What is the mean of the high temperatures, in degrees Fahrenheit, for the week? Show your work.

Answer:

80 women

Step-by-step explanation:

A ratio of men to women of 3:2 means that for 3 men that use the gym 2 women use the gym, so using a rule of three we can determinate how many women were on the gym that day if 120 men were there, like this:

  3 men   ------ 2 women

120 men  ------       X

[tex]X = \frac{(120men)(2women)}{3men}=80 women[/tex]

Then, there were 80 women for the 120 men that were in the gym.

cross multiply:

21*9 = 189

7*q = 7q

so you have 189/7q

 divide 189 by 7 to get q

189 / 7 =27

q = 27

since angle 3 = 47, then angle 1 also = 47

this would mean that both angles 5 & 7 are also 47

so angle 5 = 47 degrees

It will take approximately 1.459 years for a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.

To find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly, we can use the formula A = P(1+rn)^(nt). Plug in the values: A = 2200 + 210 = 2410, P = 2200, r = 0.10 (10%), n = 12 (compounded monthly), and t = ?

2410 = 2200(1 + 0.10/12)^(12t). Divide both sides by 2200 to isolate the expression:

1.095 = (1 + 0.10/12)^(12t). Take the natural logarithm of both sides to remove the exponent:

ln(1.095) = 12t * ln(1 + 0.10/12). Solve for t:

t = ln(1.095) / (12 * ln(1 + 0.10/12)). Use a calculator to find the value of t, which is approximately 1.459 years when rounded to 3 decimal places.

Final answer:

To solve this problem, you can set up a system of equations. There are 4 finches and 14 parrots.

Explanation:

To solve this problem, we can set up a system of equations based on the given information. Let's assume that the number of finches is 'x'. According to the problem, there are 2 more than 3 times as many parrots as finches. This can be written as:

Parrots = 3x + 2

Since the total number of parrots and finches is 18, we can set up another equation:

Parrots + Finches = 18

Substituting the first equation into the second equation, we get:

(3x + 2) + x = 18

Combining like terms, we have:

4x + 2 = 18

Subtracting 2 from both sides, we get:

4x = 16

Dividing both sides by 4, we find that:

x = 4

So, there are 4 finches and 3(4) + 2 = 14 parrots.

Answer:

Mars

Step-by-step explanation:

Sun is the brightest object in the sky of the Earth. It is a giant spherical star, composed of hot plasma that is located at the center of the Solar System. The diameter of the Sun is about 1.391 million km.

Mars, also known as the Red Planet, is one of the four terrestrial planets. It is the fourth planet of the Solar System. It is the second-smallest planet having diameter of about 6,779 km.

Now, diameter of Mars ÷ diameter of the Sun ≈ 6,779 km ÷ 1391000 km ≈ 1 ÷ 200

⇒ diameter of Mars ≈ (1 ÷ 200) × diameter of the Sun

Therefore, the diameter of Mars is approximately 1/200 of the diameter of the Sun.

Answer:

Step-by-step explanation:

They have 30 gallons of paint and for each hour that passes, they use 3 gallons of paint. Therefore, we can express that as a function:

y = -3x + 30

where y = gallons left

and x = hours passed

Therefore, the end points are (0, 30) and (10, 0)

Using our function when 0 hours has passed:

y = -3(0) + 30

y = 30

Therefore one endpoint is when x = 0 y = 30 or (0,30)

Using our function when 10 hours has passed:

y = -3(10) + 30

y = -30 + 30

y = 0

Therefore one endpoint is when x = 10 y = 0 or (10, 0)

The graph can be seen in the picture below.

Answer:m∠X’Y’Z’ = m∠XYZ

Step-by-step explanation:

Answer:

1)

t=5 hours.

2)

40960 cells.

Step-by-step explanation:

A scientist studying bacteria begins with 20 cells.

The bacteria population doubles every hour.

Let P(t) determines the population of the bacteria in 't' hours.

Hence, by the given information our function P(t) is modeled as:

[tex]P(t)=20\times 2^t[/tex]

Now, we have to find the value of 't' such that:

P(t)>500

i.e.

[tex]20\times 2^t>500\\\\\\2^t>\dfrac{500}{20}\\\\2^t>25[/tex]

on taking logarithmic function on both side we get:

[tex]t\log 2>\log 25\\\\t>\dfrac{\log 25}{\log 2}\\\\t>4.64[/tex]

i.e. after 5 hours the population of the bacteria will exceed 500.

Now we have to find the value of function P(t) when t=11.

i.e.

[tex]P(11)=20\times 2^{11}\\\\P(11)=20\times 2048\\\\P(11)=40960[/tex]

Hence , the population of bacteria after 11 hours is:

40960 cells.

divide 3 1/2 by 4

3 1/2 = 7/2

7/2 / 4 = 7/8 foot each

Answer:

[tex]\frac{7}{8}[/tex] feet.

Step-by-step explanation:

Four sister bought a total of ribbon = [tex]3\frac{1}{2}[/tex] feet

                                                           = [tex]\frac{7}{2}[/tex] feet

The sisters want to share the ribbon equally.

So we will divide the total length of the ribbon by 4.

= [tex]\frac{7}{2}[/tex] ÷ 4

= [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{4}[/tex]

= [tex]\frac{7}{8}[/tex] feet.

Each sister will receive [tex]\frac{7}{8}[/tex] feet of ribbon.

The modulo of the expressions are computed as follows: (a+a) mod 7 = 4, (a+b) mod 7 = 0, (3a) mod 7 = 6, and (2b) mod 7 = 3.

I'm sorry, but I'm afraid there might have been some confusion in your input. If you wanted the remainders of different expressions when divided by 7, here are the steps:

Given that a mod 7 = 2 and b mod 7 = 5, you can use modular arithmetic to compute the modulo of expressions including a and b:

https://brainly.com/question/13089800

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The marginal product of the second worker is b. 75 dumplings.

To find the marginal product of the second worker, we need to determine how many additional dumplings the second worker is able to produce compared to the first worker. The marginal product (MP) of a worker is calculated as follows

[tex]\[ MP = \text{Total production with two workers} - \text{Total production with one worker} \][/tex]

[tex]\[\]\[ \text{Total production with one worker} = 100 \text{ dumplings} \]\[ \text{Total production with two workers} = 175 \text{ dumplings} \][/tex]

[tex]\[\]\[ MP = 175 \text{ dumplings} - 100 \text{ dumplings} \]\[ MP = 75 \text{ dumplings} \][/tex]

Hi, here we want to "finish" a delta-epsilon proof.

We will find that the maximum delta is: δ = 0.02

We just want to find the value of δ such that:

[tex]|x - 1| < \delta[/tex]

Implies that:

[tex]|5x - 5| < \epsilon[/tex]

Well, let's start with the second expression:

[tex]|5x - 5| < \epsilon[/tex]

We can take the 5 out of the absolute value:

[tex]5*|x - 1| < \epsilon[/tex]

Now we can divide both sides by 5:

[tex]|x - 1| < \epsilon/5[/tex]

Now, if you look at the above expression, in the left side we have the same thing as in the delta inequality.

So for now we have:

[tex]|x - 1| < \epsilon/5[/tex]

[tex]|x - 1| < \delta[/tex]

From this is easy to conclude that the maximum value that delta can take is:

δ = ε/5

And we know that ε = 0.1, then we have:

δ = 0.1/5 = 0.02

δ = 0.02

The maximum value that delta can take is 0.02

Then we need to repeat it for ε = 0.01, so we get:

δ = 0.01/5 = 0.002

δ = 0.002

If you want to learn more, you can read:

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L=3W

2(3W+W)=32 feet

8W=32 feet

W=4 feet

L=3W

L=3* 4 feet

L=12 feet

The width is 4 feet, the length is 12 feet.