A carnival ride has cars that each hold 4 adult passengers. The weights of the passengers for this ride are
normally distributed with a mean of 65 kg and a standard deviation of 12 kg. Assume that the weights of
passengers are independent from each other.
Let T = the total weight of 4 randomly selected adult passengers for this ride.
Find the probability that the total weight is less than 242 kg.
You may round your answer to two decimal places.
PT <242)

Answer:

scalene triangle

Step-by-step explanation:

Step-by-step explanation:

11.

tan 30 = perpendicular / base = x/ 7

1/√3 = x/7

X= 7/√3

2.

cos 30 = 7/y

√3/2 = 7/y

y = 7×2/ √3

y= 14/√3

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Answer:

p=19

Step-by-step explanation:

since the instructions say that ([tex]x^{13}[/tex])([tex]x^{6}[/tex]) is equivalent to [tex]x^{p}[/tex], we can make the equation:

([tex]x^{13}[/tex])([tex]x^{6}[/tex])=[tex]x^{p}[/tex]

now, apply the laws of exponents; [tex]a^{m} * a^{n} =a^{m+n}[/tex]

in that case, since we're multiplying x to the 13th power by x to the 6th, the result is [tex]x^{13+6}[/tex], which is [tex]x^{19}[/tex]

the equation now:

[tex]x^{19}[/tex]=[tex]x^{p}[/tex]

since the exponents are at the same base, we can solve the equation

19=p

so p is 19

hope this helps :)

Answer:

x = - 18

Step-by-step explanation:

Let certain number = x

The difference between half of a certain number and seven

x/2 - 7

is the same as

=

with adding two to that number

x + 2

Find the number

x/2 - 7 = x + 2

x - x/2 = - 7 - 2

( 2x - x ) / 2 = -9

2x - x = -18

x = - 18

Answer:

34

Step-by-step explanation:

plug the coefficients in the equation, so

-2-2(-2)(-5)+56

Distribute the -2(-2)(-5), so it equals -20

so the equation is -2-20+56

add -20+56, so -2+36

-2+36=34

34 is your answer

Answer:

a) 25%

b) 29 - 7 = 22

c) 21

d) 26 - 15 = 11

e) 75%

Step-by-step explanation:

Answer:

the degree

Step-by-step explanation:

Answer:

x=−5/2 y+ 3/2

Step-by-step explanation:

Let's solve for x.

2x+5y=3

Step 1: Add -5y to both sides.

2x+5y+−5y=3+−5y

2x=−5y+3

Step 2: Divide both sides by 2.

2x/2

=

−5y+3

2x=

−5y+ 3/2

Answer:

x=−5/2 y+ 3/2

Answer:

x =4 , y = -1

Step-by-step explanation:

I used substitution method.

Hope I was able to help . Good luck!

Answer:

It's graph is symmetric to the origin. Cos (x) on the other hand is an even function cos (-x) = cos (x), and its graph is symmetric to the y-axis. Notice also that the graphs are exactly the same shape but horizontally shifted /2 units. They are related by: sin (x) = cos (x - /2) and cos (x) = sin (x + /2).

Step-by-step explanation:

Answer:

58.28 Sq in

Step-by-step explanation:

Area of the composite figure

=Area of trapezoid + Area of semicircle

[tex] = \frac{1}{2} (15 + 11) \times 4 +\frac{1}{2} \times 3.14\times 2^2 \\ \\ = 26 \times 2+6.28 \\ \\ = 52+6.28=58.28 \: {in}^{2} [/tex]

Answer:

x=4

Step-by-step explanation:

Answer:

[tex]x_{1} = \frac{7 - \sqrt{51} }{4} , x_{2} = \frac{7 + \sqrt{51} }{4} [/tex]

Step-by-step explanation:

attachment.

Answer:

84 and 140

Step-by-step explanation:

Jack chooses two numbers between 50 and 150

The two numbers have a Lowest Common Multiple (LCM) of 420

Factors of 420 between 50 to 150

= 60, 70, 84, 105, 140

We are also told that:

They have a Highest Common Factor (HCF) of 28

Hence, we find out of the factors above, which numbers can be divided by 28 without having any remainder.

60/28 = 2.1428571429

70/28 = 2.5

84/28 = 3

105/28 = 3.75

140/28 = 5

Therefore, the two numbers are

84 and 140

Answer:

z = 106

y = 20

Step-by-step explanation:

Answer:

c. 84

Step-by-step explanation:

120 times .70 = 84

Answer:

By using a yard stick taped together maybe

Step-by-step explanation:

Answer:

Its correct answer is sin65°/125.

Answer: Y = 7/8x+ 2.25

Step-by-step explanation:

Answer:

dive by 5 take 20 if 4×5 give u 20 the 20/4 will give you 5

Answer:

z=74

x=15

Step-by-step explanation:

74+8x-14=180

step 1 combine like terms

60+8x=180

step 2 subtract each side by 60

8x=120

step 3 divide each side by 8

x=15

Answer:

z=74

x=15

Step-by-step explanation:

z=74 because vertical angles are the same

you have to add the z and 8x-14 and set it equal to 180 because the angles at supplementary

Answer: 24

Step-by-step explanation:

32/16=2 so it cost 2 per guest.

48/2= 24 guests

Answer:

slope is -1, and y intercept is (0,7)

Step-by-step explanation:

Answer:

$72

Step-by-step explanation:

100 - 10% = 90

90 - 20% = 72

Answer:

A)

[tex]\sqrt{290}\approx 17.0\text{ units}[/tex]

B)

[tex]\sqrt{53}\approx7.3\text{ units}[/tex]

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Problem 1)

We have the two points (-4, 5) and (7, 18).

Let (-4, 5) be (x₁, y₁) and let (7, 18) be (x₂, y₂).

Substitute:

[tex]d=\sqrt{(7-(-4))^2+(18-5)^2}[/tex]

Evaluate:

[tex]\begin{aligned}d&=\sqrt{(11)^2+(13)^2}\\&=\sqrt{121+169}\\&=\sqrt{290}\approx17.0\end{aligned}[/tex]

Problem 2)

We have the two points (-2, -3) and (-4, 4).

Similarly, we will let (-2, -3) be (x₁, y₁) and (-4, 4) be (x₂, y₂).

Substitute:

[tex]d=\sqrt{(-4-(-2))^2+(4-(-3))^2[/tex]

Evaluate:

[tex]\begin{aligned}d&=\sqrt{(-2)^2+(7)^2}\\&=\sqrt{4+49}\\&=\sqrt{53}\approx7.3\end{aligned}[/tex]

Answer:

The answer is 8(a³ - 8b⁶)

Step-by-step explanation:

You have take out the common terms :

8a³ - 64b⁶

= 8(a³ - 8b⁶)

P.S.

a and b cannot be factorized because they are different terms.

Answer: x= 14

Step-by-step explanation: look at transversal ED. Angle E and angle D are alternate interior angles of this transversal. Alternate interior angles are equal. Now we need to find angle measure of D to solve. The triangle angle sum theorem states that all interior angles of a triangle sum to 180 degrees. 50+ 48 + D =180.

Measure of angle D is 82. Now that we have the two alternate interior angles, we set them equal to each other to solve.

6x-2= 82. Add 2 to both sides. 6x = 84. Divide both sides by 6. X =14