Assume the four intersecting lines are parallel. In this figure, A = 36, B = 24, and C = 60 . If D = 33,
what are the measurements of E and F?

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Equivalent functions are different functions that have equal values when evaluated and compared

The function is given as:

f(x) = 36x^2 - 1

Express 1 as 1^2

f(x) = 36x^2 - 1^2

Express 36x^2 as (6x)^2

f(x) = (6x)^2 - 1^2

Apply the difference of two squares.

This is represented as:

(a + b)(a - b) = a^2 - b^2

So, we have the following equation

f(x) = (6x - 1)(6x + 1)

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

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Based on the given table which shows the number of years with a company in relation to the employee salary, the conclusion that can be drawn is There is a weak positive correlation between the variables.

When two variables are said to be positively correlated, then it means that when one variable increases, the other variable would increase as well.

If the correlation between them is strong, then the increase between the variables would be more uniform i.e. we can tell with higher accuracy, how the increase in one variable would affect the other.

In the table, we see that with every increase in the number of years with the company, there is an increase in the salary. This means that there is a positive correlation.

The increase is not uniform however. Sometimes it increases by $1,000, and other times by $7,000. As the increase is not uniform, it means that the correlation is weak.

In conclusion, there is a weak positive correlation between number of years and salary.

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Answer: 26.39

Step-by-step explanation:

2xπxr

Answer:296 m

I’m assuming “breadth” is width and garderean is just the park.

(25+25+12+12) times 4.

A is never defined

Your net worth change by zero dollars.

Net worth is the difference between asset and liability.  

In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.

Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.

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Answer:Maria

Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.

Answer:

Here is the full list of equivalent fractions to 32.  3/2, 6/4, 96, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40

Step-by-step explanation:

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480 Ways can the letters be arranged.

What is the meaning of probability ?

First letter can't be n or l

=   4! × [tex]5P_{3}[/tex]

=    24 × 5! /3!

=     24 × 5 × 4

=         480

Therefore, 480 ways can the letters be arranged.

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Answer: 480 ways

Step-by-step explanation:

Answer: c. a-15= 20

Step-by-step explanation:

The answer is c because a represents her age and 15 less than that would mean that you have to subtract 15 from her age which is represented by a, and then 15 less than a would equal 20, so a-15=20

The probability of not choosing red when choosing one marble from the bag is 90%.

S = {1, 2, 3, 4, 5, 7}

Flipping a fair, two-sided coin.

probability that a student studied for exactly 1 hour is 0.23.

The probability of landing on yellow is less than the probability of landing on blue.

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

The experimental probability of drawing a spade is 0.15.

The probability of not choosing red when choosing one marble from the bag will be:

= (3 + 15 + 9)/30

= 27/30

= 90%

The sample space for rolling a fair seven-sided die will be S = {1, 2, 3, 4, 5, 7}.

The event that will have a sample space of S = {h, t} will be flipping a fair, two-sided coin.

The probability that a student studied for exactly 1 hour will be:

= 8/(1+8+2+5+9+7+3)

= 8/35

= 0.23

The true statement is that the probability of landing on yellow is less than the probability of landing on blue.

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%. This was 13/40 = 32.5%.

The experimental probability of drawing a spade will be:

= 3/(7+3+6+4)

= 3/20

= 0.15.

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Answer: the sample space of the experiment from simultaneously flipping a coin and rolling a die consisted of: 2 × 6 = 12 possible outcomes.

Step-by-step explanation:

The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts...etc}.

Answer:

You did not list any choices but if you simplify that the answer is 6√2x-3√2

Step-by-step explanation:

If they want you to factor it instead of simplifying the answer is 3√2(2x-1)

Answer:

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Step-by-step explanation:

So you haven't provided any options, but I'm assuming they want it in most simplified form.

To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.

So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y

[tex]5xy-3y+xy[/tex]

So in here, think of y as the variable and the 5x, -3, and x as the coefficients.

In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))

[tex](5x-3+x)y[/tex]

Simplify this expression to get

[tex](6x-3)y[/tex]

Now just plug the sqrt(2) back in as y and you get the expression

[tex](6x-3)\sqrt{2}[/tex]

Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

The minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(4) - f(1).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:

[tex]\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12[/tex]

Thus, the minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

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Answer:

slope = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 5x - 2 ← is in slope- intercept form

with slope m = - 5

Answer: 10

Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.

Answer:

5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.

The perimeter of the triangle can be express as follows:

12b + 11d + 2c

The perimeter of a figure is the sum of the whole sides of the figure.

A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.

Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.

Hence, the perimeter of the triangle can be represented as follows:

Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c

Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c

Perimeter of the triangle = 12b + 11d + 2c

Therefore, the perimeter of the triangle can be express as follows:

12b + 11d + 2c

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Answer:

There are 9 possible thousands digits, because 0 cannot be the leading digit.

There are 2 possible ones digits, 0 and 5.

If the ones digit is 5:

There are 5 possible thousands digits: 1, 2, 3, and 4.For each possible thousands digit, there are 5 possible hundreds digits. (We used one of the digits above to be the thousands digit, but 0 is a possible hundreds digit.)For each possible pair of thousands-and-hundreds digits, there are 4 possible tens digits.

So there are 5 x 5 x 4 = 100 possible 4-digit numbers that end in 5 with no repeated digit and no digit larger than 5.

If the ones digit is 0:

There are 5 possible thousands digits.For each possible thousands digit, there are 4 possible hundreds digits.For each possible pair of thousands-and-hundreds digits, there are 6 possible tens digits.

So there are 5 x 4 x 6 = 120 possible 4-digit numbers that end in 0 with no repeated digit and no digit larger than 5.

100+120=220

Answer: 220 possible numbers.

The answers are :

y = 3ˣ ⇒ b

y = 3⁻ˣ ⇒ a

y = -3ˣ ⇒ c

For y = 3ˣ, we will get a graph that will increase exponentially in the direction of positive y-axis.

For y = 3⁻ˣ, we will get a graph that will decrease exponentially in the direction of positive x-axis.

For y = -3ˣ, we will get a graph that will decrease exponentially in the direction of negative y-axis.

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a linear equation is given as:

y = mx + b

Where m is the rate of change and b is the y intercept (initial value of y)

Let y represent the amount of water Jaquan uses to wash x cars, Using the point (2, 24) and (5, 60):

y - 24 = [(60 - 24)/(5- 2)](x - 2)

y = 12x

For 6 cars:

y = 12(6) = 72

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

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Answer: Jaquan uses 72 L to wash 6 cars

Step-by-step explanation:

Answer:

original ft below sea level =88 feet

In six seconds goes to 182 feet

Amount of feet covered in 6 seconds=182-88=94 ft

Step-by-step explanation:

rate in feet per second = 94/6=15.66

rounding to nearest tenth=15.7ft/s

For Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

To calculate the sum of money they must deposit, use the compound interest formula.

From the compound interest formula;

P = A / ( 1 + r/n )^(nt)

Given that;

P = A / ( 1 + r/n )^(nt)

P = 20,000 / ( 1 + 0.12/4 )^(4×10)

P = 20,000 / ( 1.03)^40

P = 20,000 / 3.26203779

P = $6,131.14

Therefore, for Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

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Step-by-step explanation:

g(f(a))=4(a²+2a) + 5

= 4a²+8a+5

Answer:

Step-by-step explanation:

12

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

Complexes with a coordination number 4 mostly adopt tetrahedral and squar planar geometries.

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Two different integers are the same numbers, which have different signs.

An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97.

Given that,

x, y, and z are three integers. They follow the one condition: x-y-z = 0.

Any number in the number system that has only two signs, either + or -, So we consider that the third integer is 0 because 0 is a whole number that has neither a positive nor a negative sign.

The remaining two integers are the same numbers, but they have different signs to follow the given condition.

x-y-z = 0

x = y+z

Let y,z are the same numbers, They have different signs and x = 0.

Note: The value of x is always negative and y's value is always positive.

Example:

x = 0,  y = +6,  z = -6

x-y-z = 0

x = y+z

0 = +6-6

0 = 0

Hence, two different integers are the same numbers, which have different signs.

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Using the arrangements formula, it is found that:

a) There are 1365 possible outcomes that contain exactly four tails.

b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repetitions, the number of ways is given as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.

Item a:

11 heads and 4 tails, hence:

[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]

There are 1365 possible outcomes that contain exactly four tails.

Item b:

The total number is:

[tex]A_{15} = 15! = 1,307,674,400,000[/tex]

With no heads:

[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]

With one head:

[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]

With two heads:

[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]

Hence the number of outcomes with less than three heads is:

1 + 15 + 95 = 111

With at least three heads, the number of outcomes is:

[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]

There are 1,307,674,399,889 possible outcomes that contain at least three heads.

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Answer:

180

Step-by-step explanation:

If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets

The volume of the cone is  84.9 km³

Volume of a cone = 1 / 3 πr²h

where

Therefore,

radius = 3 km

height = √9.5² - 3²

height = √81.25

height = 9.01387818866

height = 9.014 km

Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014

volume of the cone = 254.732197612 / 3

volume of the cone = 84.9107325372

volume of the cone = 84.9 km³

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Answer:

The answer is B, 2.78 hours

Step-by-step explanation:

Answer:

  6 hours 15 minutes, or 6.25 hours

Step-by-step explanation:

We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.

We know that 15 minutes is 1/4 hour, so the proportion can be written ...

  hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)

Multiplying by 250 pages gives ...

  book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour

It will take Hank 6 1/4 hours to read the book.