The perimeter and the ratio of the length to the width of a rectangle are given. Find the length
and width of the rectangle. Then find the area of the rectangle.
7. Length =
7. Perimeter: 36 cm
7:w= 8:1
Width =
Area =

Answer:

its 20 (x=20)

Step-by-step explanation:

because to first is half of the second cube

The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

Answer:

69

Step-by-step explanation:

To do this, you want to first find how many pages he has read

So, to get that you want to multiply 230 by 70% or 0.7 (70% = 0.7 because to get the percent, you multiply the number by 100)

230 * 0.7 = 161

BUT, since you want to find how many pages he has left, you subtract the amount of pages he has read by how many pagest here are in total like so:

230 - 161 = 69 pages left

If you have any questions feel free to ask in the comments, and if this helped it would be appreciated if you left a brainliest :)

Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Answer:

  4.0%

Step-by-step explanation:

If we assume that potential impact sites are uniformly distributed over the area, the probability of interest is the ratio of the area of Connecticut to the area of the circle within 200 miles of Hartford.

__

The area of a circle with radius 200 miles is ...

  A = πr²

  A = π(200 mi)² = 40000π mi² ≈ 125,664 mi²

The area of a rectangle 100 miles by 50 miles is ...

  A = LW

  A = (100 mi)(50 mi) = 5000 mi²

The probability of interest is the ratio of these areas:

  p(impact in CT) = (5000 mi²)/(125664 mi²) ≈ 0.03979

The probability the meteor landed in Connecticut is about 4.0%.

Answer:

X=25

Y=25

Z=115

Step-by-step explanation:

f(x) = 3x + 5

Place 6 in X

f(6) = 3 * 6  + 5 = 23$

23 - 15 = 8$

Sara need more 8$ to rent a movie in Redbox because de sum of 15$ and 8$ is 23$ (the cost to rent 6 movies).

Answer: 4

Step-by-step explanation:

Since this inequality gives us a list, we want to choose the greatest number shown because x≤?. Because x has to be less than or equal to a number, it makes the most sense to put the greatest number there. In the list, 4 is the greatest number.

The statements about the quadrilateral and/or the transformed quadrilateral that are correct are:

The quadrilaterals will be congruent.

Option A is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

Quadrilateral WXYZ.

We see that,

Quadrilateral WXYZ is in the III Quadrant.

Step 1:

Rotated 180° about the origin.

This means,

Quadrilateral WXYZ is in the I Quadrant.

Step 2:

Reflection across the y-axis.

This means,

Quadrilateral WXYZ is in the II Quadrant.

Now,

Since there is no dilation the transformed quadrilateral will be congruent.

Thus,

The quadrilaterals will be congruent.

Quadrilateral WXYZ is in the II Quadrant.

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The complete question is:

Quadrilateral WXY will be rotated about the origin and then reflected across the y-axis. Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.

Answer:

2.25 yards per quilt

Step-by-step explanation:

if you add up all the numbers u get 58.5. then divide this by 26 to get 2.25

The number of yards that are used for each quilt will be 2.25 yards.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Dan is making quilts for the sewing class. He will utilize 22 yards of yellow texture, 11.2 yards of green texture, and 25.3 yards of blue texture. This sum makes 26 blankets.

The number of yards that are used for each quilt will be given as,

⇒ (22 / 26) + (11.2 / 26) + (25.3 / 26)

⇒ (22 + 11.2 + 25.3) / 26

⇒ 58.5 / 26

⇒ 2.25 yards

The number of yards that are used for each quilt will be 2.25 yards.

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Therefore, the area of the sketch is 56 square inches. Answer: None of the given options.

Area is a measure of the size of a two-dimensional surface or region, typically measured in square units such as square inches, square feet, or square meters. It is the amount of space inside a closed figure or shape, and is calculated by multiplying the length and width of the shape. Knowing how to calculate area is useful in a wide range of fields, including mathematics, engineering, construction, and many other areas where the measurement of space is important.

Here,

The sketch of the paper hat can be divided into two parts - a rectangle and two right triangles.

The base of each right triangle is the length of the rectangle, which is a + a = 2a = 8 inches. The height of each right triangle is b = 3 inches. Therefore, the area of each right triangle is:

(1/2) x base x height = (1/2) x 8 x 3 = 12 square inches

The area of the rectangle is:

length x width = a x 2a = 2a^2 = 2 x 4^2 = 32 square inches

To find the total area of the sketch, we add the areas of the two right triangles and the rectangle:

Total area = 2 x (area of right triangle) + area of rectangle

= 2 x 12 + 32

= 56 square inches

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Answer:

Hi there!

\(\:\mathsf{a^2\:-\:5a\:+\:6\:=\:0}\)

=> By splitting the middle term

=> \(\:\mathsf{a^2\:-\:2a\:-\:3a\:+\:6\:=\:0}\)

=> \(\:\mathsf{a(a\:-\:2)\:-\:3(a\:-\:2)\:=\:0}\)

=> \(\:\mathsf{(a\:-\:2)\:-\:(a\:-\:3)\:=\:0}\)

=> \(\:\sf{a\:=\:2\: and\: a\:=\:3}\)

\(\:\mathsf{Hope\:this\:helps\:you!\::)}\)

Thank you!

Answer:

\(a = 3 \: \: \: and \: \: a = 2\)

Step-by-step explanation:

⬇

\(a^{2} - 3a - 2a + 6 = 0\)

⬇

\(a \: (a - 3) \: \: (a - 2)\)

⬇

\({}\ a - 3 = 0 \\ a = 2{}\)

Answer:3.4

Step-by-step explanation:

Answer:

3.4

Step-by-step explanation:

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\sin Q = \frac{\text{opposite}}{\text{hypotenuse}}=\frac{x}{9.2}

sinQ=  

hypotenuse

opposite

​  

=  

9.2

x

​  

\sin 22=\frac{x}{9.2}

sin22=  

9.2

x

​  

9.2\sin 22=x

9.2sin22=x

Cross multiply.

The given equations represent the solutions of 0 = 0.25x² - 8x

An equation is a mathematical statement that shows the equality of two expressions, typically separated by an equal sign. Equations are used to solve problems and model real-world situations in many fields, including physics, engineering, and finance.

Redirecting to answer:

The equation 0 = 0.25x² - 8x can be rewritten as:

0.25x² - 8x = 0

Factoring out x gives:

x(0.25x - 8) = 0

So the solutions are x = 0 and 0.25x - 8 = 0, which gives x = 32.

Therefore, none of the given equations represent the solutions of 0 = 0.25x² - 8x

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The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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The amount of money increases by $125,000 due to the decrease in the reserve rate. The correct answer is B. It increases the amount by $125,000.

When the Federal Reserve decreases the reserve rate, it allows banks to hold a smaller portion of their deposits as reserves and lend out a larger portion. This change stimulates lending and increases the money supply in the economy through the process of fractional-reserve banking.

In this scenario, the initial deposit of $15,000 can be multiplied by the money multiplier, which is the reciprocal of the reserve rate. Initially, with a reserve rate of 6%, the money multiplier is 1/0.06 = 16.67. Therefore, the initial deposit can lead to a maximum increase in the money supply of $15,000 x 16.67 = $250,050.

When the reserve rate is decreased to 4%, the money multiplier becomes 1/0.04 = 25. Therefore, the same initial deposit of $15,000 can now result in a maximum increase in the money supply of $15,000 x 25 = $375,000.

The difference between the two scenarios is $375,000 - $250,050 = $124,950, which is approximately $125,000. Hence, the amount of money increases by $125,000 due to the decrease in the reserve rate.

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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The length of the segment is 2.4 centimeters.

The scale is 2.4 cm :24 mm.

How to change mm to cm?

One millimeter, or one-thousandth of a meter, is equal to one mm. One centimeter, also known as one hundredth of a meter, is equal to one centimeter.

Accordingly, 1 cm 10 mm. Divide the number of mm by 10 to get the number of cm when converting mm to cm.

Given that length of the segment is 24mm. now we know that,1 mm is equal to 0.1 cm,

So,

\(10 \: mm=1 \: cm \\ or, \: 1 \: mm = \frac{1}{10} \: cm \\ or, 24 \: mm × ( \frac{1}{10} ) = 2.4 \: cm.\)

The scale is 2.4 cm :24 mm.

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Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

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Answer:

I think it's J

Step-by-step explanation:

Because the ratio is 5:3:2

There are 150 raisins

And since 2 is one less than 3 my estimate would be subtracting 50 from 150 making there be 100 chocolate chips. Then if the unit is 50, 50 x 5 ( 5 in the ratio) would be 250.

I hope this helps, have a good day.

Answer:

We will begin with the graph of the tangent function, plotting points as we did for the sine and cosine functions. Recall that

tan

x

=

sin

x

cos

x

The period of the tangent function is π because the graph repeats itself on intervals of kπ where k is a constant. If we graph the tangent function on

−

π

2

to

π

2

, we can see the behavior of the graph on one complete cycle. If we look at any larger interval, we will see that the characteristics of the graph repeat.

We can determine whether tangent is an odd or even function by using the definition of tangent.

tan

(

−

x

)

=

sin

(

−

x

)

Step-by-step explanation:

Answer:

it is y=sin x

Step-by-step explanation:

i got it right on the test

Answer:

(8/9)^2

Step-by-step explanation:

8^2=64 and 9^2=81. Therefore, 8/9 x 8/9 = 64/81.

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Answer: 76 degrees

Step-by-step explanation:

m<abc = m<1 + m<2

4x+12=(2x-7)+(3x-4)

x=23

180=4x+12+m<3

m<3=76