10. The temperature underwent a change of -18 degrees Fahrenheit between noon and midnight. It changed by the same amount each hour. Write and solve an equation to find h, the hourly change in temperature.

The correct option is E, another rule that takes a line to a perpendicular line (x,y)→(4y,-4x) A B C D OE.

(x,y)→(y,-x)

E:(x,y)→(4y,-4x)→4(y,-x)

So E = (x,y)→(4y,-4x) A B C D OE.

Perpendicular lines play an important role in geometry and trigonometry. They are used to construct right angles, which are essential in measuring angles and finding distances between points. In construction, perpendicular lines are often used to ensure accuracy when building structures, such as walls or flooring.

Perpendicular lines also have real-world applications in navigation, surveying, and astronomy. For instance, in navigation, perpendicular lines are used to calculate a ship's course and location. In surveying, perpendicular lines are used to create precise measurements of land plots, while in astronomy, they are used to calculate distances between celestial objects.The slope of a perpendicular line is the negative reciprocal of the slope of the other line.

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Complete Question: -

The rule (x,y)→(y,-x) takes a line to a perpendicular line. Select all the rules that take a line to a perpendicular line.

A. (x,y)→(2y,-x)

B. (x,y)→(-y,-x)

C. (x,y)→(-y,-x)

D. (x,y)→(0.5y,-2x)

E.  (x,y)→(4y,-4x) A B C D OE

Let's first understand what's relative here, it refers to Point of reference , the point, in respect to which other's position are to be considered, which here is O, the Origin with coordinates (0,0) as we are talking about two-dimensional reference frame. What position vector means? Say, we have the point of Reference X, and we've the position vector of Y with respect to X, then it can be written as [tex]{\overrightarrow{XY}}[/tex]. Now, using this simple rule we can have,

Now, let's calculate [tex]{\overrightarrow{AC}}[/tex] firstly;

[tex]{:\implies \overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}}[/tex]

[tex]{:\implies \overrightarrow{AC}=8\hat{i}+(\lambda -7)\hat{j}}[/tex]

Now, here [tex]{AC}[/tex] just means the the magnitude of the vector [tex{\overrightarow{AC}}[/tex], and we're aware that magnitude of a vector [tex]{\overrightarrow{X}=x\hat{i}+y\hat{j}}[/tex] is given by, [tex]{X=\sqrt{x^{2}+y^{2}}}[/tex], so according to question;

[tex]{:\implies \sqrt{64+(\lambda -7)^{2}}=17}[/tex]

Squaring both sides;

[tex]{:\implies (\lambda -7)^{2}=289-64=225}[/tex]

[tex]{:\implies \lambda -7=\pm 15}[/tex]

[tex]{:\implies \boxed{\underline{\bf{\lambda =22,\:or\:-8}}}}[/tex]

The obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

What are the different quadrants of trigonometric identities?

The first quadrant has angles between 0 and 90 degrees. The second quadrant has angles between 90 and 180 degrees. The third quadrant contains angles between 180 and 270 degrees. The fourth quadrant contains angles between 270 and 360 degrees. All six trigonometric functions have positive values in the first quadrant.  The only positive values in the second quadrant are sine and cosecant. The only positive values are tangents and cotangents in the third quadrant. The only positive values in the fourth quadrant are cosine and secant.

We are asked to find an obtuse angle θ such that 0 ≤ θ ≤ 2π and has the same sine as -275°.

The value of sin(-275°) = 0.996

Since the value of sin(-275°) is positive, the angle θ should be in the first or second quadrant, because the sine of angles in the first and second quadrants is positive.

But the θ should be an obtuse angle.

So θ should be in the second quadrant.

sin(-275) = sin(360-275) = sin 85° = 0.996

sin(180 - 85) = sin(95)  = 0.996

Therefore the obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

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Kendra hits the target more often than Dalisay.

What is the hit rate?

Hit rate is a measure of performance that calculates the proportion of successful hits or positive outcomes in a given situation, usually expressed as a percentage.

To compare Kendra and Dalisay's performance in hitting the target, we need to determine the hit rate for each archer.

Kendra hits the target 3 times for every 5 misses. The hit rate for Kendra can be calculated as:

hit rate = 3 / (3 + 5) = 3/8

Dalisay hits the target 5 times for every 7 misses. The hit rate for Dalisay can be calculated as:

hit rate = 5 / (5 + 7) = 5/12

Comparing the hit rates, we see that Kendra has a higher hit rate than Dalisay.

Therefore, Kendra hits the target more often than Dalisay.

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Answer:

x = -0.01835

Step-by-step explanation:

1) Isolate the term with the variable, 910x, by subtracting 45 on both sides:

2) Divide both sides by 910 to solve for x

Answer:

B.

The equation you can use to find the area of a sphere when given radius is:

V = 4/3πr 3

Fitting 5 into the equation:

V = 4/3π5 3

V = 523.598776

Therefore, B is the correct answer.

We can see that the triangle is equilateral, thus, the value of x is 13.

We can see that it is a right triangle, and we know the value of one of the catheti and one of the angles.

Remember that the sum of the interior angles must be equal to 180°.

So if we have a right angle and a 45° angle, then the measure of the remaining angle is:

a = 180° - 90° - 45° = 45°

So we have an equilateral triangle, thus, the measure of x must be 13 units.

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Answer: 13

Step-by-step explanation: Just took the test

Let's call the number of hours of labor required to replace the water pump as "x".

The total cost of the water pump and labor was $668, so we can write an equation:

$490 + $89x = $668

Now we can solve for x by subtracting $490 from both sides:

$89x = $668 - $490

$89x = $178

And finally, dividing both sides by $89:

x = $178 / $89

x = 2 hours

So, 2 hours of labor were required to replace the water pump.

Answer: To find out how many students attend chess club on Wednesdays, we need to calculate 3% of the 800 students at Steven's high school. To do this, we multiply the number of students by 3% (which is equivalent to 0.03):

800 x 0.03 = 24

So, 24 students attend chess club on Wednesdays.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

16 students are taking Physics and 12 are taking calculus

Step-by-step explanation:

40×40%=16 students taking Physics

40×30%=12 students taking calculus

16+12=28

40-28=12 students are taking both

The shape of the distribution is normal

The probability is 0.7764

What is Standard Deviation?

The standard deviation is a measure of the spread or dispersion of a set of data around its mean. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. It is used to quantify the degree of variability or diversity in the data.

(a)

The distribution of heights of young men follows a normal distribution with a mean of 69.3 inches and a standard deviation of 2.8 inches. The distribution of heights of young women also follows a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches.

The difference between the height of a randomly selected young man (m) and a randomly selected young woman (w) follows a normal distribution with a mean of 69.3 - 64.5 = 4.8 inches (the difference in the means) and a standard deviation of √(2.8² + 2.5²) = 3.67 inches (the square root of the sum of the variances).

The shape of the distribution of the difference between the heights of a randomly selected young man and a randomly selected young woman is also normal, since the original distributions are normal. The centre of the distribution is 4.8 inches, and the spread is 3.67 inches.

(b)

We need to find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman, or in other words, we need to find P(m - w > 2).

Using the formula for the difference of two normal distributions, we have:

z = (2 - 4.8) / 3.67 = -0.76

We need to find the probability that a standard normal variable Z is greater than -0.76. Using a standard normal table or calculator, we find that P(Z > -0.76) = 0.7764.

Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is approximately 0.7764.

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The total time that tammy sent in total playing games is; 4.5 hours

The parameters given for Tammy in playing the game are;

Number of games played = 12 games

Time spent per game = ³/₈ hours

Thus;

Total time she spent playing game will be gotten by multiplying the time per game by number of games played to get;

Total time spent = ³/₈ * 12

= 9/2

= 4.5 hours

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Complete question is;

A game lasts 3/8 hours. Tammy played 12 of these games. For how long did she play in total? Write your answer in simplest form.

The length of the candle that has been burning for the total of 240 minutes would be = 9 inches.

The rate at which a candle burns = 2 in/ 2 hours

That is,

2 in = 2 hour; 2 inches = 120 minutes

X in = 240 minutes

Make X the subject of formula;

X = 2×240/120

X= 480/120

X = 4+5

X = 9 inches

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Answer:

10.00 & 0.05

Step-by-step explanation:

[tex]10.00 - 0.05 = 9.95[/tex]

The amount of money as change is $ 0.05 and the amount of money given is $ 10.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the cost of the item = $ 9.95

The amount of money given = $ 10.00

So , the amount of money received as change = amount of money given - cost of the item

On simplifying the equation , we get

The amount of money received as change = 10.00 - 9.95

The amount of money received as change = $ 0.05

Hence , the amount of change is $ 0.05

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The solutions are given in the ordered pairs.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

We have to choose a value for x to find the corresponding y value to make the equation true.

1)6x=7y

To find x:

divide both sides by 6.

We get, [tex]\frac{6x}{6} =\frac{7y}{6}[/tex]⇒[tex]x=\frac{7y}{6}[/tex]

To find y:

divide both sides by 7.

We get, [tex]\frac{6x}{7} =\frac{7y}{7}[/tex] ⇒ [tex]y=\frac{6x}{7}[/tex]

Therefore solution for the given equation is [tex](\frac{7y}{6} ,\frac{6x}{7})[/tex]

2) 5x+3y=9

To find x:

subtract 3y from both sides,

⇒ 5x=9-3y then divide 5 on both sides,

⇒ [tex]\frac{5x}{5}=\frac{9-3y}{5}[/tex]⇒ [tex]x= \frac{9-3y}{5}[/tex]

To find y:

subtract 5x from both sides.

⇒3y=9-5x, then divide by 3 on both sides we get,

[tex]\frac{3y}{3}=\frac{9-5x}{3}[/tex]⇒[tex]y=\frac{-5x}{3}+3[/tex]

The solution for this equation is [tex](\frac{9-3y}{5},\frac{-5x}{3}+3)[/tex]

3) y+5-(1/3)x =7

To find x:

subtract y-5 from both sides we get,

[tex]-\frac{1}{3}x=2-y[/tex] then multiply both sides by -3,

[tex]\frac{\frac{-1}{3}x }{\frac{-1}{3}}=\frac{2-y}{\frac{-1}{3}}[/tex]⇒x=3y-6

To find y:

Subtract 5 from both sides.[tex]y-\frac{1}{3}x = 7-5[/tex] and add [tex]\frac{1}{3} x[/tex]

we get, [tex]y=2+\frac{1}{3}x[/tex]

The solution for this equation is ([tex](3y-6, 2+\frac{1}{3})[/tex]

Hence, the solutions are given in the ordered pairs.

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Kareem's probability of attending either State or Northern is 0.88, meaning there is an 88% chance that Kareem will attend one of the universities.

Probability is a measure of the likelihood of an event occurring.

Kareem's case, the probability of attending State College is 55%, which means there is a 55% chance that Kareem will attend State College. The probability of attending Northern University is 33%, which means there is a 33% chance that Kareem will attend Northern University.

To determine the probability of attending either State or Northern, we add the individual probabilities of each event. Thus, the probability of attending either State or Northern is:

P(State) + P(Northern) = 0.55 + 0.33 = 0.88

The probability of attending either State or Northern is 0.88, which means there is an 88% chance that Kareem will attend one of these universities. It is important to note that the sum of all probabilities of all possible outcomes is always equal to 1.

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Answer:

285.50

Step-by-step explanation:

The total for the ratio of 1:4 is 5.  The ratio to the woman to the total is

4:5 or

[tex]\frac{4}{5}[/tex] = [tex]\frac{x}{2855}[/tex]  Cross multiply and solve for x

4(2855) = 5x

11420 = 5x  Divide both sides by 5

2284 =x

The woman's portion of the total is 2284.

The woman takes the 2284 and divides it in a ratio of 5:1:2.  The total is 8.

The daughter will receive the ratio of 1:8 of the total.

[tex]\frac{1}{8}[/tex] = [tex]\frac{x}{2284}[/tex]  cross multiply and solve for x

8x = 2284    Divide both sides by 8

x = 285.50

The daughter's portion is 285.50

Answer:

240/2, 360/3

Step-by-step explanation:

240/2 and 360/3 both involve division and both of their answers are equal to 120, assuming these count as number sentences.

The length of the other sides of ΔABC are AB =12 cm and BC = 16 cm.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, ΔABC ∼ΔA'B'C' and AC=20 cm A'C'=15 cm B'C'=12 cm and A'B'=9 cm.

Here, AB/A'B' = BC/B'C' = AC/A'C'

AB/9 = BC/12 = 20/15

AB/9 = BC/12 = 4/3

Now, AB/9 = 4/3

AB =12 cm

BC/12 = 4/3

BC = 16 cm

Therefore, the length of AB =12 cm and BC = 16 cm.

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Answer: Let the width of the rectangle be w and the length be l. We are given that the area of the rectangle is 45 cm^2, so we can write the equation:

w * l = 45

To find the lengths of the sides, we need to solve for w and l. We can divide both sides of the equation by any non-zero number to find an equivalent expression. For example, we can divide both sides by 9:

(w/9) * (l/9) = 45/9

Simplifying, we get:

w/9 * l/9 = 5

So, w/9 = 5/l and w = 5l/9.

Substituting the expression for w into the original equation, we get:

(5l/9) * l = 45

Expanding and simplifying, we get:

5l^2/9 = 45

Multiplying both sides by 9, we get:

5l^2 = 405

Dividing both sides by 5, we get:

l^2 = 81

Taking the square root of both sides, we get:

l = 9

So, the length of the rectangle is 9 cm. To find the width, we can substitute the value of l back into the expression we derived earlier:

w = 5l/9

w = 5 * 9 / 9

w = 5

So, the width of the rectangle is 5 cm.

The lengths of the sides of the rectangle, both exactly and approximately, are 9 cm and 5 cm.

Step-by-step explanation:

Answer:

6g+3g=11+3-5

combine like terms

9g=11+3-5

calculate the sum of difference

9g=9

Step-by-step explanation:

reduce the greatest common factor on both sides

of the equation

g=1

Answer:

The figure is made up of a rectangle and two triangles. The dimensions of the rectangle are 10 cm by 5 cm, so the area of the rectangle is 10 * 5 = 50 cm^2.

Each of the two triangles has a base of 4 cm and a height of 3 cm, so the area of each triangle is (1/2) * 4 * 3 = 6 cm^2. The total area of the two triangles is 2 * 6 = 12 cm^2.

The total area of the figure is the sum of the areas of the rectangle and the triangles: 50 + 12 = 62 cm^2.

Step-by-step explanation:

Answer:

37.437

Step-by-step explanation:

Answer:

37.437

Hope it helps

(a). Name of internet service provider is categorical variable because it cannot be quantified or measured. It can be divided into different categories according to the service they provide.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(b). Time in hours, spent surfing the internet per week is continuous numerical variable because time can be measured over an infinite number of real values within a given interval.

A variable is said to be continuous if it can assume an infinite number of real values within a given interval.

Measurement scale used for determination is ratio scale.

(c). Whether the individual uses a mobile phone to connect to the internet is categorical variable because the answer can only be yes or no and it cannot be measured numerically.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(d). Number of online purchases made in a month is discrete numerical variable because it is a value that arises through a counting process.

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation.

Measurement scale used for determination is interval scale.

(e). Where the individual uses social networks to find sought -after information is categorical variable because the answer can only be yes or no and it cannot be measured numerically. It can be either he/she uses or he/she do not.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

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The values of x, y and z are given as follows:

Similar polygons are polygons that share these two features presented as follows:

There are two similar trapezoids for this problem, hence the proportional relationship for the side lengths is given as follows:

x/15 = 10/24 = y/16 = z/12.

Applying cross multiplication, the value of x is given as follows:

24x = 15 x 10

x = 15 x 10/24

x = 6.25.

The value of y is given as follows:

y = 16 x 10/24

y = 6.67.

The value of z is given as follows:

z = 12 x 10/24

z = 5.

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The total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman is 314 ways.

We can approach this problem using the principle of inclusion-exclusion.

First, let's find the total number of ways to choose a president, vice-president, and treasurer from a group of 8 people without any restrictions. We can do this by using the permutation formula:

8P₃ = 8 x 7 x 6 = 336

Next, let's find the number of ways to choose the three positions where only freshmen are chosen. There are 4 freshmen to choose from, so we can select the president, vice-president, and treasurer in 4P₃  = 4 x 3 x 2 = 24 ways.

Similarly, there are 4 sophomores to choose from, so we can select the three positions where only sophomores are chosen in 4P₃  = 4 x 3 x 2 = 24 ways.

However, we have overcounted the cases where only freshmen or only sophomores are chosen, since the problem statement requires that at least one freshman and at least one sophomore hold at least one of the three positions. Therefore, we need to subtract the number of cases where only freshmen or only sophomores are chosen.

There is only one way to select the president, vice-president, and treasurer from the 4 freshmen, and likewise, there is only one way to select them from the 4 sophomores. Therefore, there are a total of 2 ways to select the three positions where only one class is represented.

Finally, we need to add back the cases where no freshman or no sophomore is chosen. This occurs only if all three positions are filled by juniors or seniors. There are 4 juniors and seniors to choose from, so we can select the three positions in 4P₃  = 4 x 3 x 2 = 24 ways.

Therefore, the total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions is:

336 - 24 - 24 + 2 + 24 = 314 ways.

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[tex] \frac{9}{3} = \frac{x}{2} \\ [/tex]

Cross multiply...

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3} \\ [/tex]

x = 6

Answer:

it's 6. 9 is divided by 3 and the answer is 3 .so 3=x÷2. and multiplie 2 in both side.so the answer is 6.

After dilation, the coordinates of image will be (-1,3).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

Now,

As given dilation factor= -3

that means the image will be small and x coordinate will displace from its current value - 3 that is -1.

and y coordinate will be same that is 3

Hence,

          After dilation, the coordinates of image will be (-1,3).

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