Find the value of x in each of the following
a)2x-7 = 13
b)3x+4 = 25

Sorry, I'm bad at maths.

Answer:

95% confidence interval for the true mean score is [4.6 , 6.6].

Step-by-step explanation:

We are given that a sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10.

The average rating was 5.6 and the standard deviation was 4.6.

Firstly, the pivotal quantity for 95% confidence interval for the true 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 rating = 5.6

            s = sample standard deviation = 4.6

            n = sample of tobacco smokers = 81

            [tex]\mu[/tex] = population mean score

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean score, [tex]\mu[/tex] is ;

P(-1.993 < [tex]t_8_0[/tex] < 1.993) = 0.95  {As the critical value of t at 80 degree of

                                            freedom are -1.993 & 1.993 with P = 2.5%}  

P(-1.993 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.993) = 0.95

P( [tex]-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                            = [ [tex]5.6-1.993 \times {\frac{4.6}{\sqrt{81} } }[/tex] , [tex]5.6+1.993 \times {\frac{4.6}{\sqrt{81} } }[/tex] ]

                                            = [4.6 , 6.6]

Therefore, 95% confidence interval for the true mean score is [4.6 , 6.6].

Answer:

Step-by-step explanation:

all you have to do is divide each number by 4, 41, 42, 43, 44, 45, 46, 47, 48, 49 ,and 50 until you get a remainder of 1. what I mean is do 2 divided by all the number from 40 50 and do the same with 4,5,8 and 10 until you find one of them that has a remainder of 1. (is a lot of work sorry could't tell you the anwer)

Answer:

The expected value of the random variable x is  [tex]E(x) = 5.3[/tex]

Step-by-step explanation:

From the question we are told that

 The number of occurance  is x

   The interval for the x occurance of the  event is [tex]t = 10 minutes[/tex]

Generally the expected value is the same as the mean so the expected value the random variable x is

        [tex]E(x) = 5.3[/tex]

Answer:

see below

Step-by-step explanation:

x and 80 are adjacent, supplementary angles

Supplementary angles add to 180

x+80 =180 degrees

Subtract 80 from each side

x+80-80=180-80

x=100

Answer:

Im pretty sure when your writing a question theres a place where you can upload form computer and add a picture.

Step-by-step explanation:

Hope this helps with future questions!

Answer:

See explaination

Step-by-step explanation:

Stoke theorem proposes that the surface integral of the curl of a function over any surface bounded by a closed path is equal to the line integral of a particular vector function round that path.

The Stoke Theorem can be used if you see a two dimensional region bounded by a closed curve, or if you see a single integral ie a line integral.

See attached file for further solution.

Step-by-step explanation:

Answer:

Formula could be :: (N)4 with n being the number

Step-by-step explanation:

Answer:

It's B) 0.25 * 4^n-1 and third one is B

Step-by-step explanation:

Answer:

6 pounds

Step-by-step explanation:

1/4 times 3 = 3/4

3/8 times 2: 6/8 = 3/4

1/2 times 4: 4/2 = 2

5/8 times 4: 20/8 = 2 1/2

3/4 + 3/4 = 6/4 = 1 1/2

2 + 2 1/2 + 1 1/2 = 6 pounds

Answer:

[tex]y\approx573cm[/tex]

Step-by-step explanation:

First, take a look to the picture that I attached,  however please note the triangle is not drawn to scale, the figure is just to provide visual aid. As you can see the value of [tex]\angle W =109^{\circ}[/tex] this is because of the sum of the interior angles in a triangle is always equal to 180°. So:

[tex]\angle W + \angle X + \angle Y =180\\\\\angle W = 180- \angle X -\angle Y\\\\\angle W =180-38-33\\\\\angle W=109[/tex]

Now, we can use the law of sines, which states:

[tex]\frac{w}{sin(W)} =\frac{x}{sin(X)} =\frac{y}{sin(Y)}[/tex]

Hence:

[tex]\frac{w}{sin(W)} =\frac{y}{sin(Y)}\\\\\frac{880}{sin(109)} =\frac{y}{sin(38)}\\\\Solving\hspace{3}for\hspace{3}y\\\\y=\frac{880*sin(38)}{sin(109)} \\\\y=572.9999518\approx 573 cm[/tex]

Answer:

573 cm

Step-by-step explanation:

Answer:

173

Step-by-step explanation:

Same thing as last time, just instead of 90, it's 180.

Answer:

THIS IS A RIDDLE

Step-by-step explanation:

GO TO THE RIDDLE SECTION

Answer: -1.17

Step-by-step explanation:

I guessed and got it right

Final answer:

The z-score of a baseball pitch thrown at 86.2 mph is -1.17, calculated using the z-score formula with a mean pitch speed of 89 mph and a standard deviation of 2.4 mph. Thus, option A is correct.

Explanation:

The question asks for the z-score of a baseball pitch thrown at a speed of 86.2 mph, given that the mean speed of pitches is 89 mph with a standard deviation of 2.4 mph. To find the z-score, we use the formula:

Z = (X - μ) / σ

Where Z is the z-score, X is the value in question (86.2 mph), μ is the mean (89 mph), and σ is the standard deviation (2.4 mph).

Plugging in the values, we get:

Z = (86.2 - 89) / 2.4

Z = -2.8 / 2.4

Z = -1.17

Thus, the z-score of the pitch thrown at 86.2 mph is -1.17, rounded to two decimal places.

Answer:

m = all real numbers

Step-by-step explanation:

Using this equation, you end up with 0 = 0. This means that m is all real numbers.

Answer:

it is b

Step-by-step explanation:6 square

Answer:

b

Step-by-step explanation:

Answer:  314

Step-by-step explanation:

3.14 * 100=  314

Answer:

314 feet

Step-by-step explanation:

Circumference of a circle is 2pi*r

Radius = 100/2

Circumference = 2*3.14*50 = 314 feet

Answer:

The largest value is -2 from -16/ 8

The largest absolute value is -108  from -16*8

Step-by-step explanation:

Are you asking for the greatest value?

The largest number?

-16 * 8 =   - 108

-16 / 8 = -2

-16 + 8 = -8

-16 - 8 = -24

The largest value is -2 from -16/ 8

The largest absolute value is -108  from -16*8

Answer: 24 in.2

30 in.2

20.8 in.2

Step-by-step explanation:

The expected value for the player to play one time in American roulette is -$0.05. This suggests that, on average, the player can expect to lose $0.05 every time they play the game.

The expected value for the player to play one time in American roulette can be calculated by multiplying the probability of winning by the amount the player wins and subtracting the probability of losing. In this case, the probability of winning is 1/38, since there is one winning number out of the 38 possibilities. The amount the player wins is $35. The probability of losing is 37/38, since there are 37 losing numbers out of the 38 possibilities. Using these values, the expected value can be calculated as follows:

Expected value = (1/38 * $35) - (37/38 * $1) = -$0.0526

Rounded to the nearest cent, the expected value is -$0.05. This means that, on average, the player can expect to lose $0.05 every time they play the game.

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The expected value for a player betting on a single number in American roulette is approximately -$0.03, indicating an average loss of 3 cents per play.

The question asks for the calculation of the expected value for a player betting on a single number in American roulette.

To find the expected value, we consider the winnings and the probability of winning.

In American roulette, there are 38 equally spaced slots with the numbers 00, 0, and 1 through 36, which means the probability of winning for a player when betting on a specific number is 1/38, and the probability of losing is 37/38.

The payoff for a win is $35 plus the return of the original $1 bet, for a total of $36. If the bet is lost, the player loses their $1 bet.

Using these payouts and their associated probabilities, we can calculate the expected value (EV) as follows:

→ EV = (Probability of Winning) × (Winning Amount) + (Probability of Losing) × (Loss Amount)

→ EV = (1/38) × $36 - (37/38) × $1

To calculate the exact value:

→ EV = (1/38) × 36 - (37/38) × 1

→ EV ≈ 0.9474 - 0.9737

→ EV ≈ -$0.0263

When rounding to the nearest cent, the expected value is approximately -$0.03. This means, on average, the player will lose about 3 cents per play.

Answer:25 %

Step-by-step explanation:

Given

Earlier machine was producing 52 ice cream per minute and

Now it is Producing 65 ice creams per minute

So percentage increase of the machine [tex]=\frac{\text{final-Initial}}{\text{Initial}}\times 100[/tex]

[tex]=\frac{65-52}{52}\times 100[/tex]

[tex]=\frac{13}{52}\times 100[/tex]

[tex]=\frac{1}{4}\times 100=25\ \%[/tex]

So there is increase of 25 % in speed

Answer:

The right answer is:

(i) The student who weighed the rock 20 times.

Step-by-step explanation:

Both students are taking a sample from the population. In this case, the population is all the possible weight that can be measured by the scale they are using.

Independently of the sample size, the sampling distribution mean will be centered in the population mean, so they are estimating the true weight of the rock unbiased.

But the spread of the sampling distribution, measaured by the standard deviation, depends on the sample size.

The bigger the sample, the narrower the sampling distribution is expected o be. So it is more likely to be closer to the true mean with a bigger sample.

The right answer is:

(i) The student who weighed the rock 20 times.

Answer:

100(2m)

(1+0.4)

Nathan=0.4 is the percent added =the 40 percent added to the 10 amoebas

Jennifer=the first equation is how many total amoebas Jennifer has in total

Answer:

Hope this helps!

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below for the full explanation to the above question.

The final expression for the triple integral in spherical coordinates is:

[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ

To evaluate the given integral efficiently in spherical coordinates, we'll set up the triple integral over the unit ball centered at the origin. The integral represents the volume element for a sphere, which we can express in spherical coordinates as follows:

∭D (x² + y² + z²)^(3/2) dV

In spherical coordinates, the volume element dV is given by:

dV = ρ² sin(φ) dρ dφ dθ

Here, ρ represents the radial distance from the origin, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).

The limits of integration for the triple integral in spherical coordinates can be set as follows:

ρ: 0 to 1 (since D is the unit ball, ρ ranges from 0 to the radius of the sphere, which is 1)

φ: 0 to π/2 (since we only need to consider the upper half of the sphere)

θ: 0 to 2π (covering a full revolution around the z-axis)

Now, we can express the integral using these limits and the volume element:

∭D (x² + y² + z²)[tex]^{(3/2)[/tex] dV

= ∫[0 to 2π] ∫[0 to π/2] ∫[0 to 1] (ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) dρ dφ dθ

Simplifying the integrand:

(ρ²)[tex]^{(3/2)[/tex] (ρ² sin(φ)) = ρ³ ρ sin(φ) = ρ⁴ sin(φ)

Therefore, the final expression for the triple integral in spherical coordinates is:

[tex]\int\limits^{2\pi}_0\int\limits^{\pi /2}_0 \int\limits^1_0[/tex]ρ⁴ sin(φ) dρ dφ dθ

Learn more about triple integral click;

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The music class is 4 times farther from her home than the dance class.

To find the number of times farther the music class is from her home than the dance class, we first need to determine the distance of each class from her home. The dance class is 3 miles away, and the music class is 12 miles away. To get the ratio of these distances, we divide the distance to the music class by the distance to the dance class. Therefore, the equation that represents the number of times farther the music class is from her home is:

12 miles / 3 miles = 4

So, the music class is 4 times farther from her home than the dance class.

Answer:

a) [tex]A(t) = 77000(1.01375)^{4t}[/tex]

b)

The amount of money in the account at t = 0 years is $77,000.

The amount of money in the account at t = 3 years is $90,711.

The amount of money in the account at t = 6 years is $106,864.

The amount of money in the account at t = 10 years is $132,961.

Step-by-step explanation:

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.

This means that, respectively, [tex]P = 77000, r = 0.055, n = 4[/tex]

a) Find the function for the amount to which the investment grows after t years.

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(t) = 77000(1 + \frac{0.055}{4})^{4t}[/tex]

[tex]A(t) = 77000(1.01375)^{4t}[/tex]

b) Find the amount of money in the account at t=0,3, 6, and 10 years.

[tex]A(0) = 77000(1.01375)^{4*0} = 77000[/tex]

The amount of money in the account at t = 0 years is $77,000.

[tex]A(3) = 77000(1.01375)^{4*3} = 90711[/tex]

The amount of money in the account at t = 3 years is $90,711.

[tex]A(6) = 77000(1.01375)^{4*6} = 106864[/tex]

The amount of money in the account at t = 6 years is $106,864.

[tex]A(10) = 77000(1.01375)^{4*10} = 132961[/tex]

The amount of money in the account at t = 10 years is $132,961.

The function for the investment after t years is [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex] To find the amount in the account at different times, trigger this function with the desired time intervals.

The subject of the questions is about compound interest which belongs to the finance section of Mathematics.
To solve problems related to compound interest, a simple formula can be used: [tex]A = P(1 + r/n)^{(nt)[/tex] where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is time the money is invested for in years.

a) First, identify the variables from the question:[tex]P = $77000, r = 5.5/100 = 0.055[/tex](convert the percentage to a decimal), n = 4 (since interest is compounded quarterly).
We can now plug these values into our formula to determine the function: [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex]

b) To find the amount of money in the account at different time intervals, plug the specified values for t into the function. For t = 0, 3, 6, 10 years, simply replace t in A with each of these time intervals and calculate the resulting A.

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Answer:

1/55 * 1/55 = 1/3025

Step-by-step explanation:

The probability of 2 consecutive events is:

P(A and B) = P(A) * P(B) - where P(something) is the probability of it

so:

P(picking 9) = 1 possibility out of 55 total, so 1/55

P(picking 41) = 1 possibility out of 55 total, so 1/55

Finally:

P(9 and 41) = 1/55 * 1/55 = 1/3025

The probability of drawing a specific number (e.g. 9) from 55 balls is 1/55. After one ball is drawn, the probability of drawing another specific number (e.g. 41) is 1/54. The total probability of these events happening in sequence is (1/55) * (1/54).

This problem falls under the category of probability. Probability is a mathematical way of expressing the likelihood of an event happening, using numbers from 0 (impossible) to 1 (certain).

In this case, the total number of balls is 55. Since the ball is drawn randomly, the probability of drawing any specific number (such as 9) on the first draw is 1/55. Similarly, after the first ball is drawn, there are now 54 balls left in the container, but we're again interested in drawing a specific number (41), so the probability for the second draw is also 1/54.

Our task is to find the joint probability of both these events happening - drawing the 9 first and then the 41. To do that, we multiply the probabilities of the individual events, which means the final answer will be (1/55) * (1/54).

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Step-by-step explanation:

Given:

A+B+C= π

<=> 3A+3B+3C = 3π

<=> cos(3A+3B) = - cos3C

<=> cos3A.cos3B-sin3A.sin3B = - cos3C

<=> cos3A.cos3B = sin3A.sin3B  - cos3C (1)

similarly  apply for the other two angles, we have:

Grouping three equations, (1) + (2) + (3), we have:

<=> cos3A.cos3B+cos3B.cos3C+cos3C.cos3A = sin3A.sin3B + sin3B.sin3C + sin3C.sin3A - ( cos3A  + cos3B + cos3C )

= 1  

Hope it can find you well.

Using the sum of angles in a triangle and cosine identities, we proved that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) equals 1.

Given that A + B + C = π, we will use trigonometric identities and properties to prove the required equation.

Hence, we have proven that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) = 1 for angles A, B, and C summing up to \pi.

Answer:

Length of x ~ 10.5; Option B

Step-by-step explanation:

1. There are three radii present in this problem. Of that the diamter is supposedly 42.2 units. Given that the radii should be ⇒ 42.2 / 2 ⇒ 21.2 units

2. With that being said the 3rd radii contains parts x and 10.6. By radii congruency, the length of all radii should be the same, so this 3rd radii should = 21.2 units as well. If so, by the Partition Postulate 21.2 = x + 10.6

3. Through algebra let us solve for x:

21.2 = x + 10.6,

x = 21.2 - 10.6,

Answer ~ Length of x: 10.5