4.
What is the constant of proportionality? What does it represent?

The scatter plot for the randomly selects 12 students is illustrated below.

The term called scatter plot in math is defined as a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

Here we have know that the statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade.

Here we know that the number of samples is 12.

And here we have each student's total is recorded along with their final grade.

Then the scatter plot for the following table of data is illustrated on the diagram.

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The required inequality to show how many refrigerators and how many pianos the truck could carry is  300x + 425y ≤ 7300.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have,

A truck that can carry no more than 7300 lb is being used to transport refrigerators and upright pianos.

Let x be the number of refrigerators in the truck and y be the number of pianos in the truck.

Then

300x + 425y = 7300

At x = 11 and y = 9

300(11) + 425(9)

= 7125 ib

So, the truck will not overload.

Inequality will we

300x + 425y ≤ 7300

Thus, required inequality is 300x + 425y ≤ 7300.

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By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given Equation,

y = 5x and y = 45 - 10x

So,

use the slope form is

y= mx+b , where m is slope and b is the y-intercept.

find the valued of m an b using the form y = mx+b

m = 10 and b=0

The slope of line is the value of m and y-intercept the value of b

slope = 10

y-intercept = (0,0)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.

create a table for x and y values.

x    y

0    0

1      10

and soon

Similarly for y = 45-10x

x    y

0   45

1     35

2    25

and soon

And Hence plot the points in the graph.

Therefore, By plotting the given points (0,0) , (1,10 ) for y=5x and the points for y=45-10x are (0,45) , (1,35) and (2,25) we get the required graph.

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A varied group of volunteers is frequently better able to function as a team since having a variety of viewpoints and personalities helps facilitate collaboration.

Diversity in volunteering refers to both the individuals participating and the opportunities offered. Regardless of ethnicity, gender, religion, sexual orientation, or other characteristics, volunteering should be a process that welcomes participation from people with a variety of backgrounds and talents.

People can learn from one another as a result of diversity, which introduces new ideas and experiences. Better problem-solving results from incorporating many ideas and perspectives. Working in diverse teams fosters innovation and encourages dialogue. Our culture benefits from variety as well.

Any employee, regardless of gender, race, age, ethnicity, physical ability, sexual orientation, religion, or other characteristic, has the same rights and opportunities in a diverse workplace.

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The principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width.

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). Double integrals are the integrals of a function of two variables over an area in R2 (the real-number plane).

The double integral of a positive function with two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function with one variable represents the area of the region between the graph of the function and the x-axis.

A multiple integral will produce hypervolumes of multidimensional data if there are more variables.

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the probability that at least one of the events A and B occurs is 0.72.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

The probability that event A occurs is 0.3 and the probability that event B does not occur is 0.4. To find the probability that at least one of the events A and B occurs, which states that the probability of an event occurring is equal to 1 minus the probability of it not occurring.

We can find the probability that neither event A nor event B occurs by multiplying the probability of event A not occurring (1-0.3 = 0.7) by the probability of event B not occurring (0.4). The probability that neither event A nor event B occurs is 0.7*0.4 = 0.28.

To find the probability that at least one of the events A and B occurs, we subtract the probability that neither event occurs from 1.

P(A or B) = 1 - P(neither A nor B) = 1 - 0.28 = 0.72

So the probability that at least one of the events A and B occurs is 0.72.

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The domain and the range of the relation shown to the right are given as follows:

The graph is not a function, as a vertical line for x > -5 would cross a function in multiple points.

The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, thus the domain is of:

x >= -5.

The range of a function is the set that contains all the output values of the function, hence on the graph it is the values of y, thus the domain is of:

All real values.

As there are inputs that are mapped to multiple outputs, the graph does not represent a function.

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The scatter plot shows data points that do not follow a trend, thus it shows a: nonlinear association.

A nonlinear association is a relationship between two variables, whereby a change in one does not correspond to a change in another.

Thus, on a scatter plot showing a nonlinear association, the data points do not follow a trend line and are scattered, therefore, predictions cannot be made using the scatter plot.

Thus, the scatter plot that is given shows: nonlinear association.

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The simplified exponential expression for this problem is given as follows:

(3² x 5)³ = 3^6 x 5³.

The exponential expression for this problem is defined as follows:

(3² x 5)³.

As we have a product applied to the exponent, the exponent can be applied to each factor of the exponent, as follows:

(3²)³ x 5³.

Applying the power of power rule, we have that:

(3²)³ = 3^(2 x 3) = 3^6.

Hence the simplified exponential expression for this problem is given as follows:

(3² x 5)³ = 3^6 x 5³.

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Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

The null hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is less than or equal to 57%. The alternative hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is greater than 57%.

To test this, you would use a one-sample proportion test. The test statistic is calculated using the sample proportion (60%) and the hypothesized proportion (57%) and the sample size (800).

You would then compare the calculated test statistic to the critical value from a z-table (using a two-tailed test and a 0.02 level of significance) to determine whether or not to reject the null hypothesis.

Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

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If horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F , then normal range of body temperature of a horse as an inequality 99 ≤ T ≤ 100.8  .

If the temperature of the horse denoted by "T" , is within at least 0.9 °F of 99.9 °F , then it is considered as Normal ;

To express this as an inequality, we can use the following:

⇒ 99.9 - 0.9 ≤ T ≤ 99.9 + 0.9  ;

Simplifying further , this inequality can also be written as:

⇒ 99 ≤ T ≤ 100.8

Therefore , the normal range of body temperature of a horse is 99 ≤ T ≤ 100.8 .

The given question is incomplete , the complete question is

A horse's body temperature T is considered to be normal if it is within at least 0.9 °F of 99.9 °F. Write the normal range of body temperature of a horse as an inequality .

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The correct result for the expression 3x + 10/2 + 4(x + 3/2) is solved to be

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= 3x + 10/2 + 4(x + 3/2)

parenthesis

= 3x + 10/2 + 4x + 6

division

= 3x + 5 + 4x + 6

addition

= 3x + 4x + 6 + 5

= 7x + 11

solving for x

7x = -11

x = -11/7

x = -1 4/7

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Answer:

-5

Step-by-step explanation:

Our given equation is B-A, and we know that B = 2 and A = 7. Through what we know, we can plug in the variables' values and solve:

2 - 7 (from B-A)

= -5

Dimensions of the lower floor with the given volume of 2380 cubic feet are given by : length = 34feet, width = 7feet, and height = 10 feet.

Let us consider 'y' be the width of the barn.

Lower floor with horse stall which was extends 5 feet from both the sides.

Width after having horse stall = x - 10

Barn's length is twice the barn's width

Length = 2x

Height is 7 feet less than the barn's width = x - 7

Volume = 2380 cubic feet

⇒Length × width × height = 2380

⇒ ( 2x ) (x -10 ) (x -7 ) = 2380

⇒(2x² -20x)(x-7) = 1190

⇒2x³ -34x² +140x -2380 =0

⇒ x = 17 , √70i, -√70i

x can not be imaginary.

⇒ x = 17feet ( approximately)

Required dimensions are:

Length : 2x = 34feet

Width : x -10 = 7 feet

Height : x - 7 = 10 feet

Therefore, for the given volume the required dimensions are 34feet, 7 feet , and 10 feet.

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The roots of the quadratic function f(b) = b² - 75 are Ob=5√3 and Ob=-5√3.

A quadratic function is a polynomial function of degree two, which means it is a function that can be expressed as an equation with the second-degree degree of the highest exponent of the unknown variable. It is typically expressed as ax^2 + bx + c, where a, b and c are constants, and x is an unknown variable. Quadratic functions can be used to model many real-world situations, such as the height of a projectile in motion or the area of a circle.

The Quadratic Formula can be used to solve for the roots of a quadratic function. The Quadratic Formula states that for a quadratic equation of the form ax² + bx + c = 0, the two roots are given by x = [-b ± √(b² - 4ac)]/2a.

In this case, a = 1, b = 0, and c = -75. Therefore, the two roots are given by x = [-0 ± √(0² - 4(1)(-75)]/2(1). This simplifies to x = [0 ± √(75)]/2, or x = ±5√3/2. The two roots are thus Ob=5√3 and Ob=-5√3.

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Yes, this shape belong in a group of shapes that have more than one perpendicular sides because its sides meet at a right angle.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below.

However, it should be noted that it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).

By critically observing the geometric shape, we can reasonably infer and logically deduce that it has more than one perpendicular sides.

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If vanilla cake has a diameter of 8 inches and chocolate cake has a diameter of 10 inches , then the circumference of vanilla cake is 25.12 inches and of chocolate cake is  31.4 inches .

The Circumference(C) of the circle can be found using formula: C = 2×π×r and r is the radius of the circle.

For the Vanilla cake, the diameter is 8 inches ;

and So , radius is = 8/2 = 4 inches.

The , Circumference of vanilla cake is = 2×π×4 = 8×3.14 inches.

= 25.12 inches .

For Chocolate cake, diameter is 10 inches ;

and radius is = 10/2 = 5 inches.

So , Circumference of chocolate cake is = 2×π×5 = 10×3.14 inches.

= 31.4 inches .

Therefore , To the nearest tenth, circumference of  vanilla cake is 25.13 inches and circumference of chocolate cake is 31.42 inches.

The given question is incomplete , the complete question is

A vanilla cake has a diameter of 8 inches. A chocolate cake has a diameter of 10 inches. What is the circumference the top surfaces of the two cakes to the nearest tenth? Use 3. 14 for π .

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What Meg needs to find is the whole and what Steve needs to find is the part.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

a/b * 100

(in percentage)

Since Meg already knows the part and the percent which is 10 and 33% respectively, then it means that what she needs to find is the whole which is the total number of dogs she saw.

Steve already knows the whole which is 12 dogs and the percent which is 50% and as such what he will need to do now is to find the part that makes up the percentage part.

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The equivalent expression of 6a/(2a²) is 3/a.

And none of the given option is correct.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

6a/(2a²)

Simplifying,

6a/(2a²),

= 6a /(2a×a)

= 3/a is the equivalent expression.

Therefore, 3/a is the equivalent expression.

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The unknown side BC is 2.33 units.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

A right triangle ABC.

∠ACB is a right angle.

∠ABC is twenty-five degrees.

The side AC is unknown.

Side BC is five units.

Now,

AC = x

BC = 5 units

Tan 25° = AC/BC

Tan 25° = x/5

0.47 = x/5

x = 5 x 0.47

x = 2.33

Thus,

Side BC is 2.33 units.

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Students who are proficient in math begin by defining a problem for themselves and searching for possible solutions.

They examine assumptions, limitations, connections, and objectives. Instead of just launching into a solution attempt, they formulate hypotheses regarding the structure and significance of the solution and outline a solution pathway. In order to get insight into the problem's solution, they take into account similar difficulties, try specific situations, and take the original problem in simpler forms. They track and assess their development, and if necessary, they alter their direction. A good puzzle not only involves more of the "real world" for a child than, instance, calculating the amount of paint required.

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Answer:

Answer in image

Step-by-step explanation:

Using the y-intercept, we can graph our first point at (0,5) the y-intercept. Then from there we can use the slope to continue to plot points. (This is a negative graph by the way based off of the slope -3/4).

-Hope this helped

Answer:

212

Step-by-step explanation:

277 - 68 ( I would give further explantion but it ez )

=

209

I’m so dum sorreh

Answer:

212

Step-by-step explanation:

277 - 65 =

212

An equation in slope intercept form passing through the point (-10,1) and parallel to the line 10x+5y=15 is y=-2x+19.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = mx +c

To find the slope of a line, we find the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

Given;

Line is  passing through the point (-10,1)

Parallel to the line 10x+5y=15.

So, the slope of the line is equal to the line parallel to it

Slope of given line

5y=-10x+15

y=-10x/5+15

m=-2

Equation; 1=-2x+c

c=-2*-10-1

c=19

Therefore, the equation will be y=-2x+19.

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Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

The null hypothesis is that the proportion of Americans supporting the new health policy is less than or equal to 0.5 (p <= 0.5). The alternative hypothesis is that the proportion of Americans supporting the new health policy is greater than 0.5 (p > 0.5).

The test statistic for a one-sample proportion test is:

z = (p^ - p) / sqrt((p * (1-p)) / n)

where p^ is the sample proportion (117/200 = 0.585), p is the hypothesized proportion of Americans supporting the new health policy (0.5), and n is the sample size (200).

Sample proportion of 0.585, p-value of 0.0491, not strong evidence of more than 50% support.

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Answer:

100%

Step-by-step explanation:

The mark-up percentage is the amount by which the cost price of a product is increased to arrive at the selling price. To calculate the mark-up percentage, you can use the formula:

Mark-up percentage = (selling price - cost price) / cost price x 100

In this case:

Cost price = $450

Selling price = $900

Mark-up percentage = ($900 - $450) / $450 x 100 = 100%

So the specialty shop has a mark-up of 100% on each painting.

It means that the shop is charging twice as much as the price they procured the paintings.

The number of customers when there are 576 towers will be 12.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Based on the information, it should be noted that the number of phone is proportional to the number of customers

The constant of proportionality will be:

= 252 / 5.25

= 48

Therefore, the customers when there are 576 towers will be:

= 576 / 48

= 12

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Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.

Regular Lemonade: 9

Strawberry Lemonade: 21

Regular Lemonade:

Price of Regular Lemonade = 1.50

Total earnings from Regular Lemonade = 9 x 1.50 = 13.50

Strawberry Lemonade:

Price of Strawberry Lemonade = 2

Total earnings from Strawberry Lemonade = 45 - 13.50 = 31.50

Number of Strawberry Lemonade sold = 31.50 / 2 = 15.75

Number of Regular Lemonade sold = 15.75 - 12 = 3.75

Rounded to nearest whole number,

Number of Regular Lemonade sold = 4

Number of Strawberry Lemonade sold = 16

Kallie and Jeie sold 4 regular lemonade for $1.50 amount each, and 16 strawberry lemonade for $2 each, and made a total of $45.

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Actor Albert Brook changed his surname to Albert Einstein to avoid sharing it with another well-known Al. Option C

In 1921, Albert Einstein received the Physics Nobel Prize in honor of his contributions to theoretical physics, particularly the creation of the law of the photoelectric effect. Despite moving to Switzerland in 1895 and giving up his German nationality the following year to become a citizen of the County of Württemberg, Einstein was born within the boundaries of the German Empire.

He enrolled in the program for teaching diplomas in physics and mathematics at the Swiss Federal University of Technology School in Zürich in 1897 as a 17-year-old, and he completed it in 1900.

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For the given normally distributed data, the number of children have height greater than 116 is given by 79.

Using normally distribution we have,

Z = ( X - µ ) / σ

Here,

Mean 'µ' = 110

Standard deviation 'σ' = 6 cm

n = 500

Number of children with height greater than 116 cm

P (x > 116) = 1 - P (x < 116)

For,

P( X < 116 )  

⇒ P[ (X - μ) / σ > (116 - 110)/ 6 )

⇒ P( Z < 6 / 6 )

⇒ P( Z < 1 )

Using the value from normal distribution table we have:

P (Z< 1) = 0.8413

⇒P (x > 116) = 1 - 0.8413

⇒P (x > 116) = 0.1587

Number of children with height greater than 116 is :

= 0.1587 × 500

= 79.35

= 79 ( approximately )

Therefore, the number of children have the height greater than 116 cm is equal to 79.

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