Korl spent $46.20 on 12 gallons. what was the price per gallon?​

9514 1404 393

Answer:

  b.  55°

Step-by-step explanation:

Complementary angles have a sum of 90°.

  ∠ABC +∠CBD = 90° . . . . . . the given relation

  ∠ABC + 35° = 90° . . . . . . . . . substitute the given value

  ∠ABC = 55° . . . . . . . . . . . . . . subtract 35° from both sides

  ∠ABC = ∠EBF = 55° . . . . . . vertical angles are congruent

Answer:

4 and 2

Step-by-step explanation:

thay would have the same angle area.

Answer:

<4 & <2

Step-by-step explanation:

4 and 2 are vertical angles, meaning they are congruent.

ANSWER

1:1000

EXPLANATION

1000 millimeters is equivalent to 1 meter. The scale factor is,

As a ratio, this is 1:1000

The volume of the cone is 12π or 37.70 cm²

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Given data ,

Let the volume of the cone be represented as V

Now , the equation will be

Let the length of the cone be S = 5 cm

Let the height of the cone be = H

Let the radius of the cone be R = 3 cm

From the Pythagoras theorem , S² = H² + R²

So, substituting the values in the equation , we get

Height of the cone H = √5² - 3²

Height of the cone H = √25 - 9

Height of the cone H = √16

Height of the cone H = 4 cm

Now , the volume of the cone = ( 1/3 ) πR²H

Substituting the values in the equation , we get

Volume of the cone V = ( 1/3 ) x π x ( 3 )² x 4

On simplifying the equation , we get

Volume of the cone V = 3 x 4 x π

Volume of the cone V = 12 π

Volume of the cone V = 37.70 cm²

Therefore , the value of V is 37.70 cm²

Hence , the volume of cone is 12π or 37.70 cm²

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The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.

Area = length × width

Area = 11.2 cm × 5.1 cm

Calculating the product, we get:

Area = 57.12 cm²

Therefore, the area of the rectangle is 57.12 cm².

The correct answer is: 57.12 cm².

It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.

So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

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Answer:

hopefully i got this right lol

Step-by-step explanation:

First Question:

2, 1

Second Question:

I'm assuming the lawn is the shaded region, which to solve you will need to calculate the area of the trapezoid and then subtract that by the area of the building.

EQUATION for area of building: l*w

48 * 64 = 3072^2ft

EQUATION for area of trapezoid: (a+b)/2h

subsitute

(100 + 150)/2 (80) = 10000

10000 - 3072 = 6928^2 ft

Third Question:

Answer: 26 1/4

Explanation: In order to find the volume of any rectangular prism, you need to multiply the length, width, and height. In this case, the equation is: 6 * 1 1/4 * 3 1/2 = 26 1/4

The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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Answer:

30 and 10

Step-by-step explanation:

Main concepts:

Concept 1.  Geometric Sequence

Concept 2. Common ratio

Concept 3. Finding the next terms

Concept 1.  Geometric Sequence

Geometric sequences are a specific type of sequence with a pattern where a specific number is multiplied to each term to get the next term.

For instance, a completely different geometric sequence 1,2,4,8,16,... is geometric because you multiply any term by 2 to get the next term.

Concept 2. Common ratio

In a geometric sequence, this number that you can multiply by to get the next term (in the "1,2,4,8,16,..." example, the number 2) is called the common ratio because taking the ratio of two sequential terms of the sequence (dividing two terms in a row) always gives the same answer:

This process of finding ratios will yield a common ratio only if the sequence is a Geometric Sequence.

Concept 3. Finding the next terms

Since we're told that the sequence we're given in the question is a Geometric sequence, it must have a common ratio (otherwise, it wouldn't be a geometric sequence).

Find the common ratio by dividing sequential terms:

270/810 = 1/3

90/270 = 1/3

So, for the sequence in the question, the common ratio is 1/3.  Each term is multiplied by 1/3 to get the next term in the sequence.  (This is equivalent to dividing each term by 3 to get the next term in the sequence, if you prefer division and/or to avoid fractions)

So, to get the next two terms in the sequence, multiply by the common ratio:

90 * 1/3 = 30

30 * 1/3 = 10

So, the next two terms of the sequence are 30 and 10

The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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Answer: The first three

Step-by-step explanation:

Answer:

1/72

Step-by-step explanation:

The probability of landing on heads is 1/2

The probability of rolling a 2 is 1/6

The probability of rolling a 4 is 1/6

\(\frac{1}{2} *\frac{1}{6} *\frac{1}{6} =\frac{1*1*1}{2*6*6} =\frac{1}{72}\)

Answer:

72

Step-by-step explanation:

The probability of getting both a dog and a cat image is 0.25.

The probability of getting two dog images with replacement is 0.25. This is because when selecting with replacement, each draw is independent of the previous draw. Thus, the probability of getting one dog image is 0.50 and the probability of getting a second dog image is 0.50. Thus, the probability of getting two dog images is 0.50 x 0.50 = 0.25. Similarly, the probability of getting two cat images with replacement is 0.25.

The probability of getting one dog image and one cat image with replacement is 0.50 x 0.50 = 0.25. Thus the probability of getting both a dog and a cat image is 0.25.

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The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).

To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.

A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:

A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.

B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.

C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.

D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.

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The time when Hank's Movers will cost less is the point when the total charges is both Movers are Equal, the time is at 3 hours

Given Data

For Acme, the expression for the total charges is

Total = 45+40x ----------1

For Hank, the expression for the total charges is

Total = 55x ----------------2

Equating both expressions we have

45+40x = 55x

collect like terms

45 = 55x-40x

45 = 15x

divide both sides by 15

x = 45/15

x = 3 hours

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Answer:

In this context, unique means existence of only one value for that element and no more than one value

Step-by-step explanation:

After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.

Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.

The period of compounding in a year determines the worth of the future value.

The future value can be ascertained using an online finance calculator as follows:

Interest periods: = 4 times yearly (Quarterly)

Principal = $5,000

Annual interest rate = 9%

Number of years: 18

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $24,815.83

Total Interest = $19,815.83

Interest periods: = Annually

N (# of periods) = 18 years

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,585.60

Total Interest = $18,585.60

Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)

Thus, an investment compounded periodically earns more than an investment compounded annually.

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The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

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Answer:

Overall, the steps for algebraically finding the range of a function are:

1.Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).

2.Find the domain of g(y), and this will be the range of f(x).

3.If you can't seem to solve for x, then try graphing the function to find the range.

Step-by-step explanation:

Answer:

Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).

Find the domain of g(y), and this will be the range of f(x).

If you can't seem to solve for x, then try graphing the function to find the range.

Step-by-step explanation:

Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)

Answer:

0.6

Step-by-step explanation:

4/7 can be considered a suspended division problem.  To find the answer, 4 must be divided by 7.  This yields the result 0.57142, which can be rounded to 0.6.

Answer:

\( 2ab^2 -d^3 + c \)

Step-by-step explanation:

Given the expression \( 2ab^2 - (d^3 - c) \), all you need to do to evaluate the expression is to open the bracket.

Use the negative sign to multiply all the terms within the bracket alongside the sign they carry.

Thus,

\( 2ab^2 - (d^3 - c) = 2ab^2 -d^3 + c \) (negative sign multiplied by negative sign equal positive sign)

We cannot evaluate \( 2ab^2 -d^3 + c \) further. The me three terms are different from one another. There are no like terms.

Answer:

I means that approximates a normal distribution as the sample size gets larger.

Step-by-step explanation:

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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the answer for this would be 20 percent

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

⇢∠V + ∠T = ∠x

⇢53° + 103° = 156°

⇢∠VUX = 156°

‌

‌

Hence , option b is the correct answer.

Answer:

B) 156 is correct

Hope it helps

The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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