Use the law of cosines to find each missing side. Round to the nearest tenth

Assessing the given Venn diagram and the data related to it, we can answer the required question:

Q1. How many people were surveyed = 86.

Q2. What is the probability that a customer chosen at random:

a) takes salt P(S) = 46/85.

b) takes both salt and vinegar P(S ∩ V) = 13/85.

c) takes salt or vinegar or both P(S ∪ V) = 66/85.

The number of people who take salt chips n(S) = 46.

The number of people who take vinegar chips n(V) = 33.

The number of people who takes both n(S ∩ V) = 13.

The number of people who take neither n((S ∪ V)') = 19.

Therefore, the total number of people surveyed n(U) = n(S) + n(V) - n(S ∩ V) + n((S ∪ V)') = 46 + 33 - 13 + 19 = 85.

The number of people who takes salt or vinegar or both n(S ∪ V) = n(U) - n((S ∪ V)') = 85 - 19 = 66.

The probability that a customer chosen at random takes salt P(S) = n(S)/n(U) = 46/85.

The probability that a customer chosen at random takes both salt and vinegar P(S ∩ V) = n(S ∩ V)/n(U) = 13/85.

The probability that a customer chosen at random takes salt or vinegar or both P(S ∪ V) = n(S ∪ V)/n(U) = 66/85.

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Answer:

T = 15 + 0.75c

T = $19.5

Step-by-step explanation:

Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:

T = 15 + 0.75c

Therefore, a dozen cookies plus six single cookies would cost:

T = 15 + 0.75(6)

T = 15 + 4.5

T = $19.5

Answer:

[tex]\fbox {53}[/tex]

Step-by-step explanation:

⇒ 3x² + 5

Substitute x = 4 :

⇒ 3(4)² + 5

⇒ 3(16) + 5

⇒ 48 + 5

⇒ 53

#Step1

It will result -2x-2y=-8

#2

#3

add

Find x

    Sin and cos are trigonometry functions used to find measurements in a right triangle.

         [tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]

         [tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]

Answer: Read attachment.

Step-by-step explanation: Attached below is my work. Hope it helps!

Answer:

y=10

z=18

Step-by-step explanation:

2,6,y,14,z

there are 4 years different between the childrens.

2-6-10-14-18

Answer: 12.4 x 18

-------------- = 18600

0.012

The number of hours, h it will take 5 people to build the swing set is; 2.4 hours

From the task content, it follows that it took 6 hours for 2 people to build the swing set, hence, it follows that it'd take 12 hours for 1 person to build the swing.

However, when the work is divided between 5 People, the time taken is therefore; 12/5 = 2.4hours.

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Answer:

3 square units

Step-by-step explanation:

Use BC as the base   =   2

   Use y -axis to C   (or B) as the height =  3

Area of triangle = 1/2  * base * height = 1/2 * 2 * 3 = 3 units^2

Answer:

6 + (7 + 8) = 21

Step-by-step explanation:

the associative property of addition is: (a + b) + c = a + (b + c)

So the equivalent addition sentence would be:

(6 + 7) + 8 = 6 + (7 + 8) as they both equal 21

The graph goes upwards on the left side and downwards on the right side, so the correct option is the first one.

We have the function:

[tex]y = -9*x^3 + 5*x^2 -2x[/tex]

This is a cubic polynomial with a negative leading coefficient.

So, when x takes large negative values, because the leading coefficient is negative, y will take large positive values.

And when x takes large positive values, because the leading coefficient is negative, y will take large negative values.

So the nature is:

The graph goes upwards on the left side and downwards on the right side. The correct option is the first one.

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Answer:

none

Step-by-step explanation:

please mark me as brainlest

Answer:

This is an extremely easy question bro!

1. 3²

2. 3 (Base) ² (Exponent)

3. Expanded form: (9 * 1)

   Standard form: 9

Step-by-step explanation:

Well, there's none.

Answer: 40/21

Step-by-step explanation:

[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]

350 tickets sold of children and 425 tickets sold for adult.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Let x be the number of adult tickets that were sold and y be the number of children's tickets that were sold.

Total 775 tickets were sold for the game.

So,

x + y = 775

If adults tickets sold for 2.50 and children's tickets sold for 1.50 and all the tickets were sold for a total of 1587.5, it means that

2.5x + 1.5y = 1587.5

put x = 775 - y

2.5(775 - y) + 1.5y = 1587.5

1937.5 - 2.5y + 1.5y = 1587.5

-y = 1587.5- 1937.5

y = 350

and, x = 775 - y = 775 - 350

x = 425

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The histogram is attached with the answer.

It is a mathematical representation of data in a bar shaped graph , the range is user defined.

The histogram is drawn and the shape of the histogram is left skewed as the peak of the graph lies to the left of the centre.

The histogram is attached with the answer.

The complete question is

the frequency table shows the results of a survey that asked people how many hours they spend working in the yard per month. display the data in a histogram. describe the shape of the distribution

The data is attached with the answer.

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Answer: B

Step-by-step explanation:

[tex]P(x) Q(x)=R(x) \implies Q(x)=\frac{R(x)}{P(x)}\\\\Q(x)=\frac{2x^{3}+2x^{2}+3x+3}{x+1}={2x^{2}(x+1)+3(x+1)}{x+1}=\boxed{2x^{2}+3}[/tex]

Answer:

No solution

Step-by-step explanation:

The length of BC as shown in the diagram is 6.32units

The formula for calculating the distance between two points is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the following coordinate points (3, 6) and (5, 0)

Substitute

BC = √(0-6)²+(5-3)²

BC = √(36+4)

BC = √40

BC = 6.32 units

Hence the length of BC as shown in the diagram is 6.32units

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Answer:

Step-by-step explanation:

Joe is correct as the unknown number is 6.

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

Given :

[tex](x^2)^?=x^4\times x^8[/tex]

Let the question mark exponent outside the bracket be y, which needs to be determined

[tex](x^2)^y=x^4\times x^8[/tex]

Simplify the equation by applying exponent rules to either side of the equation:

Apply the rule [tex](a^b)^c = a^{b \times c}[/tex]

[tex](x^2)^y=x^4\times x^8[/tex]

[tex](x)^{2y}=x^4\times x^8[/tex]

Now apply [tex]a^b \times a^c = a^{b+c}[/tex]

[tex](x)^{2y}=x^{4+8}\\\\(x)^{2y}=x^{12}[/tex]

So, the base is the same the exponent will be the same also,

2y = 12

y = 6

Hence, Joe is correct as the unknown number is 6.

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The expression obtained is 2g³-5g² +6 , Option C is the correct answer.

An expression is a mathematical statement that consists of constant , variable and mathematical operators.

The expression given is

[tex]\rm \dfrac{(5g^4 +5g^3 -17g^2 +6g) -(3g^4 +6g^3-7g^2 -12)}{g+2}[/tex]

On subtracting the numerator

2g⁴-g³-10g²+6g+12

Now dividing the numerator by denominator

The expression obtained is 2g³-5g² +6

Therefore Option C is the correct answer.

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Answer:

x = 10

Step-by-step explanation:

4x + 3(x - 1) = 67 ← distribute parenthesis and simplify left side

4x + 3x - 3 = 67

7x - 3 = 67 ( add 3 to both sides )

7x = 70 ( divide both sides by 7 )

x = 10

Hi. . .

✦•···················•✦•···················•✦

[tex]\boxed{\fbox{\huge{x = 10}}}[/tex]

Let's solve your equation step-by-step ~

[tex]\sf{4x \: + \: 3(x \: - \: 1) = 67}[/tex]

[tex]\sf{4x \: + \: (3)(x) \: + \: (3)(-1) = 67} \: (Distribute)[/tex]

[tex]\sf{4x \: + \: 3x \: + \: -3 = 67}[/tex]

[tex]\sf{(4x \: + \: 3x) \: + \: (-3) = 67} \: (Combine \: like \: terms)[/tex]

[tex]\sf{7x \: + \: 7 \: -3 = 67}[/tex]

[tex]\sf{7x \: - \: 3 = 67}[/tex]

[tex]\sf{7x \: - \: 3 \: + \: 3 = 67 \: + 3}[/tex]

[tex]\sf{7x = 70}[/tex]

[tex]\sf{\frac{7x}{7} = \frac{70}{7}[/tex]

[tex]\boxed{\fbox{\huge{x = 10}}}[/tex]

Hope It Helps...

Answer:

₹ 341.55

Step-by-step explanation:

Cost of 1 kg sugar = ₹ 25.30

Cost of 13.5 kg sugar = 25.30 × 13.5 = 341.55

Hence, the cost of 13.5 kg is ₹ 341.55

If you are writing, write statements too as in my school they give extra marks.

Thankyou and have a great day ahead.

Answer:341.55

Step-by-step explanation:

If one KG of sugar does cost  ₹25.3 and if you want to know how much 13.5 kg costs you just would have to multiply/times  ₹25.3 by 13.5 and what is 25.3 x 13.5.  ₹341.55 and that's your answer!

9) Diagonals of a parallelogram bisect each other, so KN=NM. Thus, KM=13.5+13.5=27 cm

10) Opposite sides of a parallelogram are congruent, so LM=KJ=17 cm

11) Based on Question 9, MN=13.5 cm

Answer:

Boys = 605

Girls = 675

Step-by-step explanation:

Let x be the number of boys in school.

So, girls = (x+70)

Total no. of students = 1280

x + x + 70 = 1280

2x + 70 = 1280

2x = 1280 - 70

2x = 1210

x = 1210/2

x = 605

Hence, no. of boys = 605

no. of girls = 605 + 70 = 675