21
There are 80 students in a class.
Each student walks to school or cycles to school or gets the bus to school.
There are 44 girls in the class.
17 of the girls walk to school.
14 of the boys cycle to school.
12 of the 20 students who get the bus to school are boys.
Find the number of these students who walk to school.

The scale factor after dilation is 2 in.

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.

Here in the given figure QRST , the length of QT = 2in.

Now after dilation the figure Q'R'S'T' , the length of Q'T'= 4in

Then scale factor is,

=> Q'T'/QT = 4/2 = 2in.

Hence the scale factor after dilation is 2 in.

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Using the standard normal distribution table, we can find that the probability of a student typing more than 50 words per minute is 0.2033 or 20.33%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

It seems like you have given me information about the distribution of typing speed for Mes Fuller's 120 keyboarding students. The distribution is normally distributed with a mean (μ) of 45 words per minute and a standard deviation (σ) of 6 words per minute.

A normal distribution is a continuous probability distribution that is symmetric around the mean value. The mean value is the center of the distribution, and the standard deviation measures the amount of variability or spread of the data.

With this information, we can calculate probabilities for different values of typing speed using the standard normal distribution table or a statistical software program.

For example, if we want to know the probability of a student typing more than 50 words per minute, we can calculate the z-score as follows:

z = (x - μ) / σ = (50 - 45) / 6 = 0.83

therefore, the standard normal distribution table, we can find that the probability of a student typing more than 50 words per minute is 0.2033 or 20.33%.

Similarly, we can calculate probabilities for other values of typing speed using the same method.

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Answer:

Question #3 *I need help*

Step-by-step explanation:

Students need to be in the top 2% in order to be eligible for the national typing competition, if Carla can type 56 wpm, is she eligible?

Answer:

Step-by-step explanation:

(a)   [tex]5\frac{1}{8} =\frac{41}{8}[/tex]

      So we get

          [tex]5\frac{1}{8}\% =\frac{41}{8}\div100[/tex]

                   [tex]= \frac{41}{8} \times \frac{1}{100}[/tex]

                   [tex]=\frac{41}{800}[/tex]  

(b)    [tex]91.4=91\frac{4}{10} =91\frac{2}{5} =\frac{457}{5}[/tex]  

       So we get

               [tex]91.4\%=\frac{457}{5} \div100[/tex]

                          [tex]=\frac{457}{5} \times \frac{1}{100}[/tex]

                          [tex]=\frac{457}{500}[/tex]                

The two random variables from this list that are continuous are: a) The average temperature in NYC during May. b) The compensation of a Top 500 CEO.

A continuous random variable is a variable whose values are any member of an uncountable set or any uncountable combination of such members. A continuous random variable has an infinite number of possible values, which are represented by an interval (a,b), where a and b can be any value on the real number line. A continuous random variable cannot take on individual values because there are an infinite number of values between any two points.For example, temperature, length, and weight are examples of continuous random variables.

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Answer:

6 hours - 5 = 2, so 15 = 6 , as its constant

The length L of the curve is approximately 185.35 units.

To find the length of the curve, we first need to find the derivative of the given function:

f'(y) = 1 - (25/32) y^(-2/3)

Next, we need to find the integrand by squaring the derivative and adding 1:

g(y) = √(1 + [1 - (25/32) y^(-2/3)]^2)

Then, we can use this integrand to set up the integral:

L = ∫[0,243] g(y) dy

L= 185.35 units

Using a calculator or software, we can evaluate this integral to find the length L of the curve, which is approximately 185.35 units. Hence the length of curve is  185.35 units

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Answer:

1.11111111

Step-by-step explanation:

Answer: 1/0.9

Step-by-step explanation:

Simply put 1 as the numerator of the given number to get the reciprocal.

Answer:

look in explanation

Step-by-step explanation:

In this equation, y can only be equal to 5 if x is labeled as 3.

Why? Because when you input the numbers into the equation, y=5 and x=3 then it will make sense.  5=3+2  If you put y as any other number the equation will not be true.

The complete table of trigonometric functions:

Row 1: θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

Row 2: θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

Row 3: θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

In this problem we must complete a table with three angles, measured in radians, and three kinds of trigonometric functions (two fundamental function and a derivate function). The procedure to complete the table is shown below:

Now we proceed to complete the table of trigonometric functions:

θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

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Answer:

18.5

Step-by-step explanation:

25-6.5=18.5

x=18.5

Therefore, the probability that the student plays neither tennis nor netball is 1/5 = 0.2 or 20%.

There are 40 students in a class. 19 students play tennis, 20 students play netball, and 8 students play neither of these sports.

A student is chosen randomly from the class, and we need to determine the probability that the student: Plays tennis If a student is randomly chosen from the class, the probability that the student plays tennis is: Probability of playing tennis= (Number of students playing tennis) /

(Total number of students in the class) Probability of playing tennis= 19 / 40Plays netball if  a student is randomly chosen from the class, the probability that the student plays netball is: Probability of playing netball= (Number of students playing netball) / (Total number of students in the class)Probability of playing netball= 20 / 40 = 1/2Plays neither of these sports a student is randomly chosen from the class, the probability that the student plays neither tennis nor netball is

:Probability of playing neither tennis nor netball= (Number of students who do not play either of the two sports) / (Total number of students in the class)Probability of playing neither tennis nor netball= 8 / 40Probability that the student plays tennis and netball

Probability of playing tennis and netball = (Number of students playing both tennis and netball) / (Total number of students in the class)We are given that none of the students play both tennis and netball, so the probability of playing both tennis and netball is 0.

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Answer:

Step-by-step explanation:

t=0

If you replace t with zero -9=-9(0+1)

0+1=1 and -9(1)=-9

so t=0

The ordered pair that describes the location of V" is (5, -2).

In mathematics, reflection is a transformation in which a geometric figure is mirrored or flipped over a line, plane or point. It is a type of transformation that changes the position of an object without changing its shape or size. Reflection can occur in any number of dimensions, including two-dimensional space (plane), three-dimensional space (solid objects), or even higher dimensions.

The reflection of point V over the x-axis will change the sign of the y-coordinate, so point V' will be located at (-5, -2).

The reflection of point V' over the y-axis will change the sign of the x-coordinate, so point V" will be located at (5, -2).

Therefore, the ordered pair that describes the location of V" is (5, -2).

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The complete question is:

Point V is located at (-5,2) on the coordinate plane. Point V is reflected

over the x-axis to create point V'. Point V' is then reflected over the y-axis

to create point V". What ordered pair describes the location of V"?*

If Person A and Person B are playing archery together. the probability that A gets more targets than B is 0.5, or 50%.

The number of targets hit by A and B follows a binomial distribution with parameters n = 201 and n = 200, respectively, and p = 0.5.

To find the probability that A gets more targets than B, we need to find the probability that A hits more than 100 targets (since 100 is the average number of targets hit by each player). We can use the normal approximation to the binomial distribution to do this.

The mean of the difference in the number of targets hit by A and B is:

E(A - B) = E(A) - E(B) = np - np = 0

The variance of the difference in the number of targets hit by A and B is:

Var(A - B) = Var(A) + Var(B) = np(1-p) + np(1-p) = 100

The standard deviation of the difference is then:

SD(A - B) = sqrt(Var(A - B)) = 10

Using the normal distribution approximation, we can standardize the difference in number of targets:

Z = (X - E(A - B)) / SD(A - B)

where X is the number of targets that A hits.

P(A hits more targets than B) = P(A - B > 0)

= P(Z > (0 - 0) / 10)

= P(Z > 0)

= 0.5

Therefore, the probability that A gets more targets than B is 0.5, or 50%. This means that there is an equal chance that A will hit more targets than B as there is that B will hit more targets than A.

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(2x10^n)+(4.02x10^5), what is n?

Step-by-step explanation:

To determine the value of n, we need to rewrite the expression as a number in scientific notation, in the form a x 10^n, where 1 ≤ a < 10.

We can start by factoring out 10^n from both terms:

(2 x 10^n) + (4.02 x 10^5) = 10^n (2 + 4.02 x 10^-5)

Now we need to divide both sides of the equation by (2 + 4.02 x 10^-5):

(2 x 10^n) + (4.02 x 10^5) / (2 + 4.02 x 10^-5) = 10^n

We can simplify the expression on the left side by multiplying the numerator and denominator by 10^5:

(2 x 10^n x 10^5 + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n

Simplifying the numerator:

(2 x 10^(n+5) + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n

Now we can cross-multiply to eliminate the fraction:

(2 x 10^(n+5) + 4.02 x 10^5) = 10^n (2 x 10^5 + 4.02)

Expanding both sides:

2 x 10^(n+5) + 4.02 x 10^5 = 2 x 10^(n+5) + 4.02 x 10^n

Subtracting 2 x 10^(n+5) from both sides:

4.02 x 10^5 = 4.02 x 10^n

Dividing both sides by 4.02:

10^5 = 10^n

Therefore, n = 5.

Answer:

The image of triangle ABC after the translation 5 units to the right and 5 units down is A'B'C' with vertices at (3, -1), (-2, -6), and (2, -8).

Step-by-step explanation:

To prove that triangle ABC is isosceles, we need to show that at least two of its sides have the same length. We can use the distance formula to calculate the length of each side:

AB = sqrt[(−7−(−2))^2 + (−1−4)^2] = sqrt[25 + 25] = 5sqrt(2)

AC = sqrt[(−3−(−2))^2 + (−3−4)^2] = sqrt[1 + 49] = sqrt(50)

BC = sqrt[(−7−(−3))^2 + (−1−(−3))^2] = sqrt[16 + 4] = 2sqrt(10)

Since AB and AC have different lengths, triangle ABC cannot be equilateral. However, if we compare AB and BC, we see that they have the same length, 5sqrt(2). Therefore, triangle ABC is isosceles.

To find the coordinates of A'B'C' after the translation 5 units to the right and 5 units down, we simply add 5 to the x-coordinates and subtract 5 from the y-coordinates of each vertex. Thus:

A' = (-2+5, 4-5) = (3, -1)

B' = (-7+5, -1-5) = (-2, -6)

C' = (-3+5, -3-5) = (2, -8)

Therefore, the image of triangle ABC after the translation 5 units to the right and 5 units down is A'B'C' with vertices at (3, -1), (-2, -6), and (2, -8).

Using the equation, the center is (-2,5) and the radius is 12 units.

Use the formula (x-a) ² + (y-b) ² = r² to determine a circle's equation when you are aware of its radius and center.

Here, stands for the circle's center, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.

The given question is:

(x - 2) ² + (y + 5) ² = 144.

Now this can be written as:

(x - 2) ² + (y + 5) ² = 12²

The circle of center (x₁, y₁) and radius r is written as:

(x - x₁) ² + (y - y₁) ² = r²

Hence, the center is (-2,5) and the radius is 12 units.

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The author develops the connection between Mourne Textiles and the history and culture of Ireland by mentioning that local Irish weavers taught Gerd Hay-Edie how to weave and make the designs. Additionally, the author highlights the significance of the landscape and natural resources in Northern Ireland to the design and production of the textiles.

Hence, the correct answer is option B.

In the article, the author describes how Gerd Hay-Edie learned traditional weaving techniques from local weavers in Northern Ireland, and how she incorporated these techniques into her designs. The author also emphasizes the importance of the Mourne Mountains and the surrounding natural resources in shaping the textiles produced by the company.

Furthermore, the author highlights how the designs and techniques used by Mourne Textiles are rooted in Irish tradition and history. Through these details and examples, the author establishes a strong connection between Mourne Textiles and the history and culture of Ireland.

Hence, the correct answer is option B.

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--The question is incomplete, answering to the question below

"How does the author develop the connection between Mourne Textiles and the history and culture of Ireland?

A. by explaining major historical events in Ireland and how Gerd Hay-Edie took part in them

B. by mentioning that local Irish weavers taught Gerd Hay-Edie how to weave and make the designs

C. by describing Gerd Hay-Edie’s career and how events in Ireland impacted the company

D. by comparing the Norwegian fjords to the Irish landscape and Gerd Hay-Edie’s fashion sense to the typical Irish style" --

Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

The functions from the graph are x = -10, y = x + 5 and y = x² + 6x + 10, while the identities are listed below

Constant function

This is a function that does not change its value irrespective of the input and/or the output

From the graph, we have the vertical line

x = -10

This is a constant function with the following identities

Domain: x = -10

Range: 0 ≤ y ≤ 12.25

Linear function

This is a function that changes constantly with x and y

From the graph, we have the points

(-4, 1) and (-2, 3)

The equation is calculated as

y = mx + c

So, we have

-4m + c = 1

-2m + c = 3

This gives

2m = 2

m = 1

So, we have

-2(1) + c = 3

-2 + c = 3

c = 5

This means that the function is y = x + 5 with the following identities

Domain: -4 ≤ x ≤ -2

Range: 1 ≤ y ≤ 3

Quadratic function

This function is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

So, we have

y = a(x + 3)² + 1

Also, we have

2 = a(-2 + 3)² + 1

a + 1 = 2

a = 1

So, we have

y = (x + 3)² + 1

y = x² + 6x + 10

This means that the function is y = x² + 6x + 10 with the following identities

Domain: -4 ≤ x ≤ -2

Range: 1 ≤ y ≤ 2

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Check the picture below.

Given the quadratic equation the condition that must apply to the constants a and c is c < 9a.

A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.

1) Remember, a quadratic function can have either a maximum or minimum value and that the value of the function at the vertex (i.e., the maximum or minimum point) is given by [tex]-b/2a[/tex].

In this case, the coefficient of x is 6, so the x-coordinate of the vertex is [tex]-6/2a = -3/a[/tex].

Since the function is always negative, the vertex must be a maximum, and the value of the function at the vertex must be negative.

Therefore, this gives us:

[tex]ax^2 + 6x + c < 0[/tex] for all x

The x-coordinate of the vertex is[tex]-3/a[/tex], so the value of the function at the vertex is:

[tex]a(-3/a)^2 + 6(-3/a) + c = 9a/a - 18/a + c = c - 9a/a[/tex]

Since the value of the function at the vertex must be negative, we thus have:

[tex]c - 9a/a < 0[/tex]

Simplifying further, we get:

[tex]c < 9a[/tex]

Therefore, we can conclude that the condition for the constants a and c to satisfy the given inequality is [tex]c < 9a.[/tex]

ii) We can choose [tex]a = 1[/tex] and [tex]c = -8[/tex].

Then, the function [tex]ax^2 + 6x + c = x^2 + 6x - 8[/tex] has a maximum value at [tex]x = -3[/tex],

Therefore, this example shows that [tex]a = 1[/tex] and [tex]c = -8[/tex]  satisfies the conditions found in part (i).

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Answer:

Step-by-step explanation:

function

slope

x value

y value

Answer:

Step-by-step explanation:

1

Answer:

180°

Step-by-step explanation:

I think they are all correct except for the last one

I think the last one should be b

The baseball game lasted 2 hours and 10 minutes.

To calculate how long the baseball game lasted, we must begin by taking the start time of 7:05. We can convert this time to a numerical value by adding 7 hours and 5 minutes, which equals 705 minutes. Next, we must do the same with the end time of 9:15. Adding 9 hours and 15 minutes gives us a total of 915 minutes. Subtracting the start time from the end time gives us a difference of 210 minutes. Finally, we must convert the minutes back to hours and minutes, which gives us 2 hours and 10 minutes. Therefore, the baseball game lasted 2 hours and 10 minutes.

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