Darius filled up his gas tank with 24 gallons of gas. For each mile that he drives, he uses 0.06 gallons of gas.

The critical t-value for a confidence level of 98% with a sample size of 30 is approximately 2.756.

To find the critical t-value for a confidence level of 98% with a sample size of 30, we'll use the t-distribution table or a statistical calculator. Here's how you can calculate it:

Determine the degrees of freedom (df) for the t-distribution. For a sample size of 30, the degrees of freedom will be df = n - 1 = 30 - 1 = 29.

Look up the critical t-value in the t-distribution table using the desired confidence level and the degrees of freedom. In this case, for a 98% confidence level, we're interested in the critical value that leaves 1% in the tails of the t-distribution. Since the distribution is symmetric, we divide the 1% by 2 to get 0.5% for each tail.

Locate the row in the t-distribution table corresponding to the degrees of freedom (29 in this case). Then, look for the column that corresponds to the desired significance level (0.005 or 0.5% in this case).

Using a statistical calculator or t-distribution table, we find that the critical t-value for a 98% confidence level and 29 degrees of freedom is approximately 2.756.

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The critical t-value for a confidence level of 98% is 2.756.

Given data:

To find the critical t-value for a confidence level of 98% with a sample size of 30,  use a t-distribution table or a calculator.

Since the sample size is small (less than 30) and the population standard deviation is unknown, we use the t-distribution instead of the standard normal distribution.

The critical t-value is determined based on the confidence level and the degrees of freedom (df), which is equal to the sample size minus 1.

For a 98% confidence level, the corresponding significance level (α) is 1 - 0.98 = 0.02. Since it's a two-tailed test, divide this significance level by 2 to find the area in each tail: 0.02 / 2 = 0.01.

With a sample size of 30, the degrees of freedom is 30 - 1 = 29.

Using a t-distribution table or a calculator, we find the critical t-value with a cumulative probability of 0.01 (in each tail) and 29 degrees of freedom.

The critical t-value for a confidence level of 98% with a sample size of 30 is approximately ±2.756.

Hence, the critical t-value is 2.756.

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Answer:

directrix: y=4

focus: (-3,2)

vertex: (-3,3)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

w² - 9 can be factored as (w + 3)(w - 3) using the difference of squares. To factor w² - 4w - 21, we need to find 2 integers that have a sum of -4 and product of -21; these integers are -7 and 3 so the factored form is (w + 7)(w - 3). Therefore, the expression becomes:

(w + 3)(w - 3) / (w + 7)(w - 3)

Both the numerator and denominator have a factor of (w - 3) so that cancels out, leaving us with (w + 3) / (w + 7).

Answer:

Everything in the option.

When you know what you are doing and what you are saying then you can be able to convince your audience.

Answer:

I can easily convince people that I'm right

I back up my opinions with facts

Step-by-step explanation:

Correct on E2020

Answer:

B=4i+4j-2k

Step-by-step explanation:

Lets find the length of vector A

IAI= sqrt(2²+2²+1²)=sqrt(9)=3

So B=2*A  = 2(2i+2j-1k)=4i+4j-2k

Answer: What is the question? You have not posted a inquiry...

Step-by-step explanation:

[tex]y = a {(x - h)}^{2} + k[/tex]

[tex]vertex = (h \: \: \: k)[/tex]

from the table

[tex]vertex = ( - 2 \: \: \: 4)[/tex]

therefore

[tex]h = - 2 \: \: and \: \: k = 4[/tex]

[tex]y = a {(x + 2)}^{2} + 4[/tex]

when x= 0, y = 3

[tex]3 = a {(2)}^{2} + 4[/tex]

[tex]3 = 4a + 4[/tex]

[tex]a = \frac{ - 1}{4} [/tex]

therefore equation of the function

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

Answer:

Associative

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Torricelli once carried out a tube and mercury experiment to test the scientific claim that nature abhors a vacuum.

In his experiment, he used glassblowers to make a long glass tube which was 4 ft long with a closed end.

He filled the tube with mercury and put his finger over the open end. Thereafter, he turned the tube upside down, dipped the open end in a bowl of mercury, and then removed his finger from the open end. He discovered that the mercury in the tube didn't completely run out as it fell to around 30 inches above the bowl before it stopped.

The gap between the sealed top end of the tube and the top end of the fallen mercury was an empty space which is a vacuum.

The hypothesis that "nature abhors a vacuum" would have implied that the vacuum would have pulled the mercury and held it up in the tube. However, that wasn't the case with his experiment and it proves that nature doesn't abhor a vacuum.

Thus, it is false.

Answer:

m∠OKG = 95°

Step-by-step explanation:

In the given question,

Angle OKL and angle OKG are the linear pairs.

And we know that sum of linear pair of angles is 180°.

Therefore, m∠OKL + m∠OKH = 180°

85° + m∠OKH = 180°

m∠OKH = 180° - 85°

              = 95°

Therefore, measure of angle OKG = 95° will be the answer.

Complete Question

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between   0  and   7  minutes. Find the probability that a randomly selected passenger has a waiting time  greater than 1.25  minutes.

Answer:

The probability is  [tex]P(X > 1.25) = 0.8214[/tex]    

Step-by-step explanation:

From the question we are told that

    The start time is  a  = 0 minutes

     The end time is  b =  7 minutes

Generally the probability that a randomly selected passenger has a waiting time  greater than 1.25  minutes is mathematically represented as

      [tex]P(X > 1.25) = 1 - P(X \le 1.25)[/tex]  

=>    [tex]P(X > 1.25) = 1 - \frac{1.25 - a}{ b- a }[/tex]  

=>    [tex]P(X > 1.25) = 1 -0.1786[/tex]

=>   [tex]P(X > 1.25) = 0.8214[/tex]    

Answer:

b. [tex]\displaystyle Law\:of\:Cosines[/tex]

Step-by-step explanation:

You would use this law under two conditions:

Hence, you have your answer.

* Just make sure to use the inverse function towards the end, or elce you will throw your answer off!

_______________________________________________

Now, you would use the Law of Sines under three conditions:

* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.

I am delighted to assist you at any time.

Answer:

Conditions for SINE RULE:

Conditions for COSINE RULE:

Step-by-step explanation:

Side is the number in m/cm.

Angle is the number with degree/in degree. Like this: ° ° °

With all these, it means you should COSINE rule.

Answer: c2 - a2 = b2

Step-by-step explanation: to isolate b2 you have to subtract a2 from both sides to get c2 - a2 = b2

Answer:

1 / 962598

Step-by-step explanation:

Let S be the sample space

total number of possible outcomes = n(S)

Let E be the event

total number of favorable outcomes = n(E)

Compute the number of ways to select 5 numbers from 0 through 42:

Total numbers to choose from = 43

So

Total number of ways to select 5 numbers from 43

= n(S) = 43C5                                                                        

= 43! / 5! ( 43-5)!                                                                      

=  43! / 5! 38!                                                                      

= 43*42*41*40*39*38! / (5*4*3*2*1)*38!

= 115511760/120

n(S) = 962598

Hence there are 962598 ways to select 5 numbers from 43

Compute the probability of being a Big Winner

In order to be a Big  Winner all 5 of the 5 winning balls are to be chosen and there is only one way you can for this event to occur. So

n(E) = 1

Here E is to be a Big Winner

So probability of being a Big Winner = P(E)

= n(E) / n(S)

= 1 / 962598

Hence

P(being a Big Winner) = P(E) = 1 / 962598

Answer:

1.1% decrease

Step-by-step explanation:

Use the formula, % change = (difference/original) x 100

Plug in the values:

% change = ((9.69 - 9.58) / 9.69) x 100

= 1.1% decrease

Answer:

[tex]\frac{1716}{132600}[/tex]

Step-by-step explanation:

Assuming they removed the jokers there are 52 cards in a deck and 13 hearts

You can calculate the odds of something by multiplying the odds together, because you don't put back the card you drew you have to subtract 1 from both the numerator and denominator

[tex](\frac{13}{52})(\frac{12}{51})(\frac{11}{50})=\frac{1716}{132600}[/tex]

Therefore the probability of pulling 3 cards that are all hearts are [tex]\frac{1716}{132600}[/tex]

Answer:

We conclude that the pulse rate for smokers and non-smokers is equal.

Step-by-step explanation:

We are given that a medical researcher wants to compare the pulse rates of smokers and non-smokers.

A sample of 75 smokers has a mean pulse rate of 76, and a sample of 73 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 9 for smokers and 10 for non-smokers.

Let [tex]\mu_1[/tex] = true mean pulse rate for smokers

[tex]\mu_2[/tex] = true mean pulse rate for non-smokers

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]    {means that the pulse rate for smokers and non-smokers is same}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]    {means that the pulse rate for smokers and non-smokers is different}

The test statistics that will be used here is Two-sample z-test statistics because we know about the population standard deviations;

                       T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2}} }[/tex]  ~  N(0,1)

where, [tex]\bar X_1[/tex] = sample mean pulse rate of smokers = 76

[tex]\bar X_2[/tex] = sample mean pulse rate of non-smokers = 72

[tex]\sigma_1[/tex] = population standard deviation of the pulse rates of smokers = 9

[tex]\sigma_2[/tex] = population standard deviation of the pulse rates of non-smokers = 10

[tex]n_1[/tex] = sample of smokers = 75

= sample of smokers = 73

So, the test statistics =  [tex]\frac{(76-72)-(0)}{\sqrt{\frac{9^{2} }{75}+\frac{10^{2} }{73}} }[/tex]

                                    =  2.56  

The value of the z-test statistics is 2.56.

Also, the P-value of the test statistics is given by;

                P-value = P(Z > 2.56) = 1 - P(Z [tex]\leq[/tex] 2.56)

                              = 1 - 0.9948 = 0.0052

For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0052 = 0.0104.

Now, at a 0.01 level of significance, the z table gives a critical value of -2.58 and 2.58 for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the pulse rate for smokers and non-smokers is equal.

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]

Div and Curl:

Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]

First, let's define what we are given:

[tex]\displaystyle \text{F} = x^2 \hat{\i} + y^2 \hat{\j} + z \hat{\text{k}}[/tex]

Region D is the solid cube cut by coordinate planes and planes [tex]x = 2[/tex]. [tex]y = 2[/tex], and [tex]z = 2[/tex]

In order to use the Divergence Theorem, we first must find div F. We use partial differentiation and differentiation properties found under "Calculus" to attain div F:

[tex]\begin{aligned}\nabla \cdot \text{F} & = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial z}(z) \\& = 2x + 2y + 1 \\\textbf{div} \ \text{F} & = \boxed{2x + 2y + 1}\end{aligned}[/tex]

∴ [tex]\displaystyle \boxed{ \textbf{div} \ \text{F} = 2x + 2y + 1 }[/tex]

In order to find the outward flux of F across region D, we now must use the Divergence Theorem. Substitute our knowns into the Divergence Theorem Formula listed under "Multivariable Calculus":

[tex]\displaystyle \iiint_D \nabla \cdot \textbf{F} \, dV = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz[/tex]

We can now evaluate the Divergence Theorem integral using basic + advanced integration techniques listed under "Calculus" and learned from "Multivariable Calculus":

[tex]\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dz \, dy \, dx \\& = \int\limits^2_0 \int\limits^2_0 {(2x + 2y + 1)z \bigg| \limits^2_0} \, dy \, dx \\& = 2 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dy \, dx \\& = 2 \int\limits^2_0 {\bigg( 2xy + y^2 + y \bigg) \bigg| \limits^2_0} \, dx \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = 2 \int\limits^2_0 {4x + 6} \, dx \\& = 2 \bigg[ 2x^2 + 6x \bigg] \bigg| \limits^2_0 \\& = 2(20) \\& = \boxed{40} \\\end{aligned}[/tex]

∴ the integrals evaluates to 40.

[tex]\displaystyle \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz = \boxed{40}[/tex]

___

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Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

Answer:

C

Step-by-step explanation:

We need to first rewrite the equation the proper way.

(-2x+4x²+5)-(x²+3x)

We need to distribute the negative thought the 2nd set of parenthesis.

-2x+4x²+5-x²-3x

combine the same terms

3x²-5x+5

Answer:

13791

Step-by-step explanation:

Take 96,537 and divide by 7

Answer:

1/204

Step-by-step explanation:

6/18 * 5/17 * 4/16 * 3/15

= 1/3 * 5/17 * 1/4 * 1/5

= 1/204

Answer:

10.9 liters

Step-by-step explanation:

cubical tank size = 30 x 30 x 30

filled with 6 cm x 30 cm x 30 cm = 5400 cu.cm

then added 5500 cu.cm.

total volume on a cubical tank = 5400 cu.cm + 5500 cu.cm

total volume on a cubical tank = 10,900 cu.cm x 1 cu.cm/0.001 liters

total volume on a cubical tank = 10.9 liters

Answer:

Step-by-step explanation:

= 10.9 liters

In a parallelogram opposite angles are identical so K and M are the same. Solve for K first:

6x +3 = -9 + 7x

Add 9 to both sides:

6x + 12 = 7x

Subtract 6x from both sides:

X = 12

K = 6(12) + 3 =72 +3 = 75

Now K + N = 180

N = 180 - 75 = 105

N = 105

Answer:

ANGLE N = 105°

Step-by-step explanation:

The opposite angles of a parallelogram are equal

Therefore,

-9+7x = 6x+3

Bringing variables to one side

7x-6x = 3+9

x= 12

Since , x = 12

So , Angle K = 6x+3= 6(12)+3

= 72+3

=75

In a parallelogram , adjacent angles are supplementary

i.e, Angle K +Angle N = 180°

75 + Angle N = 180°

Angle N = 180 -75

= 105 °

Answer:

The correct answer is: (x,y)↦(x+ 8 ,y+ 16)

Hoped I helped

The required value of the triple integral is (16/3)π.

To evaluate the triple integral ∫∫∫E z dV, where E lies above the paraboloid z = x² + y² and below the plane z = 2y, we can use cylindrical coordinates.

In cylindrical coordinates, we have:

x = r cosθ

y = r sinθ

z = z

To determine the limits of integration, we need to find the bounds for r, θ, and z.

The paraboloid z = x² + y² can be expressed in cylindrical coordinates as z = r².

The plane z = 2y can be expressed in cylindrical coordinates as z = 2r sinθ.

To find the bounds for r, we set the two equations equal to each other:

r^2 = 2r sinθ

Simplifying the equation, we have:

r = 2 sinθ

Since the paraboloid lies above the xy-plane, the lower bound for r is 0.

To find the bounds for θ, we need to determine the range of θ that corresponds to the region of interest. This can be done by plotting the two surfaces and visualizing the region. From the equations, we can see that the region lies within the range 0 ≤ θ ≤ π.

To find the bounds for z, we need to determine the range of z between the two surfaces. The paraboloid is below the plane, so the lower bound for z is the equation of the paraboloid, z = r^2. The upper bound for z is the equation of the plane, z = 2r sinθ.

Therefore, the limits of integration are as follows:

0 ≤ r ≤ 2 sinθ

0 ≤ θ ≤ π

r² ≤ z ≤ 2r sinθ

Now, we can evaluate the triple integral:

∫∫∫E z dV = ∫[0,2π] ∫[0,∞] ∫[r²,(2r sin θ)] (r cos(φ) sin(θ)) dz dr dθ
               = (16/3)π

Therefore, the value of the triple integral is (16/3)π.

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Answer:

-82°

Step-by-step explanation:

If we go 82° below 0, that means that instead of increasing by 82, we are decreasing by 82.

If we decrease to a number below 0, it becomes a negative number.

For example: If we decrease 10° from 0, we'd be at -10°.

Likewise, if we decrease 2° from 0, we'd be at -2°.

Following this pattern, if we decrease 82° from 0, we'd be at -82°.

Hope this helped!

Answer:

110 cupcakes are left

Step-by-step explanation:

200-90 is 110

Answer:

110 cupcakes

Step-by-step explanation:

If you have 200 cupcakes and you give away 90, that means you only have [tex]200-90[/tex] cupcakes left.

[tex]200 - 90 = 110[/tex]

So you have 110 cupcakes left.

Hope this helped!

Answer:

Step-by-step explanation:

Step 1: the first term a is 13

Which means a=13 let's make this equation i

And the third term ar^3-1 = 1208

= Ar²= 1208 let's make this equation ii

Step 2: subtititute equation i into equation ii

= 13r²=1208

Divide both sides by 13 it gives us

13r²/13 = 1208/13

r²= 92.92

r= 9.64

So the second term ar^2-1

=ar

= 13. 9.64

= 125.32