Kirk ran 7 1/2 miles around the track. Each lap is 2 1/2 miles. How many laps did Kirk run?

Write your answer as a fraction or as a whole or mixed number.

Answer:

0.12 = 12% probability that a randomly selected person likes both juices.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We solve this question treating these events as Venn probabilities.

I am going to say that.

Event A: Like orange juice.

Event B: Like grape juice.

In a survey 125 people, 90 people liked orange juice or grape juice.

This means that:

[tex]P(A \cup B) = \frac{90}{125}[/tex]

62 people who like orange juice and 43 people who like grape juice.

This means that:

[tex]P(A) = \frac{62}{125}, P(B) = \frac{43}{125}[/tex]

What is the probability that a randomly selected person likes both juices?

This is [tex]P(A \cap B)[/tex], which is given by:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex].

With the values in this problem:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = \frac{62}{125} + \frac{43}{125} - \frac{90}{125} = \frac{62 + 43 - 90}{125} = \frac{15}{125} = 0.12[/tex]

0.12 = 12% probability that a randomly selected person likes both juices.

Answer:

[tex]4\frac{3}{4}[/tex]

4.75

Step-by-step explanation:

0.25 + 0.25 + 0.5 + 0.25 + 0.5 + 0.125 + 0.125 + 0.5 + 1 + 1 + 0.25

0.125 + 0.125 = 0.25

0.25 + 0.25 + 0.25 + 0.25 = 1

0.5 + 0.5 + 0.5 = 1.5

1 + 1 = 2

0.25 + 1 + 1.5 + 2

4.75

Answer:

The answer is 4 3/4

           Hope this helps! good luck :)

Answer:

8. -3x+10

9. 9-4y

10. -7x+3

11. -3x+4+4y

Step-by-step explanation:

collect like terms :)

Answer:

8) -3x+10

9) 9-4y

10) -7x+3

11) -3x+4y+4

Answer:

[tex]x=26.67[/tex]

Step-by-step explanation:

From the question we are told that:

Height of Pole [tex]h_p=15 foot[/tex]

Height of Man [tex]h_m =6ft[/tex]

Distance from Pole [tex]d_p=40ft[/tex]

Generally the equation for similar Property is mathematically given by

[tex]\frac{h_p}{h_m}=\frac{d_p+x}{x}[/tex]

[tex]x=\frac{h_m*(d_p+x)}{h_p}[/tex]

[tex]x=\frac{6*(40+x)}{15}[/tex]

[tex]x=\frac{240+6x}{15}[/tex]

[tex]x=16+0.4x\\x-0.4x=16[/tex]

[tex]x=16\0.6[/tex]

[tex]x=26.67[/tex]

Answer:

s=32

Step-by-step explanation:

1. Move the constant to the right hand side and change it's sign so

s=20+12

2. Than calcuate s=20+12 which equals 32

so the solution is 32

Answer:

A=49 degree

a=13.5

b=11.7

Step-by-step explanation:

Answer:

[tex](a)\ \cos(180 - x)[/tex] --- Never true

[tex](b)\ \cos(90 -x)[/tex] --- Always true

[tex](c)\ \cos(x)[/tex] ---- Sometimes true

[tex](d)\ \cos(2x)[/tex] ---- Sometimes true

Step-by-step explanation:

Given

[tex]\sin(x )[/tex]

Required

Determine if the following expression is always, sometimes of never true

[tex](a)\ \cos(180 - x)[/tex]

Expand using cosine rule

[tex]\cos(180 - x) = \cos(180)\cos(x) + \sin(180)\sin(x)[/tex]

[tex]\cos(180) = -1\ \ \sin(180) =0[/tex]

So, we have:

[tex]\cos(180 - x) = -1*\cos(x) + 0*\sin(x)[/tex]

[tex]\cos(180 - x) = -\cos(x) + 0[/tex]

[tex]\cos(180 - x) = -\cos(x)[/tex]

[tex]-\cos(x) \ne \sin(x)[/tex]

Hence: (a) is never true

[tex](b)\ \cos(90 -x)[/tex]

Expand using cosine rule

[tex]\cos(90 -x) = \cos(90)\cos(x) + \sin(90)\sin(x)[/tex]

[tex]\cos(90) = 0\ \ \sin(90) =1[/tex]

So, we have:

[tex]\cos(90 -x) = 0*\cos(x) + 1*\sin(x)[/tex]

[tex]\cos(90 -x) = 0+ \sin(x)[/tex]

[tex]\cos(90 -x) = \sin(x)[/tex]

Hence: (b) is always true

[tex](c)\ \cos(x)[/tex]

If

[tex]\sin(x) = \cos(x)[/tex]

Then:

[tex]x + x = 90[/tex]

[tex]2x = 90[/tex]

Divide both sides by 2

[tex]x = 45[/tex]

(c) is only true for [tex]x = 45[/tex]

Hence: (c) is sometimes true

[tex](d)\ \cos(2x)[/tex]

If

[tex]\sin(x) = \cos(2x)[/tex]

Then:

[tex]x + 2x = 90[/tex]

[tex]3x = 90[/tex]

Divide both sides by 2

[tex]x = 30[/tex]

(d) is only true for [tex]x = 30[/tex]

Hence: (d) is sometimes true

Answer:

0.308

Step-by-step explanation:

Given the data:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 6

The sample mean and standard deviation :

Sample mean, xbar = (1+1+2+2+2+3+3+3+3+4+4+6) / 12 = 2.833

Sample standard deviation, s = 1.40 ( calculator)

Hypothesis :

H0 : μ = 2.4

H0 : μ ≠ 2.4

The test statistic :

(xbar - μ) ÷ (s/√(n))

(2.833 - 2.40) / (1.40/sqrt(12))

Test statistic = 1.0713

Using the Pvalue from Test score calculator :

df = n - 1 = 12 - 1 = 11

Pvalue(1.071, 11) two - tailed

= 0.3069

= 0.307

The amount paid for the bananas is $0.8775.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s.

If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Bananas are on sale for $0.39 per pound. Mr. Schurter bought 3 x 3 /4 pounds of bananas.

Cost of 1 pound of banana = $0.39

Let x be the cost of 3 × 3/4 pounds of banana.

3 × 3/4 pounds = 9/4 pounds

By proportional concept,

1 : 0.39 = 9/4 : x

1 / 0.39 = 9/4 / x

Cross multiplying, we get,

1 × x = (9/4) × 0.39

x = 3.51 / 4

x = 0.8775

Hence the cost of 3 × 3/4 pounds of banana is $0.8775.

To learn more about Proportions, click :

https://brainly.com/question/26974513

#SPJ2

Answer:

hundreds

Step-by-step explanation:

Answer:

57.8 degrees

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees so you take 32.3 and figure what plus 32.3 equals 90

Answer:

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 > 0

Test statistic = 3.96

Critical value = 1.67

Reject H0

We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans

Step-by-step explanation:

M= xbar1 = 191 ; M = xbar2 = 190 miles

n1 = 61 n2 = 61

s = 1.429 ; s2 = 1.355

Hypothesis :

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 > 0

Test statistic :

(x1 - x2) ÷ √[(s1²/n1) + (s2²/n2)]

(191 - 190) ÷ √[(1.429²/61) + (1.355²/61)]

1 ÷ √[(0.0334760) + (0.0300987)]

1 ÷ √0.0635747

1 ÷ 0.2521402

= 3.966

Degree of freedom :

df = n - 1

df = 61 - 1 = 60

Critical value :

Tcritical at 0.05%, df = 60

Tcritical = 1.67

Decision region:

Reject H0 if Tstatistic > Tcritical

Since ;

3.96 > 1.67 ; We reject H0

We can conclude that there is significant evidence to support the claim that geese do travel more Than pelicans

Answer:

Consider a circle of radius 8 centimetres. Recall that the centre angle in a circle is always 360˚ . However, a semi-circle is a circle cut in half.

Step-by-step explanation:

So, the formula for the area of a semicircle is A = pi * r^2/2. Let's use that formula to calculate the area of a semicircle with a radius of 8 inches. We'll use 3.14 as an approximation of pi. So, now we plug the values into the equation.

Answer:

b

Step-by-step explanation:

the styles of different cars are qualitative because it is not given a number, just the different styles.  

Hope this helps

Answer:

Table

Bottles Price($)

3           78

6           156

9           234

From that you can find the unit price: 78 / 3 = 156 / 6 = 234 / 9 = 26.

That means that the unit rate of this fragance is $26.

If you call x the number of bottles the equation is

Price = unit rate * number of bottles = 26x.

Now compare this information with that on your graph to compare the unit rates.

This can help you fo find the unit rate in from your grpah: the unit rate is the slope of the line =

[change in y-coordinate] / [change in the x-coordinate]

Step-by-step explanation:

Answer:

3 and 78

Step-by-step explanation:

9514 1404 393

Answer:

  60 cm

Step-by-step explanation:

July and August are 2 of the 12 months in the year. The growth for the year can be expected to be 6 times the growth in a 2-month period, so 60 cm.

_____

You could get down to particulars as to the number of days in those two months versus the total number of days in a year. You would have to specify whether it is a leap year. In a non-leap year, the growth might be ...

  365/(31+31) × 10 cm ≈ 58.9 cm

In a leap year, it would be 59.0 cm.

Answer:

3rd option is the answer

Step-by-step explanation:

hope u understand

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

The given values are :

We know,

[tex] \large\boxed{ \mathrm{slant \: \: height} = \sqrt{h {}^{2} + r {}^{2} } }[/tex]

Now,

[tex] \large \boxed{\mathrm{lateral \: \: surface \: \:a rea } = \mathrm{\pi rl}}[/tex]

Therefore the correct answer is :

D. 5π√89 in²

_________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

The lateral surface area of the cone with a radius 5 inches and height 8 inch is 5(√89)π square inches

The formula for calculating the lateral area of the cone is expressed as:

V = 1/3πr²h

where:

Given the following

r = 5in

h = 8n

Substitute

L = πrl
L = 5π(√8^2+5^2)
L = 5π(√89)

Hence the lateral surface area of the cone with a radius 5 inches and height 8 inch is 5(√89)π square inches

Learn more on lateral area here: https://brainly.com/question/1601740

Answer:

A.

Step-by-step explanation:

[tex][6\:\:1]\begin{bmatrix}-1&0\\0&1 \end{bmatrix}=[6(-1) + 1(0)\:\:6(0)+1(1)]=[-6\:1][/tex]

Answer:

A on edge

Step-by-step explanation:

Answer:

$700

Step-by-step explanation:

Adam = 250 +300(12)=3850

Mandy = 750+200(12)=3150

3850-3150=700

Answer:

P(x > 10) = 0.6981.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this question:

[tex]n = 14, p = 0.8[/tex]

P(x>10)

[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 11) = C_{14,11}.(0.8)^{11}.(0.2)^{3} = 0.2501[/tex]

[tex]P(X = 12) = C_{14,12}.(0.8)^{12}.(0.2)^{2} = 0.2501[/tex]

[tex]P(X = 13) = C_{14,13}.(0.8)^{13}.(0.2)^{1} = 0.1539[/tex]

[tex]P(X = 14) = C_{14,14}.(0.8)^{14}.(0.2)^{0} = 0.0440[/tex]

[tex]P(x > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.2501 + 0.2501 + 0.1539 + 0.0440 = 0.6981[/tex]

So P(x > 10) = 0.6981.

Answer: 27

Step-by-step explanation:

Answer:

Y = - 12.55X1 + 276.52

Step-by-step explanation:

Given the data:

Age of child :(X) : 4, 6, 10, 13, 14, 17

Time (seconds) (Y) : 230, 205, 132, 119, 108, 62

Using technology, the linear regression equation obtained using the data Given is :

Y = - 12.55X1 + 276.52

Where :

Slope = - 12.55

Intercept = 276.52

This also indicates that a negative slope is present and hence a negative relationship between age of Child and time in seconds.

Answer:

Exactly 4 pitches: 15/100

= 0.15

Answer:

2.6457513110645905905016157536393

Hope that this helps!

Answer:

2m is the answer for the missing leg

Step-by-step explanation:

Answer:

26cm

Step-by-step explanation:

7+7+6+6=26

Answer:

26 cm

Step-by-step explanation:

7x2 because of 2 sides

12x2 because of 2 sides

14+12=26

Step-by-step explanation:

sinx=20/36

x=sin-¹20/36

x=34

Answer:

Step-by-step explanation:

Guss

Answer:

Always, always.