For the following exercises, evaluate the function f at the values f(−2), f(−1), f(0), f(1), and f(2)

70. f(x) = 8x2 − 7x + 3

The length of each side of the equilateral triangle is 5x³ + 11x⁵

From the question, we are to determine the length of each side of the equilateral triangle.

An equilateral triangle has its sides equal to each other.

If the length of a side of an equilateral triangle is c,

Then, the perimeter, P, of the triangle is

P = 3c

From the given information,

P = 15x³ + 33x⁵

∴ 3c = 15x³ + 33x⁵

c = (15x³ + 33x⁵) / 3  

c = 3(5x³ + 11x⁵) / 3

c = 5x³ + 11x⁵

Hence, the length of each side of the equilateral triangle is 5x³ + 11x⁵

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Answer: 5x^3 + 11x^5

Step-by-step explanation:

The simplified form of the given expression is -18. The correct option is the third option-  -18

From the question, we are to simplify

|3-10| - (12 ÷ 4 + 2)²

Simplifying

|3-10| - (12 ÷ 4 + 2)²

|-7| - (3 + 2)²

7 - (5)²

7 - 25

= -18

Hence, the simplified form of the given expression is -18. The correct option is the third option-  -18

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Answer:

9 cm

Step-by-step explanation:

The hypotenuse is the major side of the right triangle, if you look at the options only two of them are smaller than the hypotenuse, the rest cannot be the answer.

Hypotenuse (c) = 15 cm

Cathetus (a) = 12 cm

Cathetus (b) = ?

Equation: [tex]c^{2}=a^{2} +b^{2}[/tex]

Solution: [tex]b^{2} =c^{2} -a^{2}[/tex]

[tex]b^{2} =(15)^{2} -(12)^{2}[/tex]

[tex]b^{2} =225-144[/tex]

[tex]b^{2}=81[/tex]

[tex]b=\sqrt{81}[/tex]

[tex]b=9[/tex]

Hope this helps

Answer:

x = -6

Explanation:

⇒ 9(x + 3) = 4x - 3​

apply distributive method: a(b + c) = ab + ac

⇒ 9(x) + 9(3) = 4x - 3

multiply variables

⇒ 9x + 27 = 4x - 3

collect like terms

⇒ 9x - 4x = -3 - 27

subtract like terms

⇒ 5x = -30

divide both sides by 5

⇒ x = -6

Answer:

x = -6

Step-by-step explanation:

distribute 9(x+3) = 9x+27

9x+27 = 4x-3 subtract -27 and -4x on each side

9x-4x = -3-27 combine like terms

5x = -30 divide by 5

x = -6

Answer:

0.1

Step-by-step explanation:

break 1 into 10 parts, and take one part: hence 0.1

Answer:

0.1

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf 60 \ miles}[/tex]

Step-by-step explanation:

Given that,

3 hours = 180 miles

Divide 3 to both sides

3/3 hour = 180/3 miles

1 hour = 60 miles

So, Mom drove 60 miles in one hour.

[tex]\rule[225]{225}{2}[/tex]

The value of x in the equation [tex]log_{2x + 6}8=3[/tex] gives that x = -2.

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

[tex]log_{2x + 6}8=3\\\\applying\ the\ logarithm\ rule:\\\\(2x+6)^3=8\\\\8x^3+72x^2+216+208=0\\\\x=-2[/tex]

The value of x in the equation [tex]log_{2x + 6}8=3[/tex] gives that x = -2.

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Answer:

A. The color of fire when different metals are burned.

Explanation:

Qualitative data is data that relates to a quality or characteristic of an object, and does not include any numbers.

example: colour, taste, survey answers

Quantitative data, on the other hand, relates to measurements and counting of variables, and uses numbers to convey value.

example: height of a person, number of coins

Answer:

Diameters  

Step-by-step explanation:

In spherical geometry, lines are called diameters.

Answer:

Diameter

Step-by-step explanation:

In spherical geometry, lines are called diameter .

Also this makes sense the most .

The response rate is 52.021%.

Given a random sample of 2,000 households are selected for telephone interviews in which 432 interviews are completed, 586 are refused by the respondent, 902 do not answer or are not at home and 80 are non-working numbers.

Total Number of sample, S =2000

Completed interview, C = 432

Refusal by the Respondent, R = 586

No answer/ not at home , N = 902.

Non - working Numbers, NW = 80.

From the above data, we got responses from completed interviews and refusals by respondents.

so responded number (RN) is

RN=C+R

RN= 432+ 586

RN= 1018.

The actual number of samples =Total samples - non-working samples Actual number of samples=2000-80

The actual number of samples=1920

And the response rate (RR) is

RR=1018÷1920

RR=0.52021

Hence, the response rate from 2000 households which are selected for telephone interviews is 0.52021.

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The correct steps are given below:-

a) Subtract 2 and two-thirds from both sides of the equation

b) 8 minus 2 and two-thirds = 5 and one-third

c) Substitute the value for r to check the solution.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be solved by using the following steps:-

[tex]2 \dfrac{2}{3}[/tex]  + r   = 8

Subtract [tex]2 \dfrac{2}{3}[/tex]  from each side

[tex]2 \dfrac{2}{3}[/tex]    + r  - [tex]2 \dfrac{2}{3}[/tex]     = 8 - [tex]2 \dfrac{2}{3}[/tex]  

r = 5 1/3

Check the solution,

[tex]2 \dfrac{2}{3}[/tex]   + [tex]5 \dfrac{1}{3}[/tex] =8

8 = 8

The complete question is given below:-

Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8 Subtract 2 and two-thirds from both sides of the equation. Add 2 and two-thirds to both sides of the equation. 8 minus 2 and two-thirds = 5 and one-third 8 + 2 and two-thirds = 10 and two-thirds Substitute the value for r to check the solution.

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Answer:

A,C,E >:3.

your welcome!

Answer:

A=7 B=9 C=4

Step-by-step explanation:

[tex]a\frac{b}{c} =\sqrt[c]{a^b}[/tex]

The percentage that the infuser will have to be filled to use the same amount of tea will be 90.23%.

The infuser for Lizeete is 7 cm high, 3 cm long and 1.5 cm wide. The volume will be:

= 7 × 3 × 1.5

= 31.5cm³

The tea infuser from the example, was the same except 7.9 cm high. Therefore, the volume will be:

= 7.9 × 3 × 1.5

= 35.5

Since it was filed to 80%, this will be:

= 80% × 35.5

= 31.5cm³

Therefore, the dimensions will work and the percentage to use the same amount of tea will be:

= 28.44/31.5 × 100

= 90.23%

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Answer: [tex]144\pi[/tex]

Step-by-step explanation:

The area of the base is [tex]36\pi[/tex].

If we consider the right triangle, by the Pythagorean theorem, the unknown leg, which has a length of 4, is the height.

So, the volume is [tex]144\pi[/tex].

Answer:

5

Step-by-step explanation:

This is quite some trial and error question.

Based on the question, the numbers we can use are 1,3,5,7 and 9.

We will start with the middle digit first.

Since the question has stated it is 3 times the last digit, the number has to be in multiples of 3.

So we are left with: 3 and 9.

Then, the question also states the middle digit is 4 more than the first digit. See, its a digit, so the value cannot be less than 1 (odd numbers only and no negative values), so if we subtract 4 to the middle digit to find the first, it should still be a Positive Single numerical value.

3 - 4 = -1

9 - 4 = 5

Therefore, this middle digit is = 9.

Since we know the middle digit = 9

The first digit will be 9 - 4 = 5

The whole value is now 593.

Answer:

QUESTION 1:  (-3,0), (1,1), (5, 2), (9,3)

QUESTION 2: Draw a mapping diagram (see question 3)

QUESTION 3: Yes, the image below is a function.

Step-by-step explanation:

For question 1, you can pair the domains (x-values) with any y-value. The y-values can repeat.

For question 3b, you must understand that domains cannot repeat, but ranges (y-values can). In 3b, every x-value has a unique y-value which means that it is a function. You can also determine is something is a function by seeing if its graph passes the vertical line test.

Yes

As per definition

Every domain of the function has an unique range

Here

Hence it's a function

Answer:

x

Step-by-step explanation:

2^3

Answer:

16/25 or 64%

Step-by-step explanation:

There are 12 even numbers between 1 and 25: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24

There are 8 multiples of 3 between 1 and 25: 3, 6, 9, 12, 15, 18, 21, and 24

That makes your odds 20/25. But, you can't count numbers twice! So eliminate the repeats and you get:

2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, and 24

which is 16/25 numbers that satisfy being an even number, a multiple of 3, or both

hope this helped :)

The probability that all of the next ten customers who want this racket can get the version they want from current stock is 0.821

Given: currently has seven rackets of each version.

Then the probability that the next ten customers get the racket they want is P(3≤X≤7)

Note that If less than 3 customers want the oversize, then more than 7 want the midsize and someone's going to miss out.

X ~ Binomial (n = 10, p = 0.6)

P(3≤X≤7)  = P(X≤7) - P(X≤2)

From Binomial Table:

               = 0.8333 - 0.012

               = 0.821

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Answer:

Area = ab

Step-by-step explanation:

Area is length × width, so fill in a for the length and b for the width. Multiply a and b together.

A = a×b

A = ab

The limit as x approaches three from the right of f(x)  is 3

The value a function approaches when the variable approaches its limit.

A graph is given which shows a piece  wise function ,

As when the limit approaches from the right the function can be seen approaching 3 , it is not 3 at 3 but approaching to 3

The right hand lim x--> 3 f(x)  approaches  3 .

Therefore , limit as x approaches three from the right of f(x)  is 3

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Using it's concept, the expression that can be used to find the probability that a randomly selected point is in the white area of the grid is:

[tex]\frac{7}{16}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, 7 out of 16 squares are in the white area, hence the probability is given by:

[tex]p = \frac{7}{16}[/tex].

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The whole number consisting of x in the hundreds place, y in the tens place, and 2 in the ones place is; xy2.

It follows from the task content that the whole number described has x in the hundreds place, y in the tens place, and 2 in the ones place.

The whole number in discuss can be broken down simply as: (x×100) + (y×10) +(2×1).

Hence, the whole number is; xy2.

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2) perpendicular lines form right angles

3) perpendicular lines form right angles

4) all right angles are congruent

5) reflexive property

6) ASA

7) CPCTC

8) ABCD is a rhombus because it is a parallelogram with a pair of consecutive congruent sides

The probability that a simple random sample of 45 unemployed individuals will provide is 0.7372

Here, μ = 17.5, σ = 0.8944, x1 = 16.5 and x2 = 18.5.

We need to compute P(16.5<= X <= 18.5).

The corresponding z-value is calculated using Central Limit Theorem.

z = (x - μ)/σ

z1 ⇒ (16.5 - 17.5)/0.8944 = -1.12

z2 ⇒ (18.5 - 17.5)/0.8944 = 1.12

Therefore, we get

P(16.5 <= X <= 18.5) = P((18.5 - 17.5)/0.8944) <= z <= (18.5 - 17.5)/0.8944)

⇒ P(-1.12 <= z <= 1.12) = P(z <= 1.12) - P(z <= -1.12)

⇒ 0.8686 - 0.1314 = 0.7372

The principal limit theorem states that if you have a population with imply μ and trendy deviation σ and take sufficiently huge random samples from the populace with alternative, then the distribution of the pattern method may be about usually distributed.

The relevant limit theorem (CLT) states that the distribution of pattern manner approximates a normal distribution as the pattern size gets larger, regardless of the population's distribution. sample sizes identical to or extra than 30 are often considered enough for the CLT to preserve.

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The probability that the sum of both rolls is at least 9 is 2/36.

Probability is the chance that a given event will occur.  the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Given:

Total sample spaces: 36.

Number on one dice: 6

For sum of both rolls to be 9 , the only possible way is (6,3)(3,6)

Using probability formula,

Thus The probability that the sum of both rolls is at least 9 is 2/36.

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Answer:

[32, ∞]

Step-by-step explanation:

c - 32 ≥ 0 can be rewritten as c ≥ 32 (adding 32 on both sides)
So for any value of between 32 and infinity both inclusive is a solution

Six less than the quotient of two and a number "W"

Let's take this step-by-step. First, change the written-out numbers to numerals:

6 less than the quotient of 2 and a number "W"

Next, combine the smallest part. In this case, it would be:

the quotient of 2 and a number "W"

Here, you are finding the quotient of a specific part: 2 and W. When we have specific sections like this in math, we put parentheses around them, like this:

6 less than the quotient of (2 and a number "W")

Now we need to remember what a "quotient" is. This means that there is division between the two numbers mentioned - in this case, 2 and the number W. But which is being divided into which? The number 2 comes first, so we think of 2 as being the first number used. Therefore, we are looking at:

6 less than (2 divided by W)

Division problems are exactly the same as fractions. For example, 3 divided by 1 is the same as 3 ÷ 1, which is also the same as 3/1 (which equals 3). In our case, 2 divided by W is the same as 2/W (your teacher might want this written as 2 ÷ W, but they mean the same thing). Now, we can write the equation as:

6 less than (2/W)

Which can also be written as:

6 less than 2 ÷ W

To finish this up, let's take a step back for a moment Imagine you have 10 jelly beans, and you eat 7 of them. You now have 7 less than 10, or 3 jelly beans. This can also be written as 10-7 = 3.

In our example, we have 6 less than (2/W). If we use the jelly bean equation we found as a starting point, we can change the 7 to 6 and the 10 to (2/W). Then, we get this:

(2/W) - 6

Which can also be written as:

2 ÷ W - 6

And that's your answer! Both of those mean the same thing so they're both correct. Your teacher might prefer you write it one way or the other, though. If this is the case, make sure to choose the solution that best fits your teacher's request.

Answer:

if i subtract 3/8 with 2/5 i get 1/40

Step-by-step explanation:

i dont know if this is correct but it seems so

Step-by-step explanation:

—Let the unknown number is x, so we can write the equation like below.

[tex] \frac{2}{5} \times x = \frac{3}{8} [/tex]

[tex] \: [/tex]

—Find x.

[tex] \frac{2}{5} \times x = \frac{3}{8} [/tex]

[tex]x = \frac{3}{8} \div \frac{2}{5} [/tex]

[tex]x = \frac{3}{8} \times \frac{5}{2} [/tex]

[tex]x = \frac{15}{16} [/tex]

[tex] \: [/tex]

—Let's prove that it's true.

[tex] \frac{2}{5} \times x = \frac{3}{8} [/tex]

[tex] \frac{2}{5} \times \frac{15}{16} = \frac{3}{8} [/tex]

[tex] \frac{30}{80} = \frac{3}{8} [/tex]

[tex] \frac{30 \div 10}{80 \div 10} = \frac{3}{8} [/tex]

[tex] \frac{3}{8} = \frac{3}{8} \: \: \text{proved}[/tex]

[tex] \: [/tex]

So, the other number or the value of x is [tex]\frac{15}{16}[/tex]