The local library is undergoing a renovation to make the ramp safe for hand-powered wheelchairs. To do so, they will need to make the angle of elevation no greater than $4. 8\degree$. If the ramp remains $1. 5$ feet high, what is the minimum length the ramp will need to be so that it is safe for hand-powered wheelchairs?

Answer:

1 : 2

Step-by-step explanation:

First, find the GCF of 6 and 12, which is 6.

So divide both sides by 6:

6 / 6, 12 / 6

= 1 : 2

Answer:

121.2 calories.

Step-by-step explanation:

Weight of one packet of crisps = 864/36

= 24 grams.

So, by proportion, the number of calories in one packet

= 24 * 505/100

= 121.2 calories.

Varying 'a' in the equation og graph [tex]y = a(x-2)^2 + 5[/tex] changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).

A graph is a visual representation of data or information that displays a relationship or pattern between two or more variables.

The graph of [tex]y = a(x-2)^2 + 5[/tex] is a quadratic function that has been shifted 2 units to the right and 5 units up from the standard form of [tex]y = x^2.[/tex] The variable 'a' represents the vertical stretch or compression factor of the parabola.

In summary, varying 'a' in the equation [tex]y = a(x-2)^2 + 5[/tex] changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).

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Outside of this range, the relationship's range may differ, and outliers or other significant points may also have an impact.

A variable in mathematics is a symbol or letter that designates a number or value that is subject to change or variation. In order to solve problems and generate expressions and equations that represent the relationships between different quantities, variables are employed. X and Y are variables in the equation y = 3x + 2, for instance. The variable value of x determines the value of y. In order to express unknown numbers that we want to solve for, we can also utilize variables.

given

The scatterplot's depicted relationship is a positive linear relationship. These are some possible descriptions of the relationship's scope:

As the independent variable (x-axis) rises, so too does the dependent variable (y-axis).

There is not much scatter around the trendline, suggesting that the link is reasonably strong. From the lowest value on the y-axis to the greatest value on the y-axis, the relationship's range is defined.

The scatterplot only depicts the relationship between the two variables within the observed range of the data, it is crucial to remember this. Outside of this range, the relationship's range may differ, and outliers or other significant points may also have an impact.

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Answer: 300/π°, or ~95.49°

Step-by-step explanation:

In order to find the central angle of the arc, we first find the ratio of the arc length to the circumference of the circle, since it is proportional to the ratio of the central angle to the total inside angle, 360°.

Finding the circumference
Circumference is equal to 2πr, and r (radius) in this case is 3, so

C=2π*3, or 6π

The ratio of the arc length to circumference is then 5/6π

Finding the angle

Since the ratio of lengths and ratio of angles are proportional, we can set up this equation:

5/6π=x/360

solving for x gets us:

x=300/π°, or ~95.49°

Answer: 23/42

Step-by-step explanation:  

your messageHELP URGENT !!!A bag contains 16 red marbles, 7 yellow marbles, and 19 green marbles. What is the probability that a marble drawnfrom the bag is red or yellow? Write your answer as a simplifed fraction.Sure, I can help you with that! The probability of drawing a red marble is 16/42 (since there are 16 red marbles out of a total of 42 marbles), and the probability of drawing a yellow marble is 7/42. To find the probability of drawing a red or yellow marble, we simply add those two probabilities: 16/42 + 7/42 = 23/42 So the probability of drawing a red or yellow marble is 23/42, which is already in simplified fraction form.

In conclusion, the chance of having HIV, assuming a positive test result, is 0.4%. It is important to remember that this number could vary depending on the accuracy and false positive rate of the test, as well as the number of people infected with HIV in the given area.

Assuming you tested positive for HIV, the chance of having the virus is higher than 2.5%, since the test has a false positive rate of 2.5%.

Out of the 10,000 people, 250 are likely to test positive, of which only one person actually has the virus. This means that the actual chance of having HIV, assuming a positive test result, is 1 in 250 or 0.4%.

It is important to note that this calculation only applies to the specific case of the 10,000 people in question, and the false positive rate of the test. Different tests have different levels of accuracy and false positive rate, which could alter the result. Furthermore, the number of people infected with HIV may differ significantly in different areas, which could also change the probability.

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18:8, 27:12 and 45:20 are ratios are equivalent to 9:4.

A ratio is a mathematical comparison between two or more quantities that indicates how many times one quantity is contained within another. Ratios are expressed in the form of a fraction, with the first quantity being the numerator and the second quantity being the denominator.

three ratios that are equivalent to 9:4

All of these ratios are equivalent to 9:4, because they represent the same ratio of 9 parts to 4 parts.

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Answer:

<ICJ

Step-by-step explanation:

Vertical angles are congruent.

Answer: <ICJ

Answer: ∠JCI

Step-by-step explanation:

   ∠JCI and ∠FCE are vertical angles. We know that vertical angles are congruent, so the answer to this question is;

            ∠JCI

The Scatterplot has no correlation.

What is scatterplot?

Data visualization that depicts the relationship between two numerical variables is known as a scatterplot. The values for the two variables are used to depict each member of the dataset as a point with ( x , y ) coordinates that correspond to those values.

We know that A positive correlation between the variables is present when the y variable tends to grow as the x variable increases and a negative correlation is when x variables increase but y variable decreases.

No correlation means there is no clear relationship between two variables.

In the given scatter plot represent the relationship between month and cost.

Here for 6 months cost is $0.5 , for 7 months cost is $1 and for 5 months  cost is also $1. Then there is no clear relationship between month and cost.

Hence the scatterplot has no correlation.

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Answer:

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

perimeter = 2(length + width)

In this case, the length is 14.3 yards and the width is 12 yards. Substituting these values into the formula, we get:

perimeter = 2(14.3 + 12)

perimeter = 2(26.3)

perimeter = 52.6 yards

Therefore, the perimeter of the rectangle is 52.6 yards.

The area of a rectangle is given by the formula:

area = length x width

Substituting the length and width values, we get:

area = 14.3 x 12

area = 171.6 square yards

Therefore, the area of the rectangle is 171.6 square yards.

The best graphical representation for the given data would be a histogram. A histogram is a graph that displays the distribution of continuous numerical data. It consists of a series of bars, where each bar represents a range of values and the height of the bar represents the frequency or proportion of data points that fall within that range. Since the variable of interest in this case is the number of hours slept per night, which is a continuous numerical variable, a histogram would be an appropriate way to display the distribution of the data. A stem-and-leaf plot is another way to display numerical data, but it is better suited for smaller data sets. Circle graphs and bar graphs are used to display categorical data.

Step-by-step explanation:

We can prove that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1, using mathematical induction.

Base case: n = 1 When n = 1, we have X^1 + Y^1 = X + Y, which is clearly divisible by X + Y.

Inductive step: Assume that X^k + Y^k is divisible by X + Y for some odd natural number k ≥ 1. We will show that X^(k+2) + Y^(k+2) is divisible by X + Y.

We can expand X^(k+2) + Y^(k+2) using the binomial theorem: X^(k+2) + Y^(k+2) = (X^2)(X^k) + (Y^2)(Y^k)

We can factor out X + Y from the first term and Y + X from the second term, since X + Y = Y + X: X^(k+2) + Y^(k+2) = (X + Y)(X^k + XY^k) + (X + Y)(Y^k + XY^k)

We can then simplify this expression by factoring out XY^k from the first term and X^kY from the second term: X^(k+2) + Y^(k+2) = (X + Y)XY^k + (X + Y)X^kY X^(k+2) + Y^(k+2) = (X + Y)XY^k + (X + Y)X^kY

We can then factor out (X + Y) from this expression to get: X^(k+2) + Y^(k+2) = (X + Y)(XY^k + X^kY)

Since X + Y is a common factor of X^(k+2) + Y^(k+2), we have shown that X^(k+2) + Y^(k+2) is divisible by X + Y.

Therefore, by mathematical induction, we have proven that X^n + Y^n is divisible by X + Y for any odd natural number n, where n ≥ 1.

The relative frequency of a class is computed by dividing the frequency of the class by the total number of observations in the data set. This statement (C) is true.

What is the relative frequency?

The relative frequency is a statistical term that represents the percentage of times a certain event occurs in an experiment or study. It is calculated by dividing the number of times an event occurred by the total number of trials in the experiment or study.

The class width is the difference between the upper limit and lower limit of a class. Class width is used to construct frequency histograms, cumulative frequency curves, and frequency polygons.The frequency of a class is the number of times the data falls within a certain class.

So, to compute the relative frequency of a class, divide the frequency of the class by the total number of observations in the data set. Therefore, option c, "dividing the frequency of the class by the total number of observations in the data set," is correct.

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Answer:

100

Step-by-step explanation:

[tex]\frac{40}{6} = \frac{x}{15}[/tex]

x = (40 x 15) / 6

x = 100

The equation of the line perpendicular to y = 1/3 x + 5 and passing through (2,6) is y = -3x + 12, which is option 3.

To find the equation of a line perpendicular to y = 1/3 x + 5 and passing through the point (2,6), we first need to determine the slope of the original line and the slope of y = 1/3 x + 5 is 1/3.

To find the slope of a line perpendicular to this, we can use the fact that the product of the slopes of two perpendicular lines is -1 and therefore, the slope of the line we want is the negative reciprocal of 1/3, which is -3.

Now that we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line passing through (2,6) with slope -3:

y - 6 = -3(x - 2)

y = -3x + 12

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Answer:

X= -2x - 1,2x + 3

Step-by-step explanation:

1)Break down the problem into these 2 equations.

(2x-3) - X+ 1 = 4x − 1

-(-(2x-3) - X + 1) = 4x − 1

2)Solve the 1st equation: (2x-3) - X + 1 = 4x − 1.

X=-2x 1

3)Solve the 2nd equation: -(-(2x-3) − X + 1) = 4x – 1.

X = 2x + 3

4)Collect all solutions.

X= -2x - 1,2x + 3

h(2) = 3(2) = 6

The output is six

The final equation of the line is   y = (-2/3)x - 3   in the coordinate system.

what is coordinate system?

A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in space. In mathematics, the most common coordinate system is the Cartesian coordinate system

what is equation ?

In mathematics, an equation is a statement that shows the equality between two expressions. It contains an equals sign (=) between the two expressions that are being compared. Equations can be used to describe relationships between variables, to solve problems, or to represent real-world situations.

In the given question,

To draw the line going through (-6,1) with a slope of -2/3, we can follow these steps:

Plot the point (-6,1) on a coordinate system. This will be one point on the line.

From that point, use the slope to find another point on the line. A slope of -2/3 means that for every 3 units to the right we move, we must move 2 units down. So starting from (-6,1), we can move 3 units to the right and 2 units down to get to the point (-3,-1). This is another point on the line.

Draw a straight line through the two points to represent the line going through (-6,1) with a slope of -2/3.

To write the equation of the line, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1,y1) is one point on the line, m is the slope, and (x,y) are the coordinates of any other point on the line. Let's choose (-6,1) as our point:

y - 1 = (-2/3)(x - (-6))

Simplifying, we get:

y - 1 = (-2/3)x - 4

Adding 1 to both sides, we get the final equation of the line:

y = (-2/3)x - 3

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Answer:

WE CAN WRITE IN STANDARD FORM IN THE FOLLOWING WAY..

LMX0

We can conclude that the linear relationship between x and y in this table is described by the phrase "y is 3 more than x."

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

The given table shows two variables, x, and y, with corresponding values. A linear relationship between two variables means that a change in one variable causes a proportional change in the other variable.

If we look at the table, we can see that as the value of x increases by 1 unit from 3 to 4, the value of y also increases by 3 units from 9 to 12. Similarly, as the value of x increases by 1 unit from 4 to 5, the value of y increases by 3 units from 12 to 15.

This means that for every 1 unit increase in x, the value of y increases by a constant amount of 3 units.

In other words, the slope of the line connecting these points is constant and equal to 3.

Therefore, we can conclude that the linear relationship between x and y in this table is described by the phrase "y is 3 more than x."

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It will take approximately 1.386*t days until only 1/2 ounces of element X remain.

If the half-life of element X is t days, it means that after every t days the amount of element X will be reduced by half.

Initially, we have a 1-ounce sample of element X.

After t days, the amount of element X remaining will be 1/2 ounces.

After 2t days, the amount of element X remaining will be (1/2)*(1/2) = 1/4 ounces.

Similarly, after 3t days, the amount of element X remaining will be (1/2)(1/2)(1/2) = 1/8 ounces.

After n*t days, the amount of element X remaining will be (1/2)^n ounces.

We want to find the value of n such that (1/2)^n = 1/2^(n/2) ounces.

Taking the logarithm of both sides, we get:

n*log(1/2) = (n/2)*log(1/2)

Simplifying, we get:

n = 2*log(2) = 1.386

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Answer and Step-by-step explanation:

You can start off your answer by comparing each gallon/mile of each car given. Compare the values that both cars have in common.

For Car M, the car drives a distance of 50.4 miles and used 2 gallons of gasoline.

For Car P, the car drives a distance of approximately 65 miles and used 2 gallons of gasoline.

For Car M, the car drives a distance of 80.5 miles and used 3 gallons of gasoline.

For Car P, the car drives a distance of approximately 90 miles and used 3 gallons of gasoline.

For Car M, the car drives a distance of 137.5 miles and used 5 gallons of gasoline.

For Car P, the car drives a distance of approximately 160 miles and used 5 gallons of gasoline.

After looking at the given information, we can conclude that for every gallon of gasoline used, Car P drives a farther distance than Car M.

We can see this at the points 2, 3, and 5 gallons, where Car M drives 50.4 miles, 80.5 miles, and 137.5 miles (respectively), and Car P drives 65 miles, 90 miles, and 160 miles (respectively).

Have a good day!

The correct option is A.

y  ≥ -3

The range is defined as the set of possible outputs, so just look at the vertical axis, you can see it goes from x = -3 up, then the range is just the set of all values larger than -3

it is written as:

y  ≥ -3

The correct option is a-.

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Answer: 43

43 x 0.7 = 30.1

Answer:

70 % is salty water and 30% IS DRINKING WATER in which 2.1% comes from glaciers

The measure of the angle is 81 degrees, and the measure of its supplementary angle is 99 degrees.

Let x be the measure of the angle in question, and let y be the measure of its supplementary angle.

By definition, supplementary angles add up to 180 degrees, so we have:

x + y = 180

We also know from the problem statement that:

x = y - 18

We can substitute the second equation into the first equation to eliminate y, giving:

(y - 18) + y = 180

Simplifying this equation, we get:

2y - 18 = 180

Adding 18 to both sides, we get:

2y = 198

Dividing both sides by 2, we get:

y = 99

Finally, we can use the equation x = y - 18 to find the measure of the angle in question:

x = 99 - 18 = 81

Therefore, the measure of the angle is 81 degrees, and the measure of its supplementary angle is 99 degrees.

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Answer:

A) Red

Step-by-step explanation:

We can find the probability of the spinner landing on each color by dividing the number of sections for that color by the total number of sections.

Probability of landing on red: 3/6 = 1/2

Probability of landing on yellow: 1/6

Probability of landing on blue: 1/6

Probability of landing on purple: 1/6

The spinner is most likely to land on red because it has the highest probability, 1/2 or 50%. Therefore, the answer is A. Red.

A, red

It would frequently land on 3 because 3 takes up the bigger portion of the spinner

A larger sample size will result in a more reliable estimate of the population mean, lowering the variability and resulting in a higher F-ratio, which will result in the null hypothesis being rejected. As a result, both options A and B are correct.

Here we want to find,

the likelihood of rejecting the null hypothesis using anova is increased by which.

To increase the likelihood of rejecting the null hypothesis using ANOVA, a decrease in SSWITHIN and an increase in sample sizes are needed.

In statistics, analysis of variance (ANOVA) is a technique for comparing the means of two or more samples. ANOVA is an extension of the t-test and z-test methods, which can be used to compare only two means.

ANOVA compares the variation within the groups to the variation between the groups to see whether or not there is a statistically significant difference between them.

The null hypothesis ([tex]H_0[/tex]) in ANOVA is that the means of all groups are equal, while the alternative hypothesis (Ha) is that at least one group's mean is different from the others.

In ANOVA, a low value of SSWITHIN is desirable because it reflects that the data points are clustered around their respective means.

As a result, ANOVA will result in a higher F-ratio, which means that the null hypothesis will be rejected.

So, both a and b options are correct.

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The system of inequalities that matches the given word problem is:

5x + 2y <= 80

x >= 8

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Let's break down the problem and identify the key information:

The budget for food is 80 dollars

Little Cesar's pizzas cost 5 dollars each

McDonald's McChicken's cost 2 dollars each

At least 8 Little Cesar's pizzas are needed to feed everyone that wants pizza

Let x represent the number of pizzas bought and y represent the number of McChicken's bought. The total cost of pizzas and McChicken's should be less than or equal to 80 dollars, which gives us the first inequality:

5x + 2y <= 80

Additionally, we know that at least 8 pizzas should be bought, which gives us the second inequality:

x >= 8

Therefore, the system of inequalities that matches the word problem is:

5x + 2y <= 80

x >= 8

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