after developing a frequency distribution for a quantitative variable, a histogram can be developed with the horizontal axis representing the values of the variable and the vertical axis representing the frequency of occurrence in each class or group.

Step-by-step explanation:

To find the points of a parabola given the quadratic equation using substitution, follow these steps:

1. Write the quadratic equation in standard form: y = ax^2 + bx + c

2. Substitute the x-coordinate of the point you want to find into the equation.

3. Solve for the y-coordinate using algebraic operations.

4. Write the point as (x, y).

For example, let's say we have the quadratic equation y = 2x^2 - 4x + 3 and we want to find the point when x = 1.

1. The equation in standard form is y = 2x^2 - 4x + 3

2. We substitute x = 1: y = 2(1)^2 - 4(1) + 3

3. We solve for y: y = 2 - 4 + 3 = 1

4. The point is (1, 1)

Repeat the process for other x-values to find more points on the parabola.

Answer:

c

Step-by-step explanation:

\(a) (1/6)^{-8}=6^8>1 \\ \\ b) (5^{-4})^{-9}=5^{36}>0 \\ \\ c) 2^{-3}=1/8<1 \\ \\ (d) \frac{6^{-4}}{6^{-5}}=6>1\)

Answer:

6 games

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

Step-by-step explanation:

5,1, 9

Answer:

5,1 and 9 like said above sksksk

Step-by-step explanation:

Answer:

Step-by-step explanation:

Shell spend at most 95 dollars on lemon cakes. However she wont have enough to buy a chocolate cake. This question needs to be more clear on what its talking about.

Answer:

Both trains would meet in 6 hours time.

Step-by-step explanation:

Train A = 50 miles per hour

Train B = 60 miles per hour

Train B leaves 1 hour later than Train A: This means Train A started the journey first.

When will the 2 trains meet?

Both trains would meet when they both cover equal distance.

Distance = Speed * Time

First Hour

Train A = 50 miles

Train B = 0 miles

Second Hour

Train A = 100 miles

Train B = 60 miles

Third Hour

Train A = 150 miles

Train B = 120 miles

Fourth Hour

Train A = 200 miles

Train B = 180 miles

Fifth Hour

Train A = 250 miles

Train B = 240 miles

Sixth Hour

Train A = 300 miles

Train B = 300 miles

Both trains would meet in 6 hours time.

Answer:

20x+10=y

Step-by-step explanation:

The expressions below best represent within the context of the word problem is x + (x - 24) = 68, Sarah's age is 46 years. Mother's age is 46 - 24 = 22. Therefore, Sarah is 46 years old, and her mother is 22 years older than her, making her mother 68 years old.

In the given word problem, we are given two pieces of information about Sarah and her mother's ages. Firstly, we know that Sarah is 24 years younger than her mother. Secondly, we know that the sum of their ages is 68. To find out Sarah's age, we need to represent it using an expression. Let's say Sarah's age is 'x'. Therefore, the expression that best represents Sarah's age is 'x'.

Now, we also need to represent Sarah's mother's age using an expression. As we know that Sarah's mother is 24 years older than her, we can subtract 24 from Sarah's age to get her mother's age. So, the expression that best represents Sarah's mother's age is 'x - 24'.

To find Sarah's age, we can use the sum of their ages, which is 68. We know that Sarah's age is 'x', and her mother's age is 'x - 24'. Therefore, we can write an equation:

x + (x - 24) = 68

Solving this equation, we get:

2x - 24 = 68

2x = 92

x = 46

Hence, Sarah is 46 years old.

In the given word problem, we are asked to find the age of Sarah, knowing that she is 24 years younger than her mother and the sum of their ages is 68. We can use the expressions x and x - 24 to represent Sarah's and her mother's ages, respectively.

Let x represent Sarah's age. Since Sarah is 24 years younger than her mother, we can represent her mother's age as x - 24. According to the problem, the sum of their ages is 68. We can now set up an equation using this information:

x (Sarah's age) + (x - 24) (Mother's age) = 68

Solve the equation to find the value of x, which represents Sarah's age:

x + x - 24 = 68
2x - 24 = 68

Now, add 24 to both sides of the equation:

2x = 92

Next, divide both sides by 2:

x = 46

So, Sarah's age is 46 years. To find her mother's age, we can substitute the value of x in the expression x - 24:

Mother's age = 46 - 24 = 22

Therefore, Sarah is 46 years old, and her mother is 22 years older than her, making her mother 68 years old.

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Answer:

$5193.77

Step-by-step explanation:

You want to figure out what x is.

Since x is the number of years after 1996, you can do 2005 - 1996 = 9 years.

Then, plug x = 9 into the equation:

y = 11,000(0.92)^9

Plug this into a calculator and you get: y = $5193.77

Step-by-step explanation:

c=32.50+4.95p

you can put numbers in this formula and count

Answer:

y = 2x + 2

Step-by-step explanation:

Find the slope of the line that passes through the points (-2, 1) and (0, 5):

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-1}{0-(-2)}=\dfrac{4}{2}=2\)

If two lines are parallel they have the same slope.  

Therefore, the slope of the other line that passes through point (1, 4) is also 2.

To find the equation of the parallel line that passes through the point (1, 4), substitute the found slope of 2 and the point (1, 4) into the point-slope formula:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-4=2(x-1)\)

\(\implies y-4=2x-2\)

\(\implies y=2x+2\)

In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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Answer:

15) 9

16) WZ

17) Congruent

The equation for a circle with a radius of r and center at (h, k) is given by \((x - h)^2 + (y - k)^2 = r^2\).The correct answer is option B.

In this equation, (x, y) represents any point on the circle's circumference. The center of the circle is denoted by (h, k), which specifies the horizontal and vertical positions of the center point.

The radius, r, represents the distance from the center to any point on the circle's circumference.

This equation is derived from the Pythagorean theorem. By considering a right triangle formed between the center of the circle, a point on the circumference, and the x or y-axis, we can determine the relationship between the coordinates (x, y), the center (h, k), and the radius r.

The lengths of the triangle's sides are (x - h) for the horizontal distance, (y - k) for the vertical distance, and r for the hypotenuse, which is the radius.

By squaring both sides of the equation, we eliminate the square root operation, resulting in the standard form of the equation for a circle.

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Answer:

\( \sin(x) = \frac{a}{b} \\ \sin(90 - x) = \sin(90) \cos(x) - \cos(90) \sin(x) \\ \sin(90 - x) = \cos(x) \\ { \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ { \cos(x) }^{2} = 1 - {( \frac{a}{b})}^{2} = \frac{ {b}^{2} - {a}^{2} }{ {b}^{2} } \\ \cos(x) = \frac{ \sqrt{ {b}^{2} - {a}^{2} } }{ \sqrt{ {b}^{2} } } \\ \boxed{ \sin(90 - x) =\cos(x) = \frac{ \sqrt{ {b}^{2} - {a}^{2} } }{ b} } \\ \)

The value equal to the given trigonometric expression sin(90°-x)​ is √(b²-a²)/b.

Given that, sinx=a/b.

We know that, sinθ=Opposite/Hypotenuse

Here, Opposite = a and Hypotenuse = b

Let the adjacent side be x.

Here, x=√(b²-a²)

Given that, sin(90°-x)​ = cosx

Now, cosx=x/b

cosx=√(b²-a²)/b

Therefore, the value equal to the given trigonometric expression sin(90°-x)​ is √(b²-a²)/b.

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Answer:

Option D: 7/3x

Step-by-step explanation:

Because this line passes through the origin (0,0), we know that there is know b-value according to the equation y = mx + b. To figure out the equation, we must first calculate the slope of the linear function.

Slope = △y/△x

△y (change in y) = -7

△x (change in x) = -3

Therefore, the slope is 7/3 and the equation is y = 7/3x.

(a) The probability that it loses money on a single policy is 0.025

(b) The probability that the company makes a profit on these policies is 3.75%

Here we have given that that an insurance company found that 2.5% of male drivers between the ages of 18 and 25 are involved in serious accidents annually.

Now for a single policy as we are given the probability of accident here is calculated as,

=> 25/1000 = 0.025

Where as suppose that the company writes 1,000 such policies to a collection of drivers, then the probability that the company makes a profit on these policies is calculated as,

=> 2000 - [65,000 x 25/1000]/100

=> [2000 - 1625]/100

=> 375/100

=> 3.75%

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Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

The equation for the plane through P0(8,1,−4) perpendicular to the following line is x + 4y + 5z - 8 = 0

The slope of the perpendicular line should be a/b, and if one line is perpendicular to this line, the product of slopes should be -1. The equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + = 0, where is a constant.

The given parameters are

x=8−t​, y=1−2t​, z=3t​,

P0(- 9, 6, - 5).

Direction vector of line is < -1, 4, 5>,

This vector is normal vector for unknown plane.

So, equation of plane: -1(x - (-9)) + 4(y - 6) + 5(z - (-5)) = 0; - x - 9 + 4y - 24 + 5z + 25 = 0;

In conclusion the equation is given as  -x + 4y + 5z - 8 = 0

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Answer:

2

Step-by-step explanation:

The parent graph is the one used to create a new function by any of the transformations (reflection about an axis, horizontal/vertical shifts, stretches/compressions).

Start with the square root function

\(f(x)=\sqrt{x}\)

Multiply by 3 (vertical stretch)

\(h(x)=3\sqrt{x}\)

Replace  x  with  x - 2 (shift to right 2 units)

\(g(x)=3\sqrt{x-2}\)

Answer:

Step-by-step explanation:

(0.061)(0.43) =0.02623

Solution:

As, two set of data are each symmetrical and do not contain outliers.

To find the center , the best way is to find Median of data set.Median of Data set is the mid value of Data that is center of Data.

As, you have to find variability , mean can't measure variability. Mean deviation would have been better option.

So, MAD=Median absolute Deviation , would be better tool to measure variability. Because it is Absolute difference between median and Each value of data set.

So, Option (C) median and MAD, would be best way to compare the two given data set.

Answer:

C = number of chickens

P = number of pigs

C + P = 13

2C + 4P = 46

Solve for C and P and get

C = 3

P = 10