Kyle uses a calculator to figure out
the total cost of a $1.60 cookie jar.
Including sales tax, the total is
$1.62. What is the sales tax
percentage?

Answer:

(a) y=x             YES

(b) y=-9            YES

(c) y=4x²¹ +8    NO

(d) y=-4x+7       YES

Step-by-step explanation:

See attached worksheet.

He utilized about 39.9 KG of clay per pot, or 38% of the 315 KG of clay, using 119.7 KG for 3 pots.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value indicating hundredth parts of any quantity, is a relative value that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Here,

Weight of clay=315 KG

Weight of clay he used,

=38%*315

=119.7 KG

Number of pots=3

Clay used in each pot,

=119.7/3

=39.9 KG

He used around 39.9 KG of clay to make each pot using 119.7 KG of clay for  3 pots out of 38% of 315 KG of clay.

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Answer:

95

Step-by-step explanation:

x = 38 over 0.4 = 95

38 over x 100=40%

Answer: 1134 m^2

Step-by-step explanation:

First, you would plug in "9" to replace the variable. It would be 7(9) and 4(9). Parenthesis means multiplication.

Then, you would multiply. 7 x 9 = 63, 4 x 9 = 36

The area of a triangle is bh/2. So, 63x36=2268, 2268/2=1134.

I believe the answer is 1134 m^2.

The addition is 5x - 2. We can find out our answer using simple arithmetic calculations.

What are arithmetic calculations?

Arithmetic calculations are mathematical operations used to solve equations and perform numerical calculations. They include addition, subtraction, multiplication, and division. Arithmetic is a fundamental part of mathematics, and it is an important part of everyday life. Arithmetic is used to solve problems in a variety of fields, such as engineering, finance, and science. It is also used in everyday tasks such as grocery shopping and budgeting. Arithmetic calculations are essential for most people and can help them understand and solve a variety of problems. By mastering basic arithmetic calculations, people can make more informed decisions and better understand the world around them.

In algebraic expressions ,

same variables are added together and constants together.

In given equation,

2x and 3x are added i.e. 5x

and 5 and -7 are added  i.e. -2

So, the equation is 5x-2.

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0.0076 is  the probability that the first 30 igniters tested do not fail .

What is probability in math?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.

a)if the failure rate for the super igniters is 15% then the probability that each igniter fails is 0.15,and the probability that it does not fail is 0.85.Therefore the probability that the first 30 igniters tested do not fail is       (0.85)30= 0.0076.

b)given that there are no failures in the first 30 tries,the probabilities occurs on 31st try is 0.15 and the probability that it does not occur on 31st but occurs on 32nd try is (0.85)(0.15)=0.1275.therefore the probability of one or the other is 0.15+0.1275=0.2775.

c)the result of the probability calculation in part(a) provides reason to believ the failure rate of the super igniters is less than 15%.The calculated proability of 0.0076 shows that there is less than a 1% chance that 30 or more igniters in a row would not fail if the failured rate was 15%.This probability is smaller than conventional significance levels such as alpha=0.05 and 0.01 and thus is small enough to make it reasonable to believe that the failure rate of the super igniters is less than 15%.

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The coordinates of C are (5, 4).

What is a coordinate point?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Given, A(-4,-2) and B(8,6)

Point C is 3/4 of the way from point A to B. Then,

C = A +3/4(B -A)

or, C = (3B +A)/4

or, C = (3(8, 6) +(-4, -2))/4

or, C = (24 -4, 18 -2)/4

or, C = (5, 4)

Hence, the coordinates of C are (5, 4).

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The unit rate for the ratio 100 points/ 4 games is 25 points per game

From the question, we have the following parameters that can be used in our computation:

Ratio = 100 points/ 4 games

The unit rate is simply the value of the above ratio

However, with a denominator of 1

This means that we evaluate the quotient in the above expression

So, we have the following representation

Ratio = 25 points/ 1 game

Express as unit rate

Unit rate = 25 points per game

Hence, the unit rate is 25 points per game

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Answer:

$115.4

Step-by-step explanation:

V = Pert ( Substitution p . r. t into formula )

= 103 x e^9%x6

=103 x e0.114

=115.4

Do not reject H(0). There is not sufficient evidence to a manufacturer of transistors claims that its transistors will last an average of different than 1000 hours. at 0.01 significance level.

In the given question, a manufacturer of transistors claims that its transistors will last an average of 1000 hours.

To maintain this average, 25 resistors are tested each month.

We may assume that the distribution of the lifetime of a transistor is normal.

We have to calculate a sample that has a mean of 1010 and a standard deviation of 60.

So let us consider

X : Life time of a transistor

So we have

N=25

x=1010

s=60

Since sample size n(25≤30) is small and population standard is unknown so we use t statistic for hypothesis testing.

Now our null and alternate hypotheses are given as:

H(0): μ=1000

H(1): μ≠1000 (two tailed test)

Under Null hypothesis our test statistic is;

t=(x-μ)/(s/√n)

t=(1010-1000)/(60/√25)

t=0.83

Critical Value:

t(α,(n-1))=t(0.01, 24)

t(α,(n-1))=2.80

We have given level of significance α=0.01 and also we find the t-score 0.83 and degree of freedom=24

p value

The Excel formula is used to calculate the p value is:

P value =2×(1- (t(24) > 0.83))

P value =2×(1-0.7926)

P value =2×0.2074

P value =0.4147

Since p value=0.42 greater than α=0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected and we claims that its transistors will last an average of 1000 hours.

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The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Jane bought 3 shirts and returned 2 pairs of pants

Laura bought 4 shirt and 3 pairs of pants.

Let, s = cost of shirt

and, p = cost of a pair of pants

The equation for Jane is

3s - 2p = $5

Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.

Now, the equation for Laura is

4s + 3p = $120

Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.

So, the system of equation we get

3s - 2p = $5

4s + 3p = $120

After solving  simultaneously we get the values s = 15 and p = 20.

Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,

for 1st equation,

3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)

for 2nd equation,

4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)

Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.

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Answer:

Step-by-step explanation:3

The HA Theorem is a special case of proving that two triangles are congruent. The HA theorem is a special case of the AAS theorem.

The HA congruence theorem for right triangles says that if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle then the two triangles are congruent.

It states that if both hypotenuses and a pair of acute angles of two right triangles are congruent, then the triangles are congruent.

The HA Theorem is a special case of proving that two triangles are congruent.

AAS theorem says that if two angles and any side of a triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent.

Hence, the HA theorem is a special case of the AAS theorem.

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Using equation of motion to calculate the distance covered during acceleration is 540m

Distance is the total length between two points, while displacement is the length between two points, but it also takes into account the direction of the motion. Distance is a scalar quantity, while displacement is a vector quantity.

In this problem, we can either draw a velocity - time graph or proceed to solve using equations of motions.

We are required to calculate the distance covered during the period of acceleration.

Data;

a = v - u / t

a = acceleration

a = (60 - 30) / 12

a = 30 / 12

a = 2.5 m/s²

But we have another equation as

v² = u² + 2as

s = distance

60² = 30² + 2*2.5*s

x = 540

The distance covered is 540m

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The dinner party needs 400 pieces of silverware for 10 tables and 8 seats at each table. By evaluating the given expression, we get the required value.

The given expression is,

A dinner party with tables t' and seats at each table 's' needs "5ts" pieces of silverware.

I.e., number of pieces of silverware = 5ts

Thus, the given expression gives the required value.

If Aaron is planning for a dinner party with t = 10 tables and s = 8 seats at each table, then the number of pieces of silverware required for the dinner party is

5ts = 5 × 10 × 8 = 40 × 10 = 400

Therefore, it needs 400 piece of silverware.

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The current population density  is 125 people / square kilometers.

Given :

plumeria island is an island in the indian ocean. the island is 4,000 square kilometers in size. currently, 500,000 people live there. last year, 150,000 children were born and 50,000 people immigrated. 100,000 people died and 10,000 emigrated. it is believed that the island could support up to 350 people per square kilometer.

Total people =  500000

Area = 4000 square kilometers

we know that ,

Population density = total people / area

= 500000 / 4000

= 500 / 4

= 125

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The linear equation that models how much Carolina earns depending on the number of hours that she works is:

y = 6*x + 8

Here we know that for every mowing job, Carolina charges $6, plus an initial fee. So if that initial fee is b, we can write the equation as:

y = 6*x + b

We also know that for a 4 hours job she charges $32, then we can replace x by 4 and y by 32 in the equation above.

32 = 6*4 + b

32 = 24 + b

32 - 24 = b

8 = b

Then the linear equation we wanted to find is:

y = 6*x + 8

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The value of x = 50

Exterior angle:

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.

If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex.

In contrast, an exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.

given that

m∠6 = x

m∠7 = x-20

m∠11 = 80

we solve this by using exterior angles

sum of 2 interior angles is equal to one  exterior angle

m∠6 + m ∠7 = m∠11

x + x - 20 = 80

2x = 80 + 20

2x = 100

x = 100/2

the value of x = 50

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The rate at which the angle between the ladder and the wall of the house is changing is ≈ 0.083 deg/s when the base of the ladder is 7 feet from the wall.

Trigonometric The values of all trigonometric functions based on the ratio of sides in a right-angled triangle are defined as ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

sine, cosine, tangent, cotangent, secant, and cosecant are all trigonometric ratios.

Given:

Length of ladder = 25 feet

The base of the ladder pulled at the rate of = 2 feet per sec

Distance of the base of the ladder from the wall =7 feets

According to the question,

By using trigonometric ratios - sine ratio

[tex]sine = \frac{opposite}{hypotenuse} \\[/tex]

from the position of A, the opposite side is x and the hypotenuse is 25. hence

[tex]sin A = \frac{x}{25}[/tex]

Differentiating it with respect to the time t we have,

[tex]cos A= \frac{dA}{dt} = \frac{1}{25} \frac{dx}{dt} ...... (3)[/tex]

at x = 7

[tex]sin A = \frac{7}{25}\\cos A = \frac{24}{25}[/tex]

plugging in [tex]\frac{dx}{dt} = 2, cos A = \frac{24}{25}\\[/tex] into eq no (3) gives us rate of change

[tex]\frac{24}{25} \frac{dA}{dt} = \frac{1}{25} (2)\\\frac{dA}{dt} = \frac{25}{25} \frac{1}{25} (2)\\\frac{dA}{dt} = \frac{1}{12}\\[/tex]

[tex]\frac{dA}{dt}[/tex] ≈ 0.083

Therefore, the rate at which the angle between the ladder and the wall of the house is changing is ≈ 0.083 deg/s when the base of the ladder is 7 feet from the wall.

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A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

[tex]Distance = r\times time[/tex]

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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In order to maximize the number of bags with 9 balls he needs at least 32 bags.

9x + 11y = 304

To begin, solve for y so that you may graph it:

y = -9x/11 +304/11

Then look for the place where x has the largest possible value and x and y are both positive integers (keeping in mind that y1).

This is an important point (24,8). There are 24 bags of nine marbles and eight bags of eleven marbles.

Anand should put 9 marbles in 24 bags and 11 marbles in 8 bags, for a total of 32 bags.

Marble is a metamorphic rock made up of recrystallized carbonate minerals, the most common of which being calcite or dolomite. There are certain exceptions to the rule that marble is not foliated (layered).

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1085 different combination of 3 movie she can rent.

What is linear equations?

Linear equations is a type of equation that is in between two variables that gives a straight line.

The calculation of  number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-

=N×(2× documentry and 1 horror movies)+N×(3 documentry)

=(6C1)×(15C2)+(6Co)×(15C3)

= 630 + 455

= 1,085

Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.

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Answer:

Step-by-step explanation:

52%

The equation of the line that passes through the point (-1,2) and has a slope of -1, in point-slope form is: y - 2 = -1(x + 1).

If we know one point (a, b), that a line passes through and its slope (m), we can write the equation of that line in point-slope form as y - b = m(x - a).

Given the following:

A point (a, b) = (-1, 2)

The slope of the line (m) = -1

To write the equation of the line, substitute m = -1, a = -1, and b = 2 into y - b = m(x - a):

y - 2 = -1(x - (-1))

y - 2 = -1(x + 1).

The answer is: y - 2 = -1(x + 1).

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The linear equation to model the scenario -

For the stated question;

Let the side of the equilateral triangle be 'x'.

Then,

Perimeter of the equilateral triangle = x + x + x

Perimeter of the equilateral triangle P = 3x

Now,

One side of rectangle = side of equilateral triangle = x.

Second side of rectangle = 6 + side of equilateral triangle = 6 + x.

Perimeter of the rectangle P = x + x + 6 + x + 6 + x

Perimeter of the rectangle P = 4x + 12

Thus, linear equation to model the scenario -

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The values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

Expression 10x – x²

The expression can be written as

10x – x² = p – (x – q)²

10x – x² = p - x² - q² + 2xq

10x – x² = - x² + 2xq + p - q²

Compare the quantities on both sides,

10x = 2xq and 0 = p - q², p = q²

q = 10x / 2x = 5

p = 5² = 25

Therefore, the values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

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The type of analysis used to identify the source of the bias is known as Differential Item Functioning Analysis.

Analysis

In statistics, analysis is to break a topic or concept down into its parts in order to inspect and understand it, and to restructure those parts in a way that makes sense to you.

Given,

Here we need to find the type of analysis used to identify sources of bias.

While we looking into the given question, we have used by ETS.

And it identifies items that are specifically biased against any ethnic, racial or gender group.

And we also know that the first analysis equates groups on the basis of overall scores.

By using these groups it evaluates differences in performance between sub groups on particular items.

And the Items that differ significantly between the groups are thrown out.

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the proportionality constant is 20 and in 8 ours it will cover 160 miles.

What is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

The slope of he given graph will be (30-10)/(2-1) = 20

So here the proportionality constant is 20.

we can write y = 20x

This means in 8 ours it will cover 8*20 = 160 miles.

Hence, the proportionality constant is 20 and in 8 ours it will cover 160 miles.

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