15. What is the sum of a number and its
opposite?

Answer:

[tex]\frac{3}{12} ,\frac{8}{12}[/tex]

Step-by-step explanation:

Given fraction: 1/4 and 2/3

To find common denominator, we will use Least common divisor (LCD) of 4 and 3.

[tex]4= 2\times 2\\3= 3\times 1[/tex]

∴ Least common divisor (LCD) = [tex]4\times 3= 12[/tex]

Now, to make denominator common for both the fractions, we need to multiply denominator with a number equal to 12.

∴ [tex]\frac{1}{4} =\frac{?}{12}[/tex]

Multiply numerator and denominator by 3

[tex]\frac{1\times 3}{4\times 3} = \frac{3}{12}[/tex]

Next solving for another fraction:

[tex]\frac{2}{3} =\frac{?}{12}[/tex]

Multiply numerator and denominator by 4

[tex]\frac{2\times 4}{3\times 4} = \frac{8}{12}[/tex]

∴ We have [tex]\frac{3}{12}\  and \ \frac{8}{12}[/tex] with common denominator.

Answer:

There are 500 staples in each package.

Step-by-step explanation:

This is a simple problem which requires us to tell number of staples each package have. The total number of staples in the catoon and the total number of staples that each package have is given in the question. So we can easily calculate total number of staples that each package have by dividing total number of staples in the cartoon by number of staples each packet have i.e.

25,000/50 = 500

Answer:  

Explanation:

The angle STV is an inscribed angle, i.e. an angle with its vertex (point T) on a circle and formed by two intersectic chords.

As per the inscribed angle therorem, this angle is half the central angle.

Thus, the central angle is 82º × 2 = 164º.

That central angle is the measure of the arc SVU.

By the construction, the measure of the arc SV plus the measure of the arc VU is equal to the measure of the arc SU.

Thus, you have:  

Answer:

[tex]x_{123} x^{2} \sqrt{x} \neq \sqrt{x} \sqrt{x} \geq \neq \pi \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]  \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] x^{2} \pi[/tex]

Step-by-step explanation:

because im smart

Answer:

see explanation

Step-by-step explanation:

The measure of arc AE is

AE = 360° - (100 + 40 + 60)° = 360° - 200° = 160°

∠ BCD = 0.5( m arc AE - m arc BD ), that is

x = 0.5(160 - 40) = 0.5 × 120 = 60

4 km = 4000 m = 400000 cm

Scale: 3:400000

answer: 3:400000

Final answer:

Scale on a map is the ratio between map distance and actual distance on Earth's surface. For the given question, the scale is found to be approximately 1 cm representing 1.33 km.

Explanation:

Scale on a map is the ratio between the distance on the map and the actual distance on Earth's surface. In this question, a scale of 3 cm representing 4 km means the ratio is 3 cm to 4 km. To find the scale, divide the map distance by the actual distance: 3 cm / 4 km = 0.75 cm/km. Therefore, the scale of the map is 1 cm representing approximately 1.33 km.

Answer:

The solution for long division of 238÷7 is 34 with remainder of 0. You may check the attached figure a to visualize step by step solution of this long division.

Step-by-step explanation:

Please check the attached figure a to visualize step by step solution of this long division.

Here is the step by step solution of 7 divided by 238.

Hence, The solution for long division of 238÷7 is 34 with remainder of 0. Please see the attached figure a to visualize step by step solution of this long division.

Keywords: long division, divide

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34 with the remainder of 0 is the result of the long division when 7 is divided by 238.  

The following steps will be taken to do the long division:

23 divided by 7 will result in 3

Divide the divisor by the quotient digit (3).

Subtract the numbers =  21 away from 23.

Bring the number as the next dividend figure.

28 divided by 7 will result in 4

Divide the divisor by the quotient digit (4).

Subtract 28 from 28 and the result is 0

The remainder after the division will be 7

The resultant will be 0.

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It will take 3 tractors approximately 2.4 hours to plow the field.

To find out how many hours it will take 3 tractors to plow the field, we can use the concept of work rates.

Given that 5 tractors can plow the field in 4 hours, we can set up a proportion:

5 tractors / 4 hours = 3 tractors / x hours

Cross-multiplying, we have:

5(x) = 3(4)

Simplifying, we get:

5x = 12

Dividing both sides by 5, we find that x = 2.4 hours.

Therefore, it will take 3 tractors approximately 2.4 hours to plow the field.

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It would take one tractor 20 hours to plow the field, so with the combined rate of three tractors, it will take them approximately 6.67 hours to plow the field together.

The subject of this question is work-rate problems in Mathematics. To solve this problem, we must first determine the rate at which a single tractor can plow the field. If five tractors can plow a field in four hours, then one tractor would take five times as long, or 20 hours, to plow that same field alone.

Knowing this, we can now calculate how long it would take three tractors to plow the field together. Since one tractor takes 20 hours to plow the field, the rate of one tractor is 1 field per 20 hours. Therefore, three tractors would work at a rate of 3 fields per 20 hours, and so, it will take them 20/3, or approximately 6.67 hours to plow the field together.

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Answer:

x=2

Step-by-step explanation:

101-13.7x=73.6

13.7x=101-73.6

13.7x=27.4

x=27.4/13.7

x=2

Answer:

Step-by-step explanation:

well....there's a few

101 - 13.7x = 73.6

can be written like :

101 - 73.6 = 13.7x

or

- 13.7x = - 101 + 73.6

or

27.4 = 13.7x

or

27.4 / 13.7 = x

Is that what you mean ?

Answer:

The original price is $25

Step-by-step explanation:

Let x represent the original price

If the shirt was sold on a 20% discount. Then the sale price is 80/100x

The original price was five dollars more than the sale price .

To put this in an equation

X= 5+ 80/100x

X-0.8X= 5

0.2x= 5

X= 5/0.2

X= $25

Answer: 40%

Step-by-step explanation: To find out what percent of shots Hanley made in the last basketball game, we need to write 14/35 as a percent.

To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. So to write 14/35 as a percent, we need to find a fraction equivalent to 14/35 with a 100 in the denominator. We can do this by setting up a proportion.

So we have [tex]\frac{14}{35} = \frac{n}{100}[/tex]

Now, we can use cross products to find the missing value.

1,400 = 35n

÷35      ÷35   ← divide by 35 on both sides of the equation

   40 = n

This means that Hanley made 40% of his shots last basketball game.

To find the percentage of how many shots Hanley made, we can divide how many shots he made to how many shots he took.

14 ÷ 35 = 0.4

Multiply by 100 to find the percentage.

0.4 * 100% = 40%

Thus, Hanley made 40% of his shots.

Best of Luck!

Answer:

A

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (2, 1), thus

y = a(x - 2)² + 1

To find a substitute (1, 0) into the equation

0 = a(1 - 2)² + 1

0 = a + 1 ( subtract 1 from both sides )

a = - 1

Hence

y = - (x - 2)² + 1 or

y = 1 - (x - 2)² → A

The equation of the parabola with its vertex at (2, 1) and that crosses the x-axis at (1, 0) is y=1-(x - 2)^2.

The vertex form of a parabola's equation is y=a(x-h)^2+k where (h, k) is the vertex. Here, the vertex is given as (2, 1). Also, it crosses the x-axis at (1,0), which makes it a downward-facing parabola(as y=0 when x=1), and hence, 'a' is negative. Now, we can compare the given options with these details.

Option A: y=1-(x - 2)^2 perfectly matches our requirements, because it's in the correct vertex form, and 'a' is negative (-1) which corresponds to a downward parabola.

So, the equation of the parabola with its vertex at (2,1) and that crosses the x-axis at (1,0) is y=1-(x - 2)^2.

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Answer:

yes it is proportional but i can't see what the rest of the answers say

Step-by-step explanation:

Answer:

average rate of change of the plane = average speed = [tex]\frac{40}{5} =8\frac{feet}{s}[/tex]

Step-by-step explanation:

we know that

average rate of change of the plane = average speed of the plane

average speed = (change in distance)/(change in time)

since th goes from 15 feet to 55 feet from 2 seconds to 7 seconds

change in time = final time - initial time = 7-2 = 5 seconds.

change in distance = final distance - initial distance

                                = 55-15 = 40 feet.

therefore average speed = [tex]\frac{40}{5} =8\frac{feet}{s}[/tex]

Answer: -6.3, -3.9, 3.4, 4.2, 7.7

Step-by-step explanation:

Use the number line.

Now remember, the highest negative is last.

So -6.3 goes first, then the next negative, -3.9.

Now use the natural order of numbers, 1,2,3,4....

So then continued, it would be 3.4, 4.2, 7.7

Answer:

This is your answer:

Step-by-step explanation:

Least to greatest:

NOTE:

Remember - when you are dealing with negative numbers and ordering them, the greater the negative number, the less value it has>

-6.3 has less value than -3.9 because -6.3 is a greater negative number, and because as you keep moving left on the number line, the values keep decreasing in value.

-6.3 has less value than -0.01

but

-6.3 has greater value than -6.5

I hope this helps!

Answer:

3

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

x*2=6

x=3

Answer:

320 cubes

Step-by-step explanation:

3 1/3 inches = 10/3 inches

There are 10 lengths of 1/3 inch in 10/3 inches.

2 2/3 inches = 8/3 inches

There are 8 lengths of 1/3 inch in 8/3 inches.

1 1/3 inches = 4/3 inches

There are 4 lengths of 1/3 inch in 4/3 inches.

In the 3 1/3 inch by 2 2/3 inch by 1 1/3 inch box, you can place 10 by 8 by 4 cubes measuring 1/3 inch on the side.

10 * 8 * 4 = 320

Answer: 320 cubes

It will take 320 cubes of size 1/3 inch  to fill the box a box with a width of 3 1/3 inches, a length of 2 2/3 inches, and a height of 1 1/3 inches

Volume of a cube of side a inch is [tex]\rm a^3\; inch^3[/tex]

Length of one side of the cube = 1/3 inch

[tex]\rm Volume\; of \; the \; cube = (1/3)^3 = 1/27 \; inch^3[/tex]

[tex]\rm Length\; of \; the \; box = 3 \dfrac{1}{3}\; inches = \dfrac{10}{3}\; inches[/tex]

[tex]\rm Width\; of \; the \; box = 2 \dfrac{2}{3}\; inches = \dfrac{8}{3} \; inches[/tex]

[tex]\rm Height\; of \; the \; box = 1 \dfrac{1}{3}\; inches = \dfrac{4}{3} \; inches[/tex]

[tex]\rm The\; volume \; of \; cuboid\; = \; Length\times Width \times Height\\\\So \; the \; volume \; of\; the\; box = (10/3)\times (8/3) \times (4/3)[/tex]

Let there be n be the number of cubes in the box so

Sum of volumes of n cubes = Volume of the box

[tex]\rm n \times (1/27 ) = (10/3)\times (8/3)\times (4/3)\\n \times (1/27) = 320 /27\\n = \bold{320}[/tex]

So, It will take 320 cubes of size 1/3 inch  to fill the box a box with a width of 3 1/3 inches, a length of 2 2/3 inches, and a height of 1 1/3 inches.

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Answer:

Exact form : 5723^9

Decimal form : 6.58587848 • 10^33

Step-by-step explanation: Evaluate.

Hope this helps you out! ☺

Answer:

g(x) is shifted 1 unit to the right and 5 units up.

Step-by-step explanation:

f(x) =,

x  --------> (original function)

(x - 1) = [x - (+1)]------>  shifted 1 unit in the positive x direction, i.e 1 unit to right

(x - 1) + 5 ----------> shifted 5 units in the positive y direction, i.e 5 units up.

combining all the steps.

g(x) is shifted 1 unit to the right and 5 units up.

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have

[tex]A=706.9\ mm^2[/tex]

Substitute:

[tex]\pi r^2=706.9[/tex]          divide both sides by π

[tex]r^2=\dfrac{706.9}{\pi}[/tex]        use π ≈ 3.14

[tex]r^2\approx\dfrac{706.9}{3.14}\\\\r^2\approx225\to r=\sqrt{225}\\\\r= 15\ mm[/tex]

The diameter d = 2r.

Therefore

[tex]d=2(15)=30\ mm[/tex]

Answer:

30mm

Step-by-step explanation:

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

Substitute 706.9 for A and [tex]\pi[/tex] for 3.14

706.9= 3.14[tex]r^{2}[/tex]             divided both sides by 706.9

when you divided 3.14 by 3.14 it will cross and when you divide 706.9 by 3.14 it will give you 225.

[tex]\sqrt{225}[/tex]

15 times 15 is 225

radius= 15

d=2r

multiply 15 by 2

the answer is 30.

Answer:

-3.5 degrees per hour

[tex] - 3.5t[/tex]

Step-by-step explanation:

The total change is temperature is -12.25 degrees.

The total time is 3.5 hours.

This means that temperature changes by -3.5 degrees per hour (-12.25 degrees ÷ 3.5 hours).

As an expression of hours, simple multiply the coefficient by a variable. I'm assuming the letter t for time (where t is the number of hours):

[tex] - 3.5t[/tex]

To determine Jordan's unit rate of swimming, divide the number of laps by the minutes taken. If Jordan swims 2 laps in 4 minutes, the unit rate is 0.5 laps per minute. This concept is widely applicable, enabling comparisons of performance across different contexts.

Jordan can swim 2 laps in a given number of minutes. To find Jordan's unit rate of laps per minute, we would simply divide the number of laps by the number of minutes. For example, if Jordan swims 2 laps in 4 minutes, the unit rate would be 0.5 laps per minute.

To find a unit rate, you always divide the first quantity (number of laps) by the second quantity (time in minutes), ensuring you have a rate reflective of one unit of time. This unit rate can then be used to calculate how many laps Jordan could swim in a different given time frame.

Examples of Unit Rates

Unit rates are beneficial for comparing performance and can apply to various scenarios like estimating how long it would take to fill a swimming pool or determining the velocity of a common garden snail.

0.222222222 is the exact decimal.

Answer:

[tex]\sqrt[4]{y}[/tex]

Step-by-step explanation:

The quotient property of radicals requires the indices of the radicals to be the same.

This statement is true and is applicable also for expressing the ((4th root of y^3)/(square root of y)) as a single radical.

The given expression is  

[tex]\frac{\sqrt[4]{y^{3}}}{\sqrt{y} }[/tex]

Now, [tex]\sqrt{y}[/tex] can also be written as [tex]\sqrt[4]{y^{2}}[/tex], and hence,

[tex]\frac{\sqrt[4]{y^{3}}}{\sqrt{y} }[/tex]

= [tex]\frac{\sqrt[4]{y^{3}}}{\sqrt[4]{y^{2}}}[/tex]

= [tex]\sqrt[4]{\frac{y^{3}}{y^{2}}}[/tex]

= [tex]\sqrt[4]{y}[/tex] (Answer)

Answer:

The radicals are the power of the same base so they can be written using rational exponents. Simplified the quotient of the exponential expression by getting a common denominator and subtracting exponents. The simplified expression is the 4th root of y

Step-by-step explanation:

Got it right on edg

Answer:

/2 and /4 because angle 1 is 90

Complementary angles in Mathematics are two angles that add up to 90 degrees. You determine this by adding the measures of two angles; if the sum is 90, the angles are complementary. An example would be angles of 30 and 60 degrees.

In the field of Mathematics, specifically geometry, complementary angles are two angles that add up to 90 degrees. Without the diagram, it's tricky to provide an accurate pair of complementary angles. Nevertheless, if you have pairs of angles in the diagram, you calculate their sum: if it equals 90 degrees, those angles are complementary. For example, if one angle measures 30 degrees and the other measures 60 degrees, those two angles are complementary because they add up to 90 degrees.

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Answer:

75 degrees

Step-by-step explanation:

Complementary angles add up to 90 degrees. If we are given that one angle is 15 degrees, we can find the other one using a simple one-step equation.

let x represent the measure of angle N

90 = 15 + x

Subtract 15 from both sides to isolate the variable

75 = x

Angle N measures 75 degrees

Answer:

118 miles

Step-by-step explanation:

Assuming that a month has 4 weeks

Each week has 5 weekdays.

The number of weekdays in a month is the number of weeks times 5.

4 X 5 = 20

Multiply the number of weekdays in a month by 5.9 miles.

20 X 5.9 miles = 118 miles

Therefore he runs 118 miles every months.

Answer:

y-5=-3(x-3)

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-3)

Answer:

A, B and C

Step-by-step explanation:

A. Adding another researcher to provide ratings will make the study less biased.

B. A quiz or exam will show which students have a better understanding of the math material. Better quiz or exam results show that the site is more effective for a student with or without the supplemental instruction.

C. Having a greater sample size is better because a greater scope of students is covered. Different students have different abilities and learning preferences.

Answer:

A. - Have another researcher provide ratings, as well.

B. - Administer a quiz or exam that gauges student understanding

C. - Increase the sample size.

Step-by-step explanation:

Option A is correct because additional researchers help identify and eliminate bias in individuals.

Option B would be very helpful in obtaining quantitative data on students improvement.

Option C will also improve the study because larger sample sizes mean more accurate results.

Option D is NOT correct, as limiting observations to students who are engaged eliminates the control group and makes it so that there is no baseline, rendering the experiments results almost meaningless.

Answer:

D (9+5-2)

Step-by-step explanation:

Monica is 9 years old, Josh is 5 years older -> 9 +5 is Josh's age

We also know that Arleta is 2 years younger than Josh -> 9+5 -2

Therefore Arleta (9+5-2) years old