write each of these ratios in lowest terms using a colon 3.0 to 1.2​

The bar model that represents the number of cousins that Sawyer has, given the cousins Hazel has is the fourth bar model.

The letter " c " is meant to represent the number of cousins that Sawyer has, in relation to those that Hazel has. This means that bar models A and C are out because they represent the cousins as B.

The question shows that Hazel has twice the number of cousins that Sawyer has. This means that if Sawyer's cousins are represented as " c " then Hazel would be 2 c. This is shown in the last bar model so this is the correct bar model.

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First part is:

Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.

How many cousins does Sawyer have?

This is not true for all functions. To prove this, an example is given below. Let f(x) = x and g(x) = x².

A function is a relation that associates each element of a set, called the domain, to exactly one element of another set, called the range. It is a type of correspondence between two sets, where each element of one set is associated with exactly one element of another set.

The first derivative of f(x) is f ' (x) = 1 and the first derivative of g(x) is g ' (x) = 2x.

Therefore, ( f ⋅ g )' = ( x ⋅ x2 )'

= 1 ⋅ 2x + x ⋅ 2

= 2x + 2 ≠ 1 ⋅ 2x + 2x

= 4x

= f ' ⋅ g '

This example proves that the statement (f⋅g)' = f'⋅g' is incorrect. It is important to note that this does not mean that the statement is not true for all functions. It simply means that for the particular example given, the statement is not correct.

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The length of the square is 1.75 inches, while the king's height is 2.25 inches.

Define length.

The length of an object or the extent of a one-dimensional object along its longest dimension is measured physically. It is a basic idea in physics and geometry and is frequently expressed in terms of meters (m), centimetres (cm), feet (ft), or inches (in).

According to the information provided, the square length to king's height ratio is 3.5 to 4.5 inches. Let's use this ratio to determine the square's length when the king is 2.25 inches tall.

We may make a proportion to get the square's length:

(square length) / (king's height) = 3.5/4.5

king's height = 2.25

Let's substitute the given values:

(square length) / 2.25 = 3.5/4.5

To solve for the length of the square, we can cross-multiply:

(square length) = (2.25) x (3.5/4.5)

(square length) = 1.75

Therefore, the length of the square is 1.75 inches, while the king's height is 2.25 inches.

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Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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The amount in the account at the end of the year is $4998.

Percentage decrease is the measure of the reduction in the value of a quantity over time, expressed as a percentage of its original value. It is calculated by taking the difference between the original value and the new value, dividing it by the original value, and then multiplying the result by 100.

We know that;

Percentage decrease = 26.5%

Then the decrease in dollars = 26.5/100 * 6800

= $1802

The amount at the end of the year = $6800 - $1802

= $4998

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Answer: (0, 3)

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Answer: 52-9 = 43 units

Step-by-step explanation:

Answer:

13.75 cm³

Step-by-step explanation:

In order to find the area of a rectangular prism you only need to multiply the width height and length together:

2.75 * 1.25 = 3.4375

3.4375 * 4 = 13.75

Hope this helps!

The probability of the sample mean being less than 25.3 is given as follows:

0.9713 = 97.13%.

The sample mean would not be considered unusual, as it has a probability that is greater than 5%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576[/tex]

The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:

Z = (25.3 - 25)/0.1576

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

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Answer:

2.362

Step-by-step explanation:

Use calculator: 2.361727836

Round: 2.362

Required Answers :

1. 2x + 4 = 10

[tex]\: :\implies [/tex] 2x = 10 - 4

[tex]\: :\implies [/tex] 2x = 6

[tex]\: :\implies [/tex] x = 6/2

[tex]\: :\implies [/tex] x = 3.

Hence, Option (A) x = 3 is the answer.

2. 25/5 × 7 = ?

[tex]\: :\implies [/tex] 5 × 7

[tex]\: :\implies [/tex] 175/5

[tex]\: :\implies [/tex] 35

Hence, The required answer is 35.

3. 100 - 50 + 10 - 5 = ?

[tex]\: :\implies [/tex] 50 + 5

[tex]\: :\implies [/tex] 55

Hence, Option (A) 55 is the answer.

4. 24 / 6 = ?

[tex]\: :\implies [/tex] 24 ÷ 6

[tex]\: :\implies [/tex] 4

Hence, Option (A) 4 is the answer.

5. A triangle has base 6 inches and height 8 inches. What is the area?

Area of triangle = ½ × Base × Height

[tex]\: :\implies [/tex] 1/2 × 6 × 8

[tex]\: :\implies [/tex] 1/2 × 48

[tex]\: :\implies [/tex] 48/2

[tex]\: :\implies [/tex] 24 sq. in

Hence, Option (A) 24 sq in is the answer.

6. What is the greatest common factor of 36 and 56?

36 = 1,2,3,4,6,9,12, 18 and 36.

56 = 1,2,4,7,8,14,28 and 56.

Hence, Option (A) 4 is the answer.

7. What is the square root of 121?

[tex]\: :\implies [/tex] 11 × 11

[tex]\: :\implies [/tex] 121

Hence, (A) 11 is the answer

8. If 2x + 4 = 14, what is x?

[tex]\: :\implies [/tex] 2x + 4 = 14

[tex]\: :\implies [/tex] 2x = 14 - 4

[tex]\: :\implies [/tex] 2x = 10

[tex]\: :\implies [/tex] x = 10/2

[tex]\: :\implies [/tex] x = 5

Hence, Option (A) 5 is the answer

9. (3x - 5) + (7x + 1) = ?

[tex]\: :\implies [/tex] 3x - 5 + 7x + 1

[tex]\: :\implies [/tex] 10x - 5 + 1

[tex]\: :\implies [/tex] 10x - 4

Hence, Option (A) 10x - 4 is the answer.

10. What fraction is 5/12?

[tex]\: :\implies [/tex] 1/2 (approximately)

Hence, Option (A) 1/2 is the answer.

a. Apples:  Lily needs 10 cups of apples for her fruit bowl.

b. Watermelons: Lily needs 13-3/4 cups of watermelons for her fruit bowl.

c. Grapes: The amount of grapes that Lily has is not given

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To make her fruit bowl, Lily needs 2½ times the amount of each fruit she currently has.

a. Apples:

2½ × 4 cups = 10 cups

Therefore, Lily needs 10 cups of apples for her fruit bowl.

b. Watermelons:

2½ × 5-½ cups = (2 × 5 + 1/2) × 5/2 cups = 13-3/4 cups

Therefore, Lily needs 13-3/4 cups of watermelons for her fruit bowl.

c. Grapes:

The amount of grapes that Lily has is not given, so we cannot calculate how much she needs for her fruit bowl.

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The elements of the sets  A ∩ (B ∪ C) is  {b, c, i}.

A universal set (U) is a set which has elements of all the related sets, without any repetition of elements.

Therefore,

U = {a, b, ….. i, j}

A = {b, c, i, j}

B = {a, c, g, i}

C = {a, b, d, i}

Therefore, let's find the elements A ∩ (B ∪ C).

Hence,

(B ∪ C) = {a, b, c, d, i, g}

A =  {b, c, i, j}

Finally,

A ∩ (B ∪ C). = {b, c, i}

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Answer:

a) x > -7

Step-by-step explanation:

an open circle (blank) means the greater than or less than symbols (< or >) and a close circle (filled in) means ≤ or ≥. the lining to your right looks more bold than the lining to your left so it's an; open circle, on -7, with the lining bold to your left.

in conclusion, x (the open circle) > -7

that L looking shape is a right angle, which is 90 degrees. and the question is saying that the part they cut off is 56 degrees. to find x you will need to subtract 90 from 56 to get 34.

The answer is 34 :)

Answer:

Option A

Concept Applied:

(g-f)(x) = g(x)-f(x)

Step-by-step explanation:

Substitute and solve

The answer of the given question based on the probability is , the probability that at least 6 adults watch the news is approximately 0.755.

Probability is  measure of likelihood or chance of  event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. Probability is used to analyze random experiments and events, and it is an essential concept in statistics, mathematics, and many other fields.

This is a binomial probability problem, where X follows a binomial distribution with n = 8 and p = 0.60. We want to find the probability that at least 6 adults watch the news, which can be written as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ...

To solve , we use  binomial probability formula:

P(X = k) =(n choose k) *p^k *(1 - p)^(n - k)

where "n choose k" is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can find the probabilities for each value of k:

P(X = 6) = (8 choose 6) * 0.60⁶ * 0.40² = 0.311

P(X = 7) = (8 choose 7) * 0.60⁷ * 0.40¹ = 0.276

P(X = 8) = (8 choose 8) * 0.60⁸ * 0.40⁰ = 0.168

Note that we can also use  binomial probability table or  calculator with  binomial probability function to find the probabilities.

Then, we can add these probabilities to get the probability that at least 6 adults watch the news:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ... = 0.311 + 0.276 + 0.168 + ...

This is a infinite series, but we can stop at P(X = 8) since the probabilities become very small after that.

P(X ≥ 6) = 0.755

Therefore, the probability that at least 6 adults watch the news is approximately 0.755.

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The length of the missing base is approximately 6.67 cm.

By applying the formula for the area of a trapezoid, we will be able to solve for the missing base.

Recall that the formula for the area of a trapezoid is:

A = [tex]\frac{1}{2} * h * (b_{1} + b_{2})[/tex]

where

A = area

h = height

b₁ and b₂ are the lengths of the parallel bases.

From the question, we are given:

A = 64 m²

h = 12 cm

b₁ = 4 cm.

Plug these values into the formula above to solve the missing base

64 = [tex]\frac{1}{2} * 12 * (4+ b_{2})[/tex]

Multiplying both sides by 2:

128 = 12(4 + b₂)

Simplifying:

128 = 48 + 12b₂

80 = 12b₂

b₂ = 80/12 = 20/3

b₂ = 6.67

Therefore, the length of the missing base is approximately 6.67 cm.

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A graph of the line with slope 3 passing through the point (5, 3) is shown in the image attached below.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (5, 3) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 3(x - 5)  

y = 3x - 15 + 3

y = 3x - 12

In conclusion, we would use an online graphing calculator to plot the equation y = 3x - 12 as shown in the graph attached below.

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The annual depreciation expense for this car is $1,833.33.

Simply deduct the vehicle's current fair market value from the purchase price, less any applicable sales tax or fees, to determine how much value has been lost.

We must determine the total depreciation throughout the vehicle's useful life and divide it by the number of years to determine the annual depreciation expense:

Total depreciation = purchase price - resale value

= $28,500 - $17,500

= $11,000

Annual depreciation expense = total depreciation / useful life = $11,000 / 6 = $1,833.33 (rounded to the nearest hundredth)

Therefore, the annual depreciation expense for this car is $1,833.33.

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An expression for the height of the cuboid is 3p - 245q/49 meters.

In Mathematics and Geometry, the volume of a cuboid with a square base can be calculated by using this following formula:

Volume of a cuboid = L² × H

Where:

By substituting the given parameters into the formula for the volume of a cuboid cuboid with a square base, we have the following;

(147p - 245q) = 7² × H

(147p - 245q) = 49 × H

Height, H = (147p - 245q)/49

Height, H = 3p - 245q/49 meters.

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Answer:

Using order of operations:

[tex] \frac{12a}{2} - 3a \times 5[/tex]

[tex]6a - 3a(5)[/tex]

[tex]6a - 15a = - 9a[/tex]

[tex] - 9 \times 4 = - 36[/tex]

Answer:

The roots of the quadratic equation x² + 4x + 7 = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 4, and c = 7. Substituting these values into the formula, we get:

x = (-4 ± √(4² - 4(1)(7))) / 2(1)

x = (-4 ± √(16 - 28)) / 2

x = (-4 ± √(-12)) / 2

x = (-4 ± 2i√3) / 2

x = -2 ± i√3

Therefore, the roots of the equation x² + 4x + 7 = 0 are: A) 2 + i√3 or 2 - i√3.

So, the correct answer is A

The surface area of the cylinder is 1851.97 square meters

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

Radius, r = 13.1 meters

Height, h = 9.4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 13.1 * (13.1 + 9.4)

Evaluate

Surface area = 1851.97

Hence, the surface area is 1851.97 square meters

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The first car consumed 15 gallons of gas

The second car consumed 30 gallons of gas during the week

Let's denote the number of gallons consumed by the first car as x, and the number of gallons consumed by the second car as y.

We know that the total gas consumption is 45 gallons, so:

x + y = 45

We also know that the total distance traveled is 1725 miles, and that the fuel efficiency (miles per gallon) of the first car is 35, and of the second car is 40. Using this information, we can write another equation:

35x + 40y = 1725

We now have two equations with two unknowns, which we can solve simultaneously to find x and y.

Multiplying the first equation by 35, we get:

35x + 35y = 1575

Subtracting this equation from the second equation, we get:

5y = 150

y = 30

Substituting y = 30 into the first equation, we get:

x + 30 = 45

x = 15

Therefore, the first car consumed 15 gallons of gas, and the second car consumed 30 gallons of gas during the week.

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The expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression: (Math Operator, Number/Variable, Math Operator).

We have a total of 10 columns and 10 rows.

Total boxes = 10×10 ⇒ 100

Number of shaded boxes = 3×10 ⇒ 30

Each box contains X's out of 100 that is:

              = 30/100

                 = 0.30

We can represent a number of columns in decimal such that:

            = 20/100  = 0.20

The expression becomes 0.20×0.30.

Thus, the expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.

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