3-107. Find common denominators and calculate each of the following sums.
b. +3
What is the least common multiple of 8 and 4? Of 5 and 3?
T
d. Explain how finding the least common multiple of two numbers can help
you add fractions.

The required value of ∠ABC in the given triangle is 50°

The relation between interior and exterior angles of the triangle are related as, the sum two interior angles of triangle is equal to the opposite exterior angle of that triangle.

As we see in the given question, the sum of angle ∠A and ∠B is equal to the exterior angle which is 145°

⇒ 2x° + 95° = 145°

⇒ 2x° = 145° - 95°

⇒ 2x = 50°

Thus, required answer of angle ∠ABC is 50°

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The hare ran 5.8 mph to win the race.

Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.

Given that, a tortoise and a hare run in the NYC marathon for 26.2 miles, the hare crosses the finish line first in a time of 4.5 hours.

Speed = distance/time

Speed of hare = 26.2/4.5 = 5.8 mph

Hence, The hare ran 5.8 mph to win the race.

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Answer: 1/12

Step-by-step explanation: If the candy jar is only 1/4 full, and there's 3 brothers, they would each receive 1/3 of 1/4. THis would be 1/12 of the jar.

The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.

A triangle is a plane shape that has three sides.

Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.

Using the formula,

Where:

From the question,

Given:

Substitute these values into equation 1

Solve for g

Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°

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Answer: I belive the answer is A

Step-by-step explanation: i could be wrong

Answer:

Step-by-step explanation:

Expand: 36e^2+12e-48=e

Subtract e from both sides 36e^2+11e-48=0

Using the quadratic formula, e=(-11+-sqrt7033)/72

The percentage increase regarding the change in visitor is 80%.

From the information, the museum had 500 visitors and on Tuesday, it had 900 visitors.

It should be noted that the increase in numbers will be:

= 900 - 500

= 400

The percentage increase will be:

= Increase / initial value × 100

= 400/500 × 100

= 0.8 × 100

= 80%

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The number of general public and students are 175 and 215 respectively.

Based on the information given:

Let p = general public

Let s = students/staff

390 people attended the concert. This will be:

p + s = 390 .... i

Tickets sold for $8.00 to the general public and for $5.50 for students and staff. Ticket sales brought in $2,582.50. This will be:

8p + 5.5s = 2582.5 .... ii

From equation i

p = 390 - s

8p + 5.5s = 2582.5 .... ii

8(390 - s) + 5.5s = 2582.5

3120 - 8s + 5.5s = 2582.5

Collect like terms

- 8s + 5.5s = 2582.5 - 3120

-2.5s = - 537.5

Divide

s = 537.5 / 2.5

s = 215

Students = 215

Note that p + s = 390

p + 215 = 390

P = 390 - 215

P = 175

Public = 175

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The expression that shows the distance you would drive from the library to the grocery store along this road is; |-5|+|7|

An absolute value inequality is defined as an expression that has absolute functions as well as inequality signs. For example, the expression |x + 5| > 1 is an absolute value inequality that contains a greater than symbol.

Now, from the inequality line graph attached, we see that the point of the library is at -5 on the line graph.

Similarly, we also see that the point of the grocery store which i will liken to the maths class is at the point 7.

Thus, the distance between both points when we take absolute values into consideration is; |-5|+|7|

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Answer:

H = 30 ft

Step-by-step explanation:

Since the triangle is 90 degrees and we have to find out how tall the streetlight is we have to subtract 90 and 40 degrees. Which we get 50 degrees, after we subtract 20 from the 50 degrees. So we get 30 ft or 30 degrees.

The solution to the equations is y = -7

From the question, we have the equation to be given as

3x - 2y = 5

The above equation is a linear equation

The domain or the replacement set is given as

{-3}

Rewrite properly as

Domain  = {-3}

or

x = -3

So, we replace the variables using the elements in the replacement set

When x = -3, we have

3 x -3 - 2y = 5

Evaluate the products

This gives

-9 - 2y = 5

Add 9 to both sides

-2y = 14

Divide both sides by -2

y = -7

So, we have

x = -3 and y = -7

Hence, the solution to the equation is y = -7

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The polynomial is, -24x⁴y⁵+16x²y³. One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method.

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The terms degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). 

Here,

The polynomial is,

=-24x⁴y⁵+16x²y³

One of the factor is (-8x²y³)

=-8x²y³*(3x²y²-2)

So other factor is 3x²y²-2.

One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method for the The polynomial -24x⁴y⁵+16x²y³.

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Answer:

see explanation

Step-by-step explanation:

m + 20 and 100 are vertically opposite angles and are congruent , then

m + 20 = 100 ( subtract 20 from both sides )

m = 80

The angles are vertically opposite angles and value of m is 80°

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Given two angles which are Vertically opposite to each others,

We know Vertically opposite angles are equal to each other, so,

m + 20° = 100°

m = 100° - 20°

m = 80°

Hence, the value of m is 80°

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Answer:

arc RP = 136°

Step-by-step explanation:

the inscribed angle PQR is half the measure of its intercepted arc, then

arc PR = 2 × ∠ PQR = 2 × 68° = 136°

Answer:

Step-by-step explanation:

The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!

The probability that it will be detected in the next hour is 0.04.

For a system, a fault test each hour is a Bernoulli with success defined as detecting a fault.

The probability of success is 0.78

Let 'x' denote the number of tests conducted up to and including the test that detected a fault.

Then x* - Geometry (0.78).

The probability mass function of the random variable x is;

P(x) = { P( 1 - P )ˣ⁻¹   x = 1,2, . . .

         { 0                 otherwise

The Probability that a fault will be detected on the third hour, given that it has gone undetected during the first two hours is;

P(X = 3 / x = 2) = P(X = 3 and x > 2) / P(x > 2)

                        = P( x = 3 ) / 1-  P(x ≤ 2)

                        = P( x = 3 ) /  1-P(x = 1) - P(x = 2)

                        = P(3) /  1-P(1) - P(2)

                        = (0.78)(0.2)² / 1 - (0·78)(0.2) - (0.78)(0.2)

                        = (0.78)(0.04) / 1 - (0.78)(0.2) - (0.78)(0.2)

                        = 0.0312 / 1 - 0.156 - 0.156

                        = 0.0312 / 0.688

                        = 0.04

The probability that it will be detected in the next hour is 0.04

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The length (in cm) of the hypotenuse is 17 cm.

According to Pythagoras' theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

H² = P² + B²

Let the hypotenuse = H

Shortest side = B

Third side = P

So, according to the question

H = 2B +1    ..... (1)

P = 2B -1     ..... (2)

Use Pythagoras' theorem,

H² = P² + B²

(2B+1)² = (2B-1)² + B²

4B² + 1 + 4B = 4B² + 1 - 4B + B²

4B = - 4B +B²

B² =-8B

B = - 8

But the length cannot be negative, so B = 8 cm

The length of the shortest side = 8 cm

So the hypotenuse will be

H = 2B + 1

= 2(8) + 1

= 17 cm

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Answer:

gradient:

y2-y1/x2-x1

1-1/9-3

0/-6

= 0

The evaluation of the expression (2.4) · (1.3) gives 3.12

From the question, we have the following expression that can be used in our computation:

(2.4) · (1.3)

Express as products

This gives

(2.4) * (1.3)

Remove the brackets

So, we have the following representation

2.4 * 1.3

Evaluate the product

3.12

Hence, the solution is 3.12

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The relationship between height and vertical jump is High positive correlation.

What is a correlation?

A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.

Main body:

To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.

If the line doesn't pass through all points it has low positive correlation.

hence this has high positive correlation .

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Answer:

-positive

-linear

-strong

-no.

Step-by-step explanation:

edge 2023

The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.

Which expression shows what the temperature was at the start of the day?

71+9+771+9+7

87−9−7

87+9+7

87+9−7

Answer:

one is 203

two is 87

Step-by-step explanation:

Answer:

  5 5/6 yards

Step-by-step explanation:

You want the perimeter of a rug that is 2 yards by 11/12 yards.

The formula for the perimeter of a rectangle is ...

  P = 2(L+W)

Using the given values, we find the perimeter to be ...

  P = 2(2 yd + 11/12 yd) = 4 22/12 yd = 5 5/6 yd

The perimeter of the rug is 5 5/6 yards.

An equation for a line that is parallel to the y - axis, based on the options, is B.x = −8.

The y - axis is a vertical line which runs straight through the x - axis. This means that the coordinates of the y - axis are expressed in terms of 0. The y - axis intercepts the x - axis at point 0 which is why the coordinates are:

x = 0

Any line that is parallel to the y - axis will therefore be expressed in terms of x as well. The equation for a line that is parallel to the y - axis is therefore:
x = -8

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An expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)

The correct answer is an option (A)

In this question we have been given an expression -4.5n + 3

We need to identify an expression which is factored form of given expression.

If we simplify the factored form then it must be a give expression.

consider ,A. −3(1.5n−1)

= -4.5n + 3

consider an expression B. −1.5(3n+2)

= -4.5n - 3

consider C. −1.5(−3n+2)

= 4.5n - 3

consider D. −3(1.5n+1)

= -4.5n - 3

Therefore, an expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)

The correct answer is an option (A)

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Answer:

TW = 16.8

Step-by-step explanation:

When two chords of a circle intersect inside the circle, then the product of the lengths of the chords of one segment equals the product of the lengths of the segments of the other chord.

Here,

TW × WS = UW × WV

TW × 30 = 18 × 28

TW = (18 × 28)/30

TW = 16.8

The value of TW is 16.8 in a circle.

The product of all the chord values of one segment, where two chords from a circle cross from within the circle, equaled the product of the chord measures of each additional segment. The value of the cord will be the distance with respect to the circle that is present in the circle.

The value of WS = 30

The value of UV = 18

The value of WV = 28

The value of TW is:

TW × WS = UW × WV

TW × 30 = 18 × 28

TW = (18 × 28)/30

TW = 16.8

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We use Inferential Statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population.

Given that;

What kind of statistics is used to gauge the likelihood that a statistical finding based on information from a random sample is representative of the population the sample is presumed to have been drawn from?

Inferential Statistics:

You attempt to conclude using inferential statistics that go beyond the immediate facts alone. For instance, we use inferential statistics to try to infer what the population would think from the sample data. Alternately, we utilize inferential statistics to assess the likelihood that an observed difference between groups in this study is a reliable one or one that may have occurred by chance. Descriptive statistics are used to simply describe what's happening in our data, while inferential statistics are used to conclude more general conditions from our data.

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The ratio of the combined volume of these pyramids to the volume of the prism as a fraction is equal to 1/3.

How to calculate the volume of a pyramid?

The volume of a pyramid can be calculated by using this formula:

Volume = 1/3 × b × h

Where:

h is the height.

b is the base area.

Here, both pyramids have the same base area as the prism, their volume is given by:

Volume of a pyramid = (1/3 × b × h) + (1/3 × b × h)

Volume of a pyramid = 2/3 × b × h

Also, the volume of this prism = 1/2 × b × h

Thus, the ratio is given by:

Ratio = (2/3 × b × h)/(1/2 × b × h)

Ratio = 2/3 × 1/2

Ratio = 1/3.

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By performing some simple mathematical operations, we know that Sophia earns $366 per hour.

So, to calculate how much Sophia earns in 1 hour:

Now, calculate earnings per hour:

Rounding off: $366

Therefore, by performing some simple mathematical operations, we know that Sophia earns $366 per hour.

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Complete question:

Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.

sophia earns $___ per hour

In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given,

Ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards:

Through combination:

²⁴C₅

24!/51(24-5)!

Simplifying:

24!/5!(19!)

24 × 23× 22× 21× 20×19!/5! × 19!
24 × 23 × 22 × 21 × 20/ 5× 4 × 3 × 2 × 1

42504

In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.

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