5.) For Valentine's Day in February, Gabriel's Appliances stocks hundreds of red heart-shaped vacuum
cleaners. The next week Gabriel still has hundreds of them in stock and tells the manager, "Discount
them 25% each week until they are gone." For the week of Valentine's Day, the vacuums were priced at
$80.
a.) What is the price the 1st week after
Valentine's Day?

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Answer:

22.22%

Step-by-step explanation:

If it is exactly a red, it means that it is removed on the first or second attempt, but only once, in this case it does not matter if it is on the first or second attempt because the marble is returned to the bag.

So suppose that on the first attempt red is drawn, the probability would be:

4 / (3 + 4 + 5) = 4/12 = 1/3

Now, on the second attempt, it is not to draw a red, it must be green or blue, so it would be:

(5 + 3) / (3 + 4 + 5) = 8/12 = 2/3

The final probability then is:

1/3 * 2/3 = 0.2222

that is, the probability is 22.22%

Answer:

can you please specify the question i mean is this like

Step-by-step explanation:

let the no. be x

ATQ

3x-7

or

3x= -7

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

answer/explanation:

hope this helps

Answer:

$80.66 and $48

Step-by-step explanation:

1.

Find the total cost of your outfit. 49+25=$74

Find 9% of 74 by doing 0.09x74, which is 6.66. This means that the sales tax is $6.66. 74+6.66=$80.66.

2.

Find 25% of 64 by doing 0.25x64=16. 64-16=$48.

the average of -1 and 0, will be 0.5.

What is inequality?

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Olivia is chosen for the 12U softball team. What age is Olivia? Because it doesn't mention "equals," you are unaware of Olivia's age. But since you already know Olivia's age to be below or equal to 12, you can write it as Olivia's Age 12. This scenario relates to disparities in the real world.

The average slope over the longer intervals will be the average of the slopes in the (same length) intervals that make up the longer interval.

-1 ≤ x ≤ 0 : average of -1 and 0, so 0.5.

Hence the average of -1 and 0, will be 0.5.

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Answer:

it is 1/2

Step-by-step explanation:

The product of a lines slope M and the slope K of a perpendicular is -1:

M*K=-1

This implies

K=-1/M

since

M * -1/M=-1

In our example we are given a line of slope M=-2 therefore the slope K of a line to perpendicular to this line is:

M*K=-1

-2*K=-1

K=-1/-2=1/2

The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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Given function y =45(0.974)ˣ is a function of exponential decay and percentage rate of decrease is 2.6%.

The exponential function is an function f(x) = a(b)ˣ

a = initial amount when x= 0

b= base that is multiplied and it is greater than 0

And x is the variable in the exponent

When b> 1 , the values of this function goes up and up and then this function shows exponential growth.

When 0< b< 1, the values of this function becomes smaller as x increases then this function shows exponential decay.

And r is the percentage rate of change where b =r +1

Given function is y = f(x) = 45(0.974)ˣ

When we compare it with standard function f(x) = a(b)ˣ

we get a = 45 and b =0.974

As b is between 0 and 1 in this case, therefore this function is exponential decay.

b =r+ 1

therefore r = b-1 = 0.974-1 = -0.026

converting 0.026 to percentage we get -0.026*100= -2.6% ( negative sign shows decrease)

Therefore, we can say that the given function represents exponential decay function and rate of decrease is 2.6%

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Answer: 1 minute and 43 seconds faster

Step-by-step explanation:

Answer:

1 minute and 43 seconds faster

Step-by-step explanation:

The order of the fraction from least of greatest are

The fractions in order from least to greatest.

7/15 3/11 13/5 4/2 4/3

converting to decimals

7/15 = 0.4667

3/11 = 0.2727

13/5 = 2.6

4/2 = 2

4/3 = 1.3333

The order is written as follows

3/11 = 0.2727

7/15 = 0.4667

4/3 = 1.3333

4/2 = 2

13/5 = 2.6

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Answer:

9.4ft²

Step-by-step explanation:

The formula for the area of a rectangle is base*height, or b*h.

Since we know the final area of the room and one of the side lengths, we can plug those into the formula I just stated so that we get

15*h=141

All that's left to do is solve for h, which is the other side that we are solving for. To do this, we will divide 15 on both sides:

15h/15=141/15

The 15s on the left side cancel out, and we simply divide 141 by 15 to get our final answer of 9.4ft².

Answer:

answer attached

Step-by-step explanation:

answer attached

hope this helps!

Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The variables which are known from the information given in the task content are; The Monthly interest amount and the Principal.

It follows from the task content that the variables which are known are to be determined.

Since it is given in the task content that the minimum monthly payment is; $22, it follows that the interest amount is; $22.

Also, since the credit card bill is; $1,000, it follows that the principal on the credit card is; $1,000.

Hence, the variables which are known are;

The variables above are therefore used to determine the interest rate of the credit card.

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The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Check the picture below.

Answers:

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

Explanation:

Let A = 50 degrees and C = 30 degrees. The side opposite angle uppercase C is lowercase c = 8. Convention usually has uppercase letters as the angles, while the lowercase letters are side lengths. A goes opposite 'a', B goes opposite b, and C goes opposite c.

Let's use the given angles to find the missing angle B

A+B+C = 180

50+B+30 = 180

B+80 = 180

B = 180-80

B = 100

Now we can apply the law of sines to find side b

b/sin(B) = c/sin(C)

b/sin(100) = 8/sin(30)

b = sin(100)*8/sin(30)

b = 15.7569240481953

b = 15.8

Make sure your calculator is in degree mode.

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

We'll do the same thing to find side 'a'

a/sin(A) = c/sin(C)

a/sin(50) = 8/sin(30)

a = sin(50)*8/sin(30)

a = 12.2567110899037

a = 12.3

Both values for 'a' and b are approximate (even before rounding).

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

Extra info (optional)

Answer:

B=100

b=15.7

a=12.25

Step-by-step explanation:

first find the missing angle:

B=180-50-30

B=100

then use the law of sines:

\( \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) ) } = \frac{c}{ \sin(c) } \)

then

\( \frac{a}{ \sin(50) } = \frac{8}{ \sin(30) } \\ \\ a = 12.25\)

use the same way to find the other side

\( \frac{b}{ \sin(100) } = \frac{8}{ \sin(30) } \\ b = 15.7\)

Answer:

simplified: 4x−28

Step-by-step explanation:

The product of 4 and the difference of a number and 7 can be written as 4(x-7) where x is the number you are looking for.

Answer:

Option A. Only Khaled

Step-by-step explanation:

To know which option is correct, we shall use the formula suggested by both Khaled and Wilma to see which will give the sequence given in the question.

For Khaled:

F(n) = 1 • 3ⁿ¯¹

n = 1

F(n) = 1 • 3ⁿ¯¹

F(1) = 1 • 3¹¯¹

F(1) = 1 • 3⁰

F(1) = 1 × 1

F(1) = 1

n = 2

F(n) = 1 • 3ⁿ¯¹

F(2) = 1 • 3²¯¹

F(2) = 1 • 3¹

F(2) = 1 × 3

F(2) = 3

n = 3

F(n) = 1 • 3ⁿ¯¹

F(3) = 1 • 3³¯¹

F(3) = 1 • 3²

F(3) = 1 × 9

F(3) = 9

For Wilma

F(n) = 1 • 3ⁿ

n = 1

F(n) = 1 • 3ⁿ

F(n) = 1 • 3¹

F(1) = 1 × 3

F(1) = 3

n = 2

F(n) = 1 • 3ⁿ

F(2) = 1 • 3²

F(2) = 1 × 9

F(2) = 9

n = 3

F(n) = 1 • 3ⁿ

F(3) = 1 • 3³

F(3) = 1 × 27

F(3) = 27

SUMMARY

Using Khaled's formula i.e F(n) = 1 • 3ⁿ¯¹ we obtained 1, 3, 9,..

Using Wilma's formula i.e F(n) = 1 • 3ⁿ

We obtained 3, 9, 27,..

Now, comparing the sequence obtained using the formula of both Khaled and Wilma, we can see that only the sequence of Khaled is the same with the one given in the question. Therefore, only Khaled's formula is correct.

Answer:

\(105\:\mathrm{m^3}\)

Step-by-step explanation:

The volume of a rectangular prism is given by \(V=l\cdot w\cdot h\). Plugging in given values, we have \(V=1.5\cdot 10\cdot 7=\boxed{105\:\mathrm{m^3}}\).

Answer:

105

Step-by-step explanation:

Length × Width × height

10×7× 1.5

(10×7) 1.5

70×1.5

=105

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

Step-by-step explanation:

Given expression which gives the distance is 16t².

Here, t = time or duration

For t = 20 seconds,

16t² = 16(20)²

      = 6400 feet

For t = 21 seconds,

16t² = 16(21)²

      = 7056 feet

For t = 22 seconds,

16t² = 16(22)²

      = 7744 feet

For t = 23 seconds,

16t² = 16(23)²

      = 8464 feet

Therefore, complete table will be,

t             20            21           22           23

h         6400       7056       7744     8464    

The side length of the triangle Elizabeth drew cannot form a right triangle.

A right triangle is a triangle that has one of its angle as 90 degrees.

The sides of a right triangles are hypotenuse side, adjacent side and the opposite side. This is base on the angle position.

Right triangle obeys Pythagoras's theorem.

a² + b² = c²

where

Therefore, let's test if the labelled side of the triangle Elizabeth drew is a right triangle.  We will use Pythagoras theorem to confirm it

5² + 8² = 14²

25 + 64 = 196

Therefore,

89 ≠ 196

Therefore, the side length cannot form a right triangle

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As per the concept of exponential decay, the initial mass of the sample is 5,254.87 kg

What is meant by Exponential decay:

In math, the term exponential decay is a very common process especially when we are talking about radioactive materials.

The standard  formula for this type of behavior which is written below:

A = Pe^-rt

where

A refers the amount left after time t

P refers the initial amount at t=0

r refers the rate

Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago.

And we need to find if the sample has a mass of today, then the initial mass of the sample.

Now, we have to substituting the values,

Then we get the equation as,

=> A = (9575 kg)(e^-0.12*5)

When we simplify this one, then we get,

=> A = 5,254.87 kg

Therefore, the initial mass of the sample is 5,254.87 kg

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The opposite angles are ∠LRE = ∠FRA and ∠TRF = ∠NRL. Then the correct options are A and D.

The complete question is attached below.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The opposite angles are given below.

∠LRE = ∠FRA

∠TRF = ∠NRL

Then the correct options are A and D.

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Answer:

155/20

Step-by-step explanation:

155/20 in decimal form is 7.75, which is only 0.25 off of 8

7.511 is 0.489 off of 8

8.3% is technically not anywhere near 8 because a percentage needs to be a percentage of something in order to make sense.