Divide: 5,108 ÷ 5
How many groups?

The union of the sets P and Q does not have the integer 5 since it is neither a multiple of 3 or a multiple of 4.

P is the set of integers between 1 and 10 and multiple of 3.

∴P = {3,6,9}

Q is the set of positive integers less than 15 and multiple of 4.

∴Q = {4,8,12}

Now the union of the sets P and Q is given by :

P∪Q = {3,4,6,8,9,12}

Now the union of the sets does not contain the integer 5.

Any collection of items, including a set of raw materials, the seven days of the week, several car types, etc., can be categorized as a set.

Any set component counts as an element of the set. Curly brackets are used to write a set. A very basic set would resemble something like this:

Q = {4,8,12}.

Therefore the integer 5 does not belong to the union of P and Q .

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Answer: 19.2, I think.

Step-by-step explanation: 10*1.2 = 12.

To keep the ratio balanced, you must also do 16*1.2, which is 19.2. Making the ratio 12 : 19.2

Answer:

-3≥11.5

Step-by-step explanation:

-3≥1/2+11

-3≥11.5

Answer:

Convergence

Step-by-step explanation:

Use the Squeeze Theorem,

I know that

[tex] \frac{k \sin {}^{2} (k) }{1 + k {}^{3} } [/tex]

lies between 0 and 1 so

[tex]0 \leqslant \frac{k \sin {}^{2} (k) }{1 + {k}^{3} } \leqslant \frac{k}{1 + k {}^{3} } [/tex]

The final series behaves like

[tex] \frac{1}{k {}^{2} } [/tex]

Using the p series, since p is 2, the series

[tex] \frac{k}{1 + k {}^{3} } \: converges[/tex]

Since the 0 and k/1+k^3 converges, the series converge.

Convergence

An amount of $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, one part of $2600 was invested at a rate of 7.5% and the other part was invested at a rate of 5%, and the total yield was $175 simple interest.

Let $x was invested at 7.5%, then $(2600-x) was invested at 5%.

Since the yield is $175, it follows,

7.5% of x + 5% of (2600-x) = 175

7.5x/100 + 5(2600-x)/100 = 175

7.5x + 13000 - 5x = 17500

2.5x = 17500-13000

2.5x = 4500

x = 1800

Now, the value of (2600-x) is,

2600-1800

=800

Hence, $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.

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William invested $1800 at 7.5% and $800 at 5% on his both accounts.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, William opened two investment accounts. In the first​ year, these​ investments, which totaled ​$2600​,

Assuming he invested $x at 7.5% on the first account and $(2600 - x) at 5% in the second account and yielded ​$175 in simple interest.

∴ (x×7.5×1)/100 + {(2600 - x)×5×1}/100 = 175.

7.5x/100 + (13000 - 5x)/100 = 175.

7.5x + 13000 - 5x = 17500.

2.5x = 4500.

x = 1800. And (2600 - x) = (2600 - 1800) = 800.

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The length of q, to the nearest 10th of a centimeter, is 8.8 cm.

We are given the following;

In ΔQRS, s = 7.9 cm, ∠Q=125° and ∠R=23°.

The third angle can be calculated using the angle sum property:

angle Q + angle R + angle S = 180 degrees

125 degrees + 23 degrees + angle S = 180 degrees

angle S = 180 - (125 + 23) degrees

angle S = 180 - 148 degrees

angle S = 32 degrees

To find the length of q we shall apply the Sine rule.

q / Sin Q = s / Sin S

q / Sin 125 = 7.9 / Sin 32

by cross multiplication we will get;

q = (7.9 x Sin 125) / Sin 32

q = (7.9 x 0.61) / 0.55

q = 8.8 cm (approximately)

So,  the length of q is 8.8 cm.

Thus, the length of q, to the nearest 10th of a centimeter, is 8.8 cm.

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The rate at which Bart read is 24/7 book/day.

Given, Bart read 4/7 of comic book in 1/6 of a day.

We have to find the rate at which he read the book in a day.

Now, Bart read 4/7th of a comic book = 1/6th of a day

4/7 comic book = 1/6 day

1 day = (4 × 6)/7 comic book

1 day = 24/7 comic book

So, the rate at which Bart read is 24/7 book/day.

Hence, the rate at which Bart read is 24/7 book/day.

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Answer:

1. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  [0, ∞)

2. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  (-∞, ∞)

3. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  (-∞, ∞)

4. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain:  (-∞, ∞); Range:  [0, ∞)

Step-by-step explanation:

Rule for end behavior of polynomials:

(a) Positive leading coefficient, even degree:  y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞

(b) Negative leading coefficient, even degree: y ⇒ -∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞  

(c) Positive leading coefficient, odd degree:  y ⇒ ∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞

(d) Negative leading coefficient, odd degree:  y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞

Domain and range for a polynomial function with an odd degree will always be all real numbers, whether or not there's a constant or not.

Domain will always be all real numbers for a polynomial function with an even, whether or not there's a constant.

For a polynomial function with an even degree, the range will extend from the y-coordinate of the vertex to ∞, if the leading coefficient is positive

For a polynomial function with an even degree, the range will extend from -∞ to the y-coordinate of the vertex if the leading coefficient is negative.

The following are the characteristics of the graph of the linear parent function:

B. It has a slope of 1.

C. It is a parabola.

D. It is a straight line.

Lets explain the meaning of linear parent function

- A linear parent function is the equation y = x or f(x) = x

- A parent function is the simplest equation of a function

- It represented by a straight line passing through the origin point O

- The x-coordinate and the y-coordinate of any points lie on it are equal

- The slope of the line is 1 because the slope is the change of Δy/Δx

and Δy = Δx

The characteristics of the graph of the linear parent  function are

∵ Linear parent function is f(x) = x and f(x) = y

∴ x = y

∵ The slope = Δy/Δx

∵ Δx = Δy because x = y

∴ The slope of it is 1

B. It has a slope of 1

∵ y = 0

∵ If x = 0 then y must = 0

∴ It goes through the origin

C. It goes through the origin

∵ It is a linear function

∵ All linear function represented by a straight line

∴ The graph of the linear parent function is a straight line

D. It is a straight line

Hence we get the right answers.

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The required value of the given expression : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100 = 5.3

The Bodmas rule is based on the BODMAS acronym, which stands for Brackets, Order of Powers or Roots, Division, and Multiplication. Subtraction is represented by the letter S, while addition is represented by the letters A and S. According to the BODMAS rule, mathematical expressions with multiple operators must be resolved in the order of BODMAS, starting from the left. As with addition and subtraction, division and multiplication are interchangeable and depend on which comes first in the expression.

Given : [tex]\frac{79 - 75 }{ 75 }[/tex] × 100

on calculating it further

we get :

[tex]\frac{4}{75}[/tex] × 100

0.0533 X 100

=> 5.3

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Answer: I don't know

Step-by-step explanation:

I have no idea

Answer:

B, C

Step-by-step explanation:

A is incorrect, it should be seventy-six hundredths.

D is incorrect, the place value for the third term is wrong - it should be 0.06.

Triangle C forms a right angle triangle.

Given:

Triangle A : 8 cm , 13 cm , 5 cm

Triangle B : 14 cm , 30 cm , 17 cm

Triangle C : 26 cm , 10 cm , 24 cm

To form a right angled triangle the longest side square is equal to the sum of squares of other sides.

In triangle A :

[tex]13^{2} = 8^{2} +5^{2}[/tex]

169 = 64 + 25

169 ≠ 89.

This is not a right angle triangle.

In triangle B:

[tex]30^{2} =17^{2} +14^{2}[/tex]

900 =  289 + 196

900 ≠ 485

This is not a right angle triangle.

In triangle C:

[tex]26^{2} = 10^{2} +24^{2}[/tex]

676 = 100 + 576

676 = 676

so it is a right angle triangle.

Therefore Triangle C forms a right angle triangle.

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Jimmy has to write 369 words per day for the next 6 days to finish the paper.

The total number of words in the paper has to be 3000

Jimmy has already written = 786 words.

3000-786 = 2214

So, Jimmy still has to write 2214 words.

He has 6 days to write the paper and he wants to write the same number of words per day.

With this in mind to find out how many words he has to write per day we can divide 2214 by 6.

2214/6 = 369 words

So, Jimmy has to write 369 words per day for the next 6 days to finish the paper.

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Answer: $1338.96

Step-by-step explanation:

The wholesale cost means the cost that the store buys the table from the supplier. To find the price that the store sells it, it is a 20% markup.

The orginal price is $1,115.80. What is 20% of $1,115.80?

$1,115.80 * .20 = $223.16

Lets add the original price to the markup.

$1,115.80 + $223.16 = $1338.96


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The linear equation that represents the hours Yuson has left after x days is (A) y = -2x + 30

Given in question,

Hours she should complete = 30 hours

Hours she complete each day = 2 hours

Hours completed in x days = 2x

Hours left after x days = 30 -2x

Hence, the linear equation that represents the hours Yuson has left after x days is y = -2x + 30.

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Answer:

percentage = 80÷4000=0.02

Answer:

The third option, as x approaches infinity y approaches infinity and as x approaches negative infinity y approaches negative infinity.

Step-by-step explanation:

Step-by-step explanation:

w = t/7

at the beginning we 0 inches of water.

after 56 minutes we have 8 inches of water.

that is a ratio of 56 minutes / 8 inches = 7/1 = 1 / 1/7.

so, in 1 minute we get 1/7 inch of water.

in 2 minutes 2×1/7 = 2/7.

in 3 minutes 3×1/7 = 3/7.

...

hence the equation.

Answer:

Step-by-step explanation:

Find the value of m and b in the equation y = mx + b.

The value of b = 0, since there is no level in the bucket initially.

Find the value of m, the slope:

So the equation is:

or

The different possibilities available for selecting an executive board in Student Council in election is 990 ways

In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6

The problem is a permutation problem trying to select 3 from 11 where order matters. The order include choosing the president the ramainig position is left 2 for 10. and so on.

This is shown in permutation as follows

₁₁P₃  = 11! / (11 - 3)!

= 11! / 8!

= 990 ways

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The probability that the person is between 67.1 and 68.3 inches, using the normal distribution, is of:

0.1056 = 10.56%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the heights of UCB students are given as follows:

[tex]\mu = 65, \sigma = 2.4[/tex]

The probability that the person is between 67.1 and 68.3 inches is the p-value of Z when X = 68.3 subtracted by the p-value of Z when X = 67.1, hence:

X = 68.3:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (68.3 - 65)/2.4

Z = 1.38.

Z = 1.38 has a p-value of 0.9162.

X = 67.1:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (67.1 - 65)/2.4

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

0.9162 - 0.8106 = 0.1056 = 10.56%.

The problem asks for the probability that the person is between 67.1 and 68.3 inches.

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Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork

Answer:

30

Step-by-step explanation:

Divide each term in 6 w = 180 by 6 and simplify. w = 30

Answer:

w = 30

Step-by-step explanation:

Given equation,

→ 6w = 180

Now the value of w will be,

→ 6w = 180

→ w = 180/6

→ [ w = 30 ]

Hence, the value of w is 30.

Answer:

X=3

Step-by-step explanation:

I'm not sure what statements below you want me to confirm that X=Y, Y=3

Answer: Symmetry Property of Equality

The measure of the exterior angle is 139 degrees.

The sum of the interior angle of a triangle is 180 degree.

The sum of angles on a straight line is 180 degrees.

From the diagram;

First, we determine the third interior angle of the triangle.

Angle 1 + Angle 2 + Angle 3 = 180

64 + 75 + Angle 3 = 180

139 + Angle 3 = 180

Angle 3 = 180 - 139

Angle 3 = 41 degrees

Now, angle 3 and the exterior angle forms a angle on a straight line.

Hence;

Angle 3 + Exterior angle = 180

41 +  Exterior angle = 180

Exterior angle = 180 - 41

Exterior angle = 139 degrees.

Therefore, 139 degrees is the exterior angle.

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The equation that can be used to find the length of the afternoon practice is B. 4(h + 3) = 20

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, during the summer the team practices 4 days per week and each of those days, they practice for 3 hours in the morning and practice again in the afternoon.

Let the afternoon practice be h.

Therefore, the equation will be:

4(h + 3) = 20

In conclusion, the correct option is B.

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