Choose the correct correspondence
D <->
Options
1.R
2.K
3.O

Answer: 1 out of 19

Step-by-step explanation:

add up all of the students, wes and maureen are two people, so it's two out of thrity eight, then just simplify it and you're done <3

The probability that both Wes and Maureen will be selected is 1/360.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, Wes is in a class of 18 students and Maureen is in a class of 20 students.

Now, this is an independent event, therefore, the probability that both Wes and Maureen will be selected will be,

= (1/18)×(1/20).

= 1/360.

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Answer:

The fan should expect the red team to win 9 more games than the blue team.

Step-by-step explanation:

Using proportions, it is found that over the entire season, the fan should expect the red team to win 9 less games.

A proportion is a fraction of a total amount.

In this problem, considering the proportions of the red and of the blue teams, the number of games they are expected to win is given by:

108 - 99 = 9, hence the fan should expect the red team to win 9 less games.

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Final answer:

To find out how many cups of orange juice Harry should use with 18 cups of soda water, set up a proportion and solve for x.

Explanation:

In this problem, we know that Harry uses 2 parts orange juice to 2 parts soda water for his fruit punch. This means that for every 2 cups of orange juice, he uses 2 cups of soda water. Since the amount of soda water is directly proportional to the amount of orange juice, we can set up a proportion to find out how many cups of orange juice Harry should use with 18 cups of soda water.

2 cups orange juice / 2 cups soda water = x cups orange juice / 18 cups soda water

To solve the proportion, we can cross multiply:

2 cups orange juice * 18 cups soda water = x cups orange juice * 2 cups soda water

36 cups orange juice = 2x cups soda water

By dividing both sides of the equation by 2, we find that Harry should use 18 cups of orange juice with 18 cups of soda water.

Answer:

[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]

Step-by-step explanation:

[tex] b^y = x \Longleftrightarrow \log_b x = y [/tex]

A logarithm is an exponent. The base of the logarithm is the base of the power.

[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]

Answer:

[tex] log_3 2 7 = 3 [/tex]

Step-by-step explanation:

We are given the following equation and we are to write it in logarithmic form:

[tex] 3 ^ 3 = 27 [/tex]

We know that [tex] a ^ n = b [/tex] is written as [tex] log _ a b [/tex] when expressed in logarithmic form.

So here we have [tex] 3 ^ 3 = 27 [/tex], converting it logarithmic form we get:

[tex] log_3 2 7 = 3 [/tex]

Answer:

STEP ONE: 2x

STEP TWO: 5=X (should be the final answer)

Step-by-step explanation:

Hi Lasagna!

So basically, this is extremely simple. In order to "solve" that equation, the x has to be on one side. The easiest way to do this would be to take the 2x to the other side. If you want the 2x to go to the other side, you need to subtract it (since it is already positive, therefore it needs to cancel out). Once you do that, you must always do the same thing to the other side: subtract 2x from 3x. That should get you one x there, which you can just write as x if it's just one. Then you're all set! :D

Answer: step 1. 2 from both sides

Step-by-step explanation:

just take away the = number by doing the opposite action for ex. if it it 2x then divide both sides by 2.

Answer:

1,2,4

Step-by-step explanation:

Factors are the numbers that we can multiply together to make 4

1*4 = 4

2*2 = 4

The factors are 1,2 and 4

Answer:

Step-by-step explanation:

[tex]Factors\ of\ 4:\ 1,\ 2,\ 4\\\\4=4\cdot\boxed{1}\\4=2\cdot\boxed2\\4=1\cdot\boxed4[/tex]

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x+2}[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The point-slope form of the equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation of a line:

[tex]y-4=\dfrac{1}{4}(x-8)\to m=\dfrac{1}{4}[/tex]

and the point (0, 2) → b = 2.

Substitute:

[tex]y=\dfrac{1}{4}x+2[/tex]

Answer:

Step-by-step explanation:

DDD

Answer:

kayla will earn $26

She will earn $36.00 in 4 hours.

27 divided by 3 = 9

9 x 4 = 36

Hope this makes sense and helps.

Cameron - х years

Josephina is five years older than Cameron = х+5 years

sum of their ages is 31

х+х+5=31

2х=31-5

2х=26

х=13 Cameron

13+5=18 Josephina

The age of Josephina and Cameron is 13 and 18.

here Cameron be х years

And, Josephina is five years older than Cameron so х+5 years

Also,

The sum of their ages is 31

Now

х+х+5=31

2х=31-5

2х=26

х=13 Cameron

13+5=18 Josephina

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Answer:

A and B

Step-by-step explanation:

When rotating a point (or any shape around a certain point), none of the diameters of the shape will change. So for example, with this circle, when you rotate it around a point, the radius and circumference will not change because it has just rotated. It wont be on the x-axis though because point P is not on the x-axis an it is being rotated 180 degrees about point P. Just know that when you are rotating, nothing about the shape changes, all angles or measurements will be the same, it is just moving to a different place.

Hope this helped ^-^

Answer:

The means is 8.5 The Median is 6

Step-by-step explanation:

1) to find the mean just Simply add all the numbers together and divided by how many numbers that is giving. (Because you are simply finding the average)

9+6+5+3+28+6+4+7=68

68 divided by 8 = 8.5

2) to find the median simply organize the numbers from least to greatest Like this: (3,4,5,6,6,7,9,28) Then keep crossing out from both sides teal you find the middle Number.

If there a odd amount of number the median will be one Number, if even 2 numbers ( if 2 numbers just add them both and divide by 2)

In This Case the Median is 6,6 but Its actually 6 Why (6+6=12) and (12/2=6) so your median is 6.

Hopes This helps!

The mean of the given data 9, 6, 5, 3, 28, 6, 4, 7 is 8.5 and the median is 6.

The mean is defined as the average of all the values or the mean can be defined as the sum of all observations by the total number of observations.

[tex]Mean =\dfrac {\ Sum \ of \ all \ observation}{Total \ number \ of \ observation}[/tex]

[tex]Mean = \dfrac{9 + 6 + 5 + 3 + 28 + 6 + 4 + 7}{8}[/tex]

Mean = [tex]\dfrac{68}{8}[/tex]

Mean  = 8.5

Therefore, the mean of the data set is 8.5.

The median is defined as:

The median is the middle value when the data set is arranged in ascending or descending order.

If there are two middle values, the median is the average of those two values.

Arrange the data set in ascending order: 3, 4, 5, 6, 6, 7, 9, 28.

Here n = 8, since n is even so the median is calculated as:

Median = [tex]\dfrac{(\dfrac{n}{2}) \ th \ observation + (\dfrac{n}{2}+1) \ th \ observation}{2}[/tex]

Median =[tex]\dfrac{( 4 \ th \ observation + 5 \ th \ observation)}{2}[/tex]

The 4th observation is 6 and the 5th observation is 6.

So, this mean will be 6.

Therefore, the median of the data set is 6.

The Mean is  8.5 and the median is  6.

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X+Y = 21 ---> Y = 21-x

X-y = 5

x - (21-x) = 5

2x - 21 = 5

2x = 26

x = 13

13 and 8

The two numbers are 13 and 8.

13 + 8 = 21

The difference (13 - 8) is 5.

Answer:

Step-by-step explanation:

If Lina supposedly bought 10 rolls, we would show it by the following equation,5*10=50, and since 25 is half of 50, we would have 5 as our solution.

25/5=5

5 rolls of films is our solution

It’s the forth one

The answer is -|x-4|.

Answer:y=-|x-4|

Step-by-step explanation:

we know the graph of y=|x| touches at x=0 and opens upward towards y axis

but this graph is facing downwards therefore it should be of form

y=-|x|

but it touches the x axis at x=4

therefore the graph is represented by

y=-|x-4|

4 is added inside the mod because it intersect x axis at x=4

The graph would be y=-|x-4|+1 if it shifts 1 unit upwards.

Answer:

See below

Step-by-step explanation:

Because her answer is greater than 2 (7/3 = 2 1/3)

We are multiplying a number less than 2 (1 2/3) by a number less than 1 (5/6), so we have less than one of the number 1 2/3, which has to be less than 1 2/3.

let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{6}\times \cfrac{5}{3}\implies \cfrac{25}{18}\implies 1\frac{7}{18}[/tex]

Answer:

Start by moving the decimal place in the number until you have a coefficient between 1 and 10. The number of places to the left that you had to move the decimal point is the exponent. so for example, 0.000345 would be 3.45(10)^4

Step-by-step explanation:

Hope that helps!

Answer:

1320 ways

Step-by-step explanation:

Here we have a situation where 3 ribbons will be awarded to 3 of the 12 contestants. We can use the permutation formula, because the order of awarding the ribbons matters.

The permutation formula is:

[tex]_{n}P_{k}=\dfrac{n!}{(n-k)!}[/tex]

n = 12

k = 3

Now that we have our variables, let's plug them into the formula.

[tex]_{12}P_{3}=\dfrac{12!}{(12-3)!}[/tex]

[tex]_{12}P_{3}=\dfrac{12!}{9!}[/tex]

[tex]_{12}P_{3}=1320[/tex]

So there are 1320 different ways that the contestants will be awarded.

Answer:

B

Step-by-step explanation:

D: You will not get a cubic function. Nothing adds to give a term with x^3 in it.

C: A rational function is of the form (x^2 + 3x + 2) / (x^2). In other words it has a numerator and a denominator that are polynomials. Unless one or both started out like that, the answer is not a rations function.

A: It can't be linear. The x^2 term will carry over after addition.

The answer is B. One of the polynomials started out as a quadratic. It will remain that way.

Answer:

[tex]\$974.83[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=10\ years\\ P=\$535\\ r=0.06[/tex]  

substitute in the formula above  

[tex]A=\$535(e)^{0.06*10}=\$974.83[/tex]  

The lengths of the legs of each triangle are:

1) Leg = √19

2) Leg = √105

3) Leg = √60

How to use Pythagoras Theorem?

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

a = √(c² - b²)

1) We are given that:

Hypotenuse = 10

Opposite side = 9

Thus, using Pythagoras Theorem, we have:

Leg = √(10²- 9²)

Leg = √19

2) We are given that:

Hypotenuse = 19

Opposite side = 16

Thus, using Pythagoras Theorem, we have:

Leg = √(19²- 16²)

Leg = √105

3) We are given that:

Hypotenuse = 8

Opposite side = 2

Using Pythagoras Theorem, we have:

Leg = √(8²- 2²)

Leg = √60

Answer:

1,350 students

Step-by-step explanation:

The number of students this year is 90% of the number from last year.  Find 90% of 1500....

90% is 0.9 as a decimal,

0.9(1500) = 1,350 students

Answer: 2i50 students

Step-by-step explanation:

Do 90% of 1,500

10% = 150

150 x 9 = 1350

We need the total amount of students

So do 1350 + 1500 = 2850 students

Answer:

Option A. [tex]SQ=7\ cm[/tex]

Step-by-step explanation:

we know that

In the figure

The triangles PTQ and RTS are similar by AA Similarity Theorem

so

Remember that

If two figure are similar, then the ratio of its corresponding sides is equal

so

[tex]\frac{PT}{RT}=\frac{QT}{ST}[/tex]

we have

[tex]PT=18\ cm[/tex]

[tex]RT=RP+PT=6+18=24\ cm[/tex]

[tex]QT=21\ cm[/tex]

[tex]SQ=ST-21\ cm[/tex] ------> equation A

substitute the values and solve for ST

[tex]\frac{18}{24}=\frac{21}{ST}[/tex]

[tex]ST=21*24/18[/tex]

[tex]ST=28\ cm[/tex]

substitute the value of ST in the equation A to find the value of SQ

[tex]SQ=28-21=7\ cm[/tex]

Answer: 77cm

Step-by-step explanation:

The difference between fixed expenses and variable expenses is that fixed expenses do not change, regardless of how many items are produced. Variable expenses change based on the number of items produced.

An example of a fixed expense is the rent. The rent is always the same amount, regardless of production.

Materials would be a variable expense. You need enough material to make each item, so the more items you produce, the more material you need.

Answer:

−2sin(2θ)cos(4θ)

Step-by-step explanation:

sin(2∅)-sin(6∅)

Sum product Identity

sinα  - sinβ  = 2cos((α+β)/2)sin((α-β)/2)

Putting α= 2∅ and β= 6∅ in the identity we get

sin(2∅)-sin(6∅) = 2cos((2∅+6∅)/2)sin((2∅-6∅)/2)

                        =2cos(8∅/2)sin(-4∅/2)

                        =2cos(4∅)sin(-2∅)

                         = -2sin(2∅)cos(4∅)

Answer:

B.  The relationship between the variables in the table is quadratic because the second differences are constant.

Step-by-step explanation:

We have to look for the differences in the y values of the given table.

The y values are:

0, 2, 6, 12, 20, 30, 42

The differences between the consecutive values are:

2, 4, 6, 8, 10, 12

These are the first differences and are not constant. This means the relationship is not linear. Now we again find the differences between the consecutive values:

2, 2, 2, 2, 2

These are the second differences. The second differences are constant. So this means the given relationship is quadratic.

Therefore, option B gives the correct answer. The relationship between the variables in the table is quadratic because the second differences are constant.

Answer:

csc θ = [tex]\sqrt{85}[/tex]/6

sec θ = [tex]\sqrt{85}[/tex]/7

tan θ = 6/7

Step-by-step explanation:

The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;

6^2 +7^2 = hypotenuse^2

hypotenuse = [tex]\sqrt{85}[/tex]

csc θ = 1/sinθ

sinθ = opposite side/hypotenuse

       = 6/[tex]\sqrt{85}[/tex]

csc θ = [tex]\sqrt{85}[/tex]/6

sec θ = 1/cosθ

cosθ = adjacent side/hypotenuse

sec θ = hypotenuse/adjacent side

         = [tex]\sqrt{85}[/tex]/7

tan θ = Opposite side/adjacent side

         = 6/7

Answer:

the answer is c

Step-by-step explanation:

Final answer:

To subtract 6 ounces from 3 pounds, convert 3 pounds to ounces (3 x 16 = 48 ounces), subtract 6 ounces (48 - 6 = 42 ounces), then convert back to pounds and ounces (42 ounces = 2 pounds and 10 ounces). The answer is 2 pounds, 10 ounces.

Explanation:

Subtracting Ounces from Pounds

The question asks to subtract 6 ounces from 3 pounds. In order to compare or subtract different units of weight, it is essential to convert them to the same unit. Firstly, we must remember the unit equivalence where 1 pound = 16 ounces. Now, to start the conversion, we multiply the number of pounds by 16 to get the total number of ounces, which is a step in solving these types of conversion problems.

Therefore, for 3 pounds:

3 pounds × 16 ounces/pound = 48 ounces.

Now subtract the given ounces: 48 ounces - 6 ounces = 42 ounces.

Since we know there are 16 ounces in a pound, we divide the total ounces by 16 to convert back to pounds and ounces.
42 ounces ÷ 16 ounces/pound = 2 pounds with a remainder of 10 ounces.

Hence, subtracting 6 ounces from 3 pounds gives us 2 pounds, 10 ounces.

The error is the way she wrote 3%

3% = 0.03

The correct equation should be y = 78,000(0.03)^x

Answer:

x < [tex]\frac{8}{3}[/tex]

Step-by-step explanation:

Given

x - 10 < 6 - 5x ( add 5x to both sides )

6x - 10 < 6 ( add 10 to both sides )

6x < 16 ( divide both sides by 6 )

x < [tex]\frac{16}{6}[/tex], that is

x < [tex]\frac{8}{3}[/tex]