Completely factor this quadratic expression: 4x2 + 12x − 72.

Answer:

because your just adding a zero at the end.

Step-by-step explanation:

Adding 6+3 is like adding 60+30 because both utilize the place value system and the commutative property of addition where units are added to units and tens to tens, respectively.

The question of adding 6+3 is similar to adding 60+30 due to the property of place value and the commutative property of addition. In both cases, you are adding units that are consistent within their respective places. In single-digit addition, such as 6+3, you are adding units to units. Similarly, in the addition of multi-digit numbers like 60+30, you are adding tens to tens. This is much like the property A+B=B+A, which holds true for ordinary numbers, meaning you'll get the same result regardless of the order in which you add them.

Answer:

[tex]7[/tex]

Step-by-step explanation:

[tex] \frac{b}{2.4} \\ \frac{16.8}{2.4} \\ = 7[/tex]

The inverse of the function is logx/log12

Given the function expressed as:
y = 12^x

To find the inverse, switch the variables to have:

x = 12^y

Take the log of both sides

logx = y log 12

y = logx/log12

Hence the inverse of the function is logx/log12

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Answer:

C = πd or 2πr

Step-by-step explanation:

2r equals d

2r = d

Answer:

  -4

Step-by-step explanation:

Use the given value of f(1) to find f(2):

  f(2) = f(1) · (-1/2) = (-16)(-1/2) = 8

Now, we can find f(3) using f(2):

  f(3) = f(2) · (-1/2) = (8)(-1/2)

  f(3) = -4

Answer:

  c.  6

Step-by-step explanation:

The degree of a vertex is the number of arc ends that intercept it. (The other end of the arc is irrelevant.)

Vertex A is connected to B (1), D (2), F (1), and itself (2). There are a total of 6 arc ends that meet vertex A. Its degree is 6.

Answer:

62

Step-by-step explanation:

length of rectangle = 2* diameter = 24

width  = diameter = 12

area = 24*12 - 2 * pi * 6^2 = 61.8

Your answer would be the second option, 62.

To answer this we need to find the area of the 2 circles, and then subtract this from the area of the rectangle to find the shaded area.

The equation for the area of a circle is πr², so for one circle this would be π × 6² = 36π. Since we're taking π = 3.14, this comes out as 113.04 as the area for once circle, which means the area for both circles would be 113.04 × 2 = 226.08.

To find the area of the rectangle, we need to notice that the height of the rectangle is the diameter of one circle, and the width is 2 multiplied by the diameter of the circle, because there are 2 diameters right next to each other. The diameter of one circle is 6 × 2 = 12, so this is the height, which means the width of the rectangle is 12 × 2 = 24. This means the area of the rectangle is 24 × 12 = 288.

Now the last step is to do 288 - 226.08 = 61.9 = 62.

I hope this helps!

Answer:

x=32, y=36, and z=25

Step-by-step explanation:

There are only two sums the equations can all add up to, 67 degrees and 113 degrees. I know that to the equation with x is equal to 67 degrees.

2x+3=67

2x=64 (subtract 3)

x=32 (divide by 2)

Now to find the measurement of the other angle, we subtract 180 and 67 since the measurement of a line is 180 degrees.

180-67=113

The equations of y and z are both equal to 113.

3y+5=113                                 4z+13=113

3y=108 (subtract 5)                 4z=100 (subtract 13)

y=36 (divide by 3)                   z=25 (divide by 4)

Final answer:

To find the area of the rectangular field in square meters, convert the dimensions from kilometers to meters and then multiply them together, resulting in 45,000 square meters.

Explanation:

To calculate the area of a rectangular field that is 0.3 kilometers long and 0.15 kilometers wide, use the following steps:

We have been given that a virus has infected 400 people in the town and is spreading to 25% more people each day. We are asked to write an exponential function to model this situation.

Since the number of infected people is increasing, so our model will be exponential growth model.

An exponential growth function is in form [tex]y=a(1+r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Growth rate in decimal form,

x = Time.

Let us convert 25% into decimal form.

[tex]25\%=\frac{25}{100}=0.25[/tex]

The initial number of infected people is [tex]400[/tex], so our function would be [tex]y=400(1+0.25)^x[/tex].

[tex]y=400(1.25)^x[/tex]

To find the number of infected in 10 days, we will substitute [tex]x=10[/tex] in our given formula as:

[tex]y=400(1.25)^{10}[/tex]

[tex]y=400(9.3132257461547852)[/tex]

[tex]y=3725.290298\approx 3725[/tex]

Therefore, there will be approximately 3725 infected people in 10 days.

The number of people that will be infected in 10 days is approximately 3725. This represents exponential growth.

Step 1

To model the spread of the virus using an exponential function, we start with the initial number of infected people and the daily growth rate. The exponential growth formula is:

[tex]\[ P(t) = P_0 \times (1 + r)^t \][/tex]

Where:

- [tex]\( P(t) \)[/tex] is the number of people infected after t days

- [tex]\( P_0 \)[/tex] is the initial number of infected people

- [tex]\( r \)[/tex] is the growth rate

- t is the time in days

Given:

- Initial number of infected people, [tex]\( P_0 = 400 \)[/tex]

- Daily growth rate, r = 0.25  (since 25% more people are infected each day)

The exponential function becomes:

[tex]\[ P(t) = 400 \times (1 + 0.25)^t \][/tex]

[tex]\[ P(t) = 400 \times (1.25)^t \][/tex]

Step 2

To find the number of people infected in 10 days [tex](\( t = 10 \))[/tex]:

[tex]\[ P(10) = 400 \times (1.25)^{10} \][/tex]

Calculating this:

[tex]\[ P(10) = 400 \times (1.25)^{10} \][/tex]

Using a calculator:

[tex]\[ (1.25)^{10} \approx 9.3132 \][/tex]

[tex]\[ P(10) = 400 \times 9.3132 \approx 3725.28 \][/tex]

So, the number of people infected in 10 days is approximately 3725.

Known :

r = 2

Asked :

C = ...?

Answer :

C = 2πr

= 2 × 3.14 × 2

= 12.56

So, tge circumference of circle is 12.56

Hope it helpful and useful :)

Answer:

[tex]4\pi[/tex]

Step-by-step explanation:

The equation for the circumference of a circle is 2[tex]\pi[/tex]r. I remember it as Cherry Pies Are (r) Square. If you plug in 2 for r, it should get you the answer

Answer:

There is a relationship between the age of a young adult and the type of movie preferred.

Step-by-step explanation:

In this case we need to test whether there is a significance relationship between the age of a young adult and the type of movie preferred.

The hypothesis can be defined as:

H₀: Age of a young adult and movie preference are independent.

Hₐ: Age of a young adult and movie preference are not independent.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

Consider the table below.

The formula to compute the expected frequencies is:

[tex]E_{i}=\frac{\text{Row Total}\times \text{Column Total}}{\text{Total}}[/tex]

The Chi-square test statistic value is:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}=2.6013[/tex]

The significance level of the test is, α = 0.05.

The degrees of freedom of the test is,

df = (r - 1)(c - 1)

   = (3 - 1)(3 - 1)

   = 2 × 2

   = 4

Compute the p-value as follows:

p-value = 0.6266

*Use a Chi square table.

As the p-value is more than the significance level the null hypothesis was failed to be rejected.

Thus, concluding that there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred.

Answer:

Step-by-step explanation:

Hello!

a)

An observational study is one where the investigator has no control or intervenes on it. He just defines the variable of interest and merely collects and documents the information. These types of studies are usually made as precursors to a more formal experimental study, to have an idea of what's to be expected from the population.

An experimental study or experiment is one where the investigator intervenes by defining the variable of interest and artificially manipulates the study factor. It is also one of its characteristics the randomization of cases or subjects in groups (two or more, depending on what is the hypothesis of study).

In this example, the investigators used a randomized block design with "Bag" as the blocking factor and assigned the bags randomly to the students of the statistic class.

The researchers manipulated all confounding factors in this experiment leaving only "the number of candies per color per bag" as the only random variable. This is an experimental study.

b)

This is an ANOVA with two factors, "Bag" and "Colour" and the treatments are all possible combinations between these two factors.

Correct Option A.

c) The response variable is the "number of candies per color per bag"

Colors: Blue, Red, Orange, Green, Brown and Yellow.

I hope you have a nice day!

Answer:

9² − x²

x(9-x)+9(9-x)

Step-by-step explanation:

The area of the shaded light gray square =

= the area of the whole square - the area of the shaded dark gray square

= 9² - x²

since x(9-x)+9(9-x) = 9x - x² + 9² - 9x = 9² - x²

then x(9-x)+9(9-x) is also a right answer.

Answer:

The answer is 9² - x² and x(9 - x) + 9(9 - x)

Step-by-step explanation:

Here, In a Figure, two square is given first which is small and shaded dark gray and second which is big and shaded light gray.

Now, For area of Small Square.

Length (l) = x

A = l²

A = (x)²

A = x²

Now, For area of Big Square.

Length (l) = 9

A = l²

A = (9)²

A = 81

Then, To find are of Shaded light gray square

Area of Big Square - Area of Small Square.

9² - x²

Thus, The answer is 9² - x² and

x(9 - x) + 9(9 - x)

-TheUnknownScientist

Answer:

[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]

The degrees of freedom are given by:

[tex] df =n-1=25-1=24[/tex]

And the p value would be given by:

[tex] p_v = P(t_{24}>2) =0.0285[/tex]

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate      

Step-by-step explanation:

Data provided

[tex]\bar X=4.2[/tex] represent the sample mean for the weigths

[tex]s=0.5[/tex] represent the sample standard deviation

[tex]n=25[/tex] sample size      

[tex]\mu_o =4[/tex] represent the value that we want to analyze

[tex]\alpha[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to conduct a hypothesis in order to check if the true mean weigth is less than 4 or not, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \leq 4[/tex]      

Alternative hypothesis:[tex]\mu > 4[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing the info given we got:

[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]  

The degrees of freedom are given by:

[tex] df =n-1=25-1=24[/tex]

And the p value would be given by:

[tex] p_v = P(t_{24}>2) =0.0285[/tex]

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate

Answer:oh yeah I remember that

Step-by-step explanation:

That’s tuff

Answer:

Corresponding Angles.

Step-by-step explanation:

When two lines are crossed by another line (called the Transversal): The angles in matching corners are called Corresponding Angles.

Answer:

it will take 1095 seconds to wash 18 dishes using a pipelined approach

Step-by-step explanation:

Let represent the identity of those three people with :

A

B

C

Now; let the function assigned to those  the people be:

A = Rinse

B =Scrub with soap

C = Dry

For the first dish pipeline

A(RInse) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

The total time taken to complete one dish to wash = (15 +30+  15+15)seconds = 75 seconds

However ; A cannot take the second dish for rinse until the first dish has not been rinse for the second time by A,   A can only start rinse from the second dish when the first dish is at C for dry

SO; for the second dish:

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

Similiarly ; for the third dish

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

B (Scrub with soap) = 30 seconds

A(RInse) = 15 seconds

C(Dry) = 15 seconds

Therefore, the total time taken to was 18 dishes = time to wash the first dish + time remaining for 17 dishes

= 75 +(30+15+15)×17

= 1095 seconds

Hence, it will take 1095 seconds to wash 18 dishes using a pipelined approach

To wash 18 dishes using a pipelined approach, you can assign each friend a different task and work on multiple dishes simultaneously. The total time taken would be 75 seconds.

In order to wash 18 dishes using a pipelined approach, you can assign each friend a different task and work on multiple dishes simultaneously. Here is the step-by-step process:

The total time taken to wash the dishes using this pipelined approach can be calculated as follows:

Total time = (15 seconds) + (30 seconds) + (15 seconds) + (15 seconds)

Total time = 75 seconds

Since the pipelined approach allows you to work on multiple dishes simultaneously, the time taken to wash 18 dishes would be the same as washing a single dish, which is 75 seconds.

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Answer:

We conclude that the new technique is not an improvement over the old technique at 5% level of significance.

Step-by-step explanation:

We are given that the average speed of a baseball line drive is 83 miles per hour.  

His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour.

Let [tex]\mu[/tex] = true average speed using the new technique.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 83 miles per hour     {means that the new technique is not an improvement over the old technique}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 83 miles per hour     {means that the new technique is an improvement over the old technique}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                           T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed using the new technique = 84.2 mph

            s = sample standard deviation = 4.7 mph

            n = sample of hits = 42

So, the test statistics  =  [tex]\frac{84.2-83}{\frac{4.7}{\sqrt{42} } }[/tex]  ~ [tex]t_4_1[/tex]

                                     =  1.655

The value of t test statistics is 1.655.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of 1.6832 at 41 degree of freedom for right-tailed test.

Since our test statistic is less than the critical value of t as 1.655 < 1.6832, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the new technique is not an improvement over the old technique.

The factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).

The given expression is 121b^4 - 49. We can recognize that it is a difference of squares, which can be factored using the formula (a^2 - b^2) = (a + b)(a - b). In this case, a is 11b^2 and b is 7.

Therefore, the factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).

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Answer:

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645*\frac{600}{\sqrt{100}} = 98.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 4500 - 98.7 = 4401.3 gallons

The upper end of the interval is the sample mean added to M. So it is 4500 + 98.7 = 4598.7 gallons

The 90% confidence interval for the average monthly residential water usage for all households in this city is between 4401.3 gallons and 4598.7 gallons.

Answer:

x=\frac{-3}{2}

Step-by-step explanation:

We have been given with the expression (1/3)^x=(27)^x+2

Now, to solve the equation firstly we have to make the base same on both sides

(1/3)^x=3^{-x}

27 can be written as 3^3

27^x=(3^3)^x=3^{3x}

Hence, given expression can be rewritten as

3^{-x}=3^{3(x+2)}

Now since, base is same we can equate the powers on both sides

-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6\Rightarrow x=\frac{-3}{2}

Therefore given expression (1/3)^x=(27)^x+2 is equivalent to x=\frac{-3}{2}

Equivalent means the simplified form of any given expression

The equation is equivalent to [tex]\(\boxed{3^x = 3^{-3x+2}}\)[/tex]

To solve the equation [tex]\((\frac{1}{3})^x = 27^{(x+2)}\)[/tex], we first need to express [tex]\(27\)[/tex] as a power of [tex]\(3\)[/tex], as [tex]\(27 = 3^3\)[/tex]. Then, we rewrite the equation as:

[tex]\[\left(\frac{1}{3}\right)^x = (3^3)^{(x+2)}\][/tex]

Now, we apply the properties of exponents, specifically the power of a power rule which states [tex]\((a^m)^n = a^{m \times n}\)[/tex], to simplify the expression:

[tex]\[\left(\frac{1}{3}\right)^x = 3^{3(x+2)}\][/tex]

Now, we have the same base on both sides of the equation. We can set the exponents equal to each other:

[tex]\[x = 3(x+2)\][/tex]

Now, let's solve for [tex]\(x\)[/tex]:

[tex]\[x = 3x + 6\][/tex]

[tex]\[x - 3x = 6\][/tex]

[tex]\[-2x = 6\][/tex]

[tex]\[x = \frac{6}{-2}\][/tex]

[tex]\[x = -3\][/tex]

Complete correct question:

Which equation is equivalent to [tex]( 1/3 )^x=27^{x+2}[/tex] ?

[tex]3^x=3^{-3x+2}[/tex]

[tex]3^x=3^{3x+6}[/tex]

[tex]3^{-x} =3^{3x+2}[/tex]

[tex]3^{-x} =3^{3x+6}[/tex]

Answer:

y = 3x - 4

Step-by-step explanation:

Start with your point-slope formula which is shown at the

top of the image that is provided below.

Then, plug in your appropriate values for the ordered pair (4, 2).

Now, simplify.

First distribute.

Then add 2 to both sides.

This leaves you with y = 3x - 10.

All my work is in the image attached.

Answer:

  (x +1)(x +24)

Step-by-step explanation:

Factors of 24 that have a sum of 25 are 1 and 24. These are the constants you need in the binomial factors:

  x^2 +25x +24 = (x +1)(x +24)

Answer:

The best point of estimate for the true mean is:

[tex]\hat \mu = \bar X = 2.55[/tex]

[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]    

[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]    

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

[tex]\bar X=2.55[/tex] represent the sample mean for the late time for a flight

[tex]\mu[/tex] population mean

[tex]\sigma=12[/tex] represent the population deviation

n=76 represent the sample size  

Confidence interval

The best point of estimate for the true mean is:

[tex]\hat \mu = \bar X = 2.55[/tex]

The confidence interval for the true mean is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level given is 0.95 or 95%, th significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got [tex]z_{\alpha/2}=1.96[/tex]

Replacing we got:

[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]    

[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]    

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Answer:

B

Step-by-step explanation:

21/25

Work Shown:

21/25 = 84/100 after multiplying top and bottom by 4

Since 84/100 = 84%, this means 21/25 = 84% as well

Alternatively, you can use a calculator or long division to find that 21/25 = 0.84 = 84%

Final answer:

Descriptive and inferential statistics both analyze research data and are used together in scientific studies to summarize, describe, and make predictions about a population based on sample data.

Explanation:

Understanding the similarities between descriptive statistics and inferential statistics is fundamental in scientific investigations. Although these two types of statistics serve different purposes, they share some common ground. Both are used to analyze data collected from a research study and help in making decisions or drawing conclusions about that data.

Descriptive statistics summarize and describe the main features of a dataset. Common descriptive measures include the mean, median, mode (measures of central tendency), and the range, standard deviation, and variance (measures of dispersion). On the other hand, inferential statistics use a random sample of data from a population to make inferences about the overall population. It includes various hypothesis tests and confidence intervals to determine the probability of the occurrence of a particular event.

Both descriptive and inferential statistics rely on the same underlying data collection principles and are often used in tandem. Descriptive statistics generally precede inferential statistics in the data analysis process, providing a foundation for further analysis. Moreover, they both employ graphical and numerical methods to present and summarize data, ensuring the findings are communicated in a clear and easily understood manner.

Ultimately, understanding both types of statistics allows researchers to accurately describe, summarize, and make predictions or generalizations regarding their data, which are crucial steps in any scientific study.

Answer:

Discrete(b,c and d)

Continuous (a and e)

Step-by-step explanation:

Discrete

Discrete Random variables are variables that can only take on integer values. Therefore the following are discrete variables.

b. The number of fish caught during a fishing tournament. e.g. 6 fishes

c. The number of statistics students now reading a book. e.g. 12 Students

d. The number of textbook authors now sitting at a computer. e.g. 9 Authors

Continuous

Continuous random variables can take on an uncountable number of values.

a. The time it takes for a light bulb to burn out. e.g.178.897 seconds

e. The height of a randomly selected giraffe. e,g 16.67 feet

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

Simple

x + 6 < - 8

x < - 8 - 6

x < - 14

x + 4 > - 8

x > - 8 - 4

x > - 12

Option B is the correct answer