So if Johnny had 3×6 amount if dish soap. How much dish soap would he have?

laiz [17]

2p+6a=$14
3p+9a=$21

3p+9a=21
Subtract 9a
3p=21-9a
divide all by 3
p=7-3a
plug it into start equations

2p+6a=14
2(7-3a)+6a=14
14-6a....+6a=14

this zeroes out...

5 0

2 years ago

What is the length of s?

vovangra [49]

Answer:

s = 16.97 units

Step-by-step explanation:

Since this is a right triangle, we can use trigonometry to figure out the lengths of the sides.

Look at the 45 degree angle. We can use the opposite side (12) and the hypotenuse (s) to solve for s.

Opposite and hypotenuse is sine, so we are using sine. The sine of 45 degrees is 0.70710678118. Make an equation like so:

0.70710678118 = $\frac{12}{s}$ , and we are solving for s.

Put a 1 in the denominator of sine(45 degrees) so you can cross-multiply.

$\frac{0.70710678118}{1} =\frac{12}{s}$

Cross multiply.

0.70710678118s = 12

Divide both sides by sine(45 degrees).

s = 16.97

The length of side s is 16.97 units.

Another way to have done this problem is to use the Pythagorean theorem: a^2 + b^2 = c^2

Substitute 12 for a and b and solve for c, the hypotenuse.

(12)^2 + (12)^2 = c^2

Evaluate the exponents.

144 + 144 = c^2

Add them together.

288 = c^2

Square root 288 to solve for c.

c = 16.97, which is the same answer as you got using trigonometry.

6 0

3 years ago

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun

QveST [7]

Answer:

We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 31.7 milligrams

Sample mean, $\bar{x}$ = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s = 2.8 milligrams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}$

We use One-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429$

Now, $t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

3 0

3 years ago

Noelle and Micah went to the bank to open new checking accounts. The equation C=0.2n+1.20 represents the monthly cost, C, in dol

Kaylis [27]

Answer:

C = $2.40

n = 6

Step-by-step explanation:

For Noelle,

Equation that represents the monthly cost 'C',

C = 0.2n + 1.20

Here, n = number of checks written in a month

For Micah,

Monthly cost for writing checks 'C' = $1.20

Number of checks 'n' = 3

Since, Cost of writing checks ∝ Number of checks written

C' ∝ n

C' = kn

k = $\frac{C'}{n}$

Here, k = proportionality constant

For C' = 1.2 and n = 3

k = $\frac{1.2}{3}$

k = 0.4

Equation will be,

C' = 0.4n

For any month C = C'

Therefore, 0.2n + 1.20 = 0.4n

0.4n - 0.2n = 1.20

0.2n = 1.20

n = 6

Number of checks written by Noelle and Micah = 6

For n = 6,

C = 0.2(6) + 1.20

C = $2.40

Cost of writing checks = $2.40

7 0

2 years ago

A park is 4.6 miles long and 2.7 miles wide. A:what is the total distance around the park? B:if a racecar drove 50 times around

Vlada [557]

Answer:

A) Total distance around the park is 14.6 miles

B) The total distance drove by racer 730 miles

Step-by-step explanation:

Given as :

The length of park = 4.6 miles

The width of park = 2.7 miles

Let the total distance cover around park = Perimeter of park = P miles

So, Perimeter of rectangular park = 2 × Length + 2 × width

or, P = 2 × 4.6 + 2 × 2.7

I.e P = 9.2 + 5.4

Or, perimeter = 14.6 miles

A ) ∴ Total distance around the park = 14.6 miles

B ) The total distance drove by racer = 50 times around the park

So, The total distance drove by car = 50 × Total distance around the park

∴The total distance drove by car = 50 × 14.6 = 730 miles

Hence A) Total distance around the park is 14.6 miles

B) The total distance drove by racer 730 miles answer

6 0

3 years ago

So if Johnny had 3×6 amount if dish soap. How much dish soap would he have?​

So if Johnny had 3×6 amount if dish soap. How much dish soap would he have?