(3b + 3)(-b² - 2b + 2)

If a < b, we can say that b is to the right of a on the number line. In other words, a is to the left of b.

A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, such as plotting a point.

If a b, then b is to the right of a on the number line. To put it another way, an is to the left of b.

This is because the number line depicts the order of real numbers, with smaller numbers to the left and larger numbers to the right. Because an is less than b, it is a smaller number and must be to the left of b on the number line.

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Answer:

-2

Step-by-step explanation:

5x/2 = -5

5 x/2=2 (-5)

5x= 2 (-5)

5x= -10

5x/5=-10/5

x=-10/5

x=-2

Answer:

m = -5/3

Y-intercept: (0, 64/3)

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (14, -2) and (5,13)​

We see the y increase by 15 and the x decrease by 9, so the slope is

m = -15/9 = -5/3
The y-intercept is located at ( 0, 64/3)

The equations in the slope-intercept form are

p = 3b + 2 and p = (5/2)b + 15/2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

From the table and scatter plot;

(a). The line for 'Build it' passes through (1, 10) and (3, 15),

then the equation of the line is,

p = (5/2)b + 15/2

Similarly, the equation of the line-'All things home' is,

p = 3b + 2.

(b) the graphs of the lines are given in the attached image.

(c) The equation in the slope-intercept form;

p = 3b + 2 and p = (5/2)b + 15/2.

(d) When b = 65,

then p = 3(65) + 2 and p = (5/2)(65) + 15/2.

So, p = 197 and p = 170

Therefore, all the required values are given above.

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The distance is 295 feet from the surfers from his eyes.

Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons),

According to the given question, we have attached a figure which represents the given situation.

Let the distance would be x from the surfers from his eyes

As per the figure, using the sine ratio to find x:

sin 29° = perpendicular/hypotenuse

Substitute the known values and solve for x:

sin 29° = 143/x

0.4848 = 143/x

x = 294.96

x ≈ 295 feet

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Answer:

-3

Step-by-step explanation:

Barbara will therefore shell out $171.36 for the cost of shipping and handling.

The amount of money, or its equivalent, for which anything being offered for sale, purchased, or otherwise transacted. A price on someone's head is a sum provided for their capture, whether they are alive or dead.

We must calculate 28% of the chandelier's original purchase price in order to calculate the value Sarah will charge for shipping and handling.

Step 1

Calculate 28% of $612

We can multiply a value by 0.28 to get 28% of it, or reduce it by 100 & then multiply the result by 28. So:

28% of $612 = 0.28 x $612 = $171.36

Step 2

Add the cost of shipping and handling to the purchase price.

Simply include the shipping & handling fee to the original price to get the chandelier's total cost with shipping and handling included:

Total cost = $612 + $171.36 = $783.36

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The value of f(1) will be 45.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a function f(n) = 45.(4/5)ⁿ⁻¹

To calculate the value of f(1) we will substitute the value of the n by 1.

f(1) = 45.(4/5)¹⁻¹

f(1) = 45.(4/5)⁰

f(1) = 45

To calculate the value of f(n -1) we will substitute the value of the n by

n - 1.

f(n -1) = 45.(4/5)ⁿ⁻¹⁻¹

that can also be written as, from the rule of power

f(n -1) = (45.(4/5)ⁿ⁻¹)/4/5

f(n -1) = (45.(4/5)ⁿ⁻¹) * 5/4

f(n -1) = f(n) * 5/4

so,

f(n) = f(n-1) * 4/5

Therefore, the value of f(1) will be 45, and the value of f(n) = f(n-11)*4/5.

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The maximum is 12 diagonals or a length of 12 × 2√2 =24√2 centimeters.

Note that the ball moves only on the diagonals of the 15 non-overlapping squares. Thus we must find the path that traverses the most diagonals.

From point 1, the path traverses 6 diagonals before ending up at D.

From point 2, the path traverses 12 diagonals before ending up at A (incidentally, it passes through point 5 in the specified direction so we do not need to check point 5).

From point 3, the path traverses 3 diagonals before ending up at B.

From point 4, the path traverses 9 diagonals before ending up at C.

From point 6, the path traverses 10 diagonals before ending up at D.

Thus the maximum is 12 diagonals, or a length of 12 × 2√2 =24√2 centimeters.

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Answer:

Slope: 1

Y-Intercept: -2

y=x-2

Graph it by plotting a point at (0,-2) and then by going up one to the right. One up and then one to the right and repeat twice. Now you can graph this easily. Hope this helped!!

Step-by-step explanation:

The measure of the angle m∠C = m∠H is equal to 35°.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Triangle ABC is similar to triangle FGH.

Therefore, m∠A = m∠F = 63° and m∠B = m∠G = 82°.

We know the sum of the measure of all the interior angles in a triangle is 180°.

Therefore, m∠C = m∠H = 180° - 63° - 82° = 35°.

Congruency can be applied to any two dimensional figure, For example,

Two circles are congruent if they have the same radius length.

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Yes You can buy 24 apples for $0.125 per pound. This price will not available except in festival or discounts sale.

what are ounces ?

An ounce is a unit of weight or mass commonly used in the United States and other countries. It is usually abbreviated as oz. One ounce is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are often used to measure small quantities of food or ingredients in recipes, as well as for measuring the weight of small objects.

According to the question:

To determine whether you can buy 24 apples for $9, we need to find the cost per apple.

If 24 apples cost $9, then the cost per apple is:

$9 / 24 apples = $0.375 per apple

Since each apple weighs about 5 ounces, there are about 3 apples per pound:

16 ounces / 5 ounces per apple ≈ 3.2 apples per pound

Therefore, the cost per pound of apples is:

$0.375 per apple / 3 apples per pound = $0.125 per pound

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The total amount that Jimmy has saved is $420.

Ratio shows the relationship between two or more numbers. It is the  number of times that one value is contained within other value.

Total amount saved = (sum of ratios x total value of R5 saved) / ratio that represents R5 saved

Sum of ratios = 2 + 5 + 7 = 14

Total value of R5 saved = 12 x 5 = R60

= (14 x 60) / 2 = $420

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Answer:

Step-by-step explanation:

Let's start by translating the given sentence into an equation:

2x + 29 ≥ -25

To solve for x, we can isolate x on one side of the inequality:

2x ≥ -25 - 29

2x ≥ -54

x ≥ -27

Therefore, the solution to the inequality is x ≥ -27.

The equation of parabola in vertex form is [tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]

To write the equation of a parabola in vertex form, we use the following formula:

[tex]$$(x-h)^2=4p(y-k)$$[/tex]

where (h,k) is the vertex and p is the distance between the focus and the vertex.

Given that the focus of the parabola is at (3, 2.5), we can determine that the vertex of the parabola is also at (3, 2.5). Let's substitute these values into the formula:

[tex]$$(x-3)^2=4p(y-2.5)$$[/tex]

To find the value of p, we need to use the fact that the distance between the focus and vertex is p. The distance formula is:

[tex]$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$[/tex]

Substituting the values we know:

[tex]$$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \ &= \sqrt{(3 - 3)^2 + (2.5 - 2.5)^2} \ &= 0 \end{aligned}$$[/tex]

Since d = 0, we know that p = 0 and the equation simplifies to:

[tex]$$(x-3)^2=0$$[/tex]

Expanding the left side:

[tex]$$x^2 - 6x + 9 = 0$$[/tex]

So the equation of the parabola in vertex form is:

[tex]$$\boxed{(x-3)^2=4 \cdot 0 (y-2.5)}$$[/tex]

Or

[tex]$$\boxed{x^2 - 6x + 9 = 0}$$[/tex]

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Answer:

Step-by-step explanation:

The answer is 120.3676. i assume you are converting between grams MgSO4 and mole. You can view more details on each measurement unit: molecular weight of MgSO4

The total volume of milk would be 1/2 gallons.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that,

Volume = 1/4 gallons

The number of weeks = 2

So, the total volume =

1/4 × 2 = 1/2 gallons

Hence, the total volume of milk would be 1/2 gallons

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Answer:

To convert 2 pints into milliliters, we need to use the conversion rate that 1 pint equals 473.176 milliliters.

Therefore, we can calculate that 2 pints is equal to 946.352 milliliters. Rounded to the nearest whole number, this would be 946 milliliters.

The approximate area of the remaining part of the fabric is given as 17.415 square feet

To get the solution, we have to solve for the area of the square shape and the area of the circle

The area of a square is given as A = a²

The area of a circle is given as πr²

We would have area of remaining fabric as

a² -  πr²

The square has its sides as a = 9 cm

the circle has π = 3.14

we  are to find the radius. But first we have to determine the diameter

The circle runs from one end of the square to the other end. This should be the diameter, because it is the length of the square as well

Diameter = 9 cm

radius = diameter / 2

= 9 / 2

= 4.5

When we put the values in the formula a² -  πr² we would have

9² - 3.14 * 4.5²

81 - 3.14 * 20.25

81 - 63.585

= 17.415

The area of the remaining part after the circle is cut is 17.415 square feet

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To convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6. Hence, the fraction of .1667 is 1/6.

To convert the decimal number 0.1667 to a fraction, we can write it as 1667/10000. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 167.

1667 ÷ 167 = 10

10000 ÷ 167 = 60 + 40/167

So, the fraction equivalent to 0.1667 is 1667/10000, which can be simplified to 10/60 + 40/167.

10/60 can be simplified to 1/6, so the final simplified fraction is:

0.1667 = 1/6 + 40/167

Therefore, the fraction equivalent to 0.1667 is 1/6.

Converting a decimal to a fraction involves expressing a decimal number as a ratio of two integers. To convert a decimal to a fraction, the decimal is written in the form of a fraction, with the decimal value as the numerator and a power of 10 as the denominator. The resulting fraction can be simplified by finding the greatest common factor between the numerator and denominator, and then dividing both by that factor. For example, to convert 0.1667 to a fraction, we write it as 1667/10000, and simplify it to 1/6.

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With the thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

a) 40% of the flanges exceeds 1.01 millimeters.

b) 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of flange thickness is 1 millimeters and the variance of flange thickness is 0.01 millimeters^2.

a) To determine the proportion of flanges that exceeds 1.01 millimeters, we need to find the area under the probability density function (pdf) of the thickness that is greater than 1.01 millimeters.

Let's call the random variable X representing the thickness of the flange. The pdf of X is uniform, so it has constant value over the interval [0.95, 1.05]. Therefore, the proportion of flanges that exceeds 1.01 millimeters can be found as follows:

P(X > 1.01) = (1.05 - 1.01) / (1.05 - 0.95) = (1.05 - 1.01) / 0.1 = 0.04 / 0.1 = 0.4

So, 40% of the flanges exceed 1.01 millimeters.

b) To find the thickness that is exceeded by 90% of the flanges, we need to solve for X in the following equation:

P(X > X) = 0.9

Substituting the values for the pdf, we get:

(X - 0.95) / (1.05 - 0.95) = 0.9

Solving for X, we get:

X = 0.95 + 0.9 * (1.05 - 0.95) = 0.95 + 0.9 * 0.1 = 0.95 + 0.09 = 1.04

So, 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of X can be calculated as follows:

Mean = (0.95 + 1.05) / 2 = 1

The variance of X can be calculated as follows:

Variance = (1.05 - 0.95)^2 / 12 = 0.01

So, the mean and variance of flange thickness are:

Mean = 1 millimeters

Variance = 0.01 millimeters^2

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The correct answer is a) No you cannot, because the lower boundary of the confidence interval is .131, which is less than .30, and so the true correlation could be less than .30.

Correlation analysis allows us to examine the strength, direction, and nature of the relationship between two variables, and to determine whether or not there is a statistically significant association between them.

Based on the information given, there appears to be a positive correlation between time spent exercising and test scores. This means that as the time spent exercising increases, the test scores also tend to increase. However, we cannot determine the strength or causality of this correlation without additional information or analysis. It is possible that other factors could be influencing both variables or that there could be confounding variables affecting the relationship.

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Correct question:

Assume a researcher found that the correlation between a test she had developed and exam performance was .5 in a study of 25 students. She had previously been informed that correlations under .30 are considered unacceptable. The 95% confidence interval was [0.131, 0.747]. Can you be confident that the true correlation is at least 0.30?

The Venn diagram shows that the number of students who offer accounting is 30 and offer Accounting and Economics are only 5.

It should be noted that a Venn diagram is an illustration which uses circles to show the relationship between the objects.

We are given that class of 50 students, the number of students who offer accounting is twice as the number who offer Economics 10 students offer neither of the two subjects and 5 students offer both subjects

The number of students who offer Economics are;

= 10 + 5

= 15

Since accounting is twice as the number who offer Economics.

The number of students who offer accounting are;

= 25 + 5

= 30

The number of students who offer only one subject will be as follows;

= 25 + 10

= 35

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The distance between the points -3,-8, and 6,-8 is 3 units.

The length of the line segment bridging two points on a plane is known as the distance between the points.

Look at the provided points.

Calculate the distance between the points using the given formula.

Given points are -3,-8 and 6,-8

Given two points lies the parallel to X-axis

The distance between the two points is

A (-3,-8) and B(6,-8) =  X₂ - X₁

6 - 3  = 3 units.

Therefore, the distance between two points -3,-8 and 6,-8 is 3 units.

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Answer:W+6

Step-by-step explanation:

The sorting algorithms that are not comparison based are counting sort, bucket sort, and radix sort.

Counting sort works by counting the number of occurrences of each element in an array and then using this information to determine the position of each element in the sorted array.

Bucket sort works by dividing the array into a number of smaller arrays, called buckets, and then sorting each of these smaller arrays separately.

Radix sort works by sorting the elements of an array based on the individual digits of each element, starting with the least significant digit and working up to the most significant digit.

These algorithms do not rely on comparisons between elements, which is why they are not considered comparison based.

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The solution for r in the equation is 428.43

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

100000 = 8000(1+ r/12000)^72

Divide through by 8000

So, we have

12.5 = (1+ r/12000)^72

Take the 72th root of both sides

So, we have

1 + r/12000 = 1.03570211065

Subtract 1

r/12000 = 0.03570211065

So, we have

r = 428.4253278

Hence, the value of r is 428.43

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Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

Answer: Jacinda has 4 cookies left over.

Step-by-step explanation:

If Jacinda divides 19 cookies into 5 equal piles using as many cookies as possible, but has some left over, we can use integer division to determine how many cookies are in each pile. Integer division divides two numbers and rounds down to the nearest integer. In this case, the number of cookies in each pile is:

19 cookies ÷ 5 piles = 3 with a remainder of 4

Answer: 4

Step-by-step explanation:

Based on the given conditions, formulate: 19-5

Calculate the sum or difference: 14

The value of DAC in the figure would be 47 degrees.

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

The angles EAD, DAC and CAB are all on a straight line which means they add up to 180 degrees.

Angle CAB is in a triangle which means all the angles add up to 180 degrees and the value of this angle is:

= 180 - 80 - 57 = 43 degrees

The value of DAC would then be;

= 180 - EAD - CAB

Substitute the known values in the above equation, so, we have the following representation

= 180 - 90 - 43

= 90 - 43  = 47 degrees

Hence, the angle is 47 degrees

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