A customer receives a discount on each purchase. If the customer's bill is $1,600 before the discount and the bill is $1,460 after the discount what is the percent discount? OA) 8.8% B) 9.5% O C) 11.4% D) 91.3%

The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.

To determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.

Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):

Number of half-lives = (Total time elapsed) / (Half-life)

Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545

Since we can't have a fraction of a half-life, we take the integer part, which is 5.

Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:

Remaining amount = Initial amount * (1/2)^(Number of half-lives)

Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:

Remaining amount = 1000 grams * \((1/2)^5\)

Remaining amount ≈ 1000 grams * 0.03125

Remaining amount ≈ 31.25 grams

Therefore, after 2 hours, approximately 31.25 grams of francium will be left.

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The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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9514 1404 393

Answer:

  1/4

Step-by-step explanation:

Each coordinate of H'J'K' is 1/4 of the value for HJK.

The scale factor is 1/4.

Answer:

1/4 would be right I am 100% sure

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

For point a:

\(\to fx_1(x_1)=\int^{x_{1}}_{0} f(x_1,x_2)\ dx\\\\\)

\(=\int^{x_{1}}_{0} e^{-x_1}\ dx_2\\\\= e^{-x_1} \ [x_2]^{x_1}_0 \\\\\therefore f x_1(x_1)=x_1e^{-x_1}; \ \ x_1>0\\\\\)

For point b:

\(\to f(x_2|x_1)=\frac{f(x_1,x_2)}{f(x_1)}\ =\frac{e^{-x_1}}{x_1\ e^{-x_1}}=\frac{1}{x_1} ; \\\\ \ \ 0\leq x_2 \leq x_1 \\\\\)

For point c:

\(P(x_1>2|x_2=7)= 1.00 \\\\\because x_2=7\to x_1>7\to x_1>2\\\\\)

h) 72 cm³

i) 160 km³

h) Volume of rectangular prism = length × width × height

length = 12cm

width = 2cm

height = 3cm

Volume of rectangular prism = 12cm × 2cm × 3cm

Volume of rectangular prism = 72 cm³

i) length = 5 km

width = 8 km

height = 4 km

Volume of rectangular prism = 5km × 8km × 4km

Volume of rectangular prism = 160 km³

Answer: 34.64 m

Step-by-step explanation:

Given: A boat is 60 m from the base of a lighthouse.

The angle of depression between the lighthouse and the boat is 37°.

By using trigonometric ratios :

\(\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}\)

here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m

\(\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64\)

Hence, the lighthouse is 34.64 m tall.

Answer:

x = 98

y = 126

Step-by-step explanation:

If you match triangle abc to triangle cde, you will match where x and y is.

168 ÷ 12 = 14

Now you multiply 14 by the other side lengths

9 • 14 = 126

7 • 14 = 98

It is similar to a dilation.

Answer:

1) Circumference = 2πr

C = 2 x π x 9

C = 18π = 56.548... = 57 inches (to the nearest inch)

2) 6h = $52.50

1h = $52.50/6 = 8.75

11h = 8.75 x 11 = $96.25 = $96 (to the nearest cent)

(57)

Answer:

Proof below

Step-by-step explanation:

Irrational and Rational Numbers

We need to use the basic property of logarithms:

\(log_b\ a=x\ \ \Rightarrow b^x=a\)

We are given:

\(log_3\ 7\)

And we will prove it's an irrational number, i.e., it's not a rational number.

Recall a rational number can always be expressed as a fraction a/b, where a and b are integer numbers. Thus, if the expression was a rational number, then:

\(\displaystyle log_3\ 7=\frac{a}{b}\)

Applying the property:

\(\displaystyle 3^{\frac{a}{b}}=7\)

Raising to the power of b:

\(3^a=7^b\)

It's not possible to find two integers a and b that satisfy the condition above. That contradiction comes from the assumption that \(log_3\ 7\) is rational, thus, it's proven \(log_3\ 7\) is irrational.

The most common number of hours volunteered is 22.

Option B is the correct answer.

We have,

A.
The number of students who volunteered more than 30 hours is greater than the number of students who volunteered fewer than 30 hours.

This can not be determined from the given stem-and-leaf plot as it only shows the frequency distribution of hours volunteered without any specific count of students.

The plot only indicates that there are some students who volunteered between 31-36 hours (stem 3, leaves 33, and 36) and one student who volunteered for 44 hours (stem 4, leaf 4).

Therefore, option A is not supported by the given data.

B.

The most common number of hours volunteered is 22.

From the stem-and-leaf plot, we can see that the mode is 22 as it has the highest frequency (stem 2, leaves 2, 5, 7, 8).

Hence, option B is supported by the given data.

C.

The number of students who volunteered between 9 and 20 hours is greater than the number of students who volunteered more than 40 hours.

This statement cannot be confirmed by the given stem-and-leaf plot as there are no leaves in stem 1, which means there are no students who volunteered less than 10 hours. Also, there are no leaves in stem 4, except for one leaf with a value of 44.

Therefore, we can not determine how many students volunteered between 9-20 hours and more than 40 hours. Hence, option C is not supported by the given data.

D.

The most common number of hours volunteered is 41.

There are no leaves in stem 4 except for the value of 44, which means there is no student who volunteered for 41 hours.

Hence, option D is not supported by the given data.

Therefore,

The most common number of hours volunteered is 22.

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The system of equations that shows the situation is option 1.  L+J=29  L=2J-10

The question tells us that the summation of the age of Latifa and Jameel is 29

Let J = Jameel

L = Latifa

L + J = 29

The question says that Latifa's age is 2 time of Jameels age = 2J with 10 years subracted

L = 2J - 10

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Answer:

120 Girls

Step-by-step explanation:

First, you have to combine the dark shade girls and the light shade girls together to get 7.

Then, you should divide 210 by 7, to get 30

Finally, using 30 as your multiplier,

you go and multiply 30 x 4 to get 120 girls :D

Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

Understanding statistical questions and data distributions is an important concept in data analysis and statistics. A statistical question is one that can be answered by collecting and analyzing data.

These questions typically ask about a population or group of individuals and are often related to trends or patterns.

Data distributions refer to the way data is spread out or distributed within a dataset. This can include measures like the mean, median, and standard deviation. Understanding data distributions is important for making accurate interpretations and predictions based on the data.

To practice understanding statistical questions and data distributions, it's important to work with real-world datasets and ask questions that can be answered using statistical analysis.

This can involve looking at trends and patterns in the data and interpreting the results in a meaningful way. By building these skills, you can become better equipped to analyze and interpret data in a variety of settings.

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The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

We have,

To find the ordered pair solutions for the system of equations, we need to solve the equations simultaneously.

The given equations are:

f(x) = x² - 2x - 3

f(x) = x + 1

Since both equations are equal to f(x), we can set them equal to each other:

x² - 2x - 3 = x + 1

Now, let's solve this quadratic equation:

x² - 2x - 3 - x - 1 = 0

x² - 3x - 4 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula.

Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation,

a = 1, b = -3, and c = -4.

Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(1)(-4))) / (2(1))

x = (3 ± √(9 + 16)) / 2

x = (3 ± √25) / 2

x = (3 ± 5) / 2

We have two possible solutions:

When x = (3 + 5) / 2 = 8 / 2 = 4

When x = (3 - 5) / 2 = -2 / 2 = -1

Therefore, the ordered pair solutions for the system of equations are:

(4, f(4)) and (-1, f(-1))

Now, let's substitute these values into either equation to find the corresponding y-values (f(x)):

For x = 4:

f(4) = 4 + 1 = 5

So, one solution is (4, 5).

For x = -1:

f(-1) = -1 + 1 = 0

So, another solution is (-1, 0).

Therefore,

The ordered pair solutions for the system of equations are:

(4, 5) and (-1, 0).

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Answer:

24

Step-by-step explanation:

Because 300 cookies / 38 cookies = 7.89,..

Then 7.89,... x 3 = 23.68,...

round to the nearest tenths= 24

In order to meet the demand for the bake sale, a total of 300 cookies will be prepared, requiring the use of precisely 24 fresh eggs.

To calculate how many eggs you need to make 300 cookies, set up a proportion based on the information given in the cookie recipe:

Number of eggs / Number of cookies = Constant ratio

Let the number of eggs needed for 300 cookies as "x."

So,  x eggs / 300 cookies = 3 eggs / 38 cookies

Now, cross-multiply and solve for "x":

x * 38 = 3 * 300

38x = 900

x = 900 / 38

x = 23.6842

x ≈ 24

Therefore, you need 24 eggs to make 300 cookies for the bake sale.

Thus, option (b) is correct.

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Jeff needs 21 oz of gelatin and 14 cups of water to make 7 boxes

The table of values is given as

Boxes          Gelatin Powder (oz)        Water (cups)

3                                           9                        6

From the above table, we can see that

Gelatin Powder = 3 * Boxes

Water  = 2 * Boxes

When there are 7 boxes, the equations become

Gelatin Powder = 3 * 7

Water  = 2 * 7

Evaluate the products in the above equation

So, we have

Gelatin Powder = 21

Water  = 14

Hence, the amount of gelatin and water needed to make 7 boxes are 21 oz and 14 cups respectively

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Answer: D: jeff will use 21 oz of powder and 14 cups of water

Step-by-step explanation:

the chart says there are

3 boxes of gelatin ) 9 oz of powder ) 6 cups of water

that equals the same as

1 box of gelatin ) 3 oz of power ) 2 cups of water

so for every box of gelatin, there is 3oz of powder and 2 cups of water

if he wants to make 7 boxes.....

7x3oz=21 oz

7x2cups=14 cups

so the Answer is D

Answer: Here, let X,Y,ZX,Y,Z indicate the amount in dollars to be invested

Step-by-step explanation: Here, let X,Y,ZX,Y,Z indicate the amount in dollars to be invested

The percentage of fares for a cab company in Chicago that fall within certain standard deviation ranges from the mean fare from O'Hare Airport to the Drake Hotel is calculated Using Chebyshev's theorem:

What is standard deviation?

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from their mean (average) value. In other words, it measures how spread out the data is from the average.

(a) According to Chebyshev's theorem, at least 75% of the fares lie between 20.87 dollars and 34.87 dollars.

(b) According to Chebyshev's theorem, at least 84% of the fares lie between $18.37 and $37.37. (Round your answer to 2 decimal places.)

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the fares lie between $14.37 and $41.37.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 95% of the fares lie between 20.87 dollars and 34.87 dollars.

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Answer:

EREREREREREEE TE RWRWRERE TE J

Solving a system of equations we will see that she deposited $18,000 at the 4.5% rate and $36,000 at the 5% rate.

First, let's define the variables:

We know that:

y = 2*x

And because the total income is $2610, then:

0.045*x + 0.05*y = $2610

So we have a little system of equations:

y = 2*x

0.045*x + 0.05*y = $2610

To solve this we can replace the first equation into the second one:

0.045*x + 0.05*(2x) = $2610

x*(0.045 + 0.1) = $2610

x*0.145 = $2610

x = $2610/0.145 = $18,000

We conclude that she deposited $18,000 at the 4.5% rate, and twice that amount (2*$18,000 = $36,000) at the 5% rate.

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A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.

A function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable = domain

The dependent variable = Range

We are given a graph where the x-axis contains the radius value and the y-axis contains the circumference value.

We can write the function as:

f(x) where x can be 4, 8, 12, 16, 20, 24, 28, 32, 36

f(0) = 0

f(4) = 22.5

f(8) = 52.5

f(12) = 75

f(16) = 105

f(20) = 127.5

f(24) = 150

The domain is between 0 to 150 and the range is between 0 and 28.

Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.

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Answer:

Kay has 7 blue balloons

Step-by-step explanation:

if Sal has 5 red balloons and 2 blue balloons and Kay has 5 more blue balloons than Sal the Kay has 7 blue balloons

The number of blue balloons does Kay have is 7.

Given that, Sal has 5 balloons. He has 3 red balloons. The rest are blue.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of blue balloons does Kay have be x.

Number of blue balloons Sal have = 5-3=2

The number of blue balloons does Kay have = Kay has 5 more blue balloons than Sal

⇒ x = 2+5 = 7

Therefore, the number of blue balloons does Kay have is 7.

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Let the number of adults equal x, and the number of children equal 5x.

26(5x) + 69x = 94908

194x = 94908

x = approx. 489

About 489 adults bought tickets.

A total of 489 adults take tickets to the circus & Fan Fair show.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the number of tickets that adults bought is a and the number of tickets that children bought is c.

Then,

26(5a) + 69c = 94908

194a = 94908

a = 489.21 but we need to take the whole number and practical number so it will be 489.

Hence "A total of 489 adults take tickets to the circus & Fan Fair show".

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Answer:

Z

Step-by-step explanation:

Using the circles:

A circle with a radius of 8 inches has an area and circumference given by:

A = πr² = π(8²) ≈ 201.06 square inches

C = 2πr = 2π(8) ≈ 50.27 inches

Rounding to the nearest hundredth:

A ≈ 201.06 square inches

C ≈ 50.27 inches

Therefore, the area is approximately 201.06 square inches and the circumference is approximately 50.27 inches.

A circle with a diameter of 20 meters has a radius of 10 meters. The area and circumference are given by:

A = πr² = π(10²) ≈ 314.16 square meters

C = 2πr = 2π(10) ≈ 62.83 meters

Rounding to the nearest hundredth:

A ≈ 314.16 square meters

C ≈ 62.83 meters

Therefore, the area is approximately 314.16 square meters and the circumference is approximately 62.83 meters.

Using these relationships, find the measures of some of the angles:

a) mJKP = mJKN (by vertical angles) and mJKP + mPKL = 90° (by complementary angles), so mJKN + mPKL = 90°.

b) mJKN = mJKP (by vertical angles) and mJKN + mKNM = 90° (by complementary angles), so mJKP + mKNM = 90°.

c) mJLK = mMPL (by alternate interior angles) and mMPL = 63°, so mJLK = 63°.

d) mKNM = 90° - mJKN (by complementary angles). We cannot determine the measure of mJKN.

e) mJLK = mMPL (by alternate interior angles) and mJLR = mJLP (by vertical angles), so:

mJLK + mKLP + mPLJ + mJLP = 360° (by the sum of angles in a quadrilateral)

63° + 90° + mPLJ + mJLP = 360°

mPLJ + mJLP = 207°

f) mJLR = mJLP (by vertical angles) and mKPL = 90°, so:

mJLR + mJLP + mKPL = 180° (by the angles in a triangle)

mJLR + mJLP + 90° = 180°

mJLR + mJLP = 90°

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Image transcribed:

Use the circle below for questions 1-7.

1. Name a radius.

2. Name a diameter.

1.

2.

3.

R

3. Name a chord that is not a diameter.

P

4. Name a central angle.

4.

S

5. Name a minor arc.

5.

6. Name a major arc.

7.

7. Name a semicircle.

For questions 8 and 9, find the area and circumference. Round to the nearest hundredth.

8.

A =

C=

9.

A =

20 m

8 in

C=

10. If m∠MPL = 63°, find each measure.

K

a) mR= =

= m KNM d) 이이

=

b) - =

c) L

=

f) mJLR =

N

M

Gina Wilson (All Things Algebra, LLC), 201

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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