A linear function as a rule shown

a) The process to find the limit is given as follows:

b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

Hence:

For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.

Applying the subtraction of perfect squares, we have that:

x² - 1 = (x - 1)(x + 1).

Then:

g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.

Meaning that the limit is then calculated as follows:

lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.

More can be learned about limits at brainly.com/question/26104792

#SPJ1

Answer:

Step-by-step explanation:

It is a real number, a rational number, a natural number, and an integer.

Answer:

It’s a real number, rational number, and a natural number.

Answer: spinning a spinner with 4 equal sections 50 times

Step-by-step explanation:

The models that one can use to simulate the outcome of guessing the correct answers to a 50-question test will be to spinn a spinner with 4 equal sections 50 times.

Flipping a coin 50 times is wrong since the coin only has two outcomes which are head and tail. Rolling a 6-sided die 50 times is also wrong.

Therefore, the correct option is B.

Answer:

174 ft²

Step-by-step explanation:

The polygon cam be decomposed into two rectangles.

The area of the polygon = rectangle A + rectangle B

Area of rectangle A = L* W

L = 18 ft

W = 9 ft

Area of rectangle A = 18*9 = 162 ft²

Area of rectangle B = L* W

L = 20 - 18 = 2 ft

W = 6 ft

Area of rectangle A = 2*6 = 12 ft²

✔️Area of the polygon = 162 + 12 = 174 ft²

Answer:

The p-value for this test is 0.1375.

Step-by-step explanation:

A student believes that the average grade on the statistics final examination was 87. The student wants to test whether the average is different from 87 at 90% level of confidence.

At the null hypothesis, we test if the average is 87, that is:

[tex]H_0: \mu = 87[/tex]

At the alternate hypothesis, we test if the average is different from 87, that is:

[tex]H_a: \mu \neq 87[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]s[/tex] is the standard deviation of the sample and n is the size of the sample.

87 is tested at the null hypothesis:

This means that [tex]\mu = 87[/tex]

The average grade in the sample was 83.96 with a standard deviation of 12. Sample of 36

This means that [tex]X = 83.96, s = 12, n = 36[/tex]

Value of the test-statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{83.96 - 87}{\frac{12}{\sqrt{36}}}[/tex]

[tex]t = -1.52[/tex]

Pvalue:

Probability of the sample mean differing of 87, which means that we have a two-tailed test, with t = -1.52 and 36 - 1 = 35 degrees of freedom.

With the help of a calculator, the pvalue is of 0.1375.

The p-value for this test is 0.1375.

Answer:

20 is the answer

Step-by-step explanation:

I did the math.hope it helps :)

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

Slope "m"

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~

( 4 , - 7 )

m = [tex]-\frac{1}{2}[/tex]

y - ( - 7 ) = [tex]-\frac{1}{2}[/tex] ( x - 4 )

y + 7 = [tex]-\frac{1}{2}[/tex] ( x - 4 )

Answer:

113

Step-by-step explanation:

The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex], where [tex]r[/tex] is the radius of the sphere. The radius of the given sphere is 3 ft, so its volume is [tex]\frac{4}{3} \pi \cdot 3^3 = 36\pi[/tex]. Using 3.14 for [tex]\pi[/tex], this is approximately equal to 113.04. Rounding to the nearest whole number, the answer is 113 cubic feet.

Answer: 113 (rounded)

Step-by-step explanation:

Hey!

So for this we just use our sphere formula and follow the steps.

Volume= 4/3 πr^3

R= radius (half of diameter)

For pi we are going to use 3.14.

Let’s work this out now.

Radius is 3 so since it is cubed, we multiply it by itself 3 times. We get 27. Now, let’s multiply this by 3.14 and get 84.78.

Lastly, multiply by 4/3. We get 112.9333. This is the volume.

Hope this helped! :D

Sorry I messed any thing up!

Comment down below for further questions!

Answer:

she saved $9.67

Step-by-step explanation:

$48.35÷ 0.20= $9.67

The cost to order 1, 000 pens and 2, 000 notebooks, by the Student Union, can  be found to be

The cost of ordering 1, 000 pens is shown to be 60 cents per pen so the total cost would be :

= Number of pens x Cost per pen

= 1, 000 x 60 cents

= $ 600

The cost of ordering 2, 000 notebooks is 76 cents per notebook which comes to a total of :

= 2, 000 x 76 cents

= $ 1, 520

The total cost of ordering the pens and notebooks is:
= 600 + 1, 520

= $ 2, 120

Find out more on ordering cost at https://brainly.com/question/18453528

#SPJ1

Answer:

[tex]y=\frac{5x}{1+2x^2}[/tex]

Step-by-step explanation:

[tex]Option ~A ~ does ~ not ~ have ~a ~ vertical~ asymptote[/tex]

--------------------------

Hope it helps...

Have a great day!!

Answer:

Step-by-step explanation:

answer is d

Answer:

Your answer is A

Step-by-step explanation:

A = pi*r²

A = 3.14*70²

A = 3.14*4900

A = 15386

Answer:

Below

Step-by-step explanation:

f(t) = 4.1 (sin pi/6 t  - pi/3) + 19.7    <===will be a maximum when the sin portion is equal to 1

   so    sin ( pi/6 t - pi/3) = 1     given that sin is equal to one   at 0 and pi and 2 pi  and 3 pi    and 4 pi   etc

              pi/6 t - pi/3 =  0  or pi , 2 pi, 3 pi  , 4 pi

                  then t = 2 and 8 and 14   and 20 hrs  ( every 6 hrs starting with t = 2)

The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

Answer:

Step-by-step explanation:buordjkdkeek

The simplest form of the given expression is (- 8n² +n +1)

Simplification is the process of making simple an expression, terms or equations so as to easy for solving or evaluating.

There are some steps for simplification such as removing parenthesis, collecting like terms, addition or subtraction of like terms and so on.

We are given an expression, ( -7n² - 8n -8) + (- n² + 9n +9)

In order to simplify, we first remove the parenthesis and get

- 7n² - 8n -8 - n² + 9n +9

in the next we will collect like terms

- 7n² - n² -8n +9n - 8 +9

We now add or subtract like terms

- 8n² + n+1

this is the simplest form of the given expression.

To learn more about simplification visit:

https://brainly.com/question/18077355

#SPJ1

Answer:

Number of year = 13 year and 6 month approx.

Step-by-step explanation:

Given:

Amount invested = $80,000

Rate of interest = 6% compounded  continuously

Future value of investment = $175,600

Find:

Number of year

Computation:

Future value of investment = Amount invested[1 + Rate of interest]ⁿ

175,600 = 80,000[1+6%]ⁿ

175,600 = 80,000[1+0.06]ⁿ

175,600 = 80,000[1.06]ⁿ

Number of year = 13.492 year

Number of year = 13 year and 6 month approx.

Answer:

depends on the size of the house

let's say the house is 10 square meter then you would need 5 gallons

let's the house is 60 square meter then you would need 30 gallons

Step-by-step explanation:

whatever the square meter just divide it with 2 and that should be your answer

Answer:c=35

Step-by-step explanation:

i just did this

Answer:

To find the radius..just divide them by two

For the diameter multiply by two

Circumference formula is

[tex]2\pi \: r[/tex]

Step-by-step explanation:

The figure is made up of an 8x8 square and 4 identical triangles with 8-ft bases and 4 ft in height. Each triangle has an area = (1/2)bh = (1/2)(8)(4) = 16 ft^2. The square part has an area of 8x8 = 64 ft^2. Therefore, the total area of the figure is

A = (area of square) + 4×(area of triangle)

= 64 ft^2 + 4(16ft^2)

= 128 sq ft

Answer:

To answer this problem, first let us calculate for the theoretical probability obtained from the study conducted:

Theoretical Probability = 6,670 / 40,000

Theoretical Probability = 0.16675 = 0.17

From the given choices, the list of words which can give this similar amount of probability is:

“to, sarcastic, epithet, for, less, corruptible, than, the, offspring, open, any, primary, loyalty, table, out, whom, example, who, mention, say”

In this set of words, the number of words starting with letter T is 4. Calculating for the probability of getting a word starting with T in this set is:

Sample probability = 4 / 20

Sample probability = 0.20

Step-by-step explanation:

The null hypothesis is rejected.

The mean is not greater than $175.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

Sample size (n) = 6

Sample mean ([tex]\bar x[/tex]) = $80

Sample standard deviation(s)=6.3

Significance level(α)=0.05

We have to test the claim that the true mean greater than $175.

The null and alternative hypotheses:

H₀ : μ = 175

H₁ : μ > 175

Here, Population Standard deviation is unknown and sample size is less than 30.

So we will use t- distribution.

Test Statistic t,

t   = ([tex]\bar x[/tex] - μ) / {s/√n}

t  =  (80−175) / (6.3 /√6)

t   =  (80−175) / (6.3 / 2.45)

t  = − 95 / 2.57196423

t = −36.937

degree of freedom (df) = n−1

                                     = 6−1

                                     = 5

p-value at  t = −36.937, df = 5 and α = 0.05

Absolute value of −36.937 = 36.937

Notice that 36.937 does not show up in the table, but it does fall between the two values 31.821 and 63.657.

So, p-value = 1

Since, p-value > α

That means, we fail to reject the null hypothesis (H₀).

Therefore, the true mean is not greater than $175.

To learn more about the hypothesis;

brainly.com/question/29519577

#SPJ1

Answer:

3.6

Step-by-step explanation:

tan61=x/2

2(tan61)=x

3.6=x

Answer:

The right answer is:

(a) 0.205

(b) 0.005425

Step-by-step explanation:

The given data is:

0.213, 0.204, 0.208, 0.200, and 0.198

(a)

The mean will be:

= [tex]\frac{Sum \ of \ all \ data}{No. \ of \ data}[/tex]

= [tex]\frac{0.213+ 0.204+ 0.208+ 0.200+0.198}{5}[/tex]

= [tex]\frac{1.023}{5}[/tex]

= [tex]0.2046[/tex]

or,

= [tex]0.205[/tex]

(b)

The standard deviation will be:

[tex]\sigma^2=\Sigma\frac{(x_i-\mu)^2}{N}[/tex]

    [tex]=\frac{(0.213-0.2046)^2+...+(0.198-0.2046)^2}{5}[/tex]

    [tex]=\frac{0.0001472}{5}[/tex]

    [tex]=2.994\times 10^{-5}[/tex]

or,

    [tex]=0.005425[/tex]

Answer:

360 cm3

Step-by-step explanation:

Option d is the right answer

Option A. They led the most powerful of the Allied countries.

Answer:

Where are the questions