Bob rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 75 cents for each mile driven. Bob had to pay $159.24
when he returned the truck. For how many miles did he drive the truck?

Here null hypothesis is rejected in this problem.

According to the statement

We have a given that the evidence at alpha level is 0.02, ANd the sample size n is 67. And mean time equal to 330 minutes and the variance that is the sigma square is equal to 529 point.

And We have to make the decision to reject or feel fail to reject the null hypothesis to solve this problem.

Firstly we solve alternative and null hypothesis

So, the null hypothesis h naught will be that mu is less than equal to 327 point and alternative hypothesis ha will be.

That mu is greater than 327 point now. This alternative hypothesis is claimed.

Next we will find the value of s which is given by sigma divided by under root n.

So, s = 67/ (529)^1/2

s = 2.8099.

Now we find the value of Z

So, Z = 327 - 330 / 2.8099

Z = 1.0677

Now the critical value of z is 2.05

Critical, we can say fail to reject the null hypothesis, and this is the result from the null hypothesis test.

With this test, we can conclude that the the data do not support that. There is evidence at 0.02 level that the drug stays in the system for more than 327 minutes. So this is the conclusion for the test for the hypothesis test and the answer to the problem.

So, Here null hypothesis is rejected in this problem.

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The polynomial function \(\(f(x) = 2(x^2+3)(x+1)^2\)\) has zeros at -3 with multiplicity 1, and -1 with multiplicity 2. The graph of the function crosses the x-axis at -3 and -1.

To find the zeros and their multiplicities, we set \(\(f(x)\)\) equal to zero and solve for \(\(x\).\)

Setting \(\(f(x) = 0\),\) we have:

\(\[2(x^2+3)(x+1)^2 = 0\]\)

Since the product of two factors is zero, at least one of the factors must be zero. Thus, we solve for \(\(x\)\) in each factor separately:

1. \(\(x^2 + 3 = 0\):\)

  This equation does not have real solutions since the square of a real number is always non-negative. Therefore, this factor does not contribute any real zeros.

2. \(\(x + 1 = 0\):\)

  Solving for \(\(x\), we find \(x = -1\).\) This gives us a zero at -1 with multiplicity 1.

Since the factor \(\((x+1)^2\)\) is squared, the zero -1 has a multiplicity of 2.

Therefore, the zeros for the polynomial function are -3 with multiplicity 1 and -1 with multiplicity 2. The graph of the function crosses the x-axis at both zeros.

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Answer: the third one

Step-by-step explanation:Hope this is correct

This situation should be analyzed using a two-sample independent method. The two-sample independent method is used when comparing two independent groups, in this case, taxi ride times in San Diego and Phoenix. The two-sample paired method is used when comparing the same group under two different conditions, which is not the case here, as the taxi ride times are taken from two separate cities. There is no common characteristic that makes these data paired.

A two-sample independent method is used to compare the means of two independent populations, which is appropriate for this situation. The independent samples t-test is a common statistical test used to compare the means of two independent populations.On the other hand, if the data were obtained from the same set of taxis in both cities or from the same set of riders in both cities, then the situation would be a paired situation, and a two-sample paired method would be more appropriate.Paired data refers to data that is collected from the same sample, subject, or group at different points in time or under different conditions. For example, if the data were obtained from the same set of taxis in both cities, then the data would be paired because each taxi in San Diego would have a corresponding taxi in Phoenix. Similarly, if the data were obtained from the same set of riders in both cities, then the data would be paired because each rider in San Diego would have a corresponding rider in Phoenix.In summary, since the data in this situation were obtained from two different cities, a two-sample independent method is appropriate. If the data were obtained from the same set of taxis or riders in both cities, a two-sample paired method would be appropriate.

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Answer:

whats the question?

Step-by-step explanation:

The statement "To determine chilling hours for an area, count the cumulative number of hours between November 1st and February 15th that the air temperature is between 32 and 45 degrees F" is true.

In horticulture, chilling hours are the number of hours in which the air temperature is between 32 and 45 degrees Fahrenheit and are commonly used in fruit crop production to determine the required winter rest period. It is calculated between November 1st and February 15th since these months are considered the winter season and are known for their cool temperatures.

Chilling hours are an essential factor in determining the growth, development, and yield of fruit trees, which require a particular amount of chilling hours to flower and bear fruit.

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Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

The absolute value is:

Work/explanation:

First, we will evaluate 2-7.

It evaluates to -5.

Now, let's find the absolute value of -5 by using these rules:

\(\sf{\mid a\mid=a}\)

\(\sf{\mid-a \mid=a}\)

Similarly, the absolute value of -5 is:

\(\sf{\mid-5\mid=5}\)

2. 8.472 * 10^5 in standard form is

3. The scientific notation of 0.000067 is 6.7 * 10^-5

4. The division gives 4.455 * 10^3

Scientific notation is a way of expressing very large or very small numbers in a compact and convenient way.

In scientific notation, a number is written as a coefficient multiplied by a power of 10.

The coefficient is a number between 1 and 10 (or between -1 and -10 for negative numbers), and the power of 10 indicates the size of the number.

Calculator can be used to get numbers to scientific notation and in standard form

The required division can be performed using calculator to get 4.455 * 10^3

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Answer:

8.5 hrs? direct variation

Step-by-step explanation:

60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator

600/60 =10

600/70 = 8.5

and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure

Answer:

His total profit is $213.00

Step-by-step explanation:

He spent $90 on tires ($45x2), $255 on rims ($85x3), and $25 on headlights ($5x5), spending a total of $370.

He sold the tires for a total of $130 ($65x2), the rims for a total of $378 ($126x3), and the headlights for a total of $75 (15x5), a total of $583.  

To find his final profit, you need to subtract what he spent from what he earned when he sold the items.  ($583-$370= $213).

The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .

As given in the question,

Total number of voters in California = 7525

x₁ = Number of voters of central valley residents approved California legislature

   = 68

n₁ = Total number of voters of central valley residents

   = 200

x₂ = Number of voters of bay area residents approved California legislature

   = 156

n₂= Total number of voters of bay area residents

   = 300

p₁ = proportion of voters of central valley

p₂= proportion of voters of bay area

p₁ = x₁/ n₁

   = 68/200

   = 0.34

p₂ = x₂/n₂

    = 156/300

    = 0.52

Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂

                        = √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300

                        = √0.001122 + 0.000832

                        = 0.044

\(p_{w}\) = (68 + 156 )/ (200 + 300)

   = 0.448

\(q_{w} = 1- p_{w}\)

    = 1 - 0.448

    = 0.552

null hypothesis p₁ - p₂ = 0

z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)

  = 4

Tabular value for confidence interval 95% = 1.96

4 > 1.96

We reject the null hypothesis.

Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.

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Answer:

-4.2

Step-by-step explanation:

-2 4/5 - 1 .4

-2.8 -1.4

-4.2

Answer:

-21/5

-4.2- decimal form

-4 1/5- mixed number form

Step-by-step explanation:

\(\sf\purple{24}\) ✅

Step-by-step explanation:-

\( - 12 \times 2 \times - 1 \\ = 24\)

Note:-

\(( - \times - ) = + \)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

Step-by-step explanation:

adding all the angles then equate it to 180

x-5+2x+2x-10=180

5x-15=180

5x=195

x=39

to check, plugin x which is 39 into the given angles.

like, 39-5=34 and 2(39)=78 and 2(39)-10= 68

and all of this must be equal to 180 because the angle in a triangle is always 180 degrees.

So, 34+78+68=180

The correct answer is option b) Bacteria in samples 2 and 3 mutated quickly to adjust to temperature change.

From the given graph it is seen that sample 1 is not showing any growth or decline despite of the temperature change. One cannot ascertain its gene expression. On the other hand, Sample 2 shows a slight change from 4cm² to 7cm² bacteria count and Sample 3 shows a wide change as per temperature change from 8cm² to 12cm². Hence it can be said that samples 2 and 3 mutated to adjust to the temperature compared to sample 1 which showed no changes.

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Complete Question

the graph below shows the growth of three samples of the different bacteria on Petri dishes incubated over 24 hours as the temperature was increased 10 degrees every eight hours: (Graph in the figure attachment) which statement best explains the data trend observed in the bacteria samples?

a) All bacteria samples grow better at higher temperatures.

b) Bacteria in samples 2 and 3 mutated quickly to adjust to temperature change.

c) Temperature changes do not affect gene expression for growth in sample 1.

d) Bacteria in sample 1 will eventually die out at higher temperatures.

The mass of 1 liter (1000 mL or 1000 cm(^3)) of Argon would be 1.78 grams.

To determine the number of atoms of Argon required to make a line 1 inch long, we need to calculate the number of atoms that can fit within that length.

First, we convert the atomic radius of Argon from picometers (pm) to inches.

1 inch = 2.54 cm = 2.54 * 10^7 pm (since there are 10^12 picometers in a meter)

The atomic radius of Argon is 188 pm, we can convert it to inches:

188 pm * (1 inch / 2.54 * 10^7 pm) = 7.40157 * 10^(-6) inches

Next, we calculate the number of atoms that can fit in 1 inch:

Since the atomic radius represents half the length of an atom, we double it to get the length of a single atom:

2 * 7.40157 * 10^(-6) inches = 1.48031 * 10^(-5) inches

To find the number of atoms that can fit in 1 inch, we divide the length of 1 inch by the length of a single atom:

1 inch / (1.48031 * 10^(-5) inches) = 6.751 * 10^4 atoms

Therefore, approximately 67,510 atoms of Argon must be lined up to make a line 1 inch long.

B. To calculate the mass of 1 liter (1000 (cm^3)) of Argon, we need to use its density:

Density = mass / volume

Rearranging the equation, we can solve for mass:

Mass = Density * Volume

Since the volume is given in cm(^3) and the density is given in g/cm^3, the resulting mass will be in grams.

Given that the density of Argon is 1.78 * 10^(-3) g/cm^3 and the volume is 1000 cm^3, we can calculate the mass:

Mass = 1.78 * 10^(-3) g/cm^3 * 1000 cm(^3) = 1.78 grams

Therefore, the mass of 1 liter (1000 mL or 1000 cm(^3) )of Argon would be 1.78 grams.

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Answer:  k = 3

Step-by-step explanation:

1

Combine multiplied terms into a single fraction

4

.

5

+

1

.

5

Answer:

Thr33

Step-by-step explanation:

3

a. Two populations.

b. Qualitative (categorical) data.

c. Proportion stats.

d. Null hypothesis: p1 = p2 (The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch). Alternative hypothesis: p1 > p2 (The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch).

e. Z-test for two proportions.

f. P-value.

g. A small P-value provides convincing evidence to support Phoebe's hunch that older students are more likely to bring a bag lunch than younger students.

h. 95% confidence interval to estimate the difference in proportions.

What is hypothesis?

A hypothesis is a proposed explanation or assumption that is tested through research and data analysis. It is a statement that suggests a relationship or difference between variables or phenomena and serves as a basis for scientific investigation.

a. There are two populations in this problem: the population of seniors and the population of sophomores.

b. This is a problem about qualitative (categorical) data since we are examining whether students bring a bag lunch or not.

c. We will use the proportion stats option in StatCrunch to complete this problem.

d. Null hypothesis (H0): The proportion of seniors who bring a bag lunch is equal to the proportion of sophomores who bring a bag lunch.

Alternative hypothesis (Ha): The proportion of seniors who bring a bag lunch is greater than the proportion of sophomores who bring a bag lunch.

e. The test statistic is the z-test for two proportions.

f. The P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

g. The strength of the P-value determines the level of evidence against the null hypothesis. If the P-value is small (below the significance level), it provides strong evidence against the null hypothesis. In this case, a P-value less than 0.05 (assuming significance level α = 0.05) would suggest convincing evidence to support Phoebe's hunch.

h. To construct a 95% confidence interval to estimate the difference in proportions, we use the formula:

Confidence interval = (p1 - p2) ± z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and z is the critical value corresponding to the desired confidence level (in this case, z value for a 95% confidence level).

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Answer:

Step-by-step explanation:

Answer:

(0, 25) or (3, 20) or (6, 15) or (9, 10) or (15, 0)

Step-by-step explanation:

Answer:

40353607

Step-by-step explanation:

just write the numbers out to find the answer

f(g(7)) = 7, and g'(7) = -14.

To calculate g'(x) where g is the inverse of f, we will use the Inverse Function Theorem.

The theorem states that if f and g are inverses, then g'(x) = 1 / f'(g(x)).

We have f(x) = (3-x) and its inverse, g, has a relation with the function f'(x) = x^3 + 2x + 3.

Let's find g(7) and g'(7)

We know that f(g(x)) = x, so f(g(7)) = 7.

Differentiate f(x) = Sqrt(3-x) with respect to x.
f'(x) = -1 / (2 * Sqrt(3-x))

we know that g(7) satisfies the equation f(g(7)) = 7.
Since f(x) = Sqrt(3-x), we have Sqrt(3-g(7)) = 7.

Now we can use this to find f'(g(7)):
f'(g(7)) = -1 / (2 * Sqrt(3-g(7))) = -1 / (2 * 7)

Using the Inverse Function Theorem, g'(7) = 1 / f'(g(7)).
So, g'(7) = 1 / (-1 / (2 * 7)) = -2 * 7 = -14

g(7) satisfies the equation f(g(7)) = 7, and g'(7) = -14.

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Answer:yes they are

Step-by-step explanation:

5.) The values of the missing side length of triangle DEF; f = 7.01; d = 7.9

To calculate the value of the missing length of the given triangles, the sine rules must be obeyed.

That is;

e/sinE = d/sinD

Where;

e=line FD = 12

E= 180-(39+34)

= 180 - 73

= 107°

d.= line FE = ?

D = 39°

That is ;

12/sin107° = d/sin39°

Make b the subject of formula;

d = 12×sin 39°/sin107°

d = 12×0.629320391/0.956304755

d = 7.9

Also;

e/sinE = f/sinF

That is;

12/sin107 = f/sin34

f= 12×0.559192903/0.956304755

f= 7.01

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