Find the distance between points P and Q.

Step-by-step explanation:

(AUB)={1,2,3,4,6 }

(AUB)nC={1,2,3,4 }

The element of the set is (AUB)’ n C= { 5}

From the information given, we have that the sets are;

U ={1,2,3,...,6}

A={1,3,4,6}

B={1,2,3}

C={1,2,3,4,5}

Now, we have to take note of the following;

From the information given, we then have;

A. (AUB) = { 1, 2, 3, 4, 6}

(AUB)' = { 5}

c = {1, 2, 3, 4, 5}

Then,  the set;

(AUB)’ n C= { 5}

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Answer:

D. 40

Step-by-step explanation:

The greater the interquartile range of a data set, the greater the variability.

Interquartile range = third quarter (Q3) - first quartile (Q1)

Interquartile range of City A = 70 - 40 = 30

Interquartile range of City B = 80 - 40 = 40.

City B has a greater interquartile range than city A, therefore, City B has the greater variability in temperature, with an interquartile range of 40.

Answer:

[tex]\%\ decrease = 9.52\%[/tex]

Step-by-step explanation:

Given

[tex]Sales\ Price = \$209.99[/tex]

[tex]Saved = \$20.00[/tex]

Required

Determine the %decrease

First, we need to determine the amount paid

[tex]Amount = Sales\ Price - Amount\ Saved[/tex]

[tex]Amount = \$209.99 - \$20.00[/tex]

[tex]Amount = \$189.99[/tex]

The percentage decrease is the calculated as follows:

[tex]\%\ decrease = -100\% * \frac{Final - Initial}{Initial}[/tex]

In this case;

[tex]Initial = Sales\ Price = \$209.99[/tex]

[tex]Final = Amount\ Paid = \$189.99[/tex]

So; we have:

[tex]\%\ decrease = -100\% * \frac{189.99 - 209.99}{209.99}[/tex]

[tex]\%\ decrease = -100\% * \frac{-20}{209.99}[/tex]

[tex]\%\ decrease = 100\% * \frac{20}{209.99}[/tex]

[tex]\%\ decrease = \frac{2000\%}{209.99}[/tex]

[tex]\%\ decrease = 9.52426306015\%[/tex]

[tex]\%\ decrease = 9.52\%[/tex] (Approximated)

Answer:

The greatest number of kits he can make is 12 kits

Step-by-step explanation:

The greatest common divisor or GCD is called the greatest number that divides exactly two or more numbers at the same time.

The greatest common divisor is usually expressed as  GCD(a,b), where a and b are numbers.

Being the divisor of a number is the value that divides the number into exact parts, that is, that the remainder is zero, one way to calculate the GCD is to determine all the divisors of each number, and from these point out the common divisors, of which the major divisor will be the GCD of those numbers. In this case:

Divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Divisors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The common divisors of 36 and 60 are 1, 2, 3, 4, 6 and 12, of which the greatest is 12. So GCD(36,60)=12

Another way to calculate the GCD is through prime factorization, which always starts with the smallest divisible number of the number being analyzed. In this case:

The decomposition of 36 is: 2*2*3*3 = 2²*3²

The decomposition of 60 is: 2*2*3*5= 2²*3*5

Now the common factors with the lowest exponent are chosen and multiplied. The result obtained is the GCD. In this case, the common factors of 36 and 60 are: 2² and 3 and their multiplication gives: 2²*3= 12. So GCD(36,60)=12

The greatest number of kits he can make is 12 kits

Answer:

6666666666/100000000000

Step-by-step explanation:

Answer:

[tex]f(3)=30[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=4x^2-6[/tex]

To find f(3), substitute 3 for x. Thus:

[tex]f(3)=4(3)^2-6[/tex]

Square:

[tex]f(3)=4(9)-6[/tex]

Multiply:

[tex]f(3)=36-6[/tex]

Subtract:

[tex]f(3)=30[/tex]

And we're done!

Answer:

Step-by-step explanation:

There is a relationship between the degree of the polynomial and the number of times its graphed curved changes direction> this change is called turning point which is a point where the graph changes from increasing to decreasing or from decreasing to increasing

A polynomial of n degree will have n-1 turning points

ex: f(x)=x³+3x²+x+1

degree of polynomial is 3, it has 2 turning points (3-1)

Answer:

The slope is -1/2

Step-by-step explanation:

-1/2 is a negative slope. Down 1 to the right 2

Answer:

the correct answer is B.

Answer:

The Factor is 1.5

Step-by-step explanation:

5.1(which is B'C') divided by 3.4(which is BC) = 1.5

3.6(A'C') divided by divided by 2.4(AC) = 1.5

2.7(A'B') divided by 1.8(AB) = 1.5

Henceforth the factor is 1.5  

Answer:

17

Step-by-step explanation:

c=15×15+8×8

c=225+64

c=289=17

Answer:

The length of the guy wire is 17ft.

Step-by-step explanation:

[tex]c = \sqrt{a^{2}+b^{2} }[/tex]

a = 15ft

b = 8ft

c = [tex]\sqrt{15^{2} + 8^{2} }[/tex]

c = [tex]\sqrt{225 + 64}[/tex]

c = [tex]\sqrt{289}[/tex]

c = 17

The length of the guy wire is 17ft.

Answer:125-1/3 can be written as : none of these

Answer:

Step-by-step explanation:

(103,581) • (%110)

= (103,581) • (1.10)

=  $113,939.1

The sales (in $) last month were $115,090 if the sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581.

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Let suppose x be the sales last month:

(x - 103581)/x = 0.1

x - 103581 = 0.1x

x - 0.1x = 103581

0.9x = 103581

x  = 103581/0.9

x = $115,090

Thus, the sales (in $) last month were $115,090 if the sales at LL Boutique decreased 10% this month compared to last month. If sales this month were $103,581.

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The correct answer is 16737 mg

Explanation:

The first step to solve this problem is to convert the weight to kilograms because the dosage of the antibiotic is given in milligrams per kilo. This can be done by multiplying the pounds by 0.453 considering each pound is equal to 0.453 kilos. The process is shown below:

123 lb x 0.453 = 55.791 kg

Now, simply multiply the kilos by the recommended dose:

55.791 kg x 300 mg/kg = 16737 mg

Also, this can be converted to grams by dividing the number into 1000 (1000 mg = 1 g)

16737mg ÷ 1000 =  16.737 grames

Answer:

Step-by-step explanation:

(-5, 4) and (0, 0)

(0 - 4)/(0 + 5) = -4/5

y - 4 = -4/5(x + 5)

y - 4 = -4/5x - 4

y = -4/5x

Answer:

x = 0

Step-by-step explanation:

x (40 °) ((3 x + 10) °)

40 x (3 x + 10) °^2

Expanded form:

120 x^2 °^2 + 400 x °^2

Roots:

x = -10/3

x = 0

Alternative forms:

40/3 (3 x + 5)^2 °^2 - (1000 °^2)/3

x (120 x °^2 + 400 °^2)

1/810 π^2 x (3 x + 10)

Geometric figure:

Parabola

HOPE I HELPED!

Answer:

[tex]x = 1.2[/tex]

See Attachment for Graph

Step-by-step explanation:

Given

[tex]y = -x + 4[/tex]

[tex]y = 4x - 2[/tex]

Required

Determine the point of intersection

To do this, we simply equate both expressions of y

i.e.

[tex]-x + 4 = 4x - 2[/tex]

Solve for x

[tex]-x - 4x = - 2 - 4[/tex]

[tex]-5x = -6[/tex]

Divide through by -5

[tex]x = \frac{-6}{-5}[/tex]

[tex]x = \frac{6}{5}[/tex]

[tex]x = 1.2[/tex]

Hence, the point of intersection is 1.2

Answer:

If x = 0, then f(0) = -15

If f(x) = 27, then x = 3

Answer:

[tex]16[/tex]

Step-by-step explanation:

[tex]2^4[/tex]

To solve, you're gonna have to multiply 4 times.

[tex]2*2*2*2[/tex]

[tex](2*4)(2*4)[/tex]

Since [tex]4*2[/tex] is [tex]8[/tex] , you will have to multiply [tex]8[/tex] by [tex]2[/tex].

[tex]8*2=16[/tex]

Your answer is [tex]16[/tex].

Hope this helps!

Answer:

x^8

Step-by-step explanation:

Answer:

[tex]x^8[/tex]

Step-by-step explanation:

[tex](x^4)^2[/tex]

To solve, we will have to multiply [tex](x^4)*(x^4)[/tex] .

[tex](x^4)*(x^4)[/tex]

Now we have to multiply x.

[tex](x*x*x*x)*(x*x*x*x)[/tex]

Let's remove the parenthesis and multiply x all together.

[tex]x*x*x*x*x*x*x*x[/tex]

We multiplied x 8 times so your answer is

[tex]x^8[/tex]

Hope this helps!

A rational number means it doesn't have a decimal that repeats. For example, 2/3 or 0.66....

There is only one number between 9.5 and 9.7. This number is 9.6.

The decimal doesn't repeat or go on forever so its rational.

Answer: 9.6

Best of Luck!

Answer:

9.6

Step-by-step explanation:

decimals are rational so ye

Answer: 122 ft

Step-by-step explanation:

s = r Ф   (Ф must be in radians)

Given: r = 50

          Ф = 140°

                 [tex]\dfrac{\pi}{180^o}=\dfrac{x}{140^o}[/tex]  

                 [tex]\dfrac{140^o\pi}{180^o}=x[/tex]

                     [tex]\dfrac{7\pi}{9}=x[/tex]

[tex]s=50\bigg(\dfrac{7\pi}{9}\bigg)\\\\\\.\quad =\dfrac{350\pi}{9}\\\\\\.\quad =122\ ft[/tex]

Answer:

105.19.

Step-by-step explanation:

Area = 1/2 ac sin B

= 1/2 * 10 * 22 * sin 107

= 105.19..

Answer:

165

Step-by-step explanation:

Answer:

27

Answer:

Answer:

Answer:

She can buy a maximum of 8 apples.

Step-by-step explanation:

Let x represent the number of apples that she wants to buy.

The grocery store sells apples for $1 each and mangos for $0.50 each.

If Gabriella decided to buy 13 mangos, it means that the cost of buying x apples and 13 mangoes is expressed as

x + 13 × 0.5 = x + 6.5

If she buy at least 19 apples, it means that

x + 13 ≥ 19

x ≥ 19 - 13

x ≥ 6

Gabriella has $15 to spend. It means that

x + 6.5 ≤ 15

x ≤ 15 - 6.5

x ≤ 8.5

Therefore, the maximum number of apples that she can buy is 8

Answer:She would only be able to buy 8 more apples

Step-by-step explanation:

First you multiply 13 by .50 and you get 6.50

Next you subtract 6.50 from 15 and get 8.50

After that you see 1 dollar per apple so she can only get 8 apples for 8 dollars.

Therefore, she can only buy 8 more apples.

Extra:She can buy an extra mango with the leftover .50cent

Steps to solve:

3(5x - 8) = 6x + 39

~Distribute left side

15x - 24 = 6x + 39

~Add 24 to both sides

15x = 6x + 63

~Subtract 6x to both sides

9x = 63

~Divide 9 to both sides

x = 7

Best of Luck!

Complete question is;

Write inequalities to represent the situations below. The temperature inside the lab refrigerator is no more than 45 °F. Use t to represent the temperature (in °F) of the refrigerator.

Answer:

t ≤ 45 °F

Step-by-step explanation:

We are told to use t to represent the temperature (in °F) of the refrigerator.

We are also told that the temperature inside the lab refrigerator is no more than 45 °F.

For the temperature inside the refrigerator to be no more than 45 °F, it means the temperature should be either less than or equal to 45 °F

Thus means that t is less than or equal to 45 °F.

Thus, it can be represented in terms of inequality as;

t ≤ 45 °F

Answer:

t ≤ 35

Step-by-step explanation:

I took the test, it was right! :)

Answer:

14, 16, 18, 20, 22

Step-by-step explanation:

14 is the smallest of 5 consecutive integers.

The next larger even integer is 16, then 18, then 20, then 22.

Answer: 14, 16, 18, 20, 22

Answer:

x-int: (-1.5, 0) and (3.5, 0)

y-int: (0, 3)

Increasing Interval: [-2, 1)

Decreasing Interval: (1, 4]

Constant Interval: [-4, -2)

Maximum: (1, 5)

Minimum: (4, -1) or (-4, -1) or (-2, -1) or (-3, -1)

Domain: [-4, 4]

Range: [-1, 5]

Step-by-step explanation:

x-intercepts are where the function f(x) crosses the x-axis when y = 0.

y-intercepts are where the function f(x) crosses the y-axis when x = 0.

Increasing interval is the set of x-values in which the graph f(x) increases in y-value.

Decreasing interval is the set of x-values in which the graph f(x) decreases in y-value.

Constant interval is the set of x-values in which the graph f(x) y-values stay constant.

Maximum is the largest y-value function f(x) can output.

Minimum is the smallest y-value function f(x) can output.

Domain is the set of x-values that can be inputted into function f(x).

Range is the set of y-values that can be outputted from function f(x).