The box plots display the scores that two different groups of students got on their last math quiz.

Answer: 0.8958

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

Answer:

90 degrees counterclockwise

Answer:

-13

Step-by-step explanation:

To add fractions, find the lowest common denominator and then combine

The correct answer is option B:

⇒ Y decreases and X increases.

Given that;

the y value starts to decrease and the x value remains the same over time.

Now, We know that;

the slope remains constant, but the y value decreases as you move along the slope in the negative y direction, while the x value increases.

Hence,

If the y value starts to decrease while the x value remains the same over time on a consistent slope,

Thus, The correct answer is option B:

⇒ Y decreases and X increases.

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Answer: x^2 + 0x + 19/5 = 0

Step-by-step explanation: The initial step involves the equation -4x - 19 = x, which can be simplified by performing the operation of subtracting x from both sides.

The given equation can be represented as -5x - 19 = 0 in standard algebraic form, where 'x' denotes the unknown variable.

The process of combining similar or like terms leads to the consolidation of terms that share the same variable and corresponding exponents.

The given expression, 5x - 19 = 0, can be rewritten in an academic manner as a linear equation. Specifically, this expression represents a linear equation in one variable, where x is the unknown. The equation can be solved to find the value of x that satisfies it. This can be done through various methods, such as isolation of x, substitution, or using algebraic properties. The solution of this equation is x = 19/5, which can be verified by plugging it back into the original equation and observing its validity.

In order to render this equation in a standard format, it is imperative to eliminate the fixed element present on the left-hand side. The aforementioned task can be accomplished by simultaneously augmenting 19 to each side of the equation.

The equation 5x = 19 can be expressed in an academic manner as a linear equation with one variable. Specifically, it states that there is a value, x, that when multiplied by the constant factor of 5, results in a final product of 19. This equation could be used as a starting point for further mathematical analysis or application, such as solving for the specific value of x or incorporating it into a larger system of equations.

The left-hand side of the expression contains the linear term and the constant term, while the right-hand side is equal to 0. In order to express this equation in a standardized form, it is necessary to perform division by a factor of negative five to isolate the variable x.

The numerical value of the variable x is equivalent to negative nineteen divided by five, expressed as x = -19/5.

The standard form of the quadratic equation can be expressed as follows:

The mathematical expression, x + 19/5 = 0, may be restated in a formal academic style as follows: "The equation is of the form x + 19/5 = 0."

In order to determine the coefficients of the squared and constant terms, it can be observed that the coefficient of the squared term equates to 1 by virtue of the squared exponent of x, while the constant term evaluates to 19/5. This analytical approach yields the appropriate identification of the relevant coefficients in the given equation. Henceforth, the standard format for the quadratic equation is expressed as follows:

The equation in question is x^2 + 0x + 19/5 = 0.

Answer:

  (d)  180° clockwise rotation

Step-by-step explanation:

Given points A(-2, -7), B(3, -2), C(2, -10) and A'(2, 7), B'(-3, 2), C'(-2, 10), you want to know the angle and direction that rotates ∆ABC to ∆A'B'C'.

We notice the signs of each of the coordinates of ABC have been reversed for the coordinates A'B'C'. For example, A(-2, -7) became A'(2, 7).

A line joining these points is a straight line through the origin. The measure of its angle at the origin is 180°. This is the angle of rotation of A'B'C' with respect to ABC.

The image is created by 180° clockwise rotation, choice D.

__

Additional comment

When rotation is 180°, the direction is immaterial. A clockwise rotation gets you to the same place as a counterclockwise rotation.

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Answer:2.71

0.43 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

-u^2 - 2u + 1 = 0

Multiplying both sides by -1, we get:

u^2 + 2u - 1 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 2, and c = -1. Substituting these values, we get:

u = (-2 ± sqrt(4 + 4)) / 2

u = (-2 ± 2sqrt(2)) / 2

Therefore, either:

The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.

The logarithmic expression given is

log₃ 55 = x

To solve for x using the change of base formula, we can use the formula

logₐ b = log c / log a

where a, b, and c are positive real numbers and a ≠ 1.

Using this formula, we can rewrite the given expression as

log x / log 3 = log 55 / log 3

We can simplify this expression by canceling out log 3 on both sides

log x = log 55

Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get

x = 55

Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.

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Answer:

Since the disease doubles every 7 days, the number of cases on day 21 will be 2^3 times the number of cases on day 14, which will be 2^2 times the number of cases on day 7, which will be 2^1 times the number of cases on day 1.

Starting with 3 cases on day 1, we can use the formula:

N = 3 * 2^(t/7)

where N is the number of cases after t days.

Plugging in t = 21, we get:

N = 3 * 2^(21/7) = 3 * 2^3 = 24

Therefore, there will be 24 cases by the end of day 21.

Step-by-step explanation:

The area of the parallelogram can be found using the formula A = base × height:

A = 6 cm × 10 cm

A = 60 cm²

The area of a triangle is given by the formula A = 1/2 × base × height. We know the height is 5 cm and the area is also 60 cm² (since it is equal to the parallelogram). So, we can solve for the base:

60 cm² = 1/2 × base × 5 cm

Dividing both sides by 1/2 × 5 cm gives:

base = 24 cm

Therefore, the base of the triangle is 24 centimeters.

Answer:

24cm

Step-by-step explanation:

Answer:

step 2 is wrong

Step-by-step explanation:

Here, The work of a student to solve the equation :

[tex]4(2x - 4) = 8 + 2x + 8[/tex]

The steps for calculating the value of x are :

Step 1: [tex]4(2x - 4) = 8 + 2x + 8[/tex]

Step 2: [tex]6x - 8 = 16 + 2x[/tex]

Step 3: [tex]6x - 2x = 16 + 8[/tex]

Step 4: [tex]4x = 24[/tex]

Step 5: [tex]x = 6[/tex]

Step 2 is incorrect, as the student instead of multiplying, adds the number as:

[tex]4(2x - 4) = 8 + 2x + 8[/tex]

Here, the correct step is:

[tex]\boxed{\bold{8x - 16 = 16 + 2x}}[/tex]

[tex]6 x = 32[/tex]

[tex]x = 5.33[/tex]

So, the error is in STEP 2 and the correct option is (B).

Answer:

[tex] {x}^{2} + 11x + 18 = [/tex]

[tex](x + 2)(x + 9)[/tex]

The two numbers are 2 and 9.

2 + 9 = 11, and 2 × 9 = 18.

The total gain at the end of the second year for both accounts combined is $509.09.

We have,

Amount saved = $8500

40% of 8500 is saved in saving account = 0.4 x 8500 = $3400

Remainder amount in stock plan = 8500 - 3400 = 5100

Working for savings plan

A = P(1 + r/n[tex])^{nt[/tex]

A = 3400(1 + 0.042/1)²

A = $3691.60

So, we gain = 3691.6 - 3400 = $291.6

Working for stock plan:  

The stock plan decreases 3% in the first year

= 5100 x 0.97

= $4947

and increases 7.5% in the second year.

= 4947 x 1.75

= $5318.03

So, we gain = 5318.03 - 5100 = $218.03

Thus, the total gain is

= 291.06 + 218.03

= $509.09

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Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:

1 2/5 = 7/5

So Rachel used 7/5 bags of lemons on Monday.

On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:

1 1/4 = 5/4

5/4 times 7/5 = 35/20 = 7/4

So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.

Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.

The computations of the net profit or loss using the following cost valuation methods are as follows:

FIFO, net profit = $20,000

Weighted Average, net profit = $17,555.54.

The inventory cost valuation methods include FIFO (First In, First Out), LIFO (Last In, First Out), WAC (Weighted Average Cost), and Specific Identification.

Under the FIFO basis, the cost of inventory is evaluated based on the assumption that inventory that are first brought in are the first to be sold.

Under the Weighted Average Cost method, the average cost is computed by dividing the total cost of goods available for sale by the number of units.

Other inventory cost valuation methods include LIFO and Specific Identification.

Cost of Goods Sold = $80,000 ($10,000 x 3 + $12,000 x 2 + $13,000 x 2)

Sales Revenue = $106,000 ($15,000 x 7)

Overhead = $6,000

Net Profit = $20,000 ($106,000 - $80,000 - $6,000)

Weighted Average Cost per tractor = $11,777.78 ($106,000 ÷ 9)

Cost of Goods Sold = $82,444.46 ($11,777.78 x 7)

Sales Revenue = $106,000 ($15,000 x 7)

Overhead = $6,000

Net Profit = $17,555.54 ($106,000 - $82,444.46 - $6,000)

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Answer:

Step-by-step explanation:

20.9 is solution

Answer:

c,,e,b,f

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

4x - 2y = 8

x - int y = 0

4x = 8

x = 2

(2, 0)

y-int, x = 0

-2y = 8

y = -4

The given images shows us that we have a total of two lines

In mathematics, a point is referred to as the particular location on a plane. A point is identified by a dot.  It has no length, shape or size.

A line is straight, without any type of thickness and it is the shortest distance that exists between 2 points. It has only length. It is without width.

A line segment has two end points. The difference that a line segment has with a line is that a line is extensive while the line segment has two end points.

Ray is defined as a line that has only one endpoint. The other end of the line just goes on. It has one start point and one end point.

From the attached image, it is vert clear that we have two lines which are the horizontal line and the line that divides it.

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The volume of the solid figure is 75 ft³

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The volume of a figure is the amount of space it occupies in its three dimensional state.

To get the surface area:

Area of base = (6 ft * 2 ft) + (7 - 6)ft * 3 ft  = 15 ft²

Volume of figure = area of base * height = 15 ft² * 5 ft = 75 ft³

The volume of the figure is 75 ft³

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Answer:

(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:

FV = P * ((1 + r)^n - 1) / r) * (1 + r)

where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.

In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:

FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)

FV ≈ €743,704.96

Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.

(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:

PV = P * ((1 - (1 + r)^(-n)) / r)

where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.

In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:

PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)

P ≈ €22,630.53

Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.

(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).

Total deposits = €22,630.53 * 30 = €678,915.90

Total withdrawals = €25,000 * 20 = €500,000

Initial balance = €743,704.96

Total interest earned = Total withdrawals - Total deposits - Initial balance

Total interest earned = €500,000 - €678,915.90 - €743,704.96

Total interest earned ≈ -€922,620.86

Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.

Step-by-step explanation:

The solution is the two dimensions will be 2121.32 by 1414.2.

Here, we have,

let X and Y be the two dimensions.

Area will be X times Y.

XY = 3000000

Y = 3000000 / X

Perimeter = 2x + 3y

substituting the values:

Perimeter = 2x + 3*3000000 / x

         = 2x + 9000000 / x

so, we get,

2 = 9000000 / x^2

x^2 = 9000000 / 2 = 4500000

x = sqrt(4,500,000)

= 2121.32

 = 1000 sqrt (4.5)

y = 3000000 / 2121.32

 = 1414.2

 = 1000 sqrt(2)

so the dimensions will be 2121.32 by 1414.2 .

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complete question:

A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

Answer: The point that satisfies the equation is E. (-3, -4).

Explanation:

To determine which point lies on the circle represented by the equation (x − 3)² + (y + 4)² = 6², we can substitute the coordinates of each point into the equation and see which one satisfies the equation.

A. (9, -2): (9 − 3)² + (-2 + 4)² = 6²

(6)² + (2)² = 36

36 + 4 = 40 ≠ 36

B. (0, 11): (0 − 3)² + (11 + 4)² = 6²

(-3)² + (15)² = 36

9 + 225 = 234 ≠ 36

C. (3, 10): (3 − 3)² + (10 + 4)² = 6²

(0)² + (14)² = 36

0 + 196 = 196 ≠ 36

D. (-9, 4): (-9 − 3)² + (4 + 4)² = 6²

(-12)² + (8)² = 36

144 + 64 = 208 ≠ 36

E. (-3, -4): (-3 − 3)² + (-4 + 4)² = 6²

(-6)² + (0)² = 36

36 + 0 = 36

The point that satisfies the equation is E. (-3, -4).

Answer: Option C.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.

The depth of the container (h) is given as 4 ft.

Plugging in these values into the formula, we get:

V = π(12^2)(4)

V = 3.14(144)(4)

V = 1808.6 cubic feet (rounded to the nearest tenth)

So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.

Step-by-step explanation:

The blanks are filled as follows

1. Commutative

2. Distributive

3. Identity

4. Associative

5. Commutative

6. Inverse

7. Identity

8. Associative

9. Distributive

10. A. Identity

11. A. Identity

12. B. Commutative

13. C. Associative

14. E. Distributive

The distributive law of multiplication is a distinct attribute in mathematics that distinguishes how multiplication interacts with the operations of addition or subtraction.

It is exemplified in the problem as

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a) From the box plot of Dwayne's data, the measure of center = 9 and the measure of spread = 5

b)  From the box plot of Mitchell's data,  the measure of center = 10 and the measure of spread = 2

c)  From the box plot of Terry's data,  the measure of center = 10 and the measure of spread = 2

We know that in the box plot the measures of spread include the interquartile range and the mean of the data set.

Whereas, the measures of center include the mean or average and median.

For the Dwayne's box plot the interquartile range is 11 - 6 = 5

And the median is 9

So, the measure of center = 9 and the measure of spread = 5

For the Mitchell's box plot the interquartile range is 11 - 9 = 2

And the median is 10

So, the measure of center = 10 and the measure of spread = 2

For the Terry's box plot the interquartile range is  11 - 9 = 2

And the median is 10

So, the measure of center = 10 and the measure of spread = 2

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The expression that is equivalent to this polynomial "x²+12" is option A. (x + 2√3i) (x — 2√3i)

In mathematics, a polynomial is an expression consisting of variables and coefficients that concern only the operations of addition, subtraction, multiplication, and nonnegative integer exponents.

A. (x + 2√3i) (x — 2√3i)

= (x² + 2√3i)² (i² = -1)

= (x² - 12x (— 1)

= x² + 12

B. (x + 6i) (x - 6i)

= (x² - (6i)²

= x² + 36

C. (x + 2√3)²

= x² + 4√3x + 12

D. (x + 2√3) (x - 2√3)

= x² - (2√3)²

= x² - 12

Therefore, the correct answer is as given above. Option A. (x + 2√3i) (x — 2√3i) is equivalent to the given polynomial.

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The complete question goes thus:

Which expression is equivalent to this polynomial?

x²+12

OA. (x + 2√3i) (x — 2√3i)

B. (x+6)(x-61)

Oc. (x + 2√3)2

OD. (x + 2√3) (x - 2√3)