write a part to part and a part to whole ratio for each problem situation of the 250 students surveyed, 142 prefer carrots and 97 prefer peas

If Katie Pittman earns a $60,840 annual salary, her weekly gross salary is $1170.

What is  weekly gross salary?

The number of hours worked multiplied by the hourly wage of an employee is how gross wages are determined for hourly workers. For instance, an employee making $12 per hour and working 25 hours per week would earn a gross weekly salary of $300 (25 x 12 = 300).

What is annual salary?

The gross pay (before tax deductions) divided by the number of pay periods in a year yields the yearly salary. For instance, a worker making $1,500 each week would make $78,000 a year (1,500 multiplied by 52).

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The simplified form of 13√5 + 3√5 is option c 16√5

Given,

The expression : 13√5 + 3√5

We have to simplify the above given expression.

Lets see the simplification of numbers with square roots.

1. Addition: a√b + c√b = (a + c) √b

2. Subtraction: a√b - c√b = (a - c) √b

3. Multiplication: a√b × c√b = a × c × b

4. Division: a√b ÷ c√b = a ÷ c

So here,

We can use addition:

That is,

a√b + c√b = (a + c) √b

Where,

a = 13, b = 5 and c = 3

Now,

13√5 + 3√5 = (13 + 3) √5 = 16√5

Therefore, the simplified form of 13√5 + 3√5 is option c 16√5

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Using the Factor Theorem, the polynomial with real coefficients that has zeros -1 and 2 - 3i is given by:

f(x) = x³ - 3x² + 9x + 13.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

Considering a leading coefficient of a = 1, the zeros of the polynomial are given as follows:

Hence the polynomial is given by:

f(x) = (x + 1)(x - 2 + 3i)(x - 2 - 3i)

f(x) = (x + 1)[(x - 2)² - (3i)²]

f(x) = (x + 1)(x² - 4x + 13), as (3i)² = 9i² = 9(-1) = -9, -(-9) = 9.

f(x) = x³ - 3x² + 9x + 13.

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The rectangular prism has the following dimensions;

The total surface area of

The total surface area of the rectangular prism is 114 square meters

The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000.

Given:

To find two numbers the exact answer is between 6×7381.

7,381 is between the numbers 7,000 and 8,000.

Rounding the number 7,381 down to 7000 and multiplying 6 by it.

6 × 7,000 is 28,000

Rounding the number 7,381 up to 8000 and multiplying 6 by it.

6 × 8,000 is 48,000

The two numbers so that the exact answer is between 6×7381 are 28,000 and 48,000 respectively.

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The converse of  t > r is r > t

A converse statement is determined when both the hypothesis and conclusion are reversed or interchanged.

In this condition, the hypothesis is written as the conclusion and the conclusion is changed to be the hypothesis.

If a conditional statement is written as: x → y

The converse is then written as y → x

Where;

Given the expression as;

t > r

We can see that;

The converse will be;

r > t

Hence, the converse is r > t

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It is proved that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7 because on solving it results in 7(n² + 2n -1).

To prove that 12n-n²+ (2n-1)(4n+ 3) - 4 is a multiple of 7.

When an algebraic expression is a multiple of 7 it should be divisible by 7.

Now, solve the algebraic expression.

12n - n²+ 8n² + 6n - 4n -3 - 4 (combine the like terms)

7n² + 14n - 7 (take out the common factor 7)

7(n² + 2n -1)

Therefore, the algebraic expression has a factor of 7 and is always a multiple of 7 for all positive integer values of n.

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Another way that people can look up how much they owe in tax is by looking it at IRS.gov/account.

A tax that you pay to the federal government in the US as opposed to a state government If income is used to pay for college, it could not be subject to federal taxes. Federal taxes are collected by the federal government.

The marginal tax rate should be used to calculate federal taxes. It only applies to taxable income. Make changes to gross revenue to arrive at a determinable Taxable income before computing Taxable income. Deductions must then be made. After deductions, taxable income is available. There is no tax due if there is no taxable income.

At IRS.gov/account, you can securely log in to access your federal tax account. Once you've logged into your account, you can see your balance and the amount you owe, as well as 18 months' worth of payment history, access Get Transcript, and see the most important data from your most recent tax return.

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The  inequality in which involves one or more rational expressions is Rational inequality.

What is inequality?

Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.

An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.

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The answer is d. Rational inequality, which includes fractions with polynomials. Other options involve exponential, linear, or logarithmic functions, without rational expressions as in inequalities.

The right choice is d. Rational inequality. An objective disparity includes at least one sane articulations, which are portions with polynomials in the numerator and denominator. These disparities can be settled by finding the basic places where the normal articulation is indistinct or changes sign.

The arrangement includes deciding the stretches where the disparity turns out as expected in view of the indication of the judicious articulation in those spans. Interestingly, dramatic, direct, and logarithmic disparities include various kinds of numerical capabilities.

Remarkable imbalances contain dramatic terms, direct disparities incorporate straight capabilities, and logarithmic imbalances contain logarithmic capabilities. Each kind of imbalance has its own qualities and strategies for settling, however just objective disparities straightforwardly manage levelheaded articulations including parts of polynomials.

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The transformations are

Transformation 1

Here, we have

The coordinates are given as

P(-5, 4), Q(2, 8), R(6, 1) and S(-1, -3)

The transformation is given as

<2, -4>

This is represented as

(x, y) ⇒ (x + 2, y - 4)

This means that the translation is (x + 2, y - 4)

When this rule is applied on the coordinates, we have

P'(-3, 0), Q'(4, 4), R'(8, -4) and S'(1, -7)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

Transformation 2

Here, we have

The coordinates are given as

E(-7, -7), F(-2, -3), G(-1, -6)

The transformation is given as

<8, 3>

This is represented as

(x, y) ⇒ (x + 8, y + 3)

This means that the translation is (x + 8, y + 3)

When this rule is applied on the coordinates, we have

E'(1, -4), F'(6, 0) and G'(7, -4)

Next, we plot the image of the transformation on a coordinate plane

See attachment for the image of the transformation

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The measure of each angles a,b and c are 32°, 74°  and 74°  respectively.

What is triangle?
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The symbol for an ΔABC triangle is A, B, and C.
Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.

Let angle b be x

Therefore angle c will also be  x [as given b and c are equal] and angle a will be x - 42°.
Now as we know that the sum of the measures of the angles of a triangle is 180° therefore,

x + x + x - 42° = 180°

=> 3x = 222°

=> x = 74°  which is angle b and c

and angle a is (74 - 42)°  =32°  

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Using the exterior angle theorem, the value of x in the triangle is: x = 8.

The exterior angle theorem states that the measure of the angle formed outside a triangle when a side is extended through one of the points of the triangle is equal to the sum of the remote interior angles of the triangle.

Triangle LMN is shown in the diagram attached below, where:

The measure of angle MNO = (5x + 2)°

The measure of angle NLM = (x + 10)°

The measure of angle LMN = (x + 16)°

Therefore:

Measure of angle MNO = measure of angle NLM + measure of angle LMN [based on the exterior angle theorem]

Substitute

(5x + 2)° = (x + 10)° +  (x + 16)°

Solve for x

5x + 2 = x + 10 +  x + 16

Combine like terms

5x + 2 = 2x + 26

5x + 2 - 2x = 2x - 2x + 26 [subtraction property of equality]

3x + 2 = 26

3x + 2 - 2 = 26 - 2  [subtraction property of equality]

3x = 24

3x/3 = 24/3 [division property of equality]

x = 8

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The journal entries to record both the dividend declaration and its distribution is : Dr Retained earnings  $44,640, Cr Common stock dividend distributable $31,000, Cr Paid-in capital in excess of par value, Common stock $13,640 .

TVX Company Journal entries

Feb 05

Dr Retained earnings  $44,640

[ (62,000 shares × 2%) ×$36 ]

Cr Common stock dividend distributable $31,000

[ (62,000 shares × 2%) ×$25 ]

Cr Paid-in capital in excess of par value, Common stock $13,640

($44,640 - $31,000)

(To record dividend declaration)

Feb 28

Dr Common stock dividend distributable$31,000

[ (62,000 shares × 2%) ×$25 ]

Cr Common stock, $25 par value $31,000

(To record dividend distribution)

Therefore the entry is  Dr Retained earnings  $44,640, Cr Common stock $31,000, Cr Paid-in capital $13,640.

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The amplitude is determined as the distance from the midline of the cosine function.

From the graph provided, the depth is shown as 3 units (between 5 units and 2 units) which puts the midline at 3.5 units. The amplitude therefore is 1.5

The value of A in the digit is 6.

The 14 digit numbers are written in the boxes.

The sum of any three consecutive digits is 20.

Therefore, from the last three digits,

5 + 9 + x = 20

14 + x = 20

subtract 14 from both sides of the equation

14 - 14 + x = 20 -14

x = 6

There the value of A is 6.

If you notice the pattern, it follows the same pattern forward and backward as follows:

69569569569569

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Reason:

87.5% of the students take the bus to school

100% - 87.5% = 12.5% of the students do not take the bus to school

The info about the "18 boys and 46 girls" is put there as a distraction since it's never used.

In linear equation, 3464.1016 feet  is the shortest length of fence that the Ranch owner can use.

What is linear equation definition and example?

Let L represent the length of the field.

Let W represent the width of the field.

Let F represent the length of fence needed.

L*W=500000

2L+3W=F Both length sides+both width sides+ fence across the width.

Let's look at the first equation again:

L*W=500000

W=(500000/L)

Now we can substitute (500000/L) for W in the second equation.

2L+3(500000/L)=F

2L+1500000/L=F

Now we have a function. We can input any length, and we'll know length needed. But how can we find the length needed so that F is as small as it can be? If you know derivatives, there's an exact way. The next easiest way to do it is to graph.

Manner 1: Derivative

Set the derivative to zero...when the length stops going down and starts coming back up, it'll be at it's lowest point.

2L+1500000^-1=F

F'=2-1500000^-2

0=2-1500000^-2

1500000/(L^2)=2

1500000=2L^2

1500000=L^2

L=866.025

Now, we know that L=500000/W

so 866.025=500000/W

W=500000/866.025

W=577.35027 feet.

Now,

2L+3W=2(866.025)+3(577.35027)

Minimum fencing needed: 3464.1016 feet.

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Answer: 3.

Step-by-step explanation:

[tex]\left \{ {{4x-3y=3 \ |[*(-4)]} \atop {5x-4y=3} \ |[*3]} \right. \ = > \ \left \{ {{-16x+12y=-12} \atop {15x-12y=9}} \right. \ = > \ \left \{ {{y=3} \atop {x=3}} \right.[/tex]

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{3}x\stackrel{\stackrel{b}{\downarrow }}{-1}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The amount in pounds of water that's been carried by Devin as described by the ratio given in the task content is; 10.5 pounds.

It follows from the task content that the amount of water Devin is carrying is to be determined.

On this note, since the backpack contains food, water, bedding, and emergency supplies are in the ratio; 2 : 3 : 1 : 4.

It therefore follows from proportion that the ratio representation of total of all supplies is; (2 + 3 + 1 + 4) = 10.

Therefore, since the total weight is; 35 pounds, it follows that the amount of water Devin is carrying can be of help as follows;

w/35 = 3/10.

w = (3 × 35)/10

w = 105/10

w = 10.5 pounds.

Ultimately, the total weight of water Devin is carrying is therefore; 10.5 pounds.

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Based on the beginning inventory to Hoover Electronics and the units to be sold, the number of units that Hoover should produce is 43, 700 units

First, find the ending inventory that Hoover Electronics would prefer which is 40% of the beginning inventory:

= Percentage of beginning inventory

= 40% x 15, 500

= 6, 200 units

The amount that Hoover should produce in units is:
= Amount to be sold + Ending inventory - Beginning inventory

= 53, 000 + 6, 200 - 15, 500

= 43, 700 units

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Answer: 2x + 3y =  33

FOR ARITHMETIC

[tex]lhs = 9 - 4 \\ lhs = 5 \\ rhs = 4 - 1 \\ rhs= 3 \\ \\ lhs \: not = rhs[/tex]

SINCE THERE IS NO COMMON DIFFERENCE LET US TEST FOR A GEOMETRIC SEQUENCE.

[tex]lhs = \frac{9}{4} \\ \\ rhs = \frac{4}{1} \\ rhs = 4 \\ \\ lhs \: not = rhs[/tex]

THERE IS NO COMMON DIFFERENCE NOR A COMMON RATION THIS MEANS THAT THE SEQUENCE IS NEITHER AN ARITHMETIC NOR A GEOMETRIC SEQUENCE.

THE OPTION IS A.NEITHER.

The two distinct lines, line l and line m, have the following relationship with line n

A. The measure of the angle where line | meets line n is 90 degrees

B. The measure of the angle where line meets line n is 90 degrees

This is a term used to refer to lines that intersect at angle 90 degrees. perpendicular lines are also found in right angle triangle. Hence it is right to say that two sides of a right angled triangle are perpendicular to each other.

The features of perpendicularity also helps in defining a squire and rectangles. This is true because the sides meet at angle 90 degrees

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We want to know which values of m satisfy ≤

5m + 1 4

Substracting 1 both sides:

-1 - 1

+03

5m ≤ 3

Dividing by 5 both sides

/5/5

m ≤ 3/5

m ≤ 0.6

Since 1 and 2 are higher than 0.6 and 0 ≤ 0.6

Then if m=0 it is satisfied

The inequality that can be used to find the domain of f(x) is x - 3 ≥ 0.

The correct answer is the second one i.e.x minus three over or equal to zero.

Given:

Function f(x) = √x-3

The fact that a negative number cannot be used as the term in the root square, so

x - 3 ≥ 0  which implies that, x ≥ 3.

From the inequality, we can tell that the domain of the function is the interval [3,∞).

Hence the inequality is x - 3 ≥ 0.

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Answer: 8 is actually the constant of proportionality, since it is the number that stays the same regardless of the change in x and y.  

Step-by-step explanation:

Let's say you want to know how many pounds of meat a male lion would eat in a month in order to purchase for the zoo the correct amount of food needed.   Let's assume the month was 30 days.  we know that 8 is the amount of food per day (that number will not change because it is a constant.  

so 30 x 8 = 240 which is what y is for the 30 days.  

if you needed two weeks, 14 days.  14 x 8 = 112 pounds for the 14 days.  

So you see 8 stays the same for each scenario, so it is the constant that is used for all values of x to find y.  

Answer:

29

Step-by-step explanation:

=5+5×5–1(5÷5=1)

Multiplication

=5+25–1(5×5=25)

Addition

=30–1

(25+5=30)

Subtraction

=29

(30-1=29)

In general, given a function g(x), a transa

The solutions to the questions are

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

For most regular quadrilaterals, you multiply the side lengths to determine the area

The area expression is given as

Area = ▢ × 102 + ▢ × 101 + 6

From the question, we can use any number

However, this number must be positive

Assume the number is 5

So, we have

Area = 5 × 102 + 5 × 101 + 6

In (a), we have:

Area = 5 × 102 + 5 × 101 + 6

Evaluate

Area = 1021

The perfect square number closest to this is

Closest = 1024

In (b), we have

Closest = 1024

Rewrite as

Area = 1024

Take the square roots

Length = 32

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