A family made three trips to the grocery store in one month.•on the first trip they spent 100 on groceries.•on the second trip they spent 20% less than they did on the first trip.•on the third trip they spent 3/4 as much as they did on the second trip.what was the total amount of money the family spent on groceries for the month?

By answering the presented question, we may conclude that In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

To determine the answer, multiply the areas of the shaded squares by the overall area of the figure.

Assuming that both squares are the same size, we may combine the fractions using a common denominator:

2/12 + 2/15 = 5/60 + 4/60 = 9/60 = 3/20

As a result, the entire shaded area is 3/20 of the total area of the diagram.

We can't discover the exact area of the graphic because it's not presented. As a result, we can only represent the answer in fractions or decimals.

In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

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Answer:

10

Step-by-step explanation:

\(1000 = {x}^{3} \\ \\ {10}^{3} = {x}^{3} \\ \\ x= 10\)

If two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the two triangles are congruent.

What is the meaning of congruent triangles?

If two triangles have both the same shape and the same size then it is said that the two triangles are congruent. In other words, two triangles are congruent if they are copies of each other.

congruent if they are copies of each other. We can prove that two triangles are congruent if they satisfy any one of the following criteria:-

SSS (side side side ):- If three sides of one triangle are equal to the corresponding three sides of the other triangle.

SAS ( side angle side ):- If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle.

ASA ( angle side angle ):- If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle.

AAS ( angle angle side ):- If two angles and a none included side of a triangle are equal to the corresponding angles and side of another triangle.

RHS (right hypotenuse side ):- If the hypotenuse and one side of the right triangle are equal to the corresponding side and the hypotenuse of another triangle.

Hence, when two angles and an included side of one triangle are equal to the corresponding pieces of another triangle then the two triangles are congruent.

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The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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Answer:

20 ft.

Step-by-step explanation:

Answer:

56 square meters I Think

The correct answer is C-60, which represents all employees' salaries at an ocean cleanup business in thousands of dollars.

The interquartile range (IQR) is just a indication of a data set's dispersion or spread. It is referred to as the disparity between the data piece's higher (Q3) and lower (Q1) quartiles. The data collection is split into four equal parts by the quartiles, with Q1 standing for the data point that represents more than or identical to 25% of the data and Q3 standing for more than or equatable to 75% of the data. As it is less susceptible to extreme values and outliers than range, which is described as the distinction between the highest and least values in the data set, the IQR is a valuable measure of spread.

given

Finding the difference between the higher quartile (Q3) and the lower quartile will help us determine the interquartile range (IQR) of the salaries (Q1).

According to the boxplot, the lower quartile (Q1) is roughly $20,000, while the higher quartile (Q3) is roughly $80,000.

Consequently, the IQR is:

Q3 - Q1 = $80,000 - $20,000 = $60,000

The correct answer is C-60, which represents all employees' salaries at an ocean cleanup business in thousands of dollars.

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Answer:

111°

Step-by-step explanation:

∠DVB and ∠AVC are both vertical angles, meaning that they have the same measure and are a pair of opposite angles formed by intersecting lines. If ∠DVB is 111°, then ∠AVC is also 111°.

Answer:your welcome

Step-by-step explanation:

The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

Answer:Asa

Step-by-step explanation:because I know

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

Each side of the original square is One-fourth the length of each side of the scale model

Step-by-step explanation:

Given that the square is a scaled copy of a smaller orginal square that was scaled up using a scale factor of 4, it means that the side length of the original square was multiplied by 4 to get the new side lenght of the scaled copy given in the question, which is 8ft.

Let original lenght be x.

x * 4 = 8 ft

4x = 8

x = 8/4 = 2.

Side lenght of the original square = 2 ft

Side of the original square to side of scale model = 2 ft to 8 ft = 2/8 = ¼.

Therefore, the statement that is true is: "Each side of the original square is One-fourth the length of each side of the scale model".

Answer:

A

Step-by-step explanation:

The lateral surface area of the walls of the warehouse is 18,000 sq ft.

Area is a measure of the size of a surface or the amount of space that a two-dimensional shape occupies. It is typically measured in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length and width of the shape together.

To find the lateral surface area of the walls of the warehouse, you need to find the combined area of all the exterior walls. To do this, you can use the formula for lateral surface area, which is:

Lateral Surface Area = 2 * (l * h + w * h)

where l is the length of the wall, w is the width of the wall, and h is the height of the wall.

Using this formula, we can find the lateral surface area of each wall and add them together to get the total lateral surface area:

Wall 1: Lateral Surface Area = 2 * (100 ft * 30 ft) = 6,000 sq ft

Wall 2: Lateral Surface Area = 2 * (200 ft * 30 ft) = 12,000 sq ft

Total Lateral Surface Area = 6,000 sq ft + 12,000 sq ft = 18,000 sq ft

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Answer: 8/9 cause we sub

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Easiest is probably to use the Quadratic Formula with

a=4  

b = - 30

c= 45

to find   x =  15/4  ±  3 sqrt(5) / 4

OR:

x=5.42705    x=2.07295

Answer:

5.42 and 2.07

Step-by-step explanation:

When ax²+bx+c =0

Quadratic formula is   x=       -b ± √(b²-4ac)

                                                      2a

In 4x²− 30x + 45 = 0

a=4, b= -30, c= 45

x=30± √(900-720)      =   30±√180    = 30±13.42    =5.42 and 2.07

           8                                 8                       8

sorry, if it is wrong

The price that corresponds to an elasticity of 1.2 for this product is $59.85.

Elasticity is a fundamental concept in economics that measures the responsiveness of demand to changes in price. In this problem, we will use the calculus-based definition of elasticity to find the price that corresponds to a specific elasticity value.

The elasticity of demand measures the percentage change in quantity demanded that results from a 1% change in price. Mathematically, the elasticity of demand is defined as:

E = (%ΔQ / %ΔP) * (P / Q)

where E is the elasticity of demand, %ΔQ is the percentage change in quantity demanded, %ΔP is the percentage change in price, P is the price of the product, and Q is the quantity demanded.

To find the price that corresponds to an elasticity of 1.2, we need to solve for P in the elasticity equation above. Since we know the demand function D(p) = -5p² + 270,000, we can find Q by taking the derivative of the demand function with respect to price:

Q = D'(p) = -10p

Then, we can plug in Q and E = 1.2 into the elasticity equation and solve for P:

1.2 = (%ΔQ / %ΔP) * (P / Q)

1.2 = (%ΔQ / -1%) * (P / (-10p))

1.2 = (%ΔQ / -0.01) * (1 / -10)

%ΔQ = -0.0144

This means that a 1% increase in price will result in a 0.0144% decrease in quantity demanded, given an elasticity of 1.2. Now, we can plug in %ΔQ and Q into the demand function to solve for P:

-0.0144 = (D(p + 0.01P) - D(p)) / D(p)

-0.0144 = (-5(p + 0.01P)² + 270,000 - (-5p² + 270,000)) / (-5p² + 270,000)

-0.0144 = (-0.1P - 0.0005p²) / (-5p² + 270,000)

P = $59.85

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15 is the value of x that will make the linear equation true .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

x + 5= 20

X = 20 - 5

x = 15

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Answer: 8 weeks

Step-by-step explanation: It would take John 8 weeks to collect more basketball cards than Frank with 67 cards for John and 66 for Frank.

Paulina will complete her math homework in 2 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now it is given that,

Number of problems assigned to Paulina = 42

Number of problems completed by Paulina = 24

Number of remaining problems to be finished per hour = 9

Therefore number of remaining problems finished in h hours = 9h

Hence, we can write,

Total number of problems completed + Total number of problems remained  = Total problems assigned

Hence the Equation is given as,

24 + 9h = 42

⇒ 9h = 42 -24

⇒ 9h = 18

⇒ h = 2

Hence, Paulina will complete her math homework in 2 hours.

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Answer:

B. 25√3

Step-by-step explanation:

Use trigonometric ratio formula to find the length and width of the rectangle

Thus:

✔️Length of diagonal:

Reference angle = 30°

Hypotenuse = 10

Let length of rectangle = x = adjacent side

Therefore:

Cos 30° = x/10

10*cos 30 = x

10*√3/2 = x (cos 30 = √3/2)

5√3 = x

x = length of rectangle = 5√3

✔️Width of diagonal:

Reference angle = 30°

Hypotenuse = 10

Let width of rectangle = y = opposite side

Therefore:

Sin 30° = y/10

10*sin 30 = y

10*½ = y (sin 30 = 1/2)

5 = y

y = width of rectangle = 5

✔️Area of rectangle = length * width = 5√3 * 5 = 25√3

Answer:

B

Step-by-step explanation:

15a + 6

= 5.3.a + 2.3

= 3(5a+2)

Answer:

\(\triangle FED\sim \triangle JEH\)

Step-by-step explanation:

Both pairs of vertical angles formed at point E are equal. Therefore, the two triangles share two angles. If two triangles share two angles, they must also share the third angle, since the sum of the interior angles of a triangle add up to 180 degrees. Therefore, all three angles of the two triangles are equal, which is a proof of similarity. \(\implies \boxed{\triangle FED\sim \triangle JEH}\)

9514 1404 393

Answer:

  ΔDEF ~ ΔHEJ

Step-by-step explanation:

The vertical angles at E are congruent, and the marked angles at F and J are congruent. The two triangles are similar by the AA postulate.

The given portion of the similarity statement names the angles in the order "unspecified", "vertical", and "50°". If we name those angles in the same order in the other triangle, the similarity statement becomes ...

  ΔDEF ~ ΔHEJ

The length of the arc defined by the central angle of 312 degrees is 26π cm.

The formula for the arc length of a circle is given by:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.

Substituting the given values, we get:

L = (312/360) × 2π(30)

L = (26/30) × π × 30

L = 26π cm

Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.

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We have two points in polar coordinates:

P1 = (-6, π)

P2 = (3, -5π/3)

The first coordinate represents the length of the line joining the origin and the point, and its sign determines the direction of the line. For the second coordinate, we have the angle between the line and the horizontal line of the coordinate system.

For the first point, we have a length of 6, a negative direction, and an angle of π. The angle of π means "half a revolution", so initially, the point is on the left side, but the sign of the first coordinate is negative, so the direction is the opposite (to the right). The first point is located 6 steps to the right of the origin. For the second point, we have a length of 3, a positive direction, and an angle of -5π/3. The negative sign of the angle means "clockwise", so the second point is located 3 steps away from the origin, and for an angle of 5π/3 below the horizontal line. Graphically, this is: