Mr. Walker, the contest sponsor, bought toy Wheels in a package of six dozen for $81. what was the unit cost of each wheel?

Answer:

0.9 / 90%

Step-by-step explanation:

54/60

=0.9

To calculate Kevin's score as a percent, we divide the number of correct answers by the total number of questions and multiply by 100. The answer, rounded to the nearest tenth of a percent, is 90.0%.

The subject of this question is Mathematics, particularly the area concerning percentage conversions. Kevin got 54 questions correct out of a total of 60 questions. To find Kevin's score as a percent, we first need to divide the number of questions he answered correctly (54) by the total number of questions (60). This gives us a decimal (0.9). To convert this decimal to a percent, we multiply by 100, which gives us 90%. This is Kevin's raw score. But the question wants the score rounded to the nearest tenth of a percent, so the final answer is 90.0%.

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Answer:

1350

Step-by-step explanation:

I added tower A and B together (90+180) Which gives me 270. Then I did;

270 * 5= 1350 ft. Hope its correct!

Final answer:

Tower C is 5 times as tall as the combined height of Tower A (90 feet) and Tower B (180 feet), which together are 270 feet tall. Multiplying this by 5 gives us the height of Tower C, which is 1350 feet.

Explanation:

The question asks us to calculate the height of Tower C given the heights of Tower A and Tower B and the relationship between their heights. Tower A is 90 feet tall, and Tower B is 180 feet tall. According to the question, Tower C is 5 times as tall as both Towers A and B combined.

To find the combined height of Towers A and B, we simply add their heights:

Now, we need to calculate the height of Tower C:

Therefore, Tower C is 1350 feet tall.

Answer:

Right and isosceles

Step-by-step explanation:

Apex

Answer:

160,281

Step-by-step explanation:

Just add the assets together.

Answer:

$160,281

Step-by-step explanation:

Assets                             Value         Liabilities         Value  

Checking and Savings $2,378    Auto Loan       $4,502  

Automobile                 $8,765       Credit Cards   $435  

House Value                 $135,000   Mortgage        $51,208  

Furniture, etc.                 $13,900    Other Loans    $1,234  

Miniature Collection $238

Their total assets is obtained adding the values of each asset, as follows:

$2,378 + $8,765 + $135,000 + $13,900 + $238 = $160,281

Answer:

Step-by-step explanation:

This line goes through the y-axis at 6; therefore, the coordinate at this point is (0, 6).

This line goes through the x-axis at 2; therefore, the coordinate at this point is (2, 0).

The rate of change of a linear function (aka a line) is the slope of the line.  We can use the slope formula to solve for the slope:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Filling in with our coordinates:

[tex]m=\frac{0-6}{2-0}=-\frac{6}{2}=-3[/tex]

The rate of change is -3.  This means that y decreases 3 with every increase in x of 1.

Answer:

The solution is the point (2,-2)

Step-by-step explanation:

we have

[tex]-4x+8y=-24[/tex] -----> equation A

[tex]7x-5y=24[/tex] -----> equation B

step 1

Multiply by 7 equation A both sides

[tex]7(-4x+8y)=7(-24)[/tex]

[tex]-28x+56y=-168[/tex] -----> equation C

step 2

Multiply equation B by 4 both sides

[tex]4(7x-5y)=4(24)[/tex]

[tex]28x-20y=96[/tex] -----> equation D

step 3

Adds equation C and equation D

[tex]-28x+56y=-168\\28x-20y=96\\-----------\\56y-20y=-168+96\\36y=-72\\y=-2[/tex]

Find the value of x

substitute the value of y in any equation

equation A

[tex]-4x+8(-2)=-24\\4x=-16+24\\4x=8\\x=2[/tex]

therefore

The solution is the point (2,-2)

Answer: the small cup cost the least per ounce

After calculating the cost per ounce for each cup size, we find that the small cup costs the least per ounce at $0.0989, making it the best value.

To determine which size cup offers the best value per ounce, we need to calculate the cost per ounce for each size. This can be done by dividing the cost of each cup by the number of ounces it holds.

For the small cup: $.89 / 9 ounces = $0.0989 per ounce

For the medium cup: $1.29 / 12 ounces = $0.1075 per ounce

For the large cup: $1.59 / 15 ounces = $0.106 per ounce

Now, comparing the cost per ounce for each cup size, we can see that the small cup offers the best value at $0.0989 per ounce.

All isosceles trapezoids have congruent base angles.

Option A

Explanation:

An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

Properties of isosceles trapezoid:

Note: Refer the attached file for the image of an isosceles trapezoid.

All isosceles trapezoids come into the category of trapezoids but all trapezoids cannot be marked as isosceles. Clearly, if a trapezoid has congruent legs, it is an isosceles trapezoid.

If a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. A trapezoid is isosceles if and only if its diagonals are congruent.

In the case of quadrilaterals, if the quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.

The shape that has congruent base angles is all isosceles trapezoids, as they have two pairs of congruent sides which result in two pairs of congruent base angles due to their geometric properties.

After excluding options such as all trapezoids, all kites, and all quadrilaterals which do not necessarily have congruent base angles, it becomes evident that the correct answer is all isosceles trapezoids.

An isosceles trapezoid is defined as a trapezoid where the non-parallel sides (legs) are congruent. According to geometric properties, these congruent non-parallel sides imply that the base angles are also congruent. So, an isosceles trapezoid always has two pairs of congruent base angles.

To support this, consider the Theorem, in an isosceles triangle the angles opposite the equal sides are equal. Similarly, by applying this to the two triangles that form when dividing an isosceles trapezoid along the line of symmetry, it becomes clear why the base angles are congruent.

Answer:

Step-by-step explanation:

40 hours per week*20 dollars per hour=800 dollars per week. This job makes 200 more dollars than the other job.  

The amount of generation of the most income in the second job offer will be more which is $800 per week.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

An employee working 40 hours per week earns a salary of $600 per week. Then the rate is given as,

Rate = $600 per week

But gets a second job offer to work 40 hours per week, hourly at $20 an hour. Then the rate is given as,

Rate = $20 x 40

Rate = $800 per week

The amount of generation of the most income in the second job offer will be more which is $800 per week.

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Answer:

I would eliminate both of the -4x because they are identical.

Step-by-step explanation:

Cancel out the both of the -4x by eliminating them. Then subtract the 3y - y. Subtract the -19 - 15. You then will be left with 2y = -34. Solve for y. Then plug y back into the equation to solve for the x.

Hope this helped. :^)

Answer:

Therefore the first option gives the correct answer of a system of equations which has exactly one solution.

Step-by-step explanation:

i) the second option is 2x + 2y = 1  and -2x -2y = 1 . these two equation can be written as 2x + 2y = 1 and 2x + 2y = -1. Therefore we can see that that the expressions for used for the variables x and y are the same but the result is different. This is not possible and so there will be no solutions for these two equations

ii) the third option is 3x + y = -1 and 6x + 2y = -2. therefore these two equations can be written as  3x + y = -1 and 3x + y = -1 (dividing the second equation by 2) and thus we see that both the equations are exactly the same and hence these two equations will have an infinite number of solutions.

iii) the last option is 3x - 2y = 4 and -3x + 2y = 4. these two equations can be written as 3x -  2y = 4 and 3x - 2y = -4. Again we can see in this case that the two equations are exactly the same and therefore these two equations will have an infinite number of solutions.

iv) the remaining option is the first one 2x + y = 3 and 5x - y = 11.  If we add the first equation to the second one we 7x = 14 and therefore x = 2. If we substitute x = 2 in the first equation we get (2 × 2) + y = 3, therefore y = -1.

Therefore the first option gives the correct answer of a system of equations which has exactly one solution.

Answer:

The second species is slower , flying at 21mph

Step-by-step explanation:

18.9/42x60=27mph

20.3/58x60=21mph

The second species is slower , flying at 21mph

0x + 1y = -5 is the standard form of equation

Solution:

Given that we have to write the equation of line passing thorugh (6, -5) and has slope 0

The equation of line in slope intercept form is given as:

y = mx + c ---------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given that, m = 0

Given point is (6, -5)

To find the y - intercept:

Substitute (x, y) = (6, -5) and m = 0 in eqn 1

-5 = 0(6) + c

c = -5

Substitute c = -5 and m = 0 in eqn 1

y = 0x + (-5)

y = -5

The standard form of equation is given as:

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

y = -5

0x + 1y = -5 is the standard form of equation

Answer:

f(x) = 6x² -25x -9

Step-by-step explanation:

6x² - 25x -9 = (2x - 9) (3x + 1)

x = (2/9) or (- 1/3)

Answer:

B. 3

Step-by-step explanation:

The shape of a box is a square. The volume for a square is lengthxwidthxheight.

For the first box it would be 2x3x6 or 36in.

For the second box, 3x4, which is 12.

Dividing 36 by 12, we get 3.

So 3x4x3 would result in 36in., the same as the first box.

The amount of pencils she bought could be 20p.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. The unitary method is a technique by which we find the value of a single unit from the value of multiple devices and It is a method that we use for most of the calculations in math.

We are given Grace bought a book for $8 and some pencils that cost $.50 each. and spent a total of $18.

when the notebook is $8 and you spend $18 which means bringing 10 worth of pencils.

50c - 1pencil

$1 - 2 pencils

$1.50 is 3

Then we have spent $5 on pencils then have 20p for $10

then $10 + 8 is $18 then spent $18 x

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Answer:

Therefore,

[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]

Step-by-step explanation:

Consider a Δ ABC with

m∠ B = 53°

BC = a = 10

AC = b = 17    

To Find:  

AC = c = ?  

m∠ A = ?

m∠ C =  ?

Solution:

We know in a Triangle Sine Rule Says that,  

In Δ ABC,

[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]

substituting the given values we get

[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]

[tex]\dfrac{10}{\sin A}= \dfrac{17}{\sin 53}\\\\\sin A=0.469\\A=\sin^{-1}(0.469)=28.02\approx 28\°[/tex]

Therefore m∠A = 28°

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

[tex]\angle A+\angle B+\angle C=180\\\\28+53+\angle C=180\\\therefore m\angle C =180-81=99\°[/tex]

Therefore m∠C = 99°

Now From Sine rule we have

[tex]\dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]

Substituting the values we get

[tex]\dfrac{17}{\sin 53}= \dfrac{c}{\sin 99}\\\\c=21.02\approx 21\ unit[/tex]

Therefore,

[tex]m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units[/tex]

Answer:

Answer 4/5 or class 2

Step-by-step explanation:

4/5=0.80    Class 3 is 70% 75+5=80, or 80%

Final answer:

After converting the pass rates of the classes to percentages, none of the classes have a pass rate that is exactly 5% greater than another class's pass rate.

Explanation:

The student's question pertains to comparing the pass rates of different math classes to determine which class had a pass rate that was exactly 5% greater than another class's pass rate. To answer this, we need to convert the pass rates for each class to a percentage and then compare them.

For class 1, the pass rate is 16 out of 24, which can be converted to a percentage by dividing 16 by 24 and then multiplying by 100, resulting in approximately 66.67%. Class 3 has a pass rate of 75%, as provided. Class 4 has a pass rate of 0.81, which is already in a decimal format comparable to a percentage; it is simply 81% when expressed as a percentage.

By comparing these percentages, we find that Class 3's pass rate is exactly 5% greater than Class 1's pass rate (75% - 66.67% = 8.33%, which is more than 5%). Therefore, none of the classes have a pass rate that is exactly 5% greater than another class's pass rate.

Answer: $22.03

Step-by-step explanation: 15% 67.8= 10.17. 67.8+10.17=77.97. x=remain balance. x=100.00-77.97=22.03.

Answer:

5/6

Step-by-step explanation:

[tex]1-\frac{2}{12}=1-\frac{1}{6}=\frac{1*6}{1*6}-\frac{1}{6}\\\\=\frac{6}{6}-\frac{1}{6}=\frac{6-1}{6}=\frac{5}{6}[/tex]

Answer:

all work is pictured and shown

Final answer:

In the given algebraic expression, 4n³ and 2n³, 2m and 6m, and 5n and 2n are identified as like terms.

Explanation:

The question asks to identify like terms in a given algebraic expression. Like terms in algebra are terms that have the exact same variables raised to the same powers, although they can have different coefficients.

For example, 4n³ and 2n³are like terms because they both contain the variable n to the third power.

On the other hand, 2m and 6m are like terms because they both contain the variable m to the first power.

Lastly, 5n and 2n are like terms because they contain the variable n to the first power.

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

a-b

On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

(c)(n)

So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

Answer:

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

a-b

On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

(c)(n)

So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

and recall the you can divide everything by 100 like 74/n  n=100 so 74/100

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Answer:

176 square yards

Step-by-step explanation:

The picture of the question in the attached figure N 1

we know that

The area of the walkway around the rectangular pool, is equal to the area of two trapezoids (#1 and #2), plus the area of two smaller rectangles (#3 and #4)

see the attached figure N 2 to better understand the problem

step 1

Find the area of the two trapezoids (#1 and #2)

[tex]A=2[\frac{1}{2}(b_1+b_2)h][/tex]

simplify

[tex]A=(b_1+b_2)h[/tex]

we have

[tex]b_1=12\ yd\\b_2=4+12+4=20\ yd\\h=4\ yd[/tex]

substitute

[tex]A=(12+20)(4)=128\ yd^2[/tex]

step 2

Find the area of the two smaller rectangles (#3 and #4)

[tex]A=2[LW][/tex]

we have

[tex]L=4\ yd\\W=6\ yd[/tex]

substitute

[tex]A=2[(4)(6)]=48\ yd^2[/tex]

step 3

Find the area of the walkway around the rectangular pool

[tex]128+48=176\ yd^2[/tex]

Answer:

176 sq yards

Step-by-step explanation:

For this case we must solve the following equation:

[tex]12y + 6 = 6 (y + 1)[/tex]

We apply distributive property on the right side of the equation:

[tex]12y + 6 = 6y + 6[/tex]

We subtract 6y on both sides of the equation:

[tex]12y-6y + 6 = 6\\6y + 6 = 6[/tex]

We subtract 6 from both sides of the equation:

[tex]6y = 6-6\\6y = 0[/tex]

Dividing by 6 on both sides of the equation:

[tex]y = 0[/tex]

So, the result is [tex]y = 0[/tex]

Answer:

[tex]y = 0[/tex]

Answer:

20 units

Step-by-step explanation:

Let the equal sides of the triangle be x.

Then the third side will be (x+5) units

Since the perimeter is 50, we have:

[tex]x + x + (x + 5) = 50[/tex]

We simplify to get:

[tex]3x + 5 = 50[/tex]

This implies that:

[tex]3x = 50 - 5[/tex]

[tex]3x = 45[/tex]

Divide both sides by 3 to get:

[tex]x = \frac{45}{3} = 15 [/tex]

The length of the third side is:

15+5=20

Answer:

The value of the expression is 19

Step-by-step explanation:

We want to find the value of the expression: [tex]-8+19+8[/tex]

We regroup the numbers to make the computation very easy for us.

[tex]-8+8+19[/tex]

Recall that -x+x  are  zero pairs.

This implies that:

[tex]-8+8+19=0+19[/tex]

Also zero is the identity element of addition of of real numbers

[tex]0+19=19[/tex]

Hence the correct answer is 19

The value of the expression and correct answer is 19

Answer:

add up the numbers and divide by the counting of the numbers. so the answer will be 56/7 equal to 8