Scale is 3in:8ft

So

Length

Width

The volume of the grain storage building is 3770. 4 m³

From the given question, it can be deduced that the grain storage is a combination of a cylinder and a cone

The volume of the grain storage = volume of the cone + the volume of the cone

The formula for finding the volume of a cylinder is given as;

Volume of cylinder = πr²h

But we know that radius is the diameter divided by 2

radius = 20/2

radius = 10 meters

height = 10 meters

Substitute the values in the formula

Volume of cylinder = 3. 142 × 10 × 10 × 10

Volume = 3. 142 × 1000

Volume = 3142 m³

The formula for finding the volume of a cone is given as;

Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]

If the cone has the same diameter, then the radius is 10 meters and the height is 6 meters

Substitute the values into the formula

Volume of the cone = 3. 142 × 10 × 10 × 6/ 3

Volume = 3. 142 × 100 × 2

Volume = 628. 4 m³

The volume of the grain storage building = 3142 + 628. 4

The volume of the grain storage building = 3770. 4 m³

Thus, the volume of the grain storage building is 3770. 4 m³

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Answer:

3770. 4 m³

Step-by-step explanation:

i took the test

Answer: 24,000

Step-by-step explanation:

This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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Answer:

30°

Step-by-step explanation:

[tex]\frac{195-(8x+17)}{2}=5x-10 \\ \\ 178-8x=10x-20 \\ \\ 198=18x \\ \\ x=11[/tex]

So, this means arc FH measures 105 degrees.

Since the circumference of a circle measures 360 degrees, arc EF measures 60 degrees.

By the inscribed angle theorem, angle EHF measures 30°.

The formula for the nth term of the arithmetic sequence is [-3]n+10

What is the nth term of an arithmetic sequence?

⇒ The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

Calculation:

It is given that the given sequence is an arithmetic sequence.

First term a1 = 7

Second term a2 = 4

Common difference d = 4-7

⇒ d=3

From the general formula,

an = a1 + (n - 1)d

On substituting,

an = 7+ (n-1)(-3)

an = 7-3n+3

an = -3n+10

⇒ Thus the general formula for the nth term of the arithmetic sequence  is -3n+10

an= [-3]n+10

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The number of strings that can be formed by ordering the letters SCHOOL using some or all of the letters is 1440 strings

Permutation can be defined as number of ways in which things can arranged.

We were given to find how many strings that can be formed by ordering the letters SCHOOL using some or all of the letters.

First of all, How many distinct letters are in the word SCHOOL ?

The distinct letters are 5 in numbers.

What is the total number of letters in the word SCHOOL ?

The total number of letters is 6.

Then

6! + 5[tex]P_{5}[/tex]

That is, 6 factorial + 6 permutation 5

( 6 x 5 x 4 x 3 x 2 x 1 ) + 6!/( 6 - 5)!

720 + 720

1440 strings

Therefore, the number of strings that can be formed by ordering the letters SCHOOL using some or all of the letters is 1440 strings

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Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

Answer: B. (-1, -5)

Step-by-step explanation:

Given equations

2x + y = -7

x - y = 4

Concept

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]

Convert into matrix

[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

Calculate the inverse of the matrix

[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]

[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]

Solve by multiplying the inverse of the matrix

[tex]A*A^{-1}=A^{-1}*A=I[/tex]

[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]

[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]

Simplify by multiplication

[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]

Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The length of the arc of the circle is 3.67 meters

The arc of a circle is a part of the circumference that makes up the circle

From the question, we have the following parameters

Diameter, d = 14 meters

Central angle = π/6 radians

Start by calculating the radius of the circle using

Radius, r = Diameter/2

This is so because radius is half the diameter

So, we have

r = 14 meters/2

Evaluate the quotient of 14 meters and 2

r = 7 meters

The length of the arc of the circle is then calculated using

L = Radius * Central angle

Substitute known values in the above equation

L = 7 meters * π/6

Evaluate the product of 7 and π/6

L = 3.67 meters

Hence, the length of the arc of the circle is 3.67 meters

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Answer:

vertex : (-5/2, -53/4)

solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)

Step-by-step explanation:

1.The vertex of the function is (-5/2, -53/4).

2.We have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.

1. Vertex:

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:

x = -b / (2a)

y = f(x) = ax^2 + bx + c

Given: a = 1, b = 5, c = -7

x = -5 / (2 * 1) = -5 / 2

Now, substitute the value of x into the equation to find y:

y = (-5/2)^2 + 5 * (-5/2) - 7

y = 25/4 - 25/2 - 7

y = 25/4 - 50/4 - 7

y = (25 - 50 - 28) / 4

y = -53 / 4

So, the vertex of the function is (-5/2, -53/4).

2. Solutions (or roots or x-intercepts):

To find the solutions (x-intercepts) of the function, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Given: a = 1, b = 5, c = -7

x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1

x = (-5 ± √(25 + 28)) / 2

x = (-5 ± √53) / 2

Now, we have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.

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