Rewrite the following polynomial in standard form. -2x^3+1/7+x^4-x^2

Answer:

6

Step-by-step explanation:

Step 1: How many males are there?

40% of 60 = 0.4 × 60 = 24

There are 24 males.

Step 2: Of the 24 males, how many wear a hat?

25% of 24 = 0.25 × 24 = 6

Answer: 6

Answer: choose Answer B

Step-by-step explanation:

because if you flip the triangle back to what it was previously A B lines up with answer B so it’s B

Best describes the translation of the figure moves Left and down.

A translation is a transformation that moves every point of a figure or object by the same distance and in the same direction without changing its shape, size, or orientation. It is a type of rigid transformation that preserves the distance between points and angles between lines.

A translation can be described using the horizontal and vertical shift or displacement of the object. If a point (x, y) is translated by a distance of 'a' units to the right and 'b' units upwards, the new location of the point would be (x + a, y + b).

Question says that a figure is translated using the mapping (x, y) → (x + a, y + b).

If the value of 'a' is negative and the value of 'b' is negative in the mapping (x, y) → (x + a, y + b), it means that the figure is being translated to the left and downwards.

The x-coordinates are being decreased by the absolute value of 'a', which means that the figure is moving left. Similarly, the y-coordinates are being decreased by the absolute value of 'b', which means that the figure is moving downwards.

Therefore, the best description of the translation is "the figure moves left and down"

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Jane can buy 20 melons for the price of 32 apples.

To find out how many melons Jane can buy for the price of 32 apples, we need to use the given ratios to find the equivalent value of melons in terms of apples.

First, we know that 6 apples are equivalent to 3 bananas. So, we can simplify this ratio to 2 apples per 1 banana.

Next, we know that 4 bananas are equivalent to 5 melons. So, we can simplify this ratio to 4/5 of a banana per 1 melon.

Now, we can use these ratios to find the equivalent value of melons in terms of apples. If 2 apples are equivalent to 1 banana, and 4/5 of a banana is equivalent to 1 melon, then we can multiply these ratios together to find the equivalent value of melons in terms of apples:

2 apples/1 banana × 4/5 banana/1 melon = 8/5 apples/1 melon

This means that 1 melon is equivalent to 8/5 apples, or 1.6 apples.

Finally, we can use this ratio to find out how many melons Jane can buy for the price of 32 apples:

32 apples × 1 melon/1.6 apples = 20 melons

Therefore, Jane can buy 20 melons for the price of 32 apples.

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Answer:

x = 9

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally.

[tex]\frac{x-1}{3x+1}[/tex] = [tex]\frac{6}{21}[/tex] = [tex]\frac{2}{7}[/tex] ( cross- multiply )

7(x - 1) = 2(3x + 1) ← distribute parenthesis on both sides

7x - 7 = 6x + 2 ( subtract 6x from both sides )

x - 7 = 2 ( add 7 to both sides )

x = 9

(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

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Answer:

θ = 78.69°

Step-by-step explanation:

As this is a right angle triangle we use trigonometric ratios/

The perpendicular i.e the height of the mast = 50 ft

The base i.e the shadow = 10 ft

tanθ = perpendicular / base

tanθ = 50/10

θ = [tex]tan^{-1}[/tex] (50/10)

θ = 78.69°

The difference in the amount of tax withheld based on his previous W-4 form and the new W-4 form is estimated to be $7 per week for federal income tax withholding, meaning $7 more will be deducted from his weekly check if he claims no allowances.

The amount of tax withheld from Jason's paycheck depends on his taxable income, which is his gross income minus any deductions and exemptions. The number of allowances claimed on his W-4 form affects the amount of his paycheck that is subject to tax withholding.

If Jason claimed 1 allowance last year, his employer withheld tax as if he had $4,300 less in taxable income than if he had claimed no allowances. For 2023, the value of each allowance is $4,350.

Therefore, if Jason claims no allowances on his W-4 form, his taxable income will be $4,350 more than if he claimed 1 allowance.

Jason's gross income is $232.50 per week, which translates to $12,090 per year. If he claimed 1 allowance last year, his taxable income was $12,090 - $4,300 = $7,790. If he claims no allowances this year, his taxable income will be $7,790 + $4,350 = $12,140.

To determine how much more tax will be withheld from his weekly paycheck, we need to calculate the difference in the amount of tax withheld based on his previous W-4 form and the amount of tax withheld based on the new W-4 form.

Assuming that Jason is paid weekly, we can use the IRS tax withholding tables to estimate the federal income tax withheld for each situation.

Based on the 2023 IRS tax withholding tables, if Jason is single and claims 1 allowance, his employer would withhold $32 per week from his paycheck for federal income tax.

If he claims no allowances, his employer would withhold $39 per week from his paycheck for federal income tax.

Therefore, if Jason claims no allowances, $39 - $32 = $7 more will be deducted from his weekly check for federal income tax withholding.

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If more than 400 sheets are duplicated, this equation will provide us with the overall expense, t.

A method that describes how two lines along both side of a sign connect each other. It typically contains an equal symbol and one variable. Similarly, 2x - 4 = 2. The variable x is present in the particular circumstance.

The equation that could be used to calculate the total cost, t, to copy p pages when p is greater than 400 is:

t = $5,000 + ($0.01 × (p - 400))

The base cost for copying the first 400 pages is $5,000. For each additional page above 400, the customer is charged $0.01 per page. Therefore, to calculate the total cost for copying p pages, we need to subtract 400 from p to determine the number of pages that are being charged at the additional rate, and then multiply that by $0.01 to determine the additional cost. This gives us:

Additional cost = $0.01 × (p - 400)

The total cost is then the sum of the base cost and the additional cost:

t = $5,000 + ($0.01 × (p - 400))

This equation will give us the total cost, t, for any number of pages greater than 400 that are copied.

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a) n = 650 and p = 0.03

b)0.954

c)0.802

d)0.0206 to 0.0594

e)The result in (d) would be more precise

(a) The sampling distribution of the sample proportion is a binomial distribution with parameters n = 650 and p = 0.03.
(b) The probability that the sample proportion of death claims is between 2% and 6% is 0.954.
(c) The probability that the sample proportion is within 0.02 of the population proportion of death claims caused by accidents is 0.802.
(d) The 95% confidence interval for the proportion of death claims caused by accidents is 0.0206 to 0.0594.
(e) If the sample size were 2000 instead of 650, the result in (d) would be more precise. This is because with a larger sample size, the confidence interval will become narrower, allowing for a more accurate estimate of the population proportion.

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The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0. The question is a bit unclear and has multiple parts, so I will answer each part separately.

Part 1: Find the exact value of each of the remaining trigonometric functions of e.

sin 0 = 3/5
cos 0 = 4/5
tan 0 = 3/4
csc 0 = 5/3
sec 0 = 5/4
cot 0 = 4/3

Part 2: Find the lengths and area A.

The length of the arc is 80 * (15/360) = 3.333 yards.
The area of the sector is (80^2 * (15/360))/2 = 266.667 square yards.

Part 3: Find the distance from A to C across the gorge illustrated in the figure.

The distance from A to C is sqrt(170^2 + 170^2) = 240.42 feet.

Part 4: Name the quadrant in which the angle o lies.

The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0.

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Answer:

The capacity of the big vase is half times bigger than the capacity of the middle sized vase, which means it is 1 + 1/2 times the capacity of the middle vase.

So, the capacity of the big vase in terms of x is:

1/2x + x = 3/2x

Therefore, the capacity of the big vase in x is 3/2x.

The capacity of the middle sized vase is four times bigger than the capacity of the small vase, which means it is 4 times the capacity of the small vase.

So, the capacity of the small vase in terms of x is:

x/4

Therefore, the capacity of the small vase in x is x/4.

The total capacity of the three vases is 5.5 liters. We can set up an equation based on this information:

x + 3/2x + x/4 = 5.5

Multiplying both sides by 4 to eliminate the fraction:

4x + 6x + x = 22

11x = 22

x = 2

Therefore, the capacity of the middle sized vase is 2 in terms of x. To find the capacity in liters, we can substitute x = 2 into any of the expressions we found earlier:

Capacity of the big vase: 3/2x = 3/2 * 2 = 3 liters

Capacity of the small vase: x/4 = 2/4 = 0.5 liters

So, the capacities of the three vases are 3 liters, 2 liters, and 0.5 liters, and their total capacity is 5.5 liters.

Anstoo blurry

Step-by-step explanation:

The reciprocal of 5/11 is: 11/5

The reciprocal of 20 is: since 20=20/1 so the reciprocal is 1/20

Answer: 11/5, 1/20

Step-by-step explanation:

The reciprocal of a value is the numerator and denominator of that value switched.

When you look at 5/11, we see that 5 is the numerator and 11 is the denominator. The reciprocal(switch numerator and denominator) is 11/5.

The reciprocal of 20 can be tricky because it isn't written with a denominator. But we know intuitively that 20 is also equal to 20/1.

Therefore we apply the same steps as in the first instance and we get that the reciprocal of 20/1 is 1/20.

No, (8, 2) is not a solution to the inequality y ≥ 3x + 4 because when we substitute x = 8 and y = 2 into the inequality, we get a false statement. In other words, the point (8, 2) does not satisfy the inequality y ≥ 3x + 4, which means it is not a valid solution to the inequality.

To determine whether (8, 2) is a solution to the inequality y ≥ 3x + 4, we need to substitute the values of x and y into the inequality and check if the inequality holds true.

y ≥ 3x + 4

Substituting x = 8 and y = 2:

2 ≥ 3(8) + 4

2 ≥ 24 + 4

2 ≥ 28

The inequality is not true since 2 is not greater than or equal to 28.

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The simplified answer is 16y² - 25x².

When multiplying conjugate binomials,

We use the formula (a+b)(a-b) = a²-b².

In this case, a = 4y and b = 5x. So,

We can pluggin these values into the formula and simplify:

(4y+5x)(4y-5x) = (4y)² - (5x)²

= 16y² - 25x²

Therefore, the simplified answer is 16y² - 25x². This is the final answer, and there are no further steps to simplify.

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The complete equation using the numbers from1 to 9 will be:

2:2 = 3×3:9 = 4×4 =16.

A contrast between two numbers in arithmetic, this is referred to as a proportion. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

In the question given:

By using the digits 1 to 9 at one time each, we have to form the equation to make the equality true.

Now,

All the numbers from 1 to 9 are = 1, 2 ,3, 4, 5, 6, 7, 8 and 9

Let the proportion be = 1

Hence, the equivalent ratios are:

1:1, 2:2. 3:3

Now, according to the question the required equation will be:

2:2 = 3×3:9 = 4×4 =16.

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The original number would be 3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider that the 10s digit = x

And the units digit = y

x +y = 11                                  

The Sum of the digits = 11

10x + y + 45 = 10y + x            

Then Reversed number is 45 more  than original,

10x - x + y + 45 = 10y              

9x + y + 45 = 10y                    

9x + 45 = 10y - y                    

9x + 45 = 9y

Now, Put x +  y = 11 into the equation just found.

9x + 45 = 9(11 - x)                    

x + 45/9 = 11 - x                      

2x + 5 =     11                          

2x = 11 - 5

2x = 6                                      

x = 6/2

x = 3

Therefore, we have;

x + y = 11

3 + y = 11        

y = 11 - 3

y = 8

Henece, we can conclude that the original number is 38 and the new number is 83 which the digits are reversed.

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By answering the above question, we may state that Hence, [tex]xy{(-4)}[/tex]is x exponents divided by y raised to the power of 4.

The mathematical process of exponentiation, frequently referred to as "b raised to the nth power," is symbolised by the symbol bn and includes two numbers: a base number, b, and an exponent, or power, n. Exponents demonstrate the number of times that a number has been multiplied by itself. For example, 2-3 (written as 23) means: 2 x 2 x 2 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Therefore, the exponent is the measurement that shows how many times a number has been multiplied by itself. For instance, multiplying 6 by 4 results in the values 6 x 6 x 6.  .

Considering that the phrase is:

[tex]xy^{-4}[/tex]

We may simplify the case when x and y both have positive exponents as follows:

[tex]xy^{(-4)} = x / y^4[/tex]

This is due to the negative exponents rule, which claims that y(-n) = 1/yn, which indicates that [tex]y(-n) = 1/yn.[/tex]

Hence, [tex]xy{(-4)}[/tex]is x divided by y raised to the power of 4.

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a) sin B = y/r = -1/5sqrt(2) and cos B = x/r = 7/5sqrt(2) (b) Since sin B is positive and cos B is negative, we found that angle B belongs in Quadrant II.

Given that cot a = 7, we know that tan a = 1/7. Since tan a = y/x, we can let x = 7 and y = -1 (since a is in Quadrant III and both x and y values are negative in this quadrant).

Using the Pythagorean Theorem, we can find r:
r = sqrt(x^2 + y^2) = sqrt(7^2 + (-1)^2) = sqrt(50) = 5sqrt(2)
Now we can find sin B and cos B:
sin B = y/r = -1/5sqrt(2)
cos B = x/r = 7/5sqrt(2)

We can use the double angle formulas for sine and cosine, sin B and cos B: sin B = sin(Phi - a) = sin Phi cos a - cos Phi sin a = (0)(-7/25) - (1)(-24/25) = 24/25 cos B = cos(Phi - a) = cos Phi cos a + sin Phi sin a = (1)(-7/25) + (0)(-24/25) = -7/25.

Since sin B is positive and cos B is negative, we know that angle B is in Quadrant II.

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The polynomial in factored form whose solutions are x = -3, 5/2, and -5i is 2(x + 3)(2x - 5)(x² + 25).

Given the solutions;

To have the solutions at x = -3 and x = 5/2, the polynomial must have factors of (x + 3) and (2x - 5), respectively.

Also, to have a solution at x = -5i, there must be a factor of (x+5i) and its complex conjugate (x-5i):

Hence;

(x + 3)(2x - 5)(x + 5i)(x - 5i)

Multiplying out these factors gives:

(x + 3)(2x - 5)(x + 5i)(x - 5i)

(x + 3)(2x - 5)(x² + 25)

= (2x² + x - 15)(x² + 25)

= 2x⁴ + x³ - 15x² + 50x² + 25x - 375

= 2x⁴ + x³ + 35x² + 25x - 375

So the polynomial in factored form is:

= 2(x + 3)(2x - 5)(x + 5i)(x - 5i)

= 2(x + 3)(2x - 5)(x² + 25)

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Jill played for 10 mins. 25+15=40 50-40=10

The point (2, –2) with x-coordinate value 2 and y-coordinate value -2, is not satisfied the equation y = x.

We have an equation, y = x --(1) and point (2,-2). We have to check that point (2, –2) satisfy the equation y = x or not. To check that, we need to put the values of the point in the equation. If the equation satisfies them, the point belong to the line. Substituting the coordinates of the given point, i.e., x = 2 and y = -2, into the defining equation(1), we get, y = x

L.H.S, y = -2

R.H.S, x = 2

but -2 ≠ 2 so, L.H.S ≠ R.H.S

We now see from the above substitution and the resultant calculation that the coordinates (x, y) of the point (2, -2) does not make the equation y = x

Hence, the point ( 2,-2) does not satisfied equation y= x .

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Answer:

$81

Step-by-step explanation:

36/4 = 9

We can deduce that each shirt costs $9 so...

9x9 = 81

So it will take 20 years for High School R and High School T to have the same enrollment.

Enrollment is the process of registering for classes at a college or university. The process usually involves submitting an application and providing transcripts and other documents to the school.

The enrollment at High School R is increasing by 15 students per year while High School T is decreasing by 10 students per year. To figure out how many years it will take for both schools to have the same enrollment, we need to calculate the difference between the two schools.
High School R currently has 200 students and High School T has 400 students. The difference between the two schools is 200 students (400-200 = 200).
Since High School R is increasing by 15 students per year and High School T is decreasing by 10 students per year, it will take 20 years for the two schools to have the same enrollment.
To calculate this, we divide the difference between the two schools (200 students) by the difference between the two schools' enrollment growth (15 students - 10 students = 5 students). This gives us 200/5 = 40. Since 40 years is too long, we divide 40 by 2 and get 20, which is the answer. So it will take 20 years for High School R and High School T to have the same enrollment.

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The expression 3^(-3) can be rewritten without an exponent as 1/27.

To rewrite the expression 3^(-3) without an exponent, we can use the rule that any expression with a negative exponent can be rewritten as the reciprocal of the expression with a positive exponent. In other words, a^(-b) = 1/a^(b).

So in this case, we can rewrite 3^(-3) as 1/3^(3).

Now, we can simplify the expression by evaluating the exponent. 3^(3) = 3*3*3 = 27.

So our final answer is 1/27.

Therefore, the expression 3^(-3) can be rewritten without an exponent as 1/27.

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The value of RU, considering the Triangle Midsegment Theorem, is given as follows:

RU = 35.

The value of RU is obtained applying the proportions in the context of the problem.

A proportion is applied as the Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to it's base, and has the length half as long.

The length of the base is of ST = 70, hence the length of the midsegement is given as follows:

RU = 0.5ST

RU = 0.5 x 70

RU = 35.

(the length of the midsegment is half the length of the base, hence we apply the proportion multiplying by 0.5).

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(\begin{bmatrix}\frac{1}{5} & -\frac{2}{5} \\-\frac{3}{5} & \frac{7}{5}\end{bmatrix}\)

To find the inverse of the given matrix 3. \( \left[\begin{array}{ll}7 & 2 \\ 3 & 1 \\ 2 & 3 \\ \text { 4. }

5 .\end{array}\right] \), use the following steps:

1. Find the determinant of the matrix by using the formula det \(A = ad-bc\). The determinant of the given matrix is \((7*1) - (2*3) = 5\).

2. Find the adjoint of the matrix by using the formula

\(A^T = \begin{bmatrix}
a & b \\c & d\end{bmatrix}^T = \begin{bmatrix}d & -b \\-c & a\end{bmatrix}\)

The adjoint of the given matrix is \\begin{bmatrix}1 & -2 \\-3 & 7\end{bmatrix}\)

3. Find the inverse of the matrix by using the formula \(A^{-1} = \frac{1}{det(A)} \cdot A^T\).

The inverse of the given matrix is \(\begin{bmatrix}\frac{1}{5} & -\frac{2}{5} \\-\frac{3}{5} & \frac{7}{5}\end{bmatrix}\)

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Since the distance between P and S is greater than 10 km, the captain is incorrect. The ship is still more than 10 km away from P.

In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.

Here,

a) To solve this problem, we can use the Law of Cosines to find the distance and the Law of Sines to find the bearing.

First, let's label the points as follows:

P: the starting point

Q: the point reached after sailing 46 km on a bearing of 104

R: the final destination reached after sailing 32 km on a bearing of 310

To find the distance QR, we can use the Law of Cosines:

QR² = PQ² + PR² - 2(PQ)(PR)cos(QPR)

where PQ is the distance sailed on the first leg, PR is the distance sailed on the second leg, and angle QPR is the angle between the two legs.

We can calculate PQ and PR using basic trigonometry:

PQ = 46cos(14)

PR = 32cos(50)

Substituting these values into the Law of Cosines, we get:

QR² = (46cos(14))² + (32cos(50))² - 2(46cos(14))(32cos(50))cos(206)

Simplifying this expression using a calculator, we get:

QR ≈ 67.7 km

To find the bearing of QR, we can use the Law of Sines:

sin(QRP) / QR = sin(QPR) / PR

where angle QRP is the bearing we want to find.

Substituting the known values, we get:

sin(QRP) / 67.7 = sin(310 - 50) / (32sin(14))

Solving for sin(QRP) and taking the inverse sine, we get:

sin(QRP) ≈ 0.493

QRP ≈ 30.1°

Therefore, the ship is approximately 67.7 km away from P on a bearing of 30.1°.

b) If the ship travels west until it is due north of P, it will reach a point S that forms a right triangle with P and Q. Let's label the angles as follows:

angle QPS: the angle between PQ and PS

angle PQS: the angle between PS and QS

angle QSP: the right angle at S

We know that angle QPS is 90° (since the ship travels due north) and that PQ = 46 km. To find PS, we can use basic trigonometry:

PS = PQtan(QPS)

PS = 46tan(90-104)

PS ≈ 26.8 km

To check if the captain is correct, we need to find the distance between P and S. We can use the Pythagorean theorem:

PS² + SP² = PQ²

SP² = PQ² - PS²

SP² = (46)² - (26.8)²

SP ≈ 38.5 km

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In interval notation, the the solution set in interval notation. (5)/(y-4)<9 is   (41/9, ∞).

Inequality is a mathematical statement that two values or expressions are not equal. It is represented by symbols, like >, <, or ≠, and is used to compare quantities or values.

To solve the inequality (5)/(y-4)<9, we need to isolate the variable on one side of the inequality. We can do this by multiplying both sides of the inequality by (y-4) and then simplifying.

(5)/(y-4)<9

5 < 9(y-4)

5 < 9y - 36

41 < 9y

y > 41/9

This means that any value of y greater than 41/9 will satisfy the inequality.

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