V(d)V, left parenthesis, d, right parenthesis models Erica's vertical distance from the top of the valley (in kilometers) after walking
d
dd kilometers along the trail.
What does the statement
V
(
2
)
=
T
V(2)=TV, left parenthesis, 2, right parenthesis, equals, T mean?

The required polynomial  [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex].

What is a polynomial ?

A polynomial is a mathematical expression that consists of variables and coefficients, combined by addition, subtraction, and multiplication, but not division by a variable.

To write a polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex], we need to include their conjugates as well. This is because complex roots always come in conjugate pairs.

The conjugate of  [tex]i\sqrt{6[/tex] is  [tex]-i\sqrt{6[/tex], so our polynomial function will have the following zeros: -1, 1,  [tex]i\sqrt{6[/tex], and  [tex]-i\sqrt{6[/tex].

To find the polynomial function, we can use the fact that the product of the factors of a polynomial is equal to the polynomial itself. So, we can start by multiplying out the factors:

[tex](x+1)(x-1)(x-i\sqrt6)(x+i\sqrt6)[/tex]

Expanding this out gives:

[tex](x^2-1)(x^2+6)[/tex]

Multiplying these two expressions gives:

[tex]x^4+5x^2-6[/tex]

So the polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex] is [tex]f(x) = x^4+5x^2-6[/tex]

To verify that this polynomial has the desired zeros, we can factor it using the difference of squares:

[tex]x^4+5x^2-6 = (x^2-1)(x^2+6) = (x-1)(x+1)(x^2+6)[/tex]

And the quadratic factor has no real roots, so it must be the factorization [tex](x-i\sqrt6)(x+i\sqrt6)[/tex].

Therefore, [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex], as required.

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Answer:

  90

Step-by-step explanation:

You want to know the number of times in 360 trials that the same letter will appear twice in a row using a fair 4-letter spinner.

The table shows 4 outcomes of the 16 possible that have the same letter repeated. That's a probability of a repeated letter of 4/16 = 1/4.

The expected number of repeated letters in 360 trials is the number of trials times the probability of a repeat:

  expected repeats = 360 × 1/4 = 90

You predict there will be 90 repetitions in 360 trials.

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Answer:

16.39 square units.

Step-by-step explanation:

The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.

To see this, we can use the Pythagorean identity for sine and cosine:

sin^2 t + cos^2 t = 1

Multiplying both sides by 9, we get:

9 sin^2 t + 9 cos^2 t = 9

Substituting x = sin t and y = 3 cos t, we get:

9 x^2 + y^2/3 = 9

This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.

The area of an ellipse is given by the formula:

Area = pi * a * b

Substituting the values of a and b, we get:

Area = pi * 3 * sqrt(3) ≈ 16.39

Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.

The interest that have been earned after two years is $25.

A type of interest known as compound interest is computed using both the original sum and any accrued interest from earlier periods. The interest that is earned on interest is, in other terms, interest.

We know that by the compound interest formula;

A = P(1 + r/n)^nt

A = amount

P = principal

r = rate

n = Number of times compounded

t = time

Thus;

A = 1100(1 + 0.0114/365)^365* 2

A = $ 1125

Thus the interest after two years is;

$ 1125 - $1100

= $25

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The calculated line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

2^x= 32

2^x=2^5

(comparing, common denominator)

therefore x=5.

The areas of each figure are 5.6 sq m, 76.8 sq km, 280.8 sq units, 173.88 sq units and 332 sq units

The area of a shape is the amount of space on it

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

Figure 7:

The area is calculated as

Area = 1/2 * (sum of parallel sides) * height

So, we have

Area = 1/2 * (3.9 + 1.7) * 2

Area = 5.6 sq m

Figure 8:

The area is calculated as

Area = Base * height

So, we have

Area = 9.6 * 8

Area = 76.8 sq km

Figure 9:

The area is calculated as

Area = 6 * 1/2 * Base * height

So, we have

Area = 6 * 1/2 * 9 * 10.4

Area = 280.8 sq units

Figure 10:

The area is calculated as

Area = 7 * 1/2 * Base * height

So, we have

Area = 7 * 1/2 * 6.9 * 7.2

Area = 173.88 sq units

Figure 11:

The area is calculated as

Area = 8 * 1/2 * Base * height

So, we have

Area = 8 * 1/2 * 10 * 8.3

Area = 332 sq units

Figure 12, 13 and 14:

The areas of the figures cannot be calculated with the available details and parameters

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Here we have an exponential growth were the increase is of 26%, and it can be written as.

[tex]y = a*(1 + 0.26)^t[/tex]

Here we want to rewrite the function

[tex]y = a*(2)^{t/3}[/tex]

In the given form for the general exponential, so let's do that.

We can expand the product to get:

[tex]y = a*(2)^{t/3}\\\\y = a*((2)^{1/3})^t\\\\y = a*(1.26)^t\\\\y = a*(1 + 0.26)^t[/tex]

To identify if it is a growth or a decay we need to see the sign of r (the thing we are adding to the 1) in this case is +0.26

When it is positive we have a growth, so here we have a growth.

And to get the percentage multiply that number by 100%, we will get:

0.25*100% = 26%

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The length of the missing diagonal is 4 miles.

Step-by-step explanation:

GIVEN :

TO FIND :

USING FORMULA :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

SOLUTION :

Substituting the given values in the formula to find the length of the missing diagonal :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

[tex] \longrightarrow{\sf{20 = \dfrac{10 \times d_2}{2}}}[/tex]

[tex] \longrightarrow{\sf{20 \times 2= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{40= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \dfrac{40}{10}}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \cancel{\dfrac{40}{10}}}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{d_2 = 4 \: miles}}}}[/tex]

Hence, the length of the missing diagonal is 4 miles.

Answer:

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

To find the length of the missing diagonal, we can use the formula for the area of a rhombus, which is:

[tex]\sf\qquad\dashrightarrow Area_{(Rhombus)} = \dfrac{(Diagonal_1 \times Diagonal_2)}{2}[/tex]

We know that the area is 20 square miles and one of the diagonals is 10 miles, so we can substitute these values into the formula as follows:

[tex]\sf\qquad\dashrightarrow20 = \dfrac{(10 \times Diagonal_2)}{2}[/tex]

Simplifying the equation, we get:

[tex]\sf\qquad\dashrightarrow 40 = 10 \times Diagonal_2[/tex]

Dividing both sides by 10, we get:

[tex]\sf\qquad\dashrightarrow \boxed{\bold{\:\:Diagonal_2 = 4\:\:}}\:\:\:\bigstar[/tex]

Therefore, the length of the missing diagonal is 4 miles.

The preimage of the quadrilateral is in the second quadrant. The quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a two-dimensional shape, also known as a 2D polygon, and can be defined as any closed shape that has four sides. There are many different types of quadrilaterals, each with its own unique set of characteristics.

The second quadrant is characterized by negative x-coordinates and positive y-coordinates, while the fourth quadrant has positive x-coordinates and negative y-coordinates.

If the preimage of the quadrilateral is in the second quadrant, then its x-coordinates are negative and its y-coordinates are positive.

When the quadrilateral is reflected across the x-axis, its x-coordinates will remain the same but its y-coordinates will become negative. Therefore, if the preimage is in the second quadrant and the quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

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The probability statement is written below:

The middle 40% of heights fall between the 10th and 90th percentiles of the standard normal distribution.

The z-scores of the 10th and 90th percentiles are -1.28 and 1.28 respectively.

The heights in the given normal distribution are found using the formula:

where

The height of the 10th percentile is:

X = 66 + (-1.28)(2.5)

X = 62.8 inches

The height of the 90th percentile is:

X = 66 + (1.28)(2.5)

X = 69.2 inches

Therefore, the middle 40% of heights fall between 62.8 inches and 69.2 inches and the probability statement will be P(62.8 ≤ X ≤ 69.2) = 0.4

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The equivalent value of the fraction is A = 11/4

Given data ,

Let the fraction be represented as A

Now , let the first fraction be p = 2 1/5

Let the second fraction be q = 4/5

Now , A = p/q

On simplifying the equation , we get

A = ( 2 1/5 ) / 4/5

A = ( 11/5 ) / ( 4/5 )

On further simplification , we get

A = ( 11/5 ) x ( 5 / 4 )

A = 11/4

Therefore , the value of A is 11/4

Hence , the fraction is A = 11/4

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Using the simple interest formula, Whitney earned an interest of $26,000 in 4 years.

The simple interest system does not charge interest on accumulated interest (unlike the compound interest system) but only on the principal for each period.

The formula for computing the simple interest amount for the period is given as I = PRT, where I is the interest earned, P is the principal (starting amount), R is the interest rate expressed as a decimal, and T is the time in years.

Principal = $50,000

Simple interest rate = 13%

Investment period = 4 years

Simple interest earned = $26,000 ($50,000 x 13% x 4)

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a. On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

b. On a 33 rpm record (12-inch diameter), the fly would travel 1,245.6 inches in 1 minute.

c. On a 78 rpm record (10-inch diameter), the fly would travel 2,430 inches in 1 minute.

Radius of 45 rpm record = 3.5 inches (7/2)

Circumference = 2 * π * r = 2 * π * 3.5 ≈ 22 inches

Distance in 1 minute = Circumference * rpm = 22 * 45 = 990 inches

Thus, it can be seen that On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.

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A box contains 5 orange pencils, 8 yellow pencils, and 8 green pencils. Two pencils are selected, one at a time, with replacement.

There are a total of 21 pencils in the box.

The probability of selecting a green pencil on the first draw is 8/21, since there are 8 green pencils out of 21 total.

After replacing the first pencil, there are still 21 pencils in the box, including 8 yellow pencils.

The probability of selecting a yellow pencil on the second draw, given that a green pencil was selected first, is 8/21.

By the Multiplication Rule of Probability, we can multiply these probabilities together to find the probability of both events occurring

P(green and yellow) = P(green) × P(yellow|green)

P(green and yellow) = (8/21) × (8/21)

P(green and yellow) = 64/441

Therefore, the probability of selecting a green pencil first and a yellow pencil second is 64/441 or approximately 0.145.

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Answer: the correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,4π3) tell us the radius r=4 and the angle θ=4π3. So the point should be on the circle labeled 4 and form an angle of 4π3 with the positive x-axis. Point B is the correct point.

Answer: 96

Step-by-step explanation: There are 16 cups in each gallon. To get how many there are in 6 gallons you would need to multiply 6 and 16.

6*16=96

or

16+16+16+16+16+16= 96

Answer:

y =- [tex]\frac{3}{4}[/tex] x + 1

Step-by-step explanation:

This is a linear equation: y = mx + b

Answer: angle b= 63

Ac= 23.6

Ab=26.4

Step-by-step explanation:

angle b= 63

Ac= 23.6

Ab=26.4

Angle B is 63 degrees, the length of AC is approximately 22.23 units, and the length of AB is approximately 26.42 units.

What is right angle triangle?

A triangle in which one of its angles measures 90 degrees is called a right-angled triangle .

The side opposite the right angle is called the hypotenuse while the other two sides are called the legs or the adjacent and opposite sides.

According to given figure angle C is a right angle, we know that the sum of angles A and B must be 90 degrees.

So, angle B = 90 - angle A = 90 - 27 = 63 degrees.

To find the length of AC, we can use trigonometry. Since we know the length of the opposite side (BC) and the angle opposite the side we want to find (angle A), we can use the tangent function:

tan A = opposite / adjacent

tan 27 = BC / AC

AC = BC / tan 27

AC = 12 / tan 27

AC ≈ 22.23

Now,

[tex]AB^2 = AC^2 + BC^2 \\ AB^2 = 22.23^2 + 12^2 \\ AB^2 ≈ 697.57 \\ AB ≈ 26.42[/tex]

Therefore, Angle B is 63 degrees, the length of AC is approximately 22.23 units, and the length of AB is approximately 26.42 units.

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Answer:you need to include the expression

Step-by-step explanation:

once you have the expression, substitute the numbers given for each variable and use order of operations to

Answer:

x = 4√3 y = 8/√2 = 4√2

(4 rad 3) (4 rad 2)

In linear equation., both quantities are different from each other.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Taking LHS

  5 2/3 - 3 3/4= 17/3 - 15/4

  17/3 - 15/4 =  68 - 45/12  = 23/12

now solving RHS

  1+2/3+3/4  = 12 + 8 + 9/12  = 29/12

clearly, LHS≠ RHS

hence both quantities are different from each other.

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The solid displayed in the image is a trapezoidal prism.

A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.

To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.

Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.

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c=25/9 for the given condition of the bionomial.

We can solve this problem by using the technique of completing the square.

First, let's assume that [tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial:

[tex](3x + b)^2 = 9x^2 + 6bx + b^2[/tex]

If we compare the above expression with [tex]9x^2 + 10x + c[/tex], we can see that:

6bx = 10x, which implies that b = 5/3

b^2 = c, which implies that [tex]c = (5/3)^2 = 25/9[/tex]

Therefore, c = 25/9 is the constant that satisfies the condition

[tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial.

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Answer:

a. 1.95 cm.

b. 3920 cm^2.

Step-by-step explanation:

(a) To find the length of the arc that subtends the central angle theta on a circle of diameter d, we can use the formula:

Arc Length = (theta / 360°) x (pi x d)

Substituting the given values, we get:

Arc Length = (1.6 / 360°) x (pi x 140 cm)

Arc Length ≈ 1.95 cm

Therefore, the length of the arc that subtends the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 1.95 cm.

(b) To find the area of the sector determined by the central angle theta, we can use the formula:

Area of Sector = (theta / 2π) x pi x (r^2)

where r is the radius of the circle.

Since the diameter of the circle is given as 140 cm, the radius is half of that, which is 70 cm.

Substituting the given values, we get:

Area of Sector = (1.6 / (2 x pi)) x pi x (70 cm)^2

Area of Sector ≈ 3920 cm^2

Therefore, the area of the sector determined by the central angle of 1.6 radians on a circle of diameter 140 cm is approximately 3920 cm^2.

Answer: The two lists that are in order from least to greatest are:

C) 0.005, 0.045, 0.102, 0.63

and

E) 7.045, 7.452, 7.599, 7.604

Step-by-step explanation:

To determine which lists are in order from least to greatest, we need to compare the values and arrange them accordingly. Here is the explanation for the two correct answers:

C) 0.005, 0.045, 0.102, 0.63

This list is already in order from least to greatest. Starting from the smallest value of 0.005, each subsequent value increases until we reach the largest value of 0.63.

E) 7.045, 7.452, 7.599, 7.604

This list is also in order from least to greatest. Starting from the smallest value of 7.045, each subsequent value increases until we reach the largest value of 7.604.

For the other options:

A) 117.51, 17.382, 17.38, 17.23 - This list is not in order from least to greatest.

B) 452.8, 45.18, 452.28, 453.71 - This list is not in order from least to greatest.

D) 2.452, 2.749, 2.981, 2.994 - This list is not in order from least to greatest.

Therefore, the two lists that are in order from least to greatest are C (0.005, 0.045, 0.102, 0.63) and E (7.045, 7.452, 7.599, 7.604).

If θ=2 rad then the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

In this problem, we are given that when the arc length is equal to the radius (S=r), the angle is 1 radian (θ = 1 rad). Now, we are asked to find the condition when the angle is 2 radians (θ = 2 rad).

If Θ=1 rad when S=r, it means that when the angle subtended by an arc of length r is 1 radian, then the radius of the circle is also r.

Now, if θ=2 rad, we can use the same proportionality to find the arc length S that corresponds to this angle. Since the angle has doubled, we can expect the arc length to double as well. Therefore, we have:

θ/Θ = S/r

2/1 = S/r

S = 2r

Thus, the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

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The income statement, and stockholders equity are given below.

We have to show the income statement

The income statement for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Income Statement

For the Year Ended December 31, 2024

Service Revenue $55,000

Less: Expenses

Salaries Expense $27,000

Rent Expense $6,000

Utilities Expense $6,000

Interest Expense $5,000

Total Expenses $44,000

Net Income $11,000

The statement of stockholders' equity for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Statement of Stockholders' Equity

For the Year Ended December 31, 2024

Retained Earnings, December 31, 2023 $35,000

Add: Net Income for 2024 $11,000

Less: Dividends $0

Retained Earnings, December 31, 2024 $46,000

Classified Balance Sheet:

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

Total Liabilities and Stockholders' Equity $119,000

Therefore, the classified balance sheet for Coyote Corporation as of December 31, 2024, is as follows:

Coyote Corporation

Classified Balance Sheet

As of December 31, 2024

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

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complete question:

Kindly check if the photo below of income statement is wrong and correct which one is wrong in a excel or anything that makes it clear to me.