The seventh-grade class is raising money
to have a class trip at the end of the year.
They began the year with $1,500. Now they
have $1,650 in the account.
What is the percent of increase for the
money the class has raised? I
a.
b.
Make Sense and Persevere The
class figured out that if the percent
increase is 99% from the beginning of
the year, the class will have enough
money for every student to go on the
field trip. How much money will the
class need to raise for every student to
go.

Answer:

Area = 72.62 m²

Step-by-step explanation:

Area of a triangle with the given three sides is given by,

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Here, s = [tex]\frac{a+b+c}{2}[/tex]

And a, b, c are the sides of the triangle.

From the question,

a = 20 m, b = 10 m and c = 15 m

s = [tex]\frac{20+10+15}{2}[/tex]

s = 22.5

Substitute these values in the formula,

Area = [tex]\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}[/tex]

        = [tex]\sqrt{22.5(2.5)(12.5)(7.5)}[/tex]

        = [tex]\sqrt{5273.4375}[/tex]

        = 72.62 m²

The distance from the origin is a.

Step-by-step explanation:

If the point is located at the coordinate [tex](a\cos \alpha, a\sin \alpha)[/tex], then its distance from the origin is given by

[tex]r = \sqrt{x^2 + y^2} = \sqrt{(a\cos \alpha)^2 + (a\sin \alpha)^2}[/tex]

[tex]\:\:\:\:=\sqrt{a^2(\cos^2\alpha + \sin^2 \alpha)}[/tex]

[tex]\:\:\:\:= a[/tex]

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.

Answer: 12°

Hope this helps!

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:

When p=2 , q=-1

3q-2p

3(-1) - 2(2)

(3)-4

-1

When p=-3 , q=4

3(4)-2(-3)

(12 )-(-6)

=18

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:

[tex]{ \tt{x + 30 \degree = 90 \degree}} \\ { \tt{x = 90 \degree - 30 \degree}} \\ { \tt{x = 60 \degree}}[/tex]

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Answer:

  4√x -7

Step-by-step explanation:

Four times the square root of x is written 4√x. Seven less than that is found by subtracting 7:

  [tex]4\sqrt{x}-7[/tex]

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Answer:

  25 (ft/s)

Step-by-step explanation:

The "rate of change" is taken to mean the "rise" divided by the "run". Here, adjacent points differ in their y-value by 25 ft and their x-value by 1 second.

The rate of change is ...

  rise/run = (25 ft)/(1 second) = 25 ft/second

Usually, we're just interested in the numerical value: 25.

_____

Additional comment

The graph is mis-labeled. It is not showing "rate of ascent." It is showing height as a function of time. The "rate of ascent" is the slope of the line on the graph, not its value.

Answer:

γ = 97.77°

Step-by-step explanation:

A = 6.8

B = 8.4

C = 11.5

To find γ, apply the angle version of the Law of Cosines:

Cos γ = (A² + B² - C²)/(2AB)

Plug in the values

Cos γ = (6.8² + 8.4² - 11.5²)/(2*6.8*8.4)

Cos γ = -15.45/114.24

Cos γ = -0.1352

γ = Cos^{-1}(-0.1352)

γ = 97.77° (nearest hundredth)

Step-by-step explanation:

He,smixing x and y values and averaging them. You add x of one point and add to the x value of the second point. Then divide by 2. Do the same with the y values.

Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

2(x + 8) = 26

Step 2: Solve for x

Answer:

{20}, {40}, {20,40}, { }

Answer:

first question is D

second question is D .875

Step-by-step explanation:

35*2.5= 87.5

7 divided by 8= .875

Answer:

D   87.5 miles

D  0.875 = 7/8 so it is a decimal that terminates after 3 dp.

Step-by-step explanation:

We write;

Scale Inch x Miles

2.5 x 35 = 87.5 miles

Why??

87.5 miles is found when we use the scale of 35 miles = 1inch

Answer = D 87.5 miles

The second one we can either multiply by 7/8 or divide by 1-7/8 = 1/8 to show that;

1/ 1/8 = 0.125

1-0.125 = 0.875  

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:

First of all, D is the supplement to the right angle. Together they equal 180 degrees providing the right angle is sitting on a line.

d + 90 = 180      Subtract 90 from both sides.

d = 180 - 90

d = 90

e is vertically opposite the 49 degree angle. Therefore e = 49 (that's what vertically opposite angles do).

f is supplementary to e. Together they add to 180

e + f = 180                     But you know e is 49 so

49 + f = 180                   Subtract 49 from both sides.

f = 180 - 49

f = 131

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:

20%

Step-by-step explanation:

The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)

The probability is: 6/30 = 1/5 = 0.2 = 20%

The probability that the student is a male given that he's a sophomore is approximately 60%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability that the student is a male given that it's a sophomore can be calculated using the formula:

P(male | sophomore) = P(male and sophomore) / P(sophomore)

The number of male sophomores is 6, and the total number of sophomores is 6+4=10.

So, the probability of selecting a sophomore is:

P(sophomore)

= (number of sophomores) / (total number of students)

= 10 / 23

The number of male sophomores is 6.

So,

The probability of selecting a male sophomore is:

P(male and sophomore) = 6 / 23

Therefore,

The probability that the student is a male given that it's a sophomore is:

P(male | sophomore)

= (6 / 23) / (10 / 23)

= 6 / 10

= 3 / 5

Rounding to the nearest whole percent, we get:

P(male | sophomore) ≈ 60%

Thus,

The probability that the student is a male given that he's a sophomore is approximately 60%.

Learn more about probability here:

https://brainly.com/question/14099682

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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:

21.2 in²

Step-by-step explanation:

The area of an equilateral triangle is given as :

Area, A = √3/4 * a²

Where, a = side length of the equilateral triangle

a = 7 inches ; Recall that all sides of an equilateral triangle are the same.

Put a = 7 in the equation :

A = √3/4 * a²

A = √3/4 * 7²

A = 0.4330127 * 49

A = 21.217 in²

Area, A = 21.2 in²

Answer:

x =5/ (1-a)

Step-by-step explanation:

3x-ax=2x+5​

Subtract 2x from each side

3x -ax-2x = 2x+5-2x

3x -ax -2x = 5

combine like terms

x-ax = 5

Factor out x

x(1-a) =5

Divide each side by 1-a

x =5/ (1-a)

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]3x-ax=2x+5\\\\3x-ax-2x=5\\\\(3-2)x-ax=5\\\\x-ax=5\\\\x(1-a)=5\\\\\dashrightarrow x=\dfrac{5}{1-a}[/tex]

Answer:

m∠y=41

m∠x=90

Step-by-step explanation:

It is an isosceles triangle, so m∠B=49 too

49+49=98

180-98=82

82÷2=41

m∠y=41

41+49=90

180-90=90

m∠x=90

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

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Answer:

  726 ft²

Step-by-step explanation:

The perimeter of the room is ...

  P = 2(L+W) = 2(18 +15) = 66 . . . . ft

Then the gross wall area (including windows) is ...

  A = LH = (66 ft)(8 ft) = 528 ft² . . . . gross wall area

The area of the 3 windows is ...

  A = 3×LW = 3×(6 ft)(4 ft) = 72 ft² . . . . window area

The area of the ceiling is ...

  A = LW = (18 ft)(15 ft) = 270 ft² . . . . ceiling area

__

Then the net area to be painted is ...

  gross wall area + ceiling area - window area

  = 528 ft² +270 ft² -72 ft² = 726 ft²

The area that Marta will paint is 726 ft².

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Answer:

  x = 64°

  y = 26°

Step-by-step explanation:

Angle x and 26° together make a right angle, so ...

  x = 90° -26° = 64°

Angles x and y together make a right angle, so ...

  y = 90° -(90° -26°) = 26°

-2y=10-5x

-2y/-2=(10-5x)/-2

Y=5/2x-2

Hello!

√7 - y = 6 <=>

<=> -y = 6 - √7 <=>

<=> y = -6 + √7 => √7 - (-6 + √7) = 6

Good luck! :)

Answer:

-29

Step-by-step explanation:

When you substitute 1 for  y  in the original equation, you get:

7−(1)−−−−−−√

=?

6

6–√

≠

6 So 1 is not a solution.

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Answer:

  (c) 16°

Step-by-step explanation:

The external angle at P is half the difference of the intercepted arcs:

  P = (90° -58°)/2 = 32°/2

  P = 16°

Answer:

The point-slope form is y - 2 = 1/2 (x - 3)

Step-by-step explanation:

The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.