2 Select all the correct answers. Which equations represent functions? 2x + 3y = 10 4x = 16 2x − 3 = 14 3y = 18 14.6 = 2x

The system of inequalities that describes this scenario is presented as follows:

One possible solution is given as follows:

(2,15).

Meaning that she has 2 dimes and 15 nickels.

The variables for the system of inequalities are given as follows:

The amounts cannot be negative, hence:

She has at least 15 coins, hence the first constraint is given as follows:

x + y ≥ 15.

A dime is worth $0.1, while a nickel is worth $0.05. The coins are worth a maximum of $1, hence:

0.1x + 0.05y ≤ 1.

The solution set of the inequality is composed by the shaded region on the graph given at the end of the answer.

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Answer: X= -2.1667 Y= 13

Answer:

1: B

2: A

3: D

4: A

5: A, B

Step-by-step explanation:

1: 6/5 is 1.2 2/10 is 1/5

2: 6/14= 3/7 or 6/14

3: 3/12 is 1/4 or 3/12

4: 28/13 is 2 2/13

5: 35/6 which is also 2 3/16

#/# means divide so 35/6 is 35 divided by 6

Answer:

5,940

Step-by-step explanation:

The sum of the interior angles of a polygon is (n-2)*180 where n is the number of sides. In this case n=35. (35-2)*180 = 33*180 = 5940.

The answer is that a risk matrix/heat map has two factors namely, likelihood and Potential Impact on its x-axis and y-axis respectively.

What is a Risk map ?

A risk heat map is a tool used to present the results of a risk assessment process visually and in a meaningful way. Risk assessment is a critical step in risk management. It involves evaluating the likelihood and potential impact of identified risks.

Risk maps are a way of representing the resulting qualitative and quantitative evaluations of the probability of risk occurrence and the impact on the organisation in the event that a particular risk is experienced.

Organisations generally map risks on a heat map using a ‘residual risk’ basis that considers the extent to which risks are reduced by risk response strategies.

So, a risk matrix/heat map plots threats on a two-dimensional grid to assess qualitative risk. it has two factors as its x and y axes , Likelihood and Potential Impact respectively.

Please find the attached image.

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A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.

The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.

Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.

Therefore,

A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.

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The independent and dependent variables in this function are order p Variable

Mathematically, discrete random variables are stated to be impartial if: P(X=x, Y=y) = P(X=x) P(Y=y), for all x,y. Intuitively, for impartial random variables understanding the price of one in every of them, does now no longer extrade the chances of the opposite. The impartial variable is the cause. Its price is impartial of different variables for your study.

The structured variable is the effect. Its price relies upon on adjustments withinside the impartial variable.An impartial variable is precisely what it sounds like. It is a variable that stands on my own and isn't always modified with the aid of using the opposite variables you are attempting to measure. For example, a persons age is probably an impartial variable.

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z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

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Answer: 392

Step-by-step explanation:

7000 x 5.6%

The original price of the instrument is $60.

Discount Price:

50% of 120 = 50/100 * 120

                   = 0.5 * 120

                   = 60

Original Price = Sale Price - Discount Price                  

                       = 120 - 60

                       = 60

Therefore, the original price of the instrument is $60.

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The Yolanda's taxable income is $62,500.

What is income tax?

An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.

Given:

In 2008, Yolanda paid $3,875 in Social Security tax.

The Social Security tax rate was 6.2% to the maximum income of $94,200 that year.

Lets assume Yolanda´s income be `x`.

Now, calculating the taxable income of Yolanda

6.2% x (x) = 3875

[tex]\frac{6.2}{100} (x) = 3875\\x = 3875(\frac{100}{6.2}) \\x = 62500[/tex]

Hence, the Yolanda's taxable income is $62,500.

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The dilated triangle is names ▲D'E'F' ,

Vertex D' → ( -8, 1)

Vertex E' → (4, 10)

Vertex F' → (7, 1)

What is dilation ?

Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though. A dilatation should either enlarge or decrease the initial form. By using the phrase "scaling factor," this transition is described.

Enlargement is the name given to a dilatation that results in a larger image.

Reduction is what happens when a dilatation results in a smaller picture.

According to question

Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':

[tex]D_{(O,k)}(x,y) = (k(x-a) +a, k(y-b) +b)[/tex]

Where "O" is the center of dilation at (a,b) and "k" is the scale factor.

In this case you can identify that:

(a,b) = (1,1)

k = 3

Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:

Vertex D' → [tex](3(-2-1) +1, 3(1-1) +1) = (-8, 1)[/tex]

Vertex E' → [tex](3(2-1) +1, 3(4-1) +1) =(4,10)[/tex]

Vertex F' →[tex](3(3-1) +1, 3(1-1) +1) =(7,1)[/tex]

hence the vertex of ▲D'E'F' are (D' → ( -8, 1),  E' → (4, 10), F' → (7, 1).)

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The carbinet has rectangular floor plan where the length is equal to 5 feet more than twice the width.  The the expression that represents the area in square feet is Option B 2w²+5. ∧where w is the width

The area of the rectangle is the floor space the rectangle can occupy at a given time.

The given parameters are

L= 2w+5

The width = w

Then area is given by the formula

A=L*W

A=2w*w+5

Simplify the expression you have

A=2w²+5 where w is the width

Therefore the area is b. 2w²+5, where w is the width

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Answer: point form: (4,3) equation form: x=4 y=3

Step-by-step explanation:

The solution is y = ( 4/5 )x - 4

The slope intercept form of the equation is y = ( 4/5 )x - 4  where the slope of the line is 4/5 and the y intercept is -4

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is given as

4x - 5y = 20   be equation (1)

On simplifying the equation , we get

Adding 5y on both sides of the equation , we get

5y + 20 = 4x

Subtracting 20 on both sides of the equation , we get

5y = 4x - 20

Divide by 5 on both sides of the equation , we get

y = ( 4/5 ) x - 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Therefore , the value of A is y = ( 4/5 ) x - 4

Hence , The slope intercept form of the equation is y = ( 4/5 )x - 4

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The Required Area of Shaded Region is 42 sq. ft.

Whhat is Area?

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

We are given that the length of side of square is 14 ft

so, we can determine thta the radius of the circle is 7 ft

To Calculate the Required Area we need to substract the area of circle from the area of square

Area of Square = Side*Side = 14*14 = 196 sq. ft.

Area of Circle = πr² = 22/7 * 7*7 = 154 sq. ft

Required Area of Shaded Region is 196 - 154 = 42 sq. ft.

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Answer:

[tex]x < -7[/tex]

Step-by-step explanation:

First subtract 2 from both sides.

[tex]-5x+2-2 > 37-2[/tex]

[tex]-5x > 35[/tex]

Then divide both sides by -5.

[tex]\frac{-5x}{-5} > \frac{35}{-5}[/tex]

For x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

Given is the inequality as follows -

- 5x + 2 > 37

The given inequality is -

- 5x + 2 > 37

- 5x + 2 > 37

- 5x + 2 - 2 > 37 - 2

- 5x > 35

x < - 7

Therefore, for x < - 7, the inequality {- 5x + 2 > 37} is satisfied.

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Answer:

57.5 milkshakes

Step-by-step explanation:

To find the number of milkshakes the ice cream shoppe sold in one hour, you can use the given information to set up the following equation: 15/4 = 71.25/X. Solving for X, we get X = 71.25 * 4/15 = 57.5. Therefore, the ice cream shoppe sold 57.5 milkshakes in one hour.

19

Step-by-step explanation:

15/4= 3.75

71.25 / 3.75=19

Answer: The inverse of a function is found by switching the positions of the input and output values in the function. For example, if the function is f(x) = 2x, the inverse would be f^-1(x) = x/2.

In the case of the given function, f(x) = 8√ x, the inverse can be found by switching the positions of the input and output values. This gives us f^-1(x) = √ x/8. This means that if x is the input value, the output value will be √ x/8. Note that the domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function. In this case, the domain of f^-1(x) is [0, ∞) and the range is [0, ∞), since these are the range and domain of the original function.

Here is the complete inverse function:

f^-1(x) = √ x/8 for x > 0.

As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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The smallest number of bags to cover the circular field is 3.0 pounds.

Area of a circle.

A circle is a shape that has a curved sides referred to as a  circumference. Its area can be determined by;

Area of a circle = [tex]\pi r^{2}[/tex]

where r is the radius of the circle

So that,

the radius of the circular field = 290/ 2

                                                 = 145 feet

The area of the circular field =  [tex]\pi r^{2}[/tex]

                                              = 22/7 x (145)(145)

The area of the circular field = 66078.57 square feet.

Given a bag has a capacity of 50 pounds, and that one pound of grass seed covers about 400 square feet.

Then,

total pounds in a bag = 50 x 400

                                    = 20000 pounds

the number of bags of grass seed needed = 66078.57 / 20000

                                                        = 3.304

The number of bags of grass seed needed = 3.30

Thus, the smallest number of bags the groundskeeper must buy to cover the circular field is 3.0 bags.

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The simplest form of Sin 30° x tan 60° is √3/2 or sin  60° or cos 30°.

What are trigonometry ratios?

Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

Given that the trigonometry function is

sin 30° x tan 60°

Putting sin 30° = 1/2 and tan 60° = √3

=  (1/2) ×√3

=  (1/2) ×(√3/1)

Now multiply the denominators and numerators:

= √3/2

Putting √3/2 = sin 60°

= sin 60°

Again sin 60° = cos 30°

= cos 30°

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Based on the rate of change, Zehra is buying 7 cans per week.

The rate of change gives the ratio between the change in one quantity to the change in another quantity.

Linear relationships have a constant rate of change and the rate of change is usually represented as the slope or gradient.

For instance, the number of cans changed from 29 to 57, a difference of 28, as the number of weeks changed from 5 to 9, a difference of 4.

The rate of change can be expressed as 28/4 or 7.

The number of cans after 5 weeks = 29

The number of cans after 9 weeks = 57

The change in weeks = 4 (9 - 5)

The change in the number of cans = 28 (57 - 29)

The rate of change = 7 (28/4)

Thus, we can conclude that Zehra buys 7 cans weekly.

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The value of the 2.6 pounds of steak cost $27.06 in the neighborhood grocery.

For the given question;

44 pounds of steak cost $45.80.

Let 'x' be the amount for the 2.6 pounds of steak.

Then, ratio of the quantity becomes,

44/45.80 = 26/x

On simplification,

x = (26 x 45.80)/44

x  = $27.06

Thus, the value of the 2.6 pounds of steak cost $27.06 in the  neighborhood grocery.

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The correct question is-

At the neighborhood grocery, 44 pounds of steak cost $45.80. How much would it cost to buy 2.6 pounds of steak?

Answer:

Below

Step-by-step explanation:

Area = pi r^2

r = sqrt ( area/pi) = sqrt( 676 ) = 26

Circumference = pi d  = 2 pi r  = 2 pi (26) = 163.4 mm

The money Trevor's family spend, in total, on shower water in the past month is $14.4

Two or more expressions with an Equal sign is called as Equation.

Given that the Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms.

In the past month, each person showered for an average of 480 minutes

an average 72 liters of shower water (over the entire month)

The cost of water per litre is 0.20 dollars.

We need to find the money Trevor's family spend, in total, on shower water in the past month

Cost of water used per minute = Water used by each person per month / Time each person spent bathing × Cost of water per liter

= 72 / 480 × 0.20

= 0.15 × 0.20

= $0.03.

Now 0.03×480=14.4.

Hence, 14.4 is the money Trevor's family spend, in total, on shower water in the past month.

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Answer:

87

Step-by-step explanation:

12x7+4-1/1

Answer: 741

Step-by-step explanation:

The biggest number Sam can make is 741. He can make this number by using the brackets and the division symbol: (12 + 1 + 1) / 4 = 741.

Our point A(x, y) becomes Something' when a point is rotated 270 degrees counterclockwise around the origin (y,-x). This implies that we reverse x and y and turn x negative.

A pair of numbers that provide the position of a point on such a coordinate plane using the horizontal as well as separations first from two reference axes. usually represented by a pair of x-values and y-values (x,y).

To find a point's coordinates in some kind of a co - ordinate system, you perform the opposite. Starting at the point, travel vertically up or down until your reach the x-axis. There seems to be your x-coordinate shown. Continue the previous procedure while staying on a horizontal line to obtain the y-coordinate.

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Answer: 13/15

Step-by-step explanation:

26/30

Simple by 2

13/15

Answer:

26/30 = 13/15

Answer:

10%

Step-by-step explanation:

percent error: p

44 - 40 = 4

4/40 × 100 = p

p = 0.1 × 100

p = 10%

Percent error is 10%