The cost of some office furniture after a 20% reduction was $3520.00. What was the original price before the furniture was discounted?

Answer:

55

Step-by-step explanation:

Answer:

Length = 30√2 yards.

Step-by-step explanation:

There is a plot of land of square shape that has 30 yards on each side. Jules owns this plot. He plans to divide the land in half by building a fence along the diagonal of the plot.

We have to calculate the length of the fence.

Now, the length of the diagonal will be the length of the fence.

So, the length = [tex]\sqrt{30^{2} + 30^{2}} = 30\sqrt{2}[/tex] yards. (Answer)

Answer:

C. 30√2 yd

Step-by-step explanation:

The value of b is -3

Explanation:

The function is [tex]f(x)=\frac{1}{4} x^{2} +bx+10[/tex] and [tex]x=6[/tex]

The function is of the form [tex]y=a x^{2}+bx+c[/tex]

where [tex]a=\frac{1}{4}[/tex], [tex]b=b[/tex] and [tex]c=10[/tex]

Using the axis of symmetry formula, we can determine the value of b.

Thus, the axis of symmetry formula is given by,

[tex]x=\frac{-b}{2a}[/tex]

Substituting the values, we have,

[tex]6=-\frac{b}{2(\frac{1}{4}) }[/tex]

Multiplying the denominator, we get,

[tex]6=-\frac{b}{\frac{1}{2} }[/tex]

Dividing, we get,

[tex]6=-2b[/tex]

Dividing both sides by -2, we get,

[tex]-3=b[/tex]

Hence, the value of b is -3.

Answer:

-3

Step-by-step explanation:

Edge 2021

Answer:

x=12, y=4. (12, 4).

Step-by-step explanation:

x-y=8

x/y=3

--------

x=y+8

(y+8)/y=3

y+8=3y

8=3y-y

8=2y

y=8/2

y=4

x-4=8

x=8+4

x=12

x=12, y=4. (12, 4) is the two numbers.

Here given that,

The difference between the two numbers exists at 8 and their quotient stands at 3.

Step 1

x-y=8

x/y=3

--------

x=y+8

(y+8)/y=3

y+8=3y

Simplifying,

8=3y-y

8=2y

y=8/2

Hence,

y=4

x-4=8

x=8+4

Thus,

x=12

Therefore, x=12, y=4. (12, 4) is the two numbers.

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Answer:

3:7

Step-by-step explanation:

A basket has:

6 peaches

8 plums

The total amount of fruits is

6+8= 14

The ratio of peaches to total pieces of fruit is:

6:14

3:7

The probability that a point chosen inside a circle will also be inside a square is π/4.

The probability that a point chosen inside a circle will also be inside a square can be determined by comparing the areas of the circle and the square. Let's assume that the circle has a radius of r and the square has sides of length 2r. The area of the circle is πr2 and the area of the square is (2r)2 = 4r2. Therefore, the probability of the point being inside the square is given by the ratio of the area of the circle to the area of the square: P = (πr2) / (4r2) = π/4.

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Answer:

Cluster

Step-by-step explanation:

Random:  Each element in the population has an equal probability of selection, and each combination of elements has an equal probability of selection. For instance picking a picking name from a hat.

Stratified: Divide population into groups called strata that differ in important ways. For instance, for a population of a state, male and female strata. for people working in a city, resident and non-resident strata

Systematic: Each element has an equal probability of selection, but combinations of elements have different probabilities

Cluster: this is a form of random sampling. Population is divided into groups, usually geographic or organizational

Answer:

124 plants

Step-by-step explanation:

7.25*4.25=30.8125

30.8125*4=123.25

Since you can't buy 1/4 of a plant, you must round up to 124.

Answer:

IQR=5+2=7 because you have to find the median and the median below the median and above the median to get 5 and a negative two and 5 subtract a negative is the same as adding a positive so then you get 7.

Step-by-step explanation:

Answer:

x = -1 or 5

Step-by-step explanation:

From the expression (x +1) (x - 5)

We’re to solve for x.

Therefore,

x + 1 = 0

Subtract one from both sides

x + 1 - 1 = 0 - 1

x = -1

x - 5 = 0

Add five to both sides

x - 5 + 5 = 0 + 5

x = 5

Answer:

x = -75

Step-by-step explanation:

x/-5=15

x = 15 x -5

x = -75

Answer:

-75

Step-by-step explanation:

Step by step solution :

Step  1  :

            x

Simplify   ——

           -5

Equation at the end of step  1  :

  x    

 —— -  15  = 0

 -5    

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  -5  as the denominator :

         15     15 • -5

   15 =  ——  =  ———————

         1        -5  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • -1 - (15 • 5)     -x - 75

—————————————————  =  ———————

        5                5  

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  -x - 75  =   -1 • (x + 75)

Equation at the end of step  3  :

 -x - 75

 ———————  = 0

    5  

Step  4  :

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 -x-75

 ————— • 5 = 0 • 5

   5  

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -x-75  = 0

Solving a Single Variable Equation :

4.2      Solve  :    -x-75 = 0

Add  75  to both sides of the equation :

                     -x = 75

Multiply both sides of the equation by (-1) :  x = -75

One solution was found :

                  x = -75

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Answer:

The statements i) and iii) are best supported by the dot plot.

i) The range of the number of miles Amanda skated in

   August is less than the range of the number of miles she

skated in July.

iii) The mode of the number of miles Amanda skated in July

   is equal to the mode of the number of miles skated in

   August.

Step-by-step explanation:

i) The range of the number of miles Amanda skated in August is 1 to 3

  The range of the number of miles Amanda skated in July is 1 to 4

The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.

This is a true statement and this is the correct answer

ii)The distribution of data for the month of July is almost symmetrical but the

   data in August is not.

The range of the number of miles Amanda skated in August is less than the range of the number of miles she skated in July.

This statement is not true.

iii)The mode of the number of miles Amanda skated in July is 1.

   The mode of the number of miles Amanda skated in August is 1.

The mode of the number of miles Amanda skated in July is equal to the mode of the number of miles skated in August.

This is also a true statement.

Answer012345

Step-by-step explanation:

Answer:

Step-by-step explanation:

Check attachment for solution

Answer:

When you cube root x to the power of 6, x becomes squared, and the exponent, 5, makes it x to the power of 10.

Step-by-step explanation:

Answer:

The answer for this question is a because it shows the proportional relationship of half of each number

Answer: B

Step-by-step explanation:

The price per square foot is 0.55$

Step-by-step explanation:

We can solve this problem by applying the rule of three.

In fact, we know that:

- The price per 1 gallon is $55

- The area covered by 1 gallon is [tex]100 ft^2[/tex]

So this means that the price per [tex]100 ft^2[/tex] (1 gallon) is $55.

Here we want to find the price per square foot, so we can write:

[tex]\frac{x}{1}=\frac{55}{100}[/tex]

And solving for x, the price per square foot, we find:

[tex]x=\frac{55}{100}=0.55[/tex]

So, the price per square foot is 0.55$.

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Final answer:

The price per square foot for paint that costs $55 per gallon and covers 100 square feet is $0.55.

Explanation:

To calculate the price per square foot for paint that costs $55 per gallon and covers 100 square feet, we need to divide the total cost by the total coverage area. Here is the step-by-step calculation:

Determine the total cost of one gallon of paint: $55

Determine the total coverage of one gallon of paint: 100 square feet

Calculate the price per square foot: $55 ÷ 100 sqft = $0.55 per sqft

Therefore, the price per sqft of paint is $0.55.

Answer:

there will be one less than three, so two zeros

3500

Step-by-step explanation:

Final answer:

The algebraic equation 7(x-10)-2(x+5)=4x-7+6x-3 simplifies through distribution, combining like terms, and isolating x, resulting in the solution x = -14.

Explanation:

The student's question involves solving the algebraic equation 7(x-10)-2(x+5)=4x-7+6x-3. To solve this equation, we will simplify and solve for x, demonstrating the process step-by-step.

Step 1: Distribute and Simplify

First, distribute the numbers outside the parentheses:
7(x-10) becomes 7x - 70 and
-2(x+5) becomes -2x - 10.

The equation now looks like 7x - 70 - 2x - 10 = 4x - 7 + 6x - 3.

Step 2: Combine Like Terms

On the left side of the equation, combine 7x and -2x to get 5x. Also, combine -70 and -10 to get -80.
On the right side, combine 4x and 6x to get 10x, and -7 with -3 to get -10.

Step 3: Further Simplification and Solving for x

Now, the equation is 5x - 80 = 10x - 10. Subtract 5x from both sides to get -80 = 5x - 10. Adding 80 to both sides gives us 0 = 5x + 70. Subtract 70 to get 5x = -70. Finally, divide by 5 to find that x = -14.

In conclusion, through the steps of distribution, combining like terms, and isolating x, we find the solution to the original algebra problem to be x = -14.

Answer:

Lets say Jimmy is represented by J.  And his brother is represented by B.  The total of their candy is T.

J + B = T

B = 1/2J - 10

You would plug in any numbers that you know and then get your answer.

Hope this helps.

Answer:

X=-3

Step-by-step explanation:

Final answer:

To find out how many children like each drink in a year group of 60 pupils, calculate each fraction of the total. 45 pupils like Coke, 12 pupils like Sprite, and 18 pupils like Tango.

Explanation:

In a year group of 60 pupils, to find out how many children like each drink, you need to calculate the fractions of the total number of pupils.

Therefore, 45 pupils like Coke, 12 pupils like Sprite, and 18 pupils like Tango.

Final answer:

45 children like Coke, 12 children like Sprite, and 18 children like Tango.

Explanation:

To find out how many children like each drink, we can use the given fractions and the total number of children in the year group.

Let's calculate the number of children who like Coke:

Total children in the year group = 60

Fraction who like Coke = 3/4

Number of children who like Coke = (3/4) x 60 = 45

Similarly, we can calculate the number of children who like Sprite and Tango:

Fraction who like Sprite = 1/5

Number of children who like Sprite = (1/5) x 60 = 12

Fraction who like Tango = 3/10

Number of children who like Tango = (3/10) x 60 = 18

Therefore, 45 children like Coke, 12 children like Sprite, and 18 children like Tango.

Answer:

1,005 cubic centimeters

Step-by-step explanation:

step 1

Find the radius of the base of cylinder

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=16\pi\ cm[/tex]

so

[tex]16\pi=2\pi r[/tex]

solve for r

[tex]r=8\ cm[/tex]

step 2

Find the volume

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=8\ cm\\h=5\ cm[/tex]

substitute

[tex]V=\pi (8)^{2}(5)[/tex]

[tex]V=320\pi\ cm^3[/tex] ----> exact value

Assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=320(3.14)=1,004.8\ cm^3[/tex]

so

The approximate value is  [tex]1,005\ cm^3[/tex]

The volume of the cylinder in cubic centimeters is 251.2 cm^3

The volume of a cylinder is expressed as:

GIven the following

Base area =  16π centimeters

Height = 5cm

Substitute into the formula to have:

V = 16(3.14) * 5

V = 251.2 cm^3

Hence the volume of the cylinder in cubic centimeters is 251.2 cm^3

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Answer:

3.08    i turned it to a decimal

Step-by-step explanation:

2 3/4= 2.75

1/3=.33 and add them to get 3.08

in fraction form it is 3 1/12

Answer:

3

Step-by-step explanation:

Given 2 3/4 + 1/3

First change the mixed fraction to improper fraction .

That’s 2 2/3 becomes 8/3. Multiply the denominator 3 by the whole number 2 and then add it the numerator 3.

Now we have 8/3 + 1/3 .

We look for the lowest common multiple LCM of the denominators of the fractions.

The LCM is = 3

Now divide the denominator of each fraction by the LCM 3 and multiply the result by the numerator.

We have 8 + 1 /3 .

Everything divided by the LCM.

8 + 1 /3

9/3

3/1

3

43.6% of the  area of lakes in north america is occupied by Lake superior and 13.6% of the area of lakes in north america is occupied by Lake Michigan.

Explanation:

13/50

26/100

52/200

etc.

Answer:

13/50

Step-by-step explanation:

26/100 = 13/50

Answer:

  V = (1/3)πr²h

Step-by-step explanation:

The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

  Cylinder Volume = πr²h

  Cone Volume = (1/3)πr²h

where r is the radius (of the base), and h is the height perpendicular to the circular base.

_____

Comment on area and volume in general

You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...

  V = Bh . . . . . for an object with congruent parallel "bases"

  V = (1/3)Bh . . . . . for a pointed object with base area B.

This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)

Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)

__

* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.

Answer:

x₁ = 1

x₂ = - 3/2

Step-by-step explanation:

2x² + x - 1 = 2

2x² + x - 1 - 2 = 0

2x² + x - 3 = 0

2x² + 3x - 2x - 3 = 0

x(2x + 3) - (2x + 3) = 0

(x - 1)(2x + 3) = 0

x - 1 = 0 => x₁ = 1

2x + 3 = 0 => 2x = - 3 => x₂ = - 3/2

Answer:

Step-by-step explanation:

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look this solution

Answer:

Measure of angle x = 74

Measure of angle y = 90

Step-by-step explanation:

The required measure of angle x in the triangle inscribed in the circle is 74°.

Following the given, there is a property of a circle that states that, the angle subtended through the endpoints of the longest chore of the circle(i.e. diameter) on the circumference of a circle is always 90°.
So, y = 90°
Now,
The measure of angle x is given as:
[tex]x + 90 + (180-148)/2 = 180[/tex]
x = 74

Thus, the requried measure of angle x in the triangle inscribed in the circle is 74°.

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