Look at the image below.

Answer: b (b²+b+4)

Step-by-step explanation:
b²=bb
b³=b²b
=b²b+bb+4b
=b(b²+b+4)

The theoretical probability of getting two tails is 1/4 = 0.25 = 25%. The experimental probability of getting two tails will change for every experiment.

The theoretical probability of getting two heads is 1/4 = 0.25 = 25%.

The theoretical probability of getting one head and one tail is 2/4 = 0.50 = 50%.

What is experimental probability?

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Given that two coins flip together. The outcomes of a coin is {H,T}.

The outcomes after flipping of two coins are

{HH, HT, TH, TT}

The total number of outcomes is 4.

The number of outcomes to get two tails is 1.

The probability of getting two tails is 1/4 = 0.25 = 25%.

The number of outcomes to get two heads is 1.

The probability of getting two heads is 1/4 = 0.25 = 25%.

The number of outcomes to get one head and one tail is 2

The probability of getting one head and one tail is 2/4 = 0.50 = 50%.

The theoretical probabilities will change for every experiment.

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Let's call the average speed for the last three hours "S".

First, we need to find the total distance that Mr. Jackson traveled in the last three hours. He traveled 300 miles in total, and he covered 64 miles in the first 90 minutes, so he had 300 - 64 = 236 miles left to travel.

Next, we need to find the time he spent traveling in the last three hours. If he traveled for three hours, and the first hour he traveled at 66 miles per hour, then he covered 66 miles in the first hour. So, he had 236 - 66 = 170 miles left to travel in the last two hours.

Finally, we can use the formula for average speed: distance divided by time. The total distance he traveled in the last three hours was 170 miles, and the time he spent traveling was 2 hours, so his average speed for the last three hours was:

S = 170 miles / 2 hours = 85 miles per hour

So, Mr. Jackson's average speed for the last three hours was 85 miles per hour.

Answer:

68 mph

Step-by-step explanation:

Let's call the average speed for the last three hours "S".

The total distance traveled for the last three hours is 300 - 64 * 1.5 = 300 - 96 = 204 miles.

So, over the last three hours, Mr. Jackson covered a distance of 204 miles at a speed of S.

The time it took him to cover that distance is 3 hours.

We can use the formula distance = speed * time to find S:

204 = S * 3

Solving for S:

S = 68 mph

So the average speed for the last three hours was 68 mph.

Answer:

Mai spent 60% of her total spending on fruit

Step-by-step explanation:

To find the percentage of the total spent on fruit, we can divide the amount spent on fruit by the total amount paid and multiply by 100 to express the answer as a percentage.

First, let's find the amount spent on things other than fruit: $15 total spent - $9 spent on fruit = $6 spent on other things.

Next, we divide the amount spent on fruit by the total amount spent: $9 on fruit / $15 total spent = 0.6.

Finally, we multiply by 100 to express the answer as a percentage: 0.6 * 100 = 60%.

So Mai spent 60% of her total spending on fruit.

Answer:

56 cola flavored gumboils

Step-by-step explanation:

Bob's 40 count of gumballs has 16 cola gumballs

Therefore the probability of a gumball being cola based on the sample size of Bob's purchase = 16/40 = 2/5

There are 140 gumballs left in the machine so we can expect that, on an average, 2/5 of them should be cola gumballs

So number of cola gumballs left is expected to be  2/5 x 140 = 56

This is only a prediction based on Bob's sample of 40 cola gumballs

Answer:  -2 ±√6
                    2

Step-by-step explanation:
Use the quadratic formula - its better to separate it into two parts
Δ = b²-4ac
   = 4² -4(2*-1)
   = 16 + 8

∴ Δ = 24
Then
x = (-b ± √Δ) ÷ 2a
  = (-4 ± √24) ÷ 4
  = (-4 ± 2√6) ÷ 4 (simplify the surd form)
∴ x = -2 ±√6   (simplify by crossing out the 2's)
             2

Answer:

(175, 175) -> $3,150

(200, 150) -> $3,300

(225, 125) -> $3,450

Explain: I hope this helps

Answer:

one fifth would be espressos so 3

Step-by-step explanation:

Answer:

2y=9-3x. 2=(3-x)3y

2=(9-3x)/y......1 2= 3y(3-x)..........2

Combining equations 1 and 2;

9-3x=3y²(3-x)

3(3-x)=3y²(3-x)

y²=1

y=√1

y= ±1

The fractions have values -

4. one-sixth plus five-sixths equals - Option 3 : 1

5. seven twelfths plus two-twelfths equals - Option 1 : 0

6. nine-tenths minus four-tenths equals - Option 4 : 2

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The first fractional statement is -

one-sixth plus five-sixths

The mathematical expression is -

1/6 + 5/6

Since the denominator is same just add the numerator.

(1 + 5) / 6

6/6

1

Therefore, the value is obtained as 1.

The second fractional statement is -

seven twelfths plus two-twelfths

The mathematical expression is -

7/12 + 2/12

Since the denominator is same just add the numerator.

(7 + 2) / 12

9/12

3/4

0.75 ≈ 0

Therefore, the value is obtained as 3/4.

The third fractional statement is -

nine-tenths minus four-tenths

The mathematical expression is -

9/10 - 4/10

Since the denominator is same just subtract the numerator.

(9 - 4) / 10

5/10

2

Therefore, the value is obtained as 2.

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4. Round each fraction to help you estimate the solution for the following equation:

one-sixth plus five-sixths equals

1. 0

2. one half

3. 1

4. 2

5. Round each fraction to help you estimate the solution for the following equation:

seven twelfths plus two-twelfths equals

1. 0

2. one half

3. 1

4. one and one half

6. Round each fraction to help you estimate the solution for the following equation:

nine-tenths minus four-tenths equals

1. one half

2. 1

3. one and one half

4. 2

the probability of picking a red ball from the bag and getting heads upon flipping a fair coin is 1/2 * 1/2 = 1/8.

There are two independent events, and therefore the probability of both occurring is calculated by multiplying the probability of each event. The probability of picking a red ball from the bag is 1/2, and the probability of getting heads upon flipping a fair coin is also 1/2. Therefore, the probability of picking a red ball from the bag and getting heads upon flipping a fair coin is 1/2 * 1/2 = 1/8.

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A statement which best describes the reflection include the following: C. a reflection over the line x = 3.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

Based on the graph of triangle ABC and triangle ΔA’B’C’, we can logically deduce the following coordinates after a reflection over the line x = 3:

A = (-2, 2)   → A' = (8,2)

B = (0, 4)    → B' = (6, 4)

C = (2,2)     → C' = (4, 2)

Therefore, the two triangles are identical (similar) because they are reflections of each other. Also, the distance between the point C and point C' is 2 units, therefore, with a line that is parallel to the y-axis and lies at point x = 3, as shown in the image attached below.

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Complete Question:

ΔA’B’C’ is a reflection of ΔABC. Which best describes the reflection?

A coordinate plane showing triangles A B C and A prime B prime C prime. The coordinates of the first figure are A negative 2 comma 2, B zero comma 4, and C 2 comma 2. The coordinates of the second figure are A prime 8 comma 2, B prime 6 comma 4, and C prime 4 comma 2.

a.)A reflection over the line x = 2

b.)A reflection over the line y = 3

c.)A reflection over the line x = 3

d.)A reflection over the y-axis

Answer:

The correct answer is:

You can map ABC to A'B'C' by translating it 6 units left and reflecting it across the x-axis, which is a series of rigid motions.

Explanation:

In ABC, the coordinates are:

A(1, -3)

B(5, 3)

C(4, -1).

In A'B'C', the coordinates are:

A'(-5, 3)

B'(-1, -3)

C'(-2, 1)

Each point is mapped to its image:

A(1, -3)→A'(-5, 3)

B(5, 3)→B'(-1, -3)

C(4, -1)→C'(-2, 1

Comparing the x-coordinates in the pre-image and image, we notice that the image has an x-coordinate that is 6 less than that of the pre-image:

1-6 = -5

5-6 = -1

4-6 = -2

This means that the figure must be translated 6 units left; that is the only way to have this change on the pre-image to form the image.

Comparing the y-coordinates of the pre-image with those of the image, we notice that they are negated:

-(-3) = 3

-(3) = -3

-(-1) = 1

This means the pre-image was reflected across the x-axis; this is the only way to negate the y-coordinate and not change the x-coordinate.

These are rigid motions because they do not change the shape or size, they simply move it and change its orientation.

Step-by-step explanation:

Hope this will help u

Answer:

1. identify the constant you will need to multiply each equation by to eliminate x

2. multiply all terms by -3 in equation 1

3. multiply all tems by 5 in equation 2

4. add the sum of the equation together to eliminate x

1. identify the constant you will need to multiply each equation by to eliminate x

2. multiply all terms by -3 in equation 1

3. multiply all tems by 5 in equation 2

4. add the sum of the equation together to eliminate x

42 adult tickets and 421 children tickets were purchased for the field trip, based on the given information that the total cost of the tickets was $995 and the children tickets cost $11 while the adult tickets cost $13, and the number of children tickets purchased was one more than ten times the number of adults tickets purchased.

Let's use variables to represent the unknown quantities in the problem:

Let x be the number of adult tickets purchased

Then the number of children tickets purchased is 10x + 1 (since it is one more than ten times the number of adults tickets purchased)

Using these variables, we can set up an equation based on the total cost of the tickets:

13x + 11(10x + 1) = 995

Simplifying and solving for x, we get:

23x + 11 = 995

23x = 984

x = 42.7826087 (rounded to 9 decimal places)

Since we can't purchase a fraction of a ticket, we'll round x down to the nearest whole number, which means 42 adult tickets were purchased. Then the number of children tickets purchased is:

10x + 1 = 10(42) + 1 = 421

So, 42 adult tickets and 421 children tickets were purchased.

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Step-by-step explanation:

let's write this properly that we are not confusing ourselves :

s = ½×a×t²

a = 30 ft/sec²

t = 6 sec

so,

s = ½ × 30 ft/sec² × (6 sec)² = ½ × 30 ft/sec² × 36 sec² =

= ½ × 30 ft × 36 = 15 ft × 36 = 540 ft

s = 540 ft

There are 12 trapezoids needed to create two hexagons with pattern blocks.

1. To create two hexagons with pattern blocks, you will need 12 trapezoids.

2. Each hexagon consists of six trapezoids.

3. Since you need two hexagons, you will need 12 trapezoids in total.

In order to create two hexagons with pattern blocks, you will need to use 12 trapezoids in total. Each hexagon consists of six trapezoids, so you will need two hexagons to use all twelve trapezoids. The two hexagons can be formed by arranging the trapezoids in a pattern of two triangles, two parallelograms, two rhombuses, and two trapezoids. With these 12 trapezoids, you will be able to create two complete hexagons.

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Answer:

Step-by-step explanation:

how many pattern blocks triangles would create 1 hexagon

Answer: 2 *(3+4)= (2x3)+ (2x4)

Step-by-step explanation:

The correct statements are Two data sets could have different means but the same standard deviation, and could have the same mean but different standard deviations. If two data sets have different means they must have different standard deviations. Correct options are A, C , D.

The mean and standard deviation are both measures of the central tendency of a data set, but they capture different aspects of the distribution. The mean represents the average value of the data, while the standard deviation measures how spread out the data is around the mean.

It is possible for two data sets to have different means but the same standard deviation if one data set is more spread out than the other, but the values are symmetrically distributed around the mean. For example, the data sets {1, 2, 3, 7, 8, 9} and {0, 4, 5, 5, 5, 9} have different means (5 and 4.67, respectively) but the same standard deviation (3.16).

Similarly, two data sets could have the same mean but different standard deviations if one data set is more spread out than the other. For example, the data sets {1, 2, 3, 4, 5} and {1, 3, 3, 3, 5} have the same mean (3) but different standard deviations (1.41 and 1.26, respectively).

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Complete question is:

Which of the following statements is true?

multiple select question.

A. two data sets could have different means but the same standard deviation.

B. if two data sets have the same mean they must have the same standard deviation.

C.  two data sets could have the same mean but different standard deviations.

D. if two data sets have different means they must have different standard deviations.

Answer:

99 square millimeters

Answer given by the other user is correct. Merely giving the steps required to solve such a problem

Step-by-step explanation:

Break up the figure into 3 rectangles as shown in the attached image

The area of the top rectangle with size 11 x 3 = 33 square millimeters

The area of the small rectangle is 2 x 5 = 10 square millimeters

The area of the vertical rectangle is 4 x 14 = 56  square millimeters

Total area = 33 + 10 + 56

= 99 square millimeters

In 30 years, the amount that Jenna will have is $411, 235

This account balance is as a result of Jenna's annuity payments.

The amount that Jenna's account will be worth in 30 years can be found by the future value of annuity formula which is :

= Annuity deposited periodically x Future value of annuity factor, 10 % , 30 years

Annuity deposited periodically = $ 2, 500

Future value of annuity factor = 164.49402268886

The value of the account balance will be:

= 2, 500 x 164.49402268886

= $411, 235

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Answer: $411,235, Annuity Payments

Step-by-step explanation:

I have took the test and know the answer is correct

The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then ∠FGN = ∠FJN.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The line segment GF = NJ and FN bisect the angle ∠GFJ.

In triangles ΔGFN and ΔJFN, then we have

GF = NJ                        (Given)

∠GFN = ∠JFN              (Given)

NF = NF                        (Common sides)

The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then we have

∠FGN = ∠FJN

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The correct statements regarding the average rate of change of the function are given as follows:

The average rate of change of a function is given by the change in the output divided by the change in the input.

From x = 1 to x = 3, we have that:

Hence the rate is given as follows:

6/2 = 3.

From x = 2 to x = 4, we have that:

Hence the rate is given as follows:

12/2 = 6.

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Given that 10 bottles were bought for a total amount of $12, the price per bottle of sport drink is $1.20.

$12 divided by ten bottles equals $1.20.

By dividing the total amount paid ($12) by the quantity of bottles bought, the price per bottle of sport drink was determined (10). As a result, each bottle cost $1.20. According to the computation, the price of 10 bottles of sport drink came to a total of $12. The cost of individual goods or greater quantities of bottles can then be determined using this cost per bottle. The price per bottle can be used to compare the costs of various sport drink brands or sizes. Customers can choose and buy sport drinks with more knowledge if they are aware of the price per bottle.

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The required, there is no highest common factor between 4454 and 121j²k. None of the options are correct.

The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.

Here,
To find the greatest common factor (GCF) of 4454 and 121j²k, we need to factor both numbers into their prime factors and then identify the common factors.

Since 4454 is an even number and 121 is an odd number so there is no prime highest common factor between the given number.

Thus, none of the options are correct.

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Variable and Coefficient of the given algebraic expression 3b + 6 is b and 3 respectively.

A variable is a symbol or letter that represents a value that can change or vary in a given context. Variables are often used to represent unknown or changing quantities in equations,

A coefficient is a numerical factor that is multiplied by a variable or variables in an algebraic expression. In other words, it is the number that appears in front of a variable.

3b + 6 identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For a variable term, identify the variable and the coefficient of the term:

The first term of the algebraic expression 3b + 6 is 3b.

This is a variable term because it contains the variable "b".

The variable is "b" and the coefficient of the term is 3.

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By working together, they can save time and complete the task faster. Therefore, Leslie and Fran can paint the room in 2.2 hours.

Leslie and Fran working together to paint a room can complete the job in 2.2 hours. This can be calculated by taking the least amount of time it would take for the job to be done (3 hrs) and dividing it by the total amount of time it would take both of them working together (7 hrs). 3 / 7 = 0.428, then multiply 0.428 by 10 to get the tenths place. 0.428 x 10 = 4.28, and round up to 2.2 hrs. Therefore, Leslie and Fran working together could paint a room in 2.2 hrs. This is significantly faster than it would take either of them working alone.

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The total cost of the aquarium that Arlington bought after markdown and including sales tax is $42.

What is meant by the markdown of the price?

The markdown is the price that separates an item's current, lowered price from its original, full price. Typically, a percentage is used to express it. Retailers can offer their products at a discount thanks to markdown.

Discounts are distinct from markdowns. Markdowns give everyone the chance to buy products for a lower price. However, some customers may only be eligible for discounts, such as students.

Markdown = (difference of prices / actual selling price) x 100

Given,

Original Cost of aquarium = $100

Marked down price = 100 - 0.60 * 100= 100 - 60 = $40

Sales tax = 5%

Sales tax is the percentage of the price at which the aquarium was bought i.e the markdown price.

Sales tax = 5% of $40 = 0.05 * 40 = $2

Total cost = marked down price + sales tax = $40 + $2 = $42

Therefore the total cost of the aquarium that Arlington bought after the markdown and including sales tax is $42.

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The amount Maggie will need in savings when she retires is $1,204,519.62 and  her payment be if she had 1.2 million is $4522.40

In investment, an annuity is a series of payments made at equal intervals

a) To calculate the amount Maggie will need in savings when she retires

Pm= {1 + r/j)pm - 1

Pm = (1+6.2%/12)4500 - 1

Pm (1+0.0052)4500 -1

Pm= (1.0052)4499

Simplifying to have

Pm = $4522.40

b) To  calculate much could her payment be if she had 1.2 million dollars in her account but her interest dropped to 5.5

Pm= {1 + r/j)pm - 1 +d

Where d is the savings

Pm = (1+5.5%/12)4500 - 1 + 1.2m

Pm= (1+5.5%/12) 4499 + 1.2m

PM = (1.0046)4499 + 1,200,000

Pm = 1,204,519.62

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