Mr. Bean puts $5000 in a mutual
fund that increases in value by 11% each
year. How many years will it take him to
reach $23,000 in his mutual fund?

question: 104=8(−8+7x)

Step-by-step explanation:

04=8(−8+7x)

Step 1: Simplify both sides of the equation.

104=8(−8+7x)

104=(8)(−8)+(8)(7x)(Distribute)

104=−64+56x

104=56x−64

Step 2: Flip the equation.

56x−64=104

Step 3: Add 64 to both sides.

56x−64+64=104+64

56x=168

Step 4: Divide both sides by 56.

56x/56 = 168/56

asnwer: x=3

Answer: Choice D

Step-by-step explanation: A dilation would result in a similar triangle because multiplying by the scale factor will create proportional sides. However, this will change the size of the triangle, making it not congruent.

Answer:

D.

Step-by-step explanation:

Congruent means that the triangles are exactly the same in shape and size.

Dilating the triangle is the only answer that will change its size.

Answer:15-A

Step-by-step explanation:

The equation of the line in fully simplified slope-intercept form is y = -x - 8.

It is assumed that a line in the graph will pass through some points on the x and y-axes.

We must determine the line's fully simplified intercept.

we know the standard form of a line that is

y = mx + b

here, m is a slope and b is the constant

On the graph, there are the y-intercept (0,-8) and the x-intercept (-8,0).

The slope of the line passing through these points is:

\(slope = \frac{y2 - y1}{x2 - x1} \\ \)

\(slope = \frac{ 8 - 0}{ 0 - 8} \)

slope = 8/(-8)

slope = -1

then find the value of b

if x = 0 y = -8 then

y = mx +b

-8 = -1(0) + b

-8 = b

the value of b is -8

After inserting the values for m and c, the line's equation will be.

y = - x - 8

Hence y = -x - 8 is the equation of the line in fully simplified slope-intercept form.

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Answer:

B) Associative Property of Multiplication

Step-by-step explanation:

The associative property states you can change where the parentheses (grouping terms) are in a multiplication statement, and you'll get the same product.

More generally:

(a * b) * c = a * (b * c)

Answer:

B) Associative Property Of Multiplication

Step-by-step explanation:

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

Therefore, changing the grouping of (8x3) or (3x4) does not change the product.

It took Paul a total of 12 hours and 40 minutes to complete all three parts of the Ironman triathlon.

Paul’s time for swimming in the Ironman triathlon was 1 hour 25 minutes. Her time for biking was 5 hours longer than her swimming time, so her biking time was (1 hour + 5 hours) = 6 hours 25 minutes. She ran for 4 hours 50 minutes. The total time it took her to complete all three parts of the race is (1 hour 25 minutes) + (6 hours 25 minutes) + (4 hours 50 minutes) = 12 hours 40 minutes.

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There are 800 students are in Collin Middle School.

As per the given data:

Collin Middle School has 280 sixth-grade students.

The sixth grade students are 35% of the total school students of Collin Middle School.

Convert the percentage to decimal numbers by dividing with 100.

We get:

35% = \($\frac{35}{100}\) = 0.35

We have to determine that how many of total number of students are there in the Collin Middle School.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Percentage formula = (Value ÷ Total value) × 100

Let the total students in the Collin Middle School be x.

x × 35% = sixth grade students

x × 0.35 = 280

x = \($\frac{280}{0.35}\)

x = 800

Therefore the total students in the Collin Middle School are 800.

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The solution for the data shows the times, in minutes and seconds, for swimmers to swim a 400-m freestyle race has been shown below.

The statistic is the study of mathematics that deals with relations between comprehensive data.

a) To convert the data to seconds, we can multiply the minutes by 60 and add the seconds. For example, 3:28 is equivalent to 3 x 60 + 28 = 208 seconds.

Here is the data converted to seconds,
208, 176, 265, 222, 333, 237, 225, 269, 303, 295, 238, 255, 257, 209, 271, 210, 252, 261, 293, 306, 287, 230, 268, 249, 301, 226, 267, 291, 312, 298

b) To find the range, we subtract the smallest value from the largest value,

Range = 333 - 176 = 157 seconds

To find the median, we need to first arrange the data in order from smallest to largest, we need to find the average of the two middle values, which are 269 and 271,

Median = (269 + 271) / 2 = 270 seconds

To find the mode, we look for the value that appears most frequently in the data

Mode = 268 seconds

c)

 1 | 7

 2 | 002256789

 3 | 00835577

 4 | 01245899

 5 | 0136

 6 | 7

 7 | 1

Interval Frequency

170-199 seconds 1

200-229 seconds 7

230-259 seconds 8

260-289 seconds 7

290-319 seconds 4

320-349 seconds 1

d) The stem-and-leaf plot displays the actual data points, while the frequency table groups the data into intervals and displays the frequency of each interval.

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The total amount that the traveler will spend if they buy the clothes in Texas is $350.50.

The first cost to the traveler is the cost of clothing which is $300.

In addition to this, there will be a sales tax of 8.5% for buying the clothes in Texas which takes the cost to:

= 300 + (300 x 8.5%)

= 300 + 25.5

= $325.50

The airline will then charge an extra $25 which takes the total to:

= 325.50 + 25

= $350.50

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Answer:

Step-by-step explanation:

The future value of $900 saved each year for 10 years at 8 percent is approximately $12,585.90.

To calculate the future value, we can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r,

where:

FV is the future value,

P is the annual payment or deposit ($900 in this case),

r is the interest rate per compounding period (8% or 0.08),

and n is the number of compounding periods (10 years).

Substituting the given values into the formula:

FV = 900 * ((1 + 0.08)^10 - 1) / 0.08,

FV ≈ $12,585.90.

Therefore, the future value of saving $900 each year for 10 years at an 8% interest rate is approximately $12,585.90.

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Answer:

-0.39794000867

Step-by-step explanation:

This is the table in which we can see the values of two squared, two cubed, and so on. This is an operation in mathematics, known as exponentiation. If we look at the numbers at the bottom line, we can try to find the power value to which 2 must be raised to get this number. For example, to get 16, it is necessary to raise two to the fourth power. And to get a 64, you need to raise two to the sixth power. Also this is totally the answer

Answer:

1

Step-by-step explanation:

\(\frac{log_{10}(2) }{log_{10}(4)-log_{10}(2) }\)

\(\frac{log_{10}(2)}{2log_{10}(2)-log_{10}(2) }\)

Add similar elements \(\frac{log_{10}(2) }{log_{10}(2) }\)

Apply rule \(\frac{a}{a}=1\)

=1

9514 1404 393

Answer:

  a = -2, h = 2, k = 1

Step-by-step explanation:

Compare the expressions. Match one pattern to the other.

  \(f(x)=-2|x-2|+1\\\\f(x)=\ \,\,a|x-h|+k \qquad\ a=-2,\ h=2,\ k=1\)

__

The transformations are ...

  Translation by (h, k) = (2, 1). That is, 2 units right and 1 unit up.

  Vertical scaling by "a", which is (i) reflection over the x-axis (because a < 0), and (ii) expansion by a factor of 2.

A table and graph are shown in the attachment.

Answer:

I believe it's 65 degrees.. I'm sry if wrong I may have fell asleep too

Step-by-step explanation:

Answer:

x = -88 + 16

x = - 72

...............................

Answer:

Step-by-step explanation: x=-72

There ya go bud

To determine the lateral magnification of an image formed by a concave mirror, we need to use the mirror formula and magnification formula.

The lateral magnification refers to the ratio of the height of the image to the height of the object.

Given that the object distance (u) is 50 cm and the radius of curvature (R) of the concave mirror is 60 cm.

Using the mirror formula: 1/f = 1/u + 1/v, where f is the focal length of the mirror and v is the image distance.

Since the mirror is concave, the focal length is half the radius of curvature: f = R/2 = 60/2 = 30 cm.

Substituting the values into the mirror formula, we can solve for v: 1/30 = 1/50 + 1/v.

Solving the equation, we find v ≈ 150 cm.

Using the magnification formula: magnification (m) = -v/u.

Substituting the values, we get m ≈ -150/50 = -3.

The negative sign indicates that the image is inverted.

The absolute value of the magnification (3) represents the ratio of the image height to the object height.

Therefore, the lateral magnification of the image is closest to 3.

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Answer:

A $0.05n< $0.45

Step-by-step explanation:

It is given that she has "less than" rather than "less than or equal to" 45 cents. Therefore, your answer will contain the "less than" sign, which is signified as <.

Therefore, being the only answer with <, your answer will be A.

A nickel is $0.05, therefore:

$0.05 of n is less than $0.45, or $0.05n< $0.45

A) $0.05n < $0.45 is your answer.

~

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Answer:

x=4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

7+2x÷3=5

7+2x=5*3

7+2x=15

15-7=2x

8=2x

x=8÷2

x=4

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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The volume of the cylnder is  9,728.5 ft³

For a cylinder of radius R and height H, the volume is given by:

V = pi*R^2*H

Where pi = 3.14

Here we know that the height is.

H = (20 + 1/2) ft = 20.5 ft

And the diameter is (1 + 1/5) times the height, then:

D = (1 + 1/5)*(20 + 1/2) ft = (1.2)*(20.5)ft = 24.6ft

And the radius is half of that, so:

R = 12.3ft

Then the volume is:

V = 3.14*(12.3ft)^2*20.5ft = 9,728.5 ft³

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Answer:

39

Step-by-step explanation:

F(x)=3x12

Plug in F(3)=3x12

Simplyfi 3x .  12    = 39

Answer:

1) D. 556 ft^2

2) B. 305

Step-by-step explanation:

1. range is the difference between the highest and lowest value

972-416=556

2. median is the middle number when all of the numbers are sorted from least to greatest

275, 280, 284, 350, 310, 321, 420

Answer:

0.9 + n = 5.2

Step-by-step explanation:

Think about it, 0.9 increased by a number is 5.2

In other words, increasing 0.9 by a number will equal 5.2

So, increasing = adding, right?

Adding 0.9 to a number will equal 5.2

0.9 + n (a number) = 5.2

Answer:

All 3 methods- graphing, elimination, and substitution- work, depending on which method you prefer. All 3 methods allows you to find the point of interaction or the variables. Graphing would let you visually see the point and line.

The carnival committee should expect to pay $218.70 for prizes at the booth.

We can start by calculating the expected number of students who win each prize:

Stuffed toy: 22% of 150 students = 0.22 x 150 = 33 students

Jump rope: 16% of 150 students = 0.16 x 150 = 24 students

T-shirt: 6% of 150 students = 0.06 x 150 = 9 students

No prize: 100% - (22% + 16% + 6%) = 56% of 150 students = 0.56 x 150 = 84 students

Next, we can calculate the total amount of money that the carnival committee should expect to pay for prizes at the booth:

Stuffed toy: 33 students x $3.60 per toy = $118.80

Jump rope: 24 students x $1.20 per rope = $28.80

T-shirt: 9 students x $7.90 per shirt = $71.10

Total cost of prizes = $118.80 + $28.80 + $71.10 = $218.70

Therefore, the carnival committee should expect to pay $218.70 for prizes at the booth.

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9514 1404 393

Answer:

  p : q = 3 : 2

Step-by-step explanation:

You are given sufficient information to write two relations involving p and q. We presume these will be sufficient to find an answer to the question. We will be able to find p and q. Then we can find their ratio, as the problem asks.

  (p-15)/(q-15) = 2/1

  (p+30)/(q+30) = 5/4

__

From the first equation, we get ...

  p -15 = 2(q -15)

  p = 2q -15 . . . . . . . add 15, simplify

From the second equation, we get ...

  4(p +30) = 5(q +30)

  4p + 120 = 5q + 150

  4p = 5q + 30

Using the first equation to substitute for p, we have ...

  4(2q -15) = 5q +30

  8q -60 = 5q +30 . . .  eliminate parentheses

  3q = 90 . . . . . . . . . . . add 60-5q to both sides

  q = 30 . . . . . . . . . . . . divide by 3

  p = 2q -15 = 2(30) -15 = 45

Then the desired ratio is ...

  p : q = 45 : 30

  p : q = 3 : 2

Answer:

  441 square feet

Step-by-step explanation:

The rug area has dimensions x-6 and x-8. Its area is ...

  A = LW

  195 = (x -6)(x -8)

  195 = x^2 -14x +48

  196 = x^2 -14x +49 . . . . . . add 1 to make this a perfect square

  14^2 = (x -7)^2

  14 = x -7 . . . . . . take the square root

  x = 14 +7 = 21

The area of the living room is ...

  A = x^2 = 21^2 = 441 . . . square feet

Answer: 2(u-3)(2u-3)

Step-by-step explanation:

4u²-18u +18           take out the greatest common factor, 2, all terms can be divided by 2

2(2u²-9u +9)         to factor, multiply the first and the last parts of the quadratic.  2(9)=18   Find 2 numbers that multiply to 18 but add to the middle number.  

-6 and -3  both multyiply to +18 but add to -9

Take those 2 numbers, -6 and -3, and replace the  middle term with those numbers

2(2u²-6u-3u +9)  we have not changed the equation, we have simply replaced the term and broke it up.  -9u = -6u-3u

2(2u²-6u-3u+9) now we "group" the first 2 terms and the last 2

2[(2u²-6u)(-3u +9)]    this is not your factor you must take out the greatest common factor from each of the groupings

2[2u(u-3)-3(u-3)]   if the parentheses are the same, then you've done a good job. the first factoring will be what is in your parentheses, the second will be what ever is left.

2(u-3)(2u-3)

We use this method because there is a coefficient, number in front of the \(u^{2}\)