A car travels at 85.5 miles in 2 hours and 15 minutes. Calculate the average speed.

Answer:

4.0 meters, ∠C = 39°, ∠A = 51°

Step-by-step explanation:

Firstly, our diagram shows us that the given triangle is actually a right triangle. So we can use the Pythagorean Theorem to solve for the height of the chain:

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

[tex](3.3)^{2} +b^{2} =(5.2)^{2}[/tex]

[tex]b^{2} =(5.2)^{2}-(3.3)^{2}[/tex]

[tex]b =\sqrt{(5.2)^{2}-(3.3)^{2}}[/tex]

[tex]b=4.0187...[/tex]

[tex]b=4.0 m[/tex]

Now, we can use the Law of Cosines to figure out one of the acute angles:

[tex]c^{2} =a^{2} +b^{2} -2ab(cos(C))[/tex]

[tex](3.3)^{2} =(4.0)^{2} +(5.2)^{2} -2(4.0)(5.2)(cos(C))[/tex]

[tex]cos(C)=\frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)}[/tex]

[tex]C=cos^{-1}( \frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)})[/tex]

[tex]C=39.3915...[/tex]

∠C = 39°

And since we know that all angles in a triangle add up to 180°:

∠A + ∠B + ∠C = 180

∠A + 90 + 39 = 180

∠A = 180 - 90 - 39

∠A = 51°

However, you should always review any answers on the Internet and make sure they are correct! Check my work to see if I made any mistakes!

Answer:

B

Step-by-step explanation:

I don't know

An appropriate test for the investigation is, One sample t-test for sample mean. So option B is correct

The process of selecting a sample of data from a population in order to draw conclusions about the population is known as random sampling. Additionally known as probability sampling. Non-probability sampling, often known as non-random sampling, is this sample's opposite. Simple random sampling, stratified sampling, cluster sampling, and multistage sampling are the main forms of this sampling. Convenience samples are often referred to as non-arbitrary samples in sampling methodologies.

Given that,

Population mean = $100

Sample = n = 56

Sample mean =  $102.30

sample standard deviation = $5.30

So, all the data mean, standard deviation is given

therefore, t-test used and one type of sample used as well

Hence, It is one-sample t-test for sample mean

To know more random sample check:

https://brainly.com/question/29852583

#SPJ6

Answer:

true

Step-by-step explanation:

Answer:

Width = 5x +3

Step-by-step explanation:

15x² - 16x - 15  =  15x² - 25x +  9x  - 3 *5

                       = 5x(3x - 5) + 3(3x - 5)

                      = (3x - 5)(5x + 3)    

Width = [tex]\frac{Area}{length}[/tex]

          [tex]= \frac{15x^{2}-16x - 15}{(3x-5)}\\\\=\frac{(3x-5)(5x+3))}{(3x-5)}\\\\=5x + 3[/tex]

Answer:

k = 3 or k = -4

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

[tex]2x=ky+2\to\ eq1\\(k+1)x=6y-3\to\ eq2\\$Change to this form: $y=mx+c\\ky=2x-2\\y=\frac{2x-2}{k}\\$gradient of eq1: $\frac{2}{k}\\6y=(k+1)x+3\\y=\frac{(k+1)x+3}{6}\\y=\frac{k+1}{6} x+\frac{3}{6}\\y= \frac{k+1}{6} x+\frac{1}{2}\\$gradient of eq1: $\frac{k+1}{6}\\$Since gradient, m, is the same for both lines,$\\\frac{2}{k}=\frac{k+1}{6}\\12=k^{2}+k\\k^{2}+k-12=0\\(k-3)(k+4)=0\\k=3 $ or $ k=-4[/tex]

Answer:

4 es esa ????k nose

Answer:

133.33, 200, 266.66

Step-by-step explanation:

GIven data

This is a ratio problem, and we will use the part to all method to get the solution

The given ratio is

= 2: 3: 4​

the total ratio

=2+3+4

=9

Hence the first part is

2/9= x/600

cross multiply

9x= 1200

x= 1200/9

x= 133.33

The second part

3/9=x/600

1/3=x/600

3x=600

x=200

The third part

4/9=x/600

4/9=x/600

9x=600*4

9x=2400

x=2400/9

x=266.66

Therefore the figures are

133.33, 200, 266.66

Answer:

29

Step-by-step explanation:

substitute 5 where the w goes in the expression.

It should look like  4 • 5 + 9

Using the order of operations ( PEMDAS ) multiply 4 • 5 to get 20 and then add 9 to get 29

Using the order of operations ( PEMDAS ), the value of the expression is 29.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

We need to find the value of the expression below when w = 5w = 5.

Using the order of operations ( PEMDAS ),

Then substitute 5 where the w goes in the expression.

4w+9 =  4 • 5 + 9

4w+9 = 20 + 9 = 29

Using the order of operations ( PEMDAS ), the value of the expression is 29.

Learn more about simplification;

https://brainly.com/question/17579585

#SPJ2

Answer:

Jessica needs 2 cases of 12 girls scout cookies plus 2 extra boxes

Step-by-step explanation:

Number of boxes sold = 26

Cases of 12 plus extra boxes needed

Number of cases of 12 needed :

Number of boxes sold / 12

= 26 /12

= 2 remainder 2

Hence, Jessica needs 2 cases of 12 girls scout cookies plus 2 extra boxes

Answer:

you can buy 4  star fruit

Step-by-step explanation:

All it is , is subtraction half of 8 is 4 and half of 16 is 8

Answer:

0.59998

Step-by-step explanation:

Number of keys = 3

Number of coins = 7

Total = 10

Number of items taken out = 2

Expected number of keys taken out:

Let x = Number of keys taken out

X = 0

1st pick = 7/10

2nd pick = 6/9

7/10 * 6/9 = 0.46666

X = 1

(7/10 * 3/9) + (3/10 * 7/9) = 0.46666

X = 2

(3/10 * 2/9) = 0.066666

X : ____ 0 ______ 1 _______ 2

P(X): _0.46666__0.46666 _0.06666

Expected value :

(0*0.46666) + (1*0.46666) + (2*0.06666)

= 0.59998

Answer:

f(3)=7

Step-by-step explanation:

just plug in the number

f(3)=2×3+1

=7

Step-by-step explanation:

I hope that is useful for you :)

Answer:

Yes, Nan pays $25 more

Step-by-step explanation:

144 hours /24 hours per day = 6 days exactly

$50 + (5 x $25) = $175

145 hours 24 hours per day = 6 days and one hour  (must pay for 7 days)

$50 + (6 x $25) = $200

$200 - $175 = $25 more

Answer:

-√(18)i, √(18)i

Step-by-step explanation:

3x^2+54 = 0

So first, no real solution, but...

x^2+18 = 0

x^2 = -18

==> x = -√(18)i, √(18)i

Answer:

(y – 4) = 2(x – 2)

Step-by-step explanation:

point slope: y – y₁ = m ( x - x₁ ).

slope: m = ∆y / ∆x.

_______________

m = ∆y / ∆x = [ 6 – 4 / 3 – 2 ] = [ 2 / 1 ]

= 2

____________________________

(2, 4) → (x₁, y₁).

2 → m.

y – y₁ = m(x – x₁) → y – 4 = 2(x – 2).

Answer:

y-4=2(x-2)

Step-by-step explanation:

Answer:

Correct

Step-by-step explanation:

The given expression is : 4n - 2

Chris says that the expression (4n-2) can be written as 2(2n - 1).

Taking 2 common on the given expression.

(4n-2) = 2(2n-1)

Hence, he has wrote it in a correct way.

Answer:

Is that your answer

Answer:

3

Step-by-step explanation:

1/6 of 18 is 3/18, and 2/3 of 18 is 12/18

So 3/18 + 12/18= 15/18

18-15=3

Hope this helps.

Answer:

pattern

Step-by-step explanation:

hope it helps............:)

Answer:

10

Step-by-step explanation:

The value of the account will reach $152,800 in 10 years.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Interest compounded continuously means there is no limit for the process of compound of interest. It is compounding infinite times.

The formula for calculating the final amount when the interest is compounded continuously is,

A = P e^(r t)

Here, A is the final amount, P is the initial or principal amount, r is the rate of interest and t is the number of years.

Given that,

A = $152,800

P = $79,000

r = 6.8% = 6.8/100 = 0.068

We have to calculate t.

152,800 = 79,000 e^(0.068 t)

152,800 / 79000 = e^(0.068 t)

1.934 = e^(0.068 t)

Taking logarithms on both sides,

㏑ 1.934 = ㏑ e^(0.068 t)

We have ㏑(a)ⁿ = n ㏑(a)

0.65968 = 0.068t ㏑ e

0.65968 = 0.068 t × 1

t = 9.7 ≈ 10 years

Hence the amount is compounded to $152,800 in 10 years.

To learn more about Compound Interest, click on the link :

https://brainly.com/question/29335425

#SPJ2

Answer:

rate

Step-by-step explanation:

r(t)=d

r=d/t

r=miles/hour=mph

r=12

Answer: I THINK it’s d

Step-by-step explanation:

Answer:

75 ft

Step-by-step explanation:

10 * 6 = 60

1/2 * 6 * 5 = 15

60 + 15 = 75 ft

Answer:

area = 25 in^2

Step-by-step explanation:

area = 1/2(10)(5) = 25 in^2

Answer:

For a triangle, we have Area = 1/2 base times height.

With a = area, b = base and h = height,

we have:

A=1/2bh

We are told that A=10 square inches and b=5 inches, so we need to solve (find h ) for:

10=1/2(5)h

We can get rid of the fraction by multiplying by 2 on both sides:

20=5h

Now divide noth sides by 5 (or multiply by 1/5 , to get

20/5=5h/5 so 4=h

The height is 4 inches.

Step-by-step explanation:

Hope it is helpful....