The width of a rectangle is 5 units less than the length. If the area is 150 square units the find the dimensions of the rectangle

The selling price for the given cost price and profit percentage is ₹420.5.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

Given that, the cost price of a bag of almonds is ₹290 and it is sold with a profit of 45%.

We know that, Selling price = (100+Profit%)/100 ×CP

Here, Selling price = (100+45)/100 ×290

= 145/100 ×290

= 1.45×290

= 420.5

Therefore, the selling price is ₹420.5.

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Answer: The area of the triangle is given by the formula:

Area = (base * height) / 2

We are told that the area is less than 18 square inches, so we can write the inequality:

(base * height) / 2 < 18

Multiplying both sides by 2, we get:

base * height < 36

To find the possible values of "a", we need to isolate "base" on one side of the inequality. Let's assume that the base is equal to "a". Then we have:

a * height < 36

Dividing both sides by height, we get:

a < 36 / height

Since the height is 6 inches, we can substitute it in the inequality:

a < 36 / 6 = 6

So the possible values of "a" are any value less than 6 inches. That is,

0 < a < 6.

Step-by-step explanation:

The height of the tree when the rock is 20 feet from the base of the tree, is equals to the 15.6 feet ( to the nearest tenth).

We have, a tree top and a rock on ground. The angle of elevation from a rock on the ground to the top of a tree = 38°.

The distance of the rock from base of tree = 20 feet

Let the height of tree be equals to "T feet". As we see in above figure, here a right angled triangle with base 20 feet , height T feet and hypothesis √400 + T² feet is formed. We have to determine the value of T. Using the Trigonometric functions, Tanθ = height / base

here, θ = 38° , height = T feet and base = 20 feet

Substitute all known values in above formula, Tan ( 38°) = T/20

=> T = 20 tan(38°)

=> T = 20× 0.7813

=> T = 15.62600 ~ 15.6 feet

Hence, required value of T is 15.6 feet..

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Answer:yes

Step-by-step explanation:

don't ask i searched it up

Answer:

see below

Step-by-step explanation:

if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

so <1 and <2 = 90

m<3 = 90

The value of y for that, the three horizontal lines would be parallel, is 7√2/ 16.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

A right-angled triangle.

Sin60° = Perpendicular/hypotenuse

Hypotenuse = 8

To find the value of y for that, the three horizontal lines be parallel:

The parallel lines are equally spaced.

So,

8 / 16 = y / 7√2/8

y =  7√2/ 16

Therefore, the value of y is 7√2/ 16.

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Answer:

0.80 m/s

Step-by-step explanation:

rate = 40 m / 50 s = 0.8 m/s

The points that can be included to keep the graph a function are given as follows:

P and U.

A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertically aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

Hence the points we can include on the graph to keep it a function are given as follows:

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The solutions of the quadratic equation 3x² – 8x + 5 = 5x² will be 0.4595 and negative 4.5495.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let the equation be ax² + bx + c = 0. Then the roots of the equation will be given as,

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]

The equation is given below.

3x² – 8x + 5 = 5x²

Simplify the equation, then we have

3x² – 8x + 5 = 5x²

2x² + 8x – 5 = 0

Then the roots of the equation are given as,

x = [ -8 ± √(8² - 4 · 2 · (-5))] / (2 · 2)

x = (- 8 ± 10.198) / 4

x = (- 8 + 10.198) / 4 , (- 8 - 10.198) / 4

x = 0.5495, -4.5495

The solutions of the quadratic equation 3x² – 8x + 5 = 5x² will be 0.4595 and negative 4.5495.

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Correct answer is H, On solving the provided question, we can say that inequality is graphed below is X less than/equal to x ≤ 15

A relationship between two expressions or values that is not equal in mathematics is referred to as an inequality. Thus, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers.

Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal ().

Values of any size can be contrasted using a variety of inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be solved.

However, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

As, the graph is pointing backwards from 15,

⇒ the values are less than equal to 15,

⇒ the inequality which follows criteria is  x ≤ 15

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The diameter of the earth is 3.66 times larger than the diameter of the moon.

The mean radius of the earth is 6.37 x 10^6 meters,

Re = 6.37 x 10^6 meters

The mean radius of the moon is 1.74 x 10^6 meters.

Rm = 1.74 x 10^6 meters

To compare the size of the diameter,

D = De/Dm = 6.37 x 10^6 / 1.74 x 10^6

Diameter of the earth is 3.66 times larger than the diameter of the moon.

In geometry, a circle's diameter is any straight line segment whose centre is on the circle and whose ends are on the circle. The longest chord of the circle is another name for it. Either of the two approaches can be used to determine the diameter of a sphere.

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Answer:

7600 if your going to nearest Hundred

Step-by-step explanation:

You have 7620. If you look at 20 it is under 50 so you would go down and if it was above 50 you would go up so therefore it is 7600

The equation representing the vertical asymptote of the graph is given as follows:

x = -8.

The vertical asymptotes of a function f(x) are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

From the graph, we can see that the function is not defined at x = 8, only to the left and to the right of x = 8, going to either negative infinity or positive infinity at both sides.

Hence the equation representing the vertical asymptote of the graph is given as follows:

x = -8.

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Answer: The expression (q + 1)^2 is equal to q^2 + 2q + 1.

The expression (q + 1)^2 can be expanded as follows: (q + 1)^2 = q^2 + 2q + 1. The "2" at the top of the parentheses is the exponent, meaning the expression inside the parentheses is being raised to the power of 2.

Step-by-step explanation:

The area and perimeter of the figure be 562.08 m² and 123.68 m.

The figure referred to is made out of a parallelogram and a crescent. The area of the parallelogram can be determined by utilizing the equation base x level, bringing about an area of 336 m².

The area of the crescent is determined utilizing the formula (π x r²)/2, calculating an area of 226.08 m². Thus, the complete area of the figure is 562.08 m².

The perimeter of the parallelogram is 86 m, while the border of the half circle is 37.68 m, giving an all-out perimeter of 123.68 m.

The area of the figure is 562.08 m², while the perimeter is 123.68 m.

This can be additionally separated into the area and perimeter of the parallelogram and half circle, which are 336 m² and 226.08 m² for the area, and 86 m and 37.68 m for the border, individually.

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the area of the shaded region is 38.8575 square centimeter.

The area of a sector is the space inside the section of the circle created by two radii and an arc. It is a fraction of the area of the entire circle.

The formula to find the area of a sector = θ/360° ×πr²

ABCD is a rectangle with AB=9 cm and BC=18 cm.

O is the midpoint of BC. Then, BO= 9 cm

a) By Pythagoras theorem,

Now, OA²=AB²+BO²

OA²=9²+9²

AO=9√2 cm

b) We know that, tanθ=Opposite/Adjacent

tanθ=18/9√2

tanθ=√2

θ=54.73°

≈55°

c) The area of the shaded region = 55°/360° ×3.14×9²

= 38.8575 square centimeter

Therefore, the area of the shaded region is 38.8575 square centimeter.

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The coordinates of the orthocenter of the triangle are (-1. 1.2)

From the question, we have the following parameters that can be used in our computation:

L(-4,3), M(2,3), and N(-1,-2).

Calculate the slopes of LM and LN.

So, we have

m₁ = (3 - 3)/(2 + 4) = 0

m₂ = (-2 - 3)/(-1 + 4) = -5/3

The slopes of the lines perpendicular to the above slopes is

m₁ = -1/0 = undefined

m₂ = -1/(-5/3) = 0.6

Next, calculate the equation of lines passing through M in which the height perpendicular to LN lay

(y - yM) = m₁(x - xM)

y - 3 = 0.6(x - 2)

Next, calculate the equation of lines passing through undefined slope

x = -1

Substitute x = -1 in y - 3 = 0.6(x - 2)

y - 3 = 0.6(-1 - 2)

y = 3 + 0.6(-1 - 2)

y = 1.2

Hence, the coordinates is (-1. 1.2)

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Answer:

N, M(2,3), L(-4,3), and (-1,-2).

Determine the LM and LN slopes.

The slopes of the lines perpendicular to the aforementioned slopes are m1 = -1/0 = undefined and m2 = -1/(-5/3) = 0.6. Hence, we obtain m1 = (3 - 3)/(2 + 4) = 0 and m2 = (-2 - 3)/(1 + 4) = -5/

Next, get the equation for lines passing through M with the height (y - yM) = m1(x - xM) y - 3 = 0.6. (x - 2)

The equation of lines running through an undefined slope, x = -1, must then be calculated.

Replace x = -1 with y - 3 = 0.6. (x - 2) y - 3 = 0.6(-1 - 2) y = 3 + 0.6(-1 - 2)\sy = 1.2

the coordinates are as a result (-1. 1.2)

Step-by-step explanation:

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As a result, the angle CBF has a 61 degree value.

When two consecutive lines or beams intersect at a single terminus, an angle is created. The apex of an arc is the location where two points come together.

Since Ray BF splits angle BCD into two equal portions because it is an angle bisector, the measures of angle CBF and angle DBF are the same. Consequently, we can write:

3z + 7 = 5z - 29

Simplifying and solving for z:

2z = 36

z = 18

Now we can substitute z = 18 into the expression for the measure of angle CBF:

3z + 7 = 3(18) + 7 = 61

Therefore, the measure of angle CBF is 61 degrees.

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The perpendicular bisector of line 7 cm is given below.

What is perpendicular bisector?

A perpendicular bisector is a line that divides the given into two halves which also makes an angle of 90° at the where it intersects the given line.

Steps to construct perpendicular bisector for the given line 7 cm.

Step 1 : Draw a line 7 cm using pencil and scale and named as AB.

Step 2: Take a measurement more than half of a line AB and draw a arc from A on both sides of the line AB.

Step 3: Repeat the step 2 from the point B.

Step 4: Join the arc by the straight line and named as MN, which is the required perpendicular bisector of line AB.

Hence the perpendicular bisector is shown in the figure.

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The cash price of the refrigerator would be $408.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that a new refrigerator has a price of $480.00. The store will discount the price by 15%.

The new price of the refrigerator would be -

{x} = 480 - {15}% of 480

{x} = 480 - (15/100) x 480

{x} = 480 - 3/20 x 480

{x} = 480 - 3 x 24

{x} = 480 - 72

{x} = 408

Therefore, the cash price of the refrigerator would be $408.

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The data given has: a) A strong correlation, b) A positive correlation

Correlation is a statistical measure that expresses the extent to which two variables are linearly related, meaning they change together at a constant rate.

We have ordered pairs in the data as:

x             y

1             2

2            3

3            8

4            10

5            26

6            38

7            46

8            50

9            68

Plotting the graph (attached)

Clearly, on plotting the scatter plot on the basis of table of values, we see that the relation is a strong correlation since we can find a relationship between variable x and y.

i.e. the points will lie above or below the curve  which is formed by connecting some points of the scatter plot and are not scattered away.

Hence, the data above has: A strong correlation.

Also, the graph is a positive correlation since with the increasing value of x the y-value also increases.

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C. The slope is negative two-thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two-thirds of an inch every hour.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The relationship of the candlestick between height and time is represented by a straight line passing through the points (0, 8) and (3, 6).

Slope(m) = (6 - 8)/(3 - 0).

Slope(m) = - 2/3.

Taking any of the points we have,

6 = - (2/3)×3 + b.

6 = - 2 + b.

b = 8.

y = - (2/3)x + 8.

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a. The values of Q1 = 355, Q2 = 510, Q3 = 910, range = 980 and IQR = 555.

b. The lower bound is not applicable and the upper bound is 1195. There are no outliers.

c.  The value at the 70th percentile is approximately 725.6 calories.

a. For the calories of each burger, we will find the Q1, Q2, and Q3, range, and IQR as follows -

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The median of the lower half (from 250 to 540) is the average of the two middle values: (300 + 410) / 2 = 355.

Therefore, Q1 = 355.

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The middle value is the median: Q2 = 510.

Arranging the calorie values in order from smallest to largest we get,

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 840, 980, 1230.

The median of the upper half (from 670 to 1230) is the average of the two middle values: (840 + 980) / 2 = 910.

Therefore, Q3 = 910.

Range = 1230 - 250 = 980.

IQR = Q3 - Q1 = 910 - 355 = 555.

b. To calculate the outlier boundaries, we need to first calculate the lower and upper limits as follows -

Lower bound: Q1 - 1.5 x IQR

Upper bound: Q3 + 1.5 x IQR

Lower bound: 430 - 1.5 x 310 = -25

Upper bound: 740 + 1.5 x 310 = 1195

Since there are no negative values for the calories of the burgers, the lower bound is not applicable. The upper bound is 1195, which is higher than the highest value in the dataset (1090). Therefore, there are no outliers.

c. To determine the value at the 70th percentile, we need to first order the calorie values from lowest to highest as follows -

250, 300, 410, 430, 445, 460, 510, 540, 670, 710, 740, 840, 980, 1090, 1230

Next, we will calculate the percentile rank of the 70th percentile -

Percentile rank = (70/100) x (n + 1) = 10.6

Since the percentile rank is not a whole number, we need to interpolate between the 10th and 11th values in the ordered list:

10th value: 710

11th value: 740

Using linear interpolation, we get:

Value at the 70th percentile = 710 + 0.6 x (740 - 710) = 725.6

Therefore, the value at the 70th percentile is approximately 725.6 calories.

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The complete question is -

For the calories of each burger:

a. find q1, q2, q3, the range, and the IQR.

b. calculate the outlier boundaries for the data set. are there any outliers? c. determine the value at the 70th percentile.

The combined area of the two rectangles is 32 square meters.

Rectangle is a two-dimensional shape with four straight sides, where all angles are right angles (90 degrees). The opposite sides of a rectangle are equal in length and parallel to each other, so rectangles have two pairs of equal sides.

The first rectangle has an area of 10 meters * 2 meters = 20 square meters.

The second rectangle has an area of 2 meters * 6 meters = 12 square meters.

When the two rectangles are joined together, the combined area of the two rectangles is 20 square meters + 12 square meters = 32 square meters.

So the combined area of the two rectangles is 32 square meters.

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The missing measures in △STU are,

⇒ ST = 4

⇒ TU = 8

And, ∠ S = 70°

∠ T = 64°

∠ U = 46°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ △PQR ~ △STU

Now, By the definition of similar of triangles;

⇒ PQ / QR = ST / TU

⇒ QR / RP = TU / US

Here, we have;

PQ = 14

PR = 21

QR = 28

SU = 6

Hence, We get;

⇒ QR / RP = TU / US

⇒ 28 / 21 = TU / 6

⇒ TU = 28 × 6 / 21

⇒ TU = 8

⇒ PQ / QR = ST / TU

⇒ 14 / 28 = ST / 8

⇒ ST = 8 / 2

⇒ ST = 4

And, All the angles are equal.

⇒ ∠ Q = 180 - (70 + 46)

           = 180 - 116

           = 64°

Hence, We get;

∠ S = 70°

∠ T = 64°

∠ U = 46°

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The inequality equation is x ≥ 48 inches

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the minimum height to ride the roller coaster be represented as x

Now , the required height to ride the roller coaster is = 48 inches

So , the individual must be equal to 48 inches tall

x = 48 inches

And , the individual could be greater than 48 inches tall

x > 48 inches

Substituting the values in the equation , we get

x ≥ 48 inches

Hence , the inequality is x ≥ 48 inches

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It will take the pump 80 minutes to fill the tank completely.

We can find the time to fill the tank by subtracting the current amount of the tank (3/8 of its capacity) from its total capacity. Then, dividing that amount by the flow rate of the pump (which is 1/16 of its capacity per minute).

The calculation is given as:

Remaining amount to fill = Total capacity - Current amount = 1 - 3/8 = 5/8

Time to fill completely = Remaining amount ÷ Flow rate = 5/8 ÷ (1/16) = 80 minutes

So, it will take the pump 80 minutes to fill the tank completely.

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____ The given question is incorrect, the correct question is given below:

If a pump fills a tank in 16 minutes and the tank currently has 3/8 of its capacity, then we can calculate how many minutes it will take to fill the tank completely.

The correct equation and solution are: D

$43. 6\ +\ 14. 3\ =\ m$

$m\ =\ 57. 9$

This equation represents the total distance traveled by the train (43.6 miles + 14.3 miles) and gives the correct answer of 57.9 miles traveled by the train.

In equation D, we add the 43.6 miles traveled with the 14.3 miles left to travel to find the total distance traveled by the train, which is 57.9 miles. This equation and solution correctly represent the number of miles traveled by the train.

The other equations and solutions  do not accurately represent the information given in the problem and do not lead to the correct answer.

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Answer: To find the profit from recent release game rentals, first multiply the number of recent release rentals by their profit per rental: 13 rentals * $3.80 per rental = $50.40

Next, multiply the profit from recent release rentals by the percentage of recent releases in the total number of rentals: $50.40 * (13/40) = $16.80.

So, the owner can expect to earn $16.80 in profit from recent release game rentals.

Step-by-step explanation: