The vector u has length 10 and points at an angle of 5°
The vector has length 16 and points at an angle of 25°

The length is 1 and width is 4 and height is 3.

In geometry, a cuboid is a solid or three-dimensional shape. A convex polyhedron bounded by 6 rectangular faces with 8 vertices and 12 sides is called a cuboid. A cuboid is also called a cuboid. A cuboid with six square faces is called a cube. An example of a real cube is a rectangular box. In mathematics, we can observe other shapes that are exactly the same as the cuboid. They are cuboid, cuboid, right prism, cuboid, cuboid, cuboid. Learn more about cuboids here

has a volume of 12cm^3

volume of cuboid is = length*width*height.

a*b*c  = 12

and the top faces has an area of 4 cm^2

op faces has an area = a*b.

ab = 4

a = length

b = width

ab = 4 = 1x4 = 2x2

and a = 1

b = 4  because the cuboid is longer than it is width

now

abc = 12

ab = 4

c = 12/ab

c = 12/4

c = 3

length = 1 width = 4 height = 3

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The area of the triangle is 72 units².

The area of a triangle can be found using sine as follows:

area of a triangle = 1 / 2 ab sin C

Hence,

Therefore,

area of a triangle = 1 / 2 × 12 × 24 × sin 30

area of a triangle = 1 / 2 × 288 × sin 30

area of a triangle = 1 / 2 × 288 × 0.5

area of a triangle = 1 / 2 × 144

area of a triangle = 72 units²

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The complete question:

Park rangers released 4 fish into a pond in year 0. Each year, there were three times as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.

An function which best represent the given scenario is,  4 x 3ˣ. So option B is correct.

In algebra, in sequence we study various progressions, one of the progression is geometric, in this progression for every two consecutive terms, the common ratio is the same.

Formula for nth term of G.P.,

Tₙ = a×rⁿ

where a is first term and r is common ratio

Given that,

Park rangers released 4 fish into a pond in year 0.

Each year, there were three times as many fish as the year before.

The number of fish after x years = ?

After 1 year,

the number of fish  =  4 x 3

After 2 year,

the number of fish  = 4 x 3 x 3

                                = 4 x 3²

After 3 year,

the number of fish = 4 x 3² x3

                               = 4 x 3³

Similarly, after x years

the number of fish =  4 x 3ˣ

Hence, the expression is  4 x 3ˣ

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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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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 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

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

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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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

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

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

Step-by-step explanation:

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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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

Equation represents the amount of money lydia spent of apples and bananas is 5x + 3y = 8.50. Equation represents the amount of money ari spent on apples and bananas is 3x + 2y = 5.25.

Let x be the cost per pound of apples, and let y be the cost per pound of bananas. Then, the system of equations representing the given situation is:

5x + 3y = 8.50 (Equation 1)

3x + 2y = 5.25 (Equation 2)

Equation 1 represents the amount of money Lydia spent on 5 pounds of apples and 3 pounds of bananas. It shows that the total cost of the apples and bananas that Lydia bought is $8.50. To find the cost per pound of each fruit, we need to solve for x and y.

Equation 2 represents the amount of money Ari spent on 3 pounds of apples and 2 pounds of bananas. It shows that the total cost of the apples and bananas that Ari bought is $5.25. To find the cost per pound of each fruit, we need to solve for x and y.

To solve for x and y, we can use the method of substitution or elimination. Once we find the values of x and y, we can substitute them back into Equation 1 or Equation 2 to find the cost of each fruit for Lydia and Ari.

In summary, the given situation can be represented by a system of two equations. Equation 1 represents the amount of money Lydia spent on apples and bananas, and Equation 2 represents the amount of money Ari spent on apples and bananas. To find the cost per pound of each fruit, we need to solve for x and y using substitution or elimination.

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Complete question is:

Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. Determine a system of equations that represents the given the situation. Let x be cost per pound of apples and let y be the cost per pound of bananas. Which equation represents the amount of money Lydia spent of apples and bananas? Which equation represents the amount of money Ari spent on apples and bananas?

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 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 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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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

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

Answer: b (b²+b+4)

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

The height of the cell phone tower in feet will be 135 feet high.

The utilization of two or more additional numbers that compares is known as the ratio.

The cell tower that casts a shadow is 100 feet long.

Lia casts shadows 3 feet and 4 inches long.

If Lia is 4 feet 6 inches tall.

Let 'h' be the height of the tower. Then the height of the tower is given as,

h / 100 = (4 + 6/12) / (3 + 4/12)

h / 100 = 4.5 / 3.33

h / 100 = 1.35

h = 135 feet

The height of the cell phone tower in feet will be 135 feet high.

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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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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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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.

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.

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:

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