Zach took a science test. He answered 42 questions correctly and 8 questions incorrectly.

What percentage of the questions did Zach answer correctly?

Answer:

Put one dot at (0,3) and the other dot at (1,0)

Step-by-step explanation:

Let x = 0

6x + 2y = 6

6(0) + 2y = 6

2y = 6  Divide both sides by 2

y = 3

(0,3)

Let y = 0

6x + 2y = 6

6x + 2(0) = 6

6x = 6  Divide both sides by 6

x = 1

(1, 0)

The probability that the area covered by a can of spray paint is 0.251

The variable of interest is:

X: are objects that can be painted with a single can of spray paint.

This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.

Symbolically:

P(X≥27)

To calculate the probability, use the standard normal distribution, so first standardize the value of X using:

Z= (X-μ)/σ

P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)

Now, because the Z-table contains cumulative probability information:

P(Zα≤Z₀)=1-α

you must perform the following conversion to calculate the requested probability:

1 - P(Z<0.67)= 1 - 0.749= 0.251

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Answer:

y = [tex]\frac{1}{6}[/tex] x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (6, 10) ← 2 points on the line

m = [tex]\frac{10-9}{6-0}[/tex] = [tex]\frac{1}{6}[/tex]

the line crosses the y- axis at (0, 9 ) ⇒ c = 9

y = [tex]\frac{1}{6}[/tex] x + 9 ← equation of line

The solution to the given set of systems of equations is (x, y) = (1, -4).

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let's determine the solution using the elimination Method

3x−2y=11  (Equation 1)

3x−y=7(Equation 2)

Multiply the second equation by 2.

6x - 2y = 14    (Equation 3)

Now subtract the first equation from third to eliminate the y.

6x - 2y - (3x - 2y) = 14 - 11

3x = 3

x = 1

Now to find the value of y,

3x−y=7

3(1) − y = 7

y = 7 - 3

y = -4

Therefore, the solution to the given set of systems of equations is (x, y) = (1, -4).

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The equation that passes (6,0) and (3,4) is -3y=4(x-6)

What are the different forms of straight lines ?

The following information about the straight line is required if we wish to obtain the equation for it.

1. The y-intercept and slope

2. Two-point and slope

3. Two things.

4. the intersection of the x- and y-axes

the straight line that passes through (6,0) and (3,4).

The equation can be expressed in a point-slope form which is ,

y/x-6=4/-3

∵ -3y=4(x-6)

Hence,

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

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Answer:

m = -5

Step-by-step explanation:

I'm not sure of the first part, but this is how to solve the second:

5m > -25

5m/5 > -25/5

m = -5

Answer:

8^18

Step-by-step explanation:

8^15

8^−3

=

8^15

8−3

= 8^15− (−3)

= 8^18

The system of equations with the solution (4, -3) is y = x - 7 and y = 2x - 11.

We are given a point. The coordinates of the point are (4, -3). We need to find a system of equations such that they pass through the given point.

We will use the slope-point form of a line. Let the slope of the equation of the straight line be "m". We need two equations. The general equation of a line using the slope-point form is given below.

(y - y1) = m(x - x1)

We know that both equations must pass through the given point for the solution to exist.

(y - (-3)) = m(x - 4)

(y + 3) = m(x - 4)

We just need to take any two values of the slope of the line.

First, we take m = 1. The corresponding equation is given below.

(y + 3) = m(x - 4)

(y + 3) = 1*(x - 4)

y + 3 = x - 4

y = x - 7

Next, we take m = 2. The corresponding equation is given below.

(y + 3) = m(x - 4)

(y + 3) = 2*(x - 4)

y + 3 = 2x - 8

y = 2x - 11

Hence, the system of equations is y = x - 7 and y = 2x - 11.

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Step-by-step explanation:

length(l)=x+4

breadth(b)=x-3

Area of rectangle(A)=l×b

60=(x+4)×(x-3)

60=x^2-3x+4x-12

60=x^2+x-12

x^2+x-12-60=0

x^2+x-72=0

x^2+9x-8x-72=0

x(x+9)-8(x+9)=0

(x+9)(x-8)=0

equating equation

x+9=0.....eq(i)

x=-9 it is not possible

x-8=0.....eq(ii)

x=8

Then,length(l)=x+4

=8+4=12

breadth(b)=x-3

=8-3=5

Part a: ΔABC≈ΔAPQ

Part b: The line segment PQ corresponds to the line segment BC.

Part c: Angle P in APQ triangle angle equates to angle B.

Part a: line segment PQ parallel to BC; PQ||BC

Thus, ∠ABC =∠APQ  AND,   ∠ACB=∠AQP

So, by (AA similarity rule)

ΔABC≈ΔAPQ

Part b: The line segment APQ on the triangle corresponds to the line segment BC:

By CPST, line segment PQ on triangle APQ equates to line segment BC (corresponding parts of similar triangle).

Part c: APQ triangle angle equates to angle B:

Angle P on triangle APQ equals angle B via CPST (corresponding parts of similar triangle).

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The confidence interval for the population mean with 99% confidence interval is (6.90;8.50).

A confidence interval is a set of values that, with a particular level of certainty, includes a population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage.

The population mean is mean [tex]\bar{x}[/tex]=7.3.

The sample's standard deviation is 2. 9

Number of samples: 42

The range of possibilities for the mean, [tex]\bar{x}[/tex]

The confidence interval for the mean is

[tex]\bar{x}[/tex] ± (σ/√n)

To calculate the critical value, we must first determine the degrees of freedom, which are given by:

df=n-1

df=42-1

df=41.

Since the confidence level is 0.99 or 99%, the values of and can be used to calculate the critical value using Excel, a calculator, or a table is 2.701

7.3-2.701(2.9/√42)=6.9013

7.3+2.701(2.9/√42)=8.5086

The 99% confidence interval in this instance would therefore be provided by (6.90;8.50).

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The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.

The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.

With regard to the above problem,

let us say L is the lenght of the rectangle and W is the width

Based on the formula for the area of a rectangle,

L x W  = 1600ft

To minimize the perimeter, of the rectangle, we must assume that:

L = W

that is L² = 1600

If we applied square root to both sides of the equation, we'd have


L = 40

Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.

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aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 5,9,13,17,21

Five comma nine comma thirteen comma seventeen comma twenty one.

We need to find the nth term of the sequence.

Firstly we need to find the sequence is AP or GP.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

so 9-5=4,

13-9=4

Hence the sequence is a Aritmetic sequence.

In arithmetic sequence the nth term can be find by using the formula

aₙ=a+(n-1)d

where a is first term and d is common difference.

Hence aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.

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Answer:

-73 +n

the first term is -73+1

the secound is -73+2

and so on

Answer:

[tex]a_{n}[/tex]= n - 73

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 71 - (- 72) = - 70 - (- 71) = - 69 - (- 70) = 1

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 72 and d = 1 , then

[tex]a_{n}[/tex] = - 72 + 1(n - 1) = - 72 + n - 1 = n - 73

The possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)

We need to find the four possible pairs of integers that has product -18

Let x and y be two required integers.

Since the product is negative, one of the integer must be negative integer.

x      y          x*y

9    -2          -18

2     -9         -18

18    -1         -18

-1     18        -18

6      -3        -18

3      -6        -18

Therefore, the possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)

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The different ways can paint the spinner is [tex]4^{6}[/tex].

Permutation and Combination:

A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

Here it is given that to paint the 6-sector spinner shown there are 4 colors to choose from.

The total number of ways to color this spinner with 6 different parts and 4 different colors is 4 × 4 × 4 × 4 × 4×4 = [tex]4^{6}[/tex] ways

Therefore the ways is [tex]4^{6}[/tex].

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Using One way ANOVA and Randomized block design, the sum of squares between groups (ssb) is equal to the sum of sum of sum of explantary variable A's sum of squares and errors sum of square.

Statistics uses one-way ANOVA to compare the means of three or more independent groups to determine if there is a statistically significant difference between the corresponding population means. It is constructed using the sum of squares measure of total variability used in the numerator of the standard deviation, subtracting the mean, squaring the difference, and adding all observations to obtain the total variability Generate a scale. For multiple groups, we focus on decomposing this total variability (total sum of squares) into the variability between means (the sum of squares of the explanatory variable A) and the variability of the residuals or errors (the error sum of squares).

SSTotal = sum of squares = ∑( yᵢ - Y )²

Total variation is assessed by the total mean (the estimated mean of all observations, available from mean-only models).

SSA = Sum of Squares of Explanatory Variable A

Also called treatment, regression, or model sum of squares. ∑∑(yᵢⱼ - Y' )²

SSE = error (residual) sum of squares

Variation of response around group mean.

Also called the sum of squared residuals.

SSE = ∑∑( Y - Y')²

The total sum of squares is always equal to the sum of the sum of the squares of the explanatory variable A and the sum of the squared errors, SST (total) = SSA + SSE. This equation means that if SSA increases, SSE must decrease if SSTotal remains the same. This result is called the sum of squares decomposition formula.

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The distance between the two points is 8.25 units

The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.

The following is the formula for the separation between two points:

d= √(x₁-x₂)²+(y₁-y₂)²

Points (x1, Y1) and (x2, Y2)

As given in the question, the points are (-6, -6) and (-8, 2)

The distance between the two points is,

d= √(-6+8)²+(-6-2)²

d=√4+64

d=√68 units= 8.25 units

Therefore, the distance between the two points is 8.25 units

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Answer:2/5=4/10 and 1/4=2/8

Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.

In accordance to Thales's theorem, the geometric system has a missing side length of 15 units.

In this problem we find a geometric system formed by two proportional trapezoids. This similarity and proportionality is defined by Thales's theorem, which states that a triangle segmented by several lines parallel to each other and parallel to the base of the figure creates triangles and quadrilaterals proportional to each other.

Then, two figures of the given trapezoids are represented by side proportionality ratios. Then, the proportionality ratio is described and its variable x is cleared within by algebra properties:

First, define the proportionality ratio associated to the geometric system:

4 / (10 + 4) = (21 - x) / 21

Second, simplify the equation and clear the variable x:

4 / 14 = 1 - x / 21

2 / 7 = 1 - x / 21

42 / 7 = 21 - x

6 = 21 - x

x = 21 - 6

x = 15

The missing length is equal to 15 units.

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Answer:

$24

Step-by-step explanation:

3(4) + 3(4) = x (the total cost)

12 + 12 = x

x = $24

Answer:

Step-by-step explanation:

A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.

The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).

Between the two variables, the number of cold, snow days, and the amount of hot chocolate sold at a ski resort, there is causation.

For two variables x and y, we have causation when a change in one of the variables causes an immediate change in the other variable as a response.

Here we have the two variables:

x = number of cold, snow days.

y = amount of hot chocolate sold at a ski resort.

Obviously, there is a correlation there, we can even assume that if the days are cold enough, a larger percentage of the people in the ski resort will decide to stay there, and then there is a larger posibility that they will consume hot chocolate there, so yes, there is causation between these two variables.

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The researchers include the scenario where subjects wear no bracelet at all are when it comes to mosquitoes, volunteers in each block should live in similar conditions.

An experiment might involve giving a novel drug to rats to see how they respond to learning about it. When you visit a new coffee shop but are unsure of how the coffee will taste, that is an example of an experiment. the act of carrying out a test like that; experimenting. An experiment is a procedure used as part of the scientific method to test a hypothesis. The independent and dependent variables are the two most important variables in every experiment. To investigate the impact of the independent variable on the dependent variable, it is either controlled or altered.

Given,

A company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment.

The researchers include the scenario where subjects wear no bracelet at all are:

When it comes to mosquitoes, volunteers in each block should live in similar conditions.

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Part A

The equation that shows the statement is

2N + 20 = 4N - 40

Part B

The value of N = 30

The number that he is thinking = N

Twice (N+10) = 2(N+10)

= 2N + 20

Four times (N-10) = 4(N - 10)

= 4N - 40

Twice (N+10) is the same as four times (N-10)

The equation that represent the given statement is

2N + 20 = 4N - 40

Part B

Solve the equation

2N + 20 = 4N - 40

4N - 2N = 20 + 40

2N =  60

N = 60/2

Divide the terms

N =30

Hence,

Part A

The equation that shows the statement is

2N + 20 = 4N - 40

Part B

The value of N = 30

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The solution to the inequality is x > 0

Inequality in mathematics differentiate two values,  if one is less than, greater than, or not equal to another value

Evaluate the equation by letting the unknow to be on one side

−1 − 10x < −1

-10x < -1+1

Add +1 to both sides

= -1-10x+1 < -1+1

= -10x < 0

Divide both sides by -10 same factor and flip the relation because  of negative factor

=  -10x /-10 > 0/-10

= x > 0

Therefore the solution to the inequality is x>0

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Answer:

7.416 is the answer

Answer: 4x+10

simplified: 2x+5

Step-by-step explanation:

Answer: 4x+10

You multiply 2 by (2x) = 4x

You multiply 2 by (5) = 10