EX 2: The diameter is 24 cm Find the length of CD

a) When x = 4, the function y = 4 has the greater numeric value.

b) The two equations have the same value for x = 6.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From graph, when x = 0, y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by two, y increases by one, hence the slope m is given as follows:

m = 1/2

m = 0.5.

Meaning that the function is given as follows:

y = 0.5x + 1.

When x = 4, the value is given as follows:

y = 0.5(4) + 1

y = 3 < 4.

The two functions will have the same value when:

0.5x + 1 = 4

0.5x = 3

x = 3/0.5

x = 6.

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The lateral surface area of the cylinder is given by the equation

S = 1,583.36 cm²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the surface area of the cylinder be represented as S

Now , the diameter of the cylinder d = 18 cm

So , the radius of the cylinder r = 18/2 = 9 cm

The height of the cylinder h = 28 cm

And , the lateral surface area of cylinder = 2πrh

Substituting the values in the equation , we get

The lateral surface area of cylinder = 2 ( 3.14 ) ( 9 ) ( 28 )

On simplifying the equation , we get

The lateral surface area of cylinder = 504π cm²

The lateral surface area of cylinder = 1,583.36 cm²

Hence , the lateral surface area is 1,583.36 cm²

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The study is a randomized controlled trial (RCT) study.

In an RCT study, participants are randomly assigned to either the treatment group or the control group. The treatment group receives the intervention (in this case, one of the two surgery procedures) being studied, while the control group does not receive the intervention.

The participants are then followed to observe the outcome of interest (in this case, the hours to recovery after surgery).

The goal of an RCT study is to determine if the intervention has an effect on the outcome. By randomly assigning participants to the treatment and control groups, any observed differences in the outcome between the two groups can be attributed to the intervention.

This helps to control for other factors that may influence the outcome and reduces the risk of bias in the results.

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The length of the smallest part of the line segment is 12 cm.

The line segment of length 96 cm is divided into 3 parts with the ratio of 2:9:5. The given ratio is a part-to-whole ratio. We can find the lengths of the parts by applying the formula:

Part = Whole × Ratio

Part 1 = 96 cm × (2/16)

= 12 cm

Part 2 = 96 cm × (9/16)

= 54 cm

Part 3 = 96 cm × (5/16)

= 30 cm

Therefore, the length of the smallest part of the line segment is 12 cm.

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Answer:A quadrilateral is a polygon having four sides, four angles, and four vertices. The word 'quadrilateral' is derived from the Latin words 'quadri,' which means four, and 'latus', which means side. The above image is an example of a quadrilateral. AB, BC, CD, and DA are the four sides of the quadrilateral ABCD.

hope this helps alot<3

Check the picture below.

The period of the function graphed is 4

The period of a trigonometric function is the length of one complete cycle of the function.

For the common trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant), the period is 2π for sine and cosine and π for the others.

In the graph the value in the domain for the function to make a complete oscillation is 4 hence the period is 4

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Answer:

x= 67

y=40

z=40

Step-by-step explanation:

 A=C        B=D

67=X    Y&?= Z&73

73+ x aka(67) = 140

180-140= y = 40

Answer: We can use the equation to find the number of dimes in Kendall's pocket:

25g + 10d = 150

25 * 4 + 10d = 150

100 + 10d = 150

10d = 50

d = 5

So Kendall has 5 dimes in her pocket.

Step-by-step explanation:

The number of grapes for 14 strawberries is 10

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

She adds 5 grapes for every 2 strawberries.

So, we have the ratio to be

Grapes : Strawberries = 5 : 2

Multiply the ratio by 7

So, we have the following representation

Grapes : Strawberries = 10 : 14

This means that 10 grapes are required for 14 strawberries

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Answer:

389 hours and 23 minutes

Step-by-step explanation:

16x24=384

384+=5=389

and 23 minutes

The experimental probability of picking a spade is 0.15 (first option)

Probability is used to determine how likely it is that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability of picking a spade = number of times a spade was drawn / number of times the experiment was repeated

3/20 = 0.15

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The system of equations is,

y = 2/3(x) and y = (-3/4)x -5.

The correct option is A.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Two lines are intersecting each other.

Line 1 passes through two points (0, 0) and (3, 2).

The equation of the line is,

y = 2/3(x)

And line 2 passes through (0, -5) and (4, -2).

The equation of the line is,

y = (-3/4)x -5.

Therefore, the equations are y = 2/3(x) and y = (-3/4)x -5.

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a) If two points on a line are A(-5,7) and B(-2,1), the rise -6, the run is of 3, and then the slope is of -2.

b) If two points on a line are A(10,-3) and B(12,9), the rise 12, the run is of 2, and then the slope is of 6.

c) If two points on a line are A(4,6) and B(8,-8), the rise -14, the run is of 4, and then the slope is of -3.5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

As the slope represents the rate of change of the output relative to the input, it is calculated as the change in the output y divided by the change in the input x, that is, the rise divided by the run.

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The value of x rounded to the nearest tenth is 10.2 units, this is found using trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

The triangle is a right-angles triangle and the given angle is 22 degrees.

Taking the cosine function, we have:

cos A = adjacent side/ hypotenuse

cos (22) = x / 11

0.927 = x/11

x = 10.2

Hence, the value of x rounded to the nearest tenth is 10.2 units, this is found using trigonometric functions.

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0.25 is greater than 0.225, the 16 ounce box of cereal has a lower price per ounce than the 20 ounce box of cereal.

The 16 ounce box of cereal has a lower price per ounce than the 20 ounce box of cereal. To calculate the price per ounce of each box of cereal, we can divide the total cost of the box by the total number of ounces in that box. For the 16 ounce box of cereal, the equation would be 4.00/16 = 0.25 per ounce. For the 20 ounce box of cereal, the equation would be 4.50/20 = 0.225 per ounce. Because 0.25 is greater than 0.225, the 16 ounce box of cereal has a lower price per ounce than the 20 ounce box of cereal.

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The wind speed and plane speed is 11 and 96  mph.

It is required to find the speed of the plane in still air and the speed of the wind.

What is arithmetic?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Let plane speed be "p".

Let wind speed be "w".

According to given question we have,

p + w = 107 mph

p - w =  85 mph

By the method of elimination we get,

2p = 192

p = 96 mph

The plane speed is 96 mph.

Solve for "w":

p + w = 107

96 + w = 107

w = 11 mph

The wind speed is  11 mph.

Therefore, the wind speed and plane speed is 11 and 96  mph.

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The troop leader can use the two categories of preference (hiking or swimming) as the row and column headings of the table.

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The troop leader can utilize the two preference categories (hiking or swimming) as the table's row and column headings.

The number of members who prefer each activity can be recorded in the cells of the table to show the distribution of preferences within each troop and the comparison between the two troops.

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The probability that the spinner will stop at an even value is: P(even) = 1/3.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. This is the fundamental theory of probability, which is applied to the probability distribution.

The probability that the spinner will stop at an even value is:

P(even) = number of even numbers on spinner / total number on spinner

P(even) = 1 / 3

Hence, the probability that the spinner will stop at an even value is: P(even) = 1/3.

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Answer:

A. 11.025

Step-by-step explanation:

1 Kilogram equals exactly 2.20462 pounds.

2.20462 multiplied by 5 is 11.025

Answer:

Y- intercept= (0, -1)

Slope = 2/3

Step-by-step explanation:

Finding the Y-Intercept is pretty much finding the Y value when X is 0

Looking at this table, when x = 0, y is -1. Which means your y intercept is (0, -1)

To find slope, you take two points (x,y) and apply it to the slope formula. We'll do the bottom 4 since those are all nice looking numbers

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

plugging it in...

[tex]slope = \frac{3 - 1}{6 - 3} [/tex]

3-1 = 2 and 6-3 = 3

Keep that in fraction form

[tex]slope = \frac{2}{3} [/tex]

The probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

Denote S= Event that a purchase bought a basic camera, then P(S)=0.32

Denote D= Event that a purchase bought a deluxe camera, then

S and D are mutually exclusive.

P(D)=1-P(S)=0.68

P(W/S)=0.4

P(W/D)=4.9

We need to calculate the probability that a randomly selected purchaser who bought an extended warranty has a basic model. By notations, this is equivalent to finding P(S/W).

P(S/W)=P(W/S)*P(S)/P(W)

Since S and D are disjoint and P(S)+P(D)=1,

P(W)=P(W∩S)+P(W∩D)

P(W)=[0.4*0.32]+[4.9*0.68]

=3.61

Hence, our required probability is: P(S/W)=P(W/S)*P(S)/P(W)

[tex]=\frac{0.4*0.32}{3.61}\\=0.0354[/tex]

Hence, the probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

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The probability of having a blue in the spin is given as; 17/200.

Probability can be calculated as the ratio of the number of favorable outcomes to the number of possible outcomes in a given scenario. It is usually expressed as a decimal or a fraction between 0 and 1.

We know that in this case we are going to look at the table to see the number of times that we land a blue.

If the total number of the outcomes is 200 and the number of the expected outcomes is 17. We would have the probability as P(blue) = 17/200.

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The measure of the arc length of the sector will be 103.62 centimeters.

Let r be the radius of the sector and θ be the angle subtends by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The central angle is 11π / 6 radian and the radius is 18 cm. Then the measure of the arc length is given as,

Arc = {(11π / 6)/2π} 2π (18)

Arc = 0.9167 x 2 x 3.14 x 18

Arc = 103.62 cm

The measure of the arc length of the sector will be 103.62 centimeters.

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Based on the data provided, the probability that one student studied for exactly one hour is 0.22.

When it comes to calculating the probability, we need to identify the frequency of a specific outcome (the probability a student studied for one hour) and compare it to the total outcome (total of students) as follows:

Total of students who studied for one hour: 8

Total of students: 1+8+2+5+9+7+3 = 35

Total of students who studied for one hour / total students

8/35 = 0.228 which can be rounded as 0.23 or 23% if expressed as a percentage.

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The probability that the three friends are seated next to each other is 1/420

The total number of ways to seat the 7 people is 7! To find the number of ways to seat the three friends next to each other, we need to consider the number of ways to seat the other 4 people around them. So the number of favorable outcomes is 4!

The probability that the three friends are next to each other is then given by the ratio of the number of favorable outcomes to the total number of outcomes: (4!)/(7!) = 4!/5040 = 1/420.

So the probability that the three friends are seated next to each other is 1/420.

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Step-by-step explanation:

[tex]x {}^{2} - 14x = - 49[/tex]

[tex]x {}^{2} - 14x - ( - 49) = 0[/tex]

Identify a, b and c in your equation and then find two numbers that when multiplied equal c, and when added equal b.

[tex]x {}^{2} - 14x + 49 = 0[/tex]

Write your equation in factored form.

[tex](x - 7) {}^{2} = 0[/tex]

Here the two factors are the same, so there will be only one solution.

[tex]x - 7 = 0[/tex]

Rearrange and isolate the variable to find each solution.

[tex]x = 7[/tex]

A, B, and D are some advantages of online surveys.

The advantages of online surveys are:

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m is usually slope

lets analyze this problem

its a linear line, meaning a straight line

i see that y, the output, increases by 4 every time x goes up 2

slope, or m, is equal to the rise/run

rise is 4, run is 2

4/2 = 2

m = 2

this means that for every x, y goes up 2

or, for every 2 x, y goes up 4

hope this helps :)

Answer: i believe its -6, 3

(if im wrong pls inform me :3