Solve the inequality 4x- 7 < 5

Given:

Given that the figure is a triangular prism.

The length of the prism is 4 m.

The base of the triangle is 2.5 m.

The height of the triangle is 2.25 m.

We need to determine the volume of the triangular prism.

Volume of the triangular prism:

The volume of the triangular prism can be determined using the formula,

[tex]V=\frac{1}{2}bhl[/tex]

where b is the base of the triangle,

h is the height of the triangle and

l is the length of the prism.

Substituting b = 2.5, h = 2.25 and l = 4 in the above formula, we get;

[tex]V=\frac{1}{2}(2.5)(2.25)(4)[/tex]

[tex]V=\frac{1}{2}(22.5)[/tex]

[tex]V=11.25 \ m^3[/tex]

Thus, the volume of the triangular prism is 11.25 m³

Answer:

Uhhhhhhhhhhhhh  yes most recipies do call for that

Step-by-step explanation:

have a nice day

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. Then, the probability of staying in the same state is 90%.

-  For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. Then, the probability of staying in the same state is 80%.

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. Then, the probability of staying in the same state is 82%.

The transition matrix becomes:

[tex]\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}[/tex]

The actual state matrix is

[tex]\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right][/tex]

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

[tex]\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right][/tex]

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

[tex]\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right][/tex]

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

[tex]\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right][/tex]

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Answer:

7  2/3

Step-by-step explanation:

Multiply 4/3 by 23/4

Answer:5

Step-by-step explanation:

Answer: $9.58

Step-by-step explanation: A pound of apples cost $1.99, so you multiply 1.99 and 1.8.(the pounds he got)

1.99x1.8= 3.58 (Cost of 1.8 pounds of apples)

A pound of strawberries cost 2.00, so you multiply 2.00 and 3 (the pounds he got)

2.00x3= $6.00

Add $3.58+$6.00= $9.58

Answer:

a movie, m is 3

a video game, v is 5.5

Brainliest would be really appreciated. (need it to unlock chat)

Feel free to ask further questions if you feel like it.

Till then, have a nice day

Step-by-step explanation:

I 5m+2v=26

II 3m+8v=53

I 5m+2v=26 devide by 2 on both sides

5/2m+v=13 subtract 5/2m om both sides

v=13-5/2m

Now put this whole thing in the other equation II, replacing the v there

3m+8(13-5/2m)=53 just calculate it

3m+104-20m=53

-17m+104=53 subtract 53 on both sides

-17m+51=0 add 17m on both sides

51=17m devide by 17

3=m

we found m, v is easy

now put m in an equation from the start, let's take equation I here

I 5m+2v=26

5*(3)+2v=26

15+2v=26 subtract 15 on both sides

2v = 11 devide by 2

v = 5.5

So we found m and v, prices for single items. we can proof this when we put m and v into a given equation and the if it equals a true value

m & v in II

II 3m+8v=53

3*(3)+8*(5.5)=53

9+44=53

53=53

Seems legit.

To find the rental cost for each movie and video game, set up a system of equations based on the given information and solve for the variables.

To find the rental cost for each movie and video game, we can set up a system of equations based on the given information.

Let's assign variables to represent the rental cost for each movie and video game. Let's use 'm' for the cost of a movie and 'g' for the cost of a video game.

Based on the first month's information, we can write the equation: 5m + 2g = 26

Based on the second month's information, we can write the equation: 3m + 8g = 53

Now we can solve this system of equations to find the values of 'm' and 'g'.

By solving the system of equations, we find that the rental cost for each movie is $4 and the rental cost for each video game is $5.

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Answer:

1) We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

2) [tex]df=n-1=8-1=7[/tex]  

Since is a one sided test the p value would be:  

[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]  

3) For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=6.5[/tex] represent the sample mean

[tex]s=1.9[/tex] represent the sample standard deviation

[tex]n=8[/tex] sample size  

[tex]\mu_o =5[/tex] represent the value that we want to test

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

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

Part 1: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is higher than 5 gpm, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

If we analyze the size for the sample is <30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{6.5-5}{\frac{1.9}{\sqrt{8}}}=2.233[/tex]    

Part 2: P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=8-1=7[/tex]  

Since is a one sided test the p value would be:  

[tex]p_v =P(t_{(7)}>2.233)=0.0304[/tex]  

Part d: Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant higher compared to the height of men in 1960 at 1% of signficance.  

Part 3

For this case is we use a significance level of 1% or 99% of confidencewe see that [tex]p_v >\alpha[/tex] and we don't have enough evidence to conclude that the specification is satified. But if we use a value of significance [tex]\alpha=0.05[/tex] or 95% of confidence we see that [tex]p_v <\alpha[/tex] and we have enough evidence to conclude that the specification is satisfied.

Answer:

y=25

Step-by-step explanation:

10*2=20

20+5=25

Final answer:

When x=10, the value of the function y=2x+5 is 25, found by substituting 10 for x and following the order of operations.

Explanation:

The value of the function y=2x+5 when x=10 can be found by substituting the value of x into the equation. To do this, multiply 2 by 10 and then add 5 to the result:

y = 2(10) + 5

y = 20 + 5

y = 25

Therefore, when x equals 10, the value of the function is 25.

Answer:

79.45

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the optimal production schedule to maximize profits, we need to create a linear programming model using the simplex method.

To determine the optimal production schedule to maximize profits, we need to create a linear programming model using the simplex method. Let's define our decision variables as follows:

Our objective is to maximize the profit, so our objective function can be written as:

Z = 2.5x + 2y

We have the following constraints:

To solve this linear programming problem with the simplex method, we will use a software or calculator that supports linear programming.

Answer:

(a)f(x)=0.8869x

(b)g(x)=143.1126x

(c)g(f(x))=126.9266x

(d)g(f(1000))=126926.6 Yen

Step-by-step explanation:

Given on a particular day

(a)If x represents the number of Dollars

Since one can purchase 0.8869 Euro with 1 USD, the function f(x) is a direct relationship where x is dollars and f(x) is in Euros.

(b)If x represents the number of Euros

Since one can purchase 143.1126 yen with 1 Euros, the function g(x) is a direct relationship where x is Euros and g(x) is in Yen.

(c)Given:

g(f(x))=143.1126(0.8869x)

(d)g(f(1000))

Answer:

5

Step-by-step explanation:

f(-4) f(x)=-2x-3

f(-4)=-2(-4)-3

f(-4)=8-3

f(-4)=5

Answer:

5

Step-by-step explanation:

you imput -4 for x then you proceed as normal solving the equation

-2(-4) - 3 since two negatives when multiplied make a positive

8 - 3

5

Answer:

Step-by-step explanation:

The first derivative is ...

  f'(x) = 30x^5 -40x^3 = 10x^3(3x^2 -4)

This will have zeros (critical points) at x=0 and x=±√(4/3).*

We don't need the second derivative to tell the nature of these critical points. Since the degree is even, the function is symmetrical about x=0. Since the leading coefficient is positive, it generally has a U-shape. This means the "outer" critical points will be minima, and the central one will be a local maximum.

__

However, since we're asked to use the 2nd derivative test first, we find the 2nd derivative to be ...

  f''(x) = 150x^4 -120x^2 = 30x^2(5x^2 -4)

For x=0, f''(0) = 0 -- as we expect for a function with a high multiplicity of the root at that point. For x either side of zero, both the function and the second derivative are negative, indicating downward concavity. That is, x = 0 is a local maximum.

For x² = 4/3, the second derivative is positive, indicating upward concavity. At x = ±√(4/3), we have local minima.

_____

* The "simplified" equivalent to √(4/3) is (2/3)√3.

The critical points of the function f(x) = 5x^6 − 10x^4 are x = 0, x = ±√(4/3). The point at x = 0 is a relative maximum while the points at x = ±√(4/3) are relative minima based on the second derivative test.

Given the function f(x) = 5x^6 − 10x^4, we first find the critical points. This is done by finding the derivative of the function and setting it equal to zero. For this function, the derivative, f'(x), is 30x^5 - 40x^3 = 0. Solving this equation for x, we get x = 0, and x = ±√(4/3).

Next, we apply the second derivative test by taking the second derivative of the original function, f''(x). This gives us f''(x) = 150x^4 - 120x^2. We substitute the obtained critical points into the second derivative. If f''(x) > 0, then the point is a relative minimum, if f''(x) < 0, it's a relative maximum. If neither, we need to consider higher order derivatives or other methods.

The second derivative is negative at x = 0, so that position is a relative maximum. The second derivative is positive at x = ±√(4/3), so these positions are relative minima.

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Answer:

a) The test statistic is z=-0.94

b) The p-value is 0.1736

c) The null hypothesis is [tex]H_0:p=0.10[/tex], we can conclude that, if the result is not significant at 0.01 level, we fail to reject the null hypothesis

d) We fail to reject the null hypothesis at 0.01 significance level.

e) We do not have sufficient  evidence to reject the claim that, less than 10​% of the treated subjects experienced headaches.

Step-by-step explanation:

The test statistic is defined by:

[tex]Z=\frac{\hat p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n} } }[/tex]

It was given that, 23 of 277 treated in the clinical trial of the​ drug subjects experienced headaches.

This means that:

[tex]\hat p=\frac{23}{277}\approx 0.083[/tex]  and n=277

The  claim is that, less than 10​% of treated subjects experienced headaches. This means:

[tex]p_0=\frac{10}{100}=0.1[/tex]

We substitute the values into the formula to obtain:

[tex]Z=\frac{0.083-0.1}{\sqrt{\frac{0.1(1-0.1)}{277} } }[/tex]

The test statistics becomes:

[tex]Z=-0.94[/tex]

b) From the normal distribution table, the p-value corresponds to Z=-0.94 .

Since this is a left-tailed test, the p-value corresponds to area under the normal curve that is to the left of z=-0.94

P(Z<-0.94)=0.173609.

c) Since the claim is that, less than 10​% of treated subjects experienced headaches, the null hypothesis is

[tex]H_0:p=0.10[/tex]

The alternate hypothesis will be:

[tex]H_1:p\:<\:0.10[/tex]

This implies that, the result is not significant at 0.01 alpha level.

d) We need to compare the p-value to the significance level. If the significance level is greater than the null hypothesis, we reject the null hypothesis.

Since 0.01<0.1736, we fail to reject the null hypothesis.

d) Conclusion: There is no enough evidence to reject the claim that, less than 10​% of treated subjects experienced headaches.

Answer:

(a)Test statistic[tex]z_{score}=-0.94[/tex]

(b) p-value=0.1736

(c)Null hypothesis,

    [tex]H_0:p=0.10[/tex]

(d)[tex]\alpha>p[/tex], we reject the null hypothesis.

(e)We have experimental values to reject the claim.

Step-by-step explanation:

Given information;

n=277

Significance level [tex]\alpha[/tex]=0.01

By normal distribution,

[tex]z_{score}=\frac{\widehat{p}-p_0}{\frac{\sqrt {p_0(1-p_0)}}{n}}[/tex]

[tex]\widehat{p}=\frac{23}{277}=0.83[/tex]

[tex]p_0=10[/tex]%=0.1

On substitution,

[tex]z_{score}=\frac{{0.83}-0.1}{\frac{\sqrt {0.1(1-0.1)}}{277}}[/tex]

Test static,

[tex]z_{score}=-0.94[/tex]

b)From the table normal distribution,

for,[tex]z_{score}=-0.94,[/tex]

[tex]P(z<-0.94)=0.173609[/tex]

(c)Null hypothesis,

    [tex]H_0:p=0.10[/tex]

     Alternate hypothesis,

    [tex]H_1:p<0.10[/tex]

It implies result is not significant at

[tex]\alpha=0.01[/tex]

(d) On compare value if

[tex]\alpha>p[/tex], we reject the null hypothesis.

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Answer:

(C)Educated people have higher savings than those who are not educated

Step-by-step explanation:

The model which is used to determine the annual savings of an individual on the basis of his annual income and education is given below:

[tex]Savings = \beta_0+\delta_0 Edu + \beta_1Inc+u[/tex]

The variable "Edu" takes a value of 1 if the person is educated. The coefficient [tex]\delta_0[/tex] measures the impact of education on a certain individual’s annual savings. If [tex]\delta_0[/tex]>0, it has a positive impact. Therefore, educated people should have higher savings than those who are not educated.

Answer:

P(Fewer than 3) = 0.05.

Step-by-step explanation:

We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.

The above situation can be represented through Binomial distribution;

[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]

where, n = number of trials (samples) taken = 10 questions

            r = number of success = fewer than 3

           p = probability of success which in our question is probability

                that question is answered correctly, i.e; 50%

LET X = Number of questions answered correctly

So, it means X ~ Binom(n = 10, p = 0.50)

Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)

P(X < 3)  = P(X = 0) + P(X = 1) + P(X = 2)

=  [tex]\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}[/tex]

=  [tex]1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}[/tex]

=  0.05

Hence, the P(Fewer than 3) is 0.05.

To find the probability of the student passing the test with at least a 70 percent, we can use the binomial probability formula. The probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).

To find the probability of the student passing the test with at least a 70 percent, we need to find the probability of the student answering 7, 8, 9, or 10 questions correctly out of the 10 questions. Since the student randomly guesses at each answer, the probability of guessing correctly is 0.5. Now we can calculate the probability using the binomial probability formula:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

P(X = k) = C(10, k) * (0.5)^k * (0.5)^(10-k), where C(n, r) is the binomial coefficient (n choose r).

Calculating each probability and summing them up, we get P(X ≥ 7) = 0.171875. Therefore, the probability of the student passing the test with at least 70 percent is 0.1719 (rounded to 2 decimal places).

Answer:

3 time 4 is 12 a and b is the same

Answer:

Dimensions of matrix:

r × c

r: no. of rows

c: no. of columns

Answer:

a) 83%

b) 0.892

Step-by-step explanation:

percentage that attends class on friday = 74%

percentage that pass because they attend class on friday = 88%

percentage that pass but did not go to school on friday = 20%

a) percentage of students expected to pass the course

  = (74% x 88%) +(88% x 20%)

   = 0.6512 + 0.176

   = 0.8272

   = 83%

b) If a person passes the course, what is the probability that he/she attended classes on Fridays

        = 74% divided by 83%

        = 0.892

Answer:

2.47 times more likely.

Step-by-step explanation:

16 out of 178 cases were reported for exposure.

And 8 out of 220 control reported for exposure.

Chances that a case would be reported for exposure = (16/178) = 0.0898876404

Chances that one control would report for exposure = (8/220) = 0.0363636364

Comparing both, how likely were cases to report an exposure compared with controls

= (0.0898876404) ÷ (0.0363636364)

= 2.4719101085 = 2.47 times more likely.

Hope this Helps!!

Answer:

Step-by-step explanation:

There are 5numbers and 3 letters. Each number can be one among the 10 possible.

Each letter is 1 among the 26 available.

a)The number of possible unique serial numbers are

10^5x 26³

The number of 5 number combinations each different (order important) is 5!(10/5)= 30240

The number of 3 letter combinations each different (order important) is 3!(26/3)=15600

The required probability (that all symbols are different if one laptop is picked at random with equal probability) is

15600x3240/ 10^5x 26³=0.2684

b) The first letter must be at least 4 to be largest among the 5 numbers. So the first letter can be one of . 4,5,6,7,8,9..

The number of 5 number combinations each different and starting with 4 (order important) is .

4!=24

The number of 5 number combinations each different and starting with 5 (order important) is .

4!(5/4)= 120

The number of 5 number combinations each different and starting with 6 (order important) is .

4!(6/4)= 360

The number of 5 number combinations each different and starting with 7 (order important) is .

4!(7/4)= 840

The number of 5 number combinations each different and starting with 8 (order important) is

4!(8/4)= 1680

The number of 5 number combinations each different and starting with 9 (order important) is .

4!(9/4)= 3024

Thus, there are

The required probability ( that all symbols are different and the first number is the largest among the numbers) is

15600* 6040/10^5x 26³= 0.0537

Answer:

20

Step-by-step explanation:

Of means multiply and is means equals

80% * 25 = ?

Change to decimal form

.80 *25 =

20

Answer:

they are called supplementary angles

Two angles whose measures add up to 180 degrees are called supplementary angles.

What are angles?

Angles are geometric figures formed by two rays that share a common endpoint called the vertex. The rays are often referred to as the sides or arms of the angle. Angles are typically measured in degrees and are used to quantify the amount of rotation or deviation between the two rays. They are commonly represented by a symbol, such as ∠ABC, where A, B, and C are points on the rays, with the vertex at point B.

The size of an angle is determined by the amount of rotation between the two rays, starting from one ray and ending at the other. A full rotation is equivalent to 360 degrees, and angles are measured counterclockwise from the initial ray. Depending on their measurement, angles can be classified into different types, such as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), and straight (exactly 180 degrees).

When two angles are supplementary, it means that they combine to form a straight angle, which is a straight line measuring 180 degrees. Supplementary angles can be adjacent (sharing a common vertex and side) or non-adjacent, but their sum will always equal 180 degrees. This property is fundamental in geometry and has various applications in solving problems involving angles and shapes.

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Answer: 480 meters. squared

Answer:

False

Step-by-step explanation:

Common sense

Answer:

90% confidence interval for the mean time per week spent listening to the radio is  [tex]11.5 \pm 1.676 \times \frac{9.2}{\sqrt{51} }[/tex] .

Step-by-step explanation:

We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

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

where, [tex]\bar X[/tex] = sample average amount of time spent listening to music = 11.5

             s = sample standard deviation = 9.2 hours

             n = sample of students = 51

             [tex]\mu[/tex] = population mean per week spent listening to the radio

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.676 < [tex]t_5_0[/tex] < 1.676) = 0.90  {As the critical value of t at 50 degree of

                                        freedom are -1.676 & 1.676 with P = 5%}  

P(-1.676 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.676) = 0.90

P( [tex]-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.676 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.676 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                  = [ [tex]11.5-1.676 \times {\frac{9.2}{\sqrt{51} } }[/tex] , [tex]11.5+1.676 \times {\frac{9.2}{\sqrt{51} } }[/tex] ]

                  = [9.34 hours , 13.66 hours]

Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].

Answer:

A prism that has a length of 2, height of 1 and one-half, and width of 2.

Step-by-step explanation:

The formula for calculating the area of a prism is base area × height

Volume = L×W×H

L is the length of the prism

W is the width

H is the height.

To determine the prism that has an area of 6 cubic units, we will substitute the values in the option in the formula.

Using option D i.e prism that has a length of 2, height of 1 and one-half, and width of 2.

L = 2units, H = 1 1/2 units , W = 2units

Substituting in the formula for finding the volume

V = 2×2×3/2

Volume of the prism = 6cubic units

Answer:

B

Step-by-step explanation:

Answer:

$12.90

Step-by-step explanation:

multiply a $1.29 by 10 pounds and you get your answer:)

Answer:

$12.90

Step-by-step explanation

10 x $1.29=$12.90

or

move the decimal 1 time to the right

Answer:

think 23 pot

Step-by-step explanation:

Answer:

Step-by-step explanation:

23

The function f(x) = 1 - x^2/3 has f(-1) = f(1) = 2/3. The derivative f'(x) = -2x/3 equals zero at x=0, which is in the interval (-1, 1). Therefore, this does not contradict Rolle's Theorem.

The function given is f ( x ) = 1 - x ^ 2 /3. To find the values f(-1) and f(1), we simply substitute these values into the function. Therefore, f(-1) = 1 - (-1) ^ 2 /3 = 1 - 1/3 = 2/3 and f(1) = 1 - 1^2/3 = 2/3. As you can see, f(-1) = f(1).

Now, to find the value 'c' such that f'(c) = 0, first we need to determine the derivative of the function, f'(x) = -2x/3. Setting this equal to zero gives the equation 0 = -2x/3, which has the solution x = 0. Therefore, f'(c) = 0 at c = 0, which is within the interval (-1, 1).

Finally, regarding Rolle's Theorem which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the interval (a, b) such that f'(c) = 0, our results are consistent with Rolle's Theorem, since f is differentiable, f(-1) = f(1), and a 'c' value exists in the interval (-1, 1) such that f'(c) = 0.

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