Find the distance between the two points

Answers

Answer 1

Answer: I got 8.1 units
.
I used the Pythagorean Theorem to find my answer. I plugged in 7 for the long side and 4 for the short side and then solved.
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Hope this helps :)

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Solve for M in the formula S= C+M. A. M= S+ C
B. M= S - C
C. M= SC
D. M= s/c

Answers

Final answer:

To solve for M in the formula S = C + M, subtract C from both sides of the equation.

Explanation:

To solve for M in the formula S = C + M, we need to isolate the variable M on one side of the equation. To do this, we can subtract C from both sides of the equation:

S - C = C + M - C

S - C = M

Therefore, the correct answer is B. M = S - C.

Learn more about Isolating Variables here:

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Answer:

im pretty sure its a

Step-by-step explanation:

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?

Answers

Answer:

The probability is $P(X > x ) = 0.19215$

Step-by-step explanation:

From the question we are told that

Th The population mean $\mu = \$ 1,999$

The standard deviation is $\sigma = \$ 574$

The values considered is $x = \$ 2,500$

Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

$P(X > x ) = P(( X - \mu)/(\sigma ) > ( x - \mu)/(\sigma ) )$

Generally

$X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )$

$P(X > x ) = P(Z > ( x - \mu)/(\sigma ) )$

substituting values

$P(X > 2500 ) = P(Z > ( 2500 - 1999)/(574 ) )$

$P(X > 2500 ) = P(Z >0.87 )$

From the normal distribution table the value of $P(Z >0.87 )$ is

$P(Z >0.87 ) = 0.19215$

Thus

$P(X > x ) = 0.19215$

Final answer:

We calculate the z-score for the amount $2,550 using the given mean and standard deviation. The z-table gives us the percentage of people who spend less than this, which we subtract from 1 to find the percentage who spend more. Approximately 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Explanation:

To compute the percentage of adults spending more than $2,550 per year, we must first find the z-score associated with this value. The z-score is a measurement of how many standard deviations a particular data point is from the mean.

The formula for calculating the z-score is: Z = (X - μ) / σ.

Where:
- X is the value we are interested in.
- μ is the mean.
- σ is the standard deviation.

Using this formula, the z-score for $2,550 is:
Z = ($2,550 - $1,999) / $574 = 0.96.

Next, we need to use a z-table or a standard normal distribution table to find out the probability that lies below the calculated z-score. Looking this up on a z-table, we get a value of 0.8315, meaning that 83.15% of the population will spend $2,550 or less per year on reading and entertainment. Since we want to know the percentage spending more than $2,550, we subtract this value from 1: 1 - 0.8315 = 0.1685.

Therefore, based on the given mean and standard deviation, about 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Learn more about Z-Score here:

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A culture started with 5000 bacteria after three hours it grew 6500 bacteria predict how many bacteria will be present after 13 hours round your answer to the nearest whole number

Answers

Answer:

15595 bacteria will be present after 13 hours.

Step-by-step explanation:

Continuous population growth:

The continuous population growth model, for the population after t hours, is given by:

$P(t) = P(0)e^(rt)$

In which P(0) is the initial population and r is the growth rate.

Started with 5000 bacteria

This means that $P(0) = 5000$

$P(t) = 5000e^(rt)$

After three hours it grew 6500 bacteria:

This means that $P(3) = 6500$ . We use this to find r.

$P(t) = 5000e^(rt)$

$6500 = 5000e^(3r)$

$e^(3r) = (65)/(50)$

$\ln{e^(3r)} = \ln{(65)/(50)}$

$3r = \ln{(65)/(50)}$

$r = \frac{\ln{(65)/(50)}}{3}$

$r = 0.0875$

$P(t) = 5000e^(0.0875t)$

How many bacteria will be present after 13 hours?

This is P(13). So

$P(13) = 5000e^(0.0875*13) = 15594.8$

Rounding to the nearest whole number

15595 bacteria will be present after 13 hours.

What is a3 if an=64(12)n−1

Answers

Answer:

$\huge\boxed{a_3=9,216}$

Step-by-step explanation:

$a_n=64(12)^(n-1)\n\n\text{substitute}\ n=3:\n\na_3=64(12)^(3-1)=64(12)^2=64(144)=9,216$

If a car travels at a constant speed of 45km/hr how long will a journey of 270km take?

Answers

the answer is 6hours because 270 divided by 45 is 6

Answer:

I think the answer is "6" but I could be wrong.

Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8

Answers

Answer: The required equation of the ellipse in standard form is $(y^2)/(25)+(x^2)/(16)=1.$

Step-by-step explanation: We are given to find the equation of an ellipse in standard form with the vertical major axis of length 10 units and minor axis of length 8 units.

Since the major axis is vertical, so it will lie on the Y-axis. Let the standard form of the ellipse be given by

$(y^2)/(a^2)+(x^2)/(b^2)=1,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where the length of major axis is 2a units and length of minor axis is 2b units.

According to the given information, we have

$2a=10\n\n\Rightarrow a=(10)/(2)\n\n\Rightarrow a=5$

and

$2b=8\n\n\Rightarrow b=(8)/(2)\n\n\Rightarrow b=4$

Substituting the values of a and b in equation (i), we get

$(y^2)/(5^2)+(x^2)/(4^2)=1\n\n\n\Rightarrow (y^2)/(25)+(x^2)/(16)=1.$

Thus, the required equation of the ellipse in standard form is $(y^2)/(25)+(x^2)/(16)=1.$

(x/h)^2+(y/v)^2=1 where h is the horizontal radius and v is the vertical radius

In this question it seem that they are saying the length of the axis and not radius so I would cut them in half so that they are radii...then:

(x/4)^2+(y/5)^2=1

x^2/16+y^2/25=1

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