If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.

Answer:

Subtractive Property of equality

Step-by-step explanation:

Since x = y, When you subtract anything from x, you must do the same to y for them to stay equal.

Answer:

Subtraction property of equality

2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.

That means the 2 sides of the right triangle are 2 and -3

Area of triangle= 1/2×base×height

                         = 1/2×-3×2

                         =-3

∴ Area of the triangle=-3

The area of the asked triangle is 3 sq units.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.

When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3

Hence, the height and base of the triangle will be 2 and 3 respectively.

Area of a triangle = 1/2 (base) (height)

Area = 1/2 (2)(3)

Area = 3

Hence, the area of the asked triangle is 3 sq units.

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Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.

He needs 80 L of 30% solution, so that

x + y = 80

0.20x + 0.60y = 0.30 (80) = 24

Solve for y in terms of x :

y = 80 - x

Substitute this into the second equation and solve for x :

0.20x + 0.60 (80 - x) = 24

0.20x + 48 - 0.60x = 24

24 = 0.40x

x = 60

Solve for y :

y = 80 - 60

y = 20

Answer:

The appropriate solution is "259".

Step-by-step explanation:

According to the question,

[tex]\sigma = 300[/tex]

[tex]M.E=25[/tex]

At 82% CI,

[tex]\alpha = 0.18[/tex]

Critical value,

[tex]Z_c=1.341[/tex]

Now,

The sample size will be:

⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]

By substituting the values, we get

      [tex]=(1.341\times \frac{300}{25} )^2[/tex]

      [tex]=(1.341\times 12)^2[/tex]

      [tex]=259[/tex]

Answer:

isisis

Step-by-step explanation:

ISO’s

Answer:

-2/3

Answer: The constant of variation k for y = kx through (-3, 2) is k = -2/3.

Answer:

B

Step-by-step explanation:

an = a+(n-1)d

an=13+(n-1)14

d=14

Answer:

One

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Solving systems of equations

Step-by-step explanation:

Step 1: Define

Identify systems

y = 3x + 5

y = 4x

Step 2: Solve

If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.

∴ the systems should have only one solution.

Answer:

B

Step-by-step explanation:

Answer:

1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.

2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.

3)Certain problems arise with self reporting of distances, such as recording error or poor recall.

Step-by-step explanation:

1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.

2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.

3)Certain problems arise with self reporting of distances, such as recording error or poor recall.

Answer: 25.6 servings (partial serving) / 25 servings (whole serving)

Step-by-step explanation:

Concepts:

As we can see from the question, there are two units applied. [Quarts] and [cups]; therefore, we need to do the unit conversion.

1 quart = 4 cups

Solve:

Step one: Convert quarts into cups

Step two: Divide the cups to find the number of servings

**Disclaimer** I am not sure about the rules that you apply in mathematics. Here, the answer is not an integer. I am concerned whether you would allow partial servings. In my understanding, the servings shall be a whole, thus should be rounded. However, if you are fine with decimals, then you have the choice.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Answer:

the

Step-by-step explanation:

it's fairly easy actually. You just have to use sin

Answer:

Exact heights of the next 100 babies born in a region.

Step-by-step explanation:

A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.

C. Dilation.

Dilation can resize the image.

Translation will shift the imagine's position but won't change its actual size.

Rotation will mangle with image's orientation but also won't change its size.

Reflection is just a type of rotation which as established, also won't change its size.

Hope this helps.

66 because you have to solve the problem next time

Answer:

= c^4 d^8 a^2

Step-by-step explanation:

Apply exponent rule: aa= a^2

= c^3 da^2 cd^7

= c^4 da^2 d^7

= c^4 d^8 a^2

Answer:

29Kg

Step-by-step explanation:

P1=2Kg

P2=7Kg

P3=31Kg

P3-P1=29Kg

To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.

I was lucky and I got the result after few steps :-)

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The two right triangles share angle A, so the similarity statement can be written ...

  ΔABC ~ ΔADE

Corresponding sides are proportional, so we have ...

  BC/DE = AB/AD

  x/12 = 3/(3+9)

  x = 3 . . . . . . . . . . multiply by 12

Answer:

x=3

this is correct!!!

Answer:

b 25x6 = 150

25 decreases every month so

150 decreses every 6 month

800-150

650 are the bees remaining after 6 month

Given:

In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.

To find:

The length of the missing side.

Solution:

In a right angle triangle,

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.  

Substituting Perpendicular = 8 inches and Base = 12 inches, we get

[tex]Hypotenuse^2=8^2+12^2[/tex]

[tex]Hypotenuse^2=64+144[/tex]

[tex]Hypotenuse^2=208[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=\sqrt{208}[/tex]

[tex]Hypotenuse=14.422205[/tex]

[tex]Hypotenuse\approx 14.4[/tex]

The length of the missing side is 14.4 inches. Therefore, the correct option is D.

Answer:

Moving upwards with an acceleration.

Step-by-step explanation:

weight of the person  = 195 pounds

Apparent weight = 205 pounds

As the weight increases so the scale is moving upwards with some acceleration.

The scale is in elevator which is moving upwards.

Answer:

a) Their average weight is of 187 pounds.

b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?

8228/44 = 187

Their average weight is of 187 pounds.

b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For men, we have that [tex]\mu = 186, \sigma = 60[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]

This probability is 1 subtracted by the p-value of Z when X = 187. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

1 - 0.5438 = 0.4562

0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For women, we have that [tex]\mu = 157, \sigma = 69[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]

[tex]Z = 2.88[/tex]

[tex]Z = 2.88[/tex] has a p-value of 0.998.

1 - 0.998 = 0.002.

0.002 = 0.2% probability that the maximum safe weight will be exceeded

Answer:

(11.847 ; 15.813)

Step-by-step explanation:

We are given 12 samples which are :

8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25

We use a T-distribution to find the confidence interval since the sample size. is small, n < 30

Using a calculator :

The sample mean, xbar = 13.83

Sample standard deviation, s = 6.87

The confidence interval, C.I

C.I = xbar ± Tcritical * s/√n)

Tcritical at 95%, df = n - 1, 12 - 1 = 11

Tcritical(0.05, 11) = 2.20

Hence,

C.I = 13.83 ± 2.20(6.87/√12)

C.I = 13.83 ± 1.9831981

C. I = (13.83 - 1.983 ; 13.83 + 1.983)

C. I = (11.847 ; 15.813)

Answer:

Step-by-step explanation:

Part A

The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)

The given parameters are;

The values of the function, f(x) = The company's profit

The values of the independent variable, "x" = The price of erasers

Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)

2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4

3) The intervals where the function is increasing is 0 ≤ x ≤ 4

At the interval where the function is increasing, the sale price is increasing and the profits are increasing

The intervals where the function is decreasing is 4 ≤ x ≤ 8

At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing

Part B

The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows

Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50

The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00

THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!

Answer:

Matthew travels 0.0161 meters per second.

Step-by-step explanation:

Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:

42/50 = 0.84

26/30 = 0.86

0.86 x 60 = 52

0.84 meters in 52 seconds

0.84 / 52 = 0.01615

Therefore, Matthew travels 0.0161 meters per second.

Answer:

(52.30 ; 52.62)

Step-by-step explanation:

Given :

Sample size, n = 20

Mean, xbar = 52.46

Standard deviation, s = 0.42

We assume a t - distribution

The 90% confidence interval

The confidence interval relation :

C.I = xbar ± Tcritical * s/√n

To obtain the Tcritical value :

Degree of freedom, df = n - 1 ; 20 - 1 = 19 ; α = (1 - 0.90) /2 = 0.1/2 = 0.05

Using the T-distribution table, Tcritical = 1.729

We now have :

C.I = 52.46 ± (1.729 * 0.42/√20)

C. I = 52.46 ± 0.1624

C.I = (52.30 ; 52.62)

Answer:

The volume of water is 396 cubic meter.

Step-by-step explanation:

Area of water, A = 132000 square meter

Height, h = 3 mm = 0.003 m

The volume of water is given by

V = Area x height

V = 132000 x 0.003

V = 396 cubic meter.

Following are the responses to the given points:

For point a:

[tex]Diameter\ (d)= 16\ m\\\\[/tex]

Calculating the 3 rotations for every minute:

Calculating time for completing 1 rotation:

[tex]1\ rotation=\frac{60}{3}= 20\ second\\\\period=20 \ second\\\\[/tex]

The standard form of the equation of the sine and cosine function is:

[tex]y=A \sin \{ B(x-c)\} +D\\\\y=A \cos \{ B(x-c)\} +D\\\\[/tex]

Calculating the Amplitue:

[tex]A=\frac{max-min}{2}=\frac{17-1}{2}=\frac{16}{2}=8\\\\Period=\frac{2\pi}{B}\\\\20=\frac{2\pi}{B}\\\\B=\frac{2\pi}{20}\\\\B=\frac{\pi}{10}\\\\[/tex]

Calculating the phase shift:

for [tex]\sin[/tex] function: [tex]c=5[/tex]

for [tex]\cos[/tex] function: [tex]c=10[/tex]

Calculating the vertical shift:

[tex]\to D=\frac{max+ min }{2}=\frac{17+ 1}{2}=\frac{18}{2}=9\\\\y=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\y=8 \cos \{ \frac{\pi}{10}(t-10)\} +9\\\\[/tex]

For point b:

[tex]y> 12\ m\\\\12=8 \sin \{ \frac{\pi}{10}(t-5)\} +9\\\\12-9=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\3=8 \sin \{ \frac{\pi}{10}(t-5)\} \\\\\frac{3}{8}=\sin \{ \frac{\pi}{10}(t-5)\} \\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (0.38439677)=(t-5) \\\\1.22357+5=t \\\\t=6.22357\ second\\\\t=6.22\ second\\\\\sin^{-1}\frac{3}{8}=\frac{\pi}{10}(t-5) \\\\\frac{\pi}{10} (2.7571961)=(t-5) \\\\t=8.7764+5\\\\t=13.78\ second\\\\t_2-t_1=13.7764-6.22357= 7.55283\approx 7.55\ second \\\\[/tex]

Learn more:

Rotation: brainly.in/question/39626227

Look at one side of the triangle. It forms a right triangle with 45 degree angles.

A 45 degree triangle the base and height are the same, so the height would also be 26.

The hypotenuse(x) of a 45 degree right triangle is the side length time the sqrt(2)

The answer is: 26 sqrt(2)