A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is (x with a line over it), while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.


Confidence Level. 90%. 95%. 99%
z*-score. 1.645. 1.96. 2.58

Answer:

45 m

Step-by-step explanation:

The height at time of launch is at x = 0

Substitute x = 0 into f(x)

f(0) = - 5(0 + 1)(0 - 9) = - 5(1)(- 9) = 45 m

Answer: The greatest distance, in feet is the first one 3ft.

Answer: 3 feet

Step-by-step explanation:

Given: The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation describes the boundary within which motion can be sensed. :

[tex](x+14)^2+(y-6)^2=9[/tex] → which is a equation of a CIRCLE.

When we compare it to the standard form of equation of circle i.e. [tex](x-(-14))^2+(y-6)^2=3^2[/tex] , we get the radius of the circle = 3

Consider the lamp post as the center of the area covered by the detector.

Then the greatest distance a person could be from the lamp and be detected = Radius of the circular area

=3 feet.

Answer:

So like terms are terms that have the same VARIABLE...

Step-by-step explanation:

So 2n + 3n is 5n and you can do that because they are like terms. you only need like terms for adding and subtracting

multiplying: 2n * 3n^2 = 6n^3

hope this helps!

The x-coordinates of points P and Q, where lines y=2x+8 and y=2x-12 intersect the x-axis, are -4 and 6 respectively. Therefore, the distance between them, PQ, is 10 units.

The two given lines are y = 2x + 8 and y = 2x - 12. These lines intersect the x-axis when y = 0. Setting y=0 in these two equations, we find the x co-ordinates of the intersection points P and Q.

For y = 2x + 8, solving 2x + 8 = 0 gives x = -4. Hence, Point P is at (-4,0).

Similarly, for y = 2x - 12, solving 2x - 12 = 0 gives x = 6. Hence, Point Q is at (6,0).

The distance PQ can then be calculated using the distance formula: "PQ = |Q - P| = |6 - (-4)| = 10 units".

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Answer:

upper left

Step-by-step explanation:

The generic equation for a circle centered at (h, k) with radius r is ...

(x -h)^2 +(y -k)^2 = r^2

Comparing that equation to the one you have, you can see that ...

-h = 0

-k = +3

r^2 = 9

Then you have (h, k) = (0, -3) and a radius of 3.

The circle has its center on the y-axis 3 units below the x-axis and just touches the x-axis. This is a description of the graph at upper left.

Answer:

19.4

Step-by-step explanation:

40^2=35^2+b^2

(Pythagorean Theorem)

b^2=375

b=19.4

In this situation of selling two properties for the same price but with different gain and loss percentages, the real estate agent does not break even but incurs an overall loss of 6.25%.

This is essentially a problem in profit and loss calculations in the domain of Mathematics. Since the selling price of both the sites is the same, the loss and gain percent will cancel out each other, resulting in no overall gain or loss. Here's why:

The total cost price is Rs. 14400 + Rs. 24000 = Rs. 38400 and the total selling price is Rs. 18000 + Rs. 18000 = Rs. 36000. So, the real estate agent has incurred an overall loss. To find the percentage of loss, use the formula face: [(Loss) / (Cost Price)] * 100 = [(Rs. 38400 - Rs. 36000) / Rs. 38400] * 100 = 6.25% loss.

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Answer:

x∈B

x∈A∪B

x∈A∪C

x∈A∩B

Step-by-step explanation:

As can be seen from the Venn diagram, x is the shaded portion between the intersection of 3 circles A, B and C.

hence x belong to b, and x belong to A union B, x belong to A union C and x belong to A intersection B !

Answer:

The following are correct:

B

C

D

E

F

Step-by-step explanation

Answer:

Option A) 0.02

Step-by-step explanation:

The probability p that one of the questions is correct is

[tex]P = \frac{1}{4}[/tex]

The number of questions that will answer (number of trials) is [tex]n = 3[/tex].

We want to find out the probability that [tex]x = 3[/tex] three questions will be answered correctly.

To calculate this probability we use the binomial formula:

[tex]P(x) = \frac{n!}{x!(n-x)!} p^x(1-p)^{n-x}[/tex]

Where

[tex]x=3\\n=3\\p=0.25[/tex]

Then:

[tex]P(x=3) = \frac{3!}{3!(3-3)!} 0.25^3(1-0.25)^{3-3}[/tex]

[tex]P(3) =0.25^3[/tex]

[tex]P(3) = 0.0156[/tex]

P(3) = 0.0156≈0.02

Answer:

Final answer is $12696.

Step-by-step explanation:

Given that initial amount P = $28000

Interest rate r = 5.8% = 0.058

Time = 1 year

Then future value is given by :

[tex]A=P\left(1+r\right)^t[/tex]

[tex]A=28000\left(1+0.058\right)^1=29624[/tex]

Similarly calculate future value for 2nd case:

Given that initial amount P = $16000

Interest rate r = 5.8% = 0.058

Time = 1 year

Then future value is given by :

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

[tex]A=16000\left(1+0.058\right)^1=16928[/tex]

then difference = 29624 - 16928 = 12696

Hence final answer is $12696.

Answer:

$696.

Step-by-step explanation:

We are asked to find the amount of interest earned on $28,000 than $16,000 with APYs of 5.8% for a year.

We will use simple interest formula to solve our given problem.

[tex]I=Prt[/tex]

[tex]I[/tex] = Amount of interest,

P = Principal amount,

r = Interest rate in decimal form,

t = Time in years.

[tex]5.8\%=\frac{5.8}{100}=0.058[/tex]

Let us find difference of interests as:

[tex]\$28,000\times 0.058-\$16,000\times 0.058[/tex]

[tex](\$28,000-\$16,000)\times 0.058[/tex]

[tex](\$12,000)\times 0.058[/tex]

[tex]\$696[/tex]

Therefore, it will earn $696 more in interest.

ANSWER

[tex]n=\frac{5}{6} [/tex]

EXPLANATION

The given equation is

[tex] \frac{4}{5}n =\frac{2}{3} [/tex]

We multiply both sides of the equation by:

[tex]\frac{5}{4}[/tex]

[tex] \frac{5}{4}\times \frac{4}{5}n =\frac{2}{3}\times\frac{5}{4} [/tex]

Multiply and cancel out common factors

This implies that:

[tex]n=\frac{5}{6}[/tex]

Option B is correct.

My answer would be 8.. I may not be correct, but I tried. So, I placed the numbers from least to greatest and split it 1’s and 2’s VS 3’s and 4’s. I just added 1 plus 2 plus 2 and a half plus 2 and a half and got 8. I also added (3+3+3)+3 and a half plus 3

Answer:

Step-by-step explanation:

start with 35 and add 1 repeatedly.

y=x+1 for ex, y= 35+ 1 and so on

In solving the inequality, 3x+8/x-4 <= 0, we identify critical points and assign intervals based on them. The solution offers two possible scenarios: x is less than or equal to -8/3 or x is greater than 4.

The inequality 3x+8/x-4 =< 0 can be divided into two possible scenarios by clarifying the critical points. To solve this inequality, you first need to identify where the expression equals zero, that's where 3x+8=0 and x=4. Solving 3x+8=0 yields x=-8/3, which is the first

possible solution. Another critical point is where the denominator is zero, which is x=4.

Next, we need to check the signs of these intervals: (-inf, -8/3), (-8/3, 4) and (4, inf). Testing these intervals on the given inequality gives us the

solution that x is less than or equal to -8/3 or x is greater than 4 . Remember, x cannot be equal to 4 because it makes denominator zero in the origin expression which is undefined in mathematics.

Therefore, the correct solution is 'x less than or equal to -8/3 or x greater than 4'.

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Answer:

The expression is equivalent to x^2-17x-60 would be (x - 20)(x + 3)

Step-1 : Multiply the coefficient of the first term by the constant   1 • -60 = -60 

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -17 .

-60+1= -59

-30+2= -28

-20+3= -17

Final (x + 3) • (x - 20)

Answer:

8[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Rationalise the denominator by multiplying both the numerator and denominator by the radical on the denominator, that is

[tex]\frac{32}{\sqrt{8} }[/tex]

= [tex]\frac{32\sqrt{8} }{8 }[/tex] → ([tex]\sqrt{8}[/tex])² = 8

= [tex]\frac{32\sqrt{4(2)} }{8}[/tex]

= 4× 2[tex]\sqrt{2}[/tex]

= 8[tex]\sqrt{2}[/tex]

Answer:

I think it is a but it is hard to see

Step-by-step explanation:

Answer:

the first option

Step-by-step explanation:

Given the triangle is right, then use Pythagoras' theorem

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

The hypotenuse is 5, hence

5² = 4² + b² OR 4² + b² = 5²

Answer: 0.22

Step-by-step explanation:

Answer:Jason is not correct  as Jason changed the terms.

Step-by-step explanation:

Given the expression 34+5.6b+9.Jason used the commutative property to write the above expression changed to 9.0 + 56b + 3.4

We have to tell Jason work is correct or not.

Commutative property states that order does not matters but the terms remains same i.e a+b=b+aJason change the expression 34+5.6b+9 to 9.0 + 56b + 3.4here, Jason change the terms as well as order Jason is not correct  as Jason changed the terms.

If you would like to show the questions to us, would be fine!

Answer:

[tex]\large\boxed{4x+6y^3}[/tex]

Step-by-step explanation:

[tex]2x+x+x+2y\times3y\times y\\\\=(2x+x+x)+(2y\times3y\times y)\\\\=4x+(2\times3)(y\times y\times y)\\\\=4x+6y^3[/tex]

The likelihood of an event stating the 30% chance of snow means that, in 100 identical weather circumstances, we would predict it to snow during 30. This does not deliver any information on the quantity of snow.

The likelihood of an event given its probability represents the chance of that event taking place. When we say that there is a 30% chance of snow tomorrow, this means that out of every 100 similar weather scenarios, we would expect it to snow in 30 of them. Hence, the likelihood of it snowing tomorrow is 30%. It's important to understand that probability is a way to quantify the uncertainty associated with events predicted to occur, based on the known conditions.

Regarding the example, if we know that 'If it snows more than three inches, the schools are mandated to close.' and we see that 'The schools closed.' we can infer that 'It snowed more than three inches.' This however has no direct relation to the probability of snow tomorrow.

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Answer:

22 feet²

Step-by-step explanation:

We are given:

height of tree h = 45 inches

Circumference= πd × inches

But d = 22.2inches

Therefore area will be

Area = 22.2π × 45 inches²

Area = 3137 inches²

Let's convert from inches² to feet², we have:

1 foot = 12 inches.

Therefore,

1 square foot = 1foot × 1foot = 12inches×12inches

= 3137inches² / 144 inches²

= 22feet²

Note: I attached missing data which states that diameter at year 13 is 22.2inches

To calculate the square footage of the tree wrap needed, we multiply the circumference of the tree trunk by the desired height. Assuming the tree trunk is cylindrical, we use the formula for the circumference of a circle: C = 2πr. Then, we convert the height to feet and calculate the square footage.

To calculate the square footage of the tree wrap needed, we need to find the circumference of the tree trunk and multiply it by the desired height. Assuming the tree trunk is cylindrical, we can use the formula for the circumference of a circle: C = 2πr. We can then multiply the circumference by the desired height to get the square footage. Since we know the height is 45 inches, we need to convert it to feet by dividing by 12. Let's say the circumference of the tree trunk is 10 feet. The square footage of the tree wrap needed would be C * H = (2πr) * H = (2π * 5) * 3.75 = 47.12 square feet (rounded to the nearest square foot).

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Answer:

Option C (Median: 347 and Mode: 347 and 348)

Step-by-step explanation:

Median is the middle point of the data and mode is the most repeated observation is the data. The first step involved in calculating the median it to list the observations in the ascending order. This gives:

335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359

The second step is to identify the middle number (in case the observations are in odd numbers) or numbers (in case the observations are in even numbers) after the ascending order step has been done. It can be observed that the middle numbers in this data set are 347 and 347. Since there are two numbers, so their average will be the median of this data set. Therefore, the median is 347. It can be seen that maximum repetitions are 2 times for 347 and 348. So the mode is 347 and 348.

Therefore, Option C is the correct answer!!!

The correct option is c: Median: 347, Mode: 347 AND 348. This is determined by sorting the numbers and finding that 347 is the median and both 347 and 348 are the modes.

This question involves identifying measures of central tendency, specifically the median and the mode, from a list of numbers.

To determine the correct answer, we proceed step-by-step to calculate the median and mode from the provided sequence: 359, 357, 348, 347, 337, 347, 340, 335, 338, 348, 339, 356, 336, 358.

Step 1: Sorting the List
The sorted list is: 335, 336, 337, 338, 339, 340, 347, 347, 348, 348, 356, 357, 358, 359

Step 2: Finding the Median
The median is the middle value of a sorted list. For a list of 14 numbers, it is the average of the 7th and 8th values:
Median = (347 + 347) / 2 = 347

Step 3: Finding the Mode
The mode is the number that appears most frequently. Here, 347 and 348 each appear twice.
Mode = 347 and 348

Based on these calculations, the correct option is Option c: Median: 347, Mode: 347 AND 348.

Answer:

Step-by-step explanation:

You subtract 310 from 25 and get 285 then you multiply 285 x 21 and I believe that should solve this equation.

To find the value of 'y' when 'x' equals 21 in this equation, we substitute 21 for 'x', perform the multiplication 25*21 first, and then subtract this result from 310, yielding a 'y' value of -215.

This question pertains to the mathematical equation y=310-25x. To find the value of 'y' when 'x' equals 21, we simply substitute 21 for 'x' in the equation. So, y = 310 - 25*(21). Multiplication happens first (due to the order of operations), yielding 525. When you subtract this from 310 (310-525), you get -215. Therefore, the value of 'y' when 'x' is 21 in this equation is -215.

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It is D.) 237 and 2/3... glad I was able to help!

2852/12 is ———————> (A) 237

Answer:

So we can write an equation to solve this:

12/100 = 36/x

And then we are going to solve for x

x(12/100) = 36

36 x (100/12) = 300

The total number of candy bars was 300

Jillian sold 12% of the class's candy bars, which amounts to 36 bars. To find the total, calculate what 1% would be by dividing 36 by 12, and then multiply by 100 to find that the class sold 300 candy bars in total.

The student is asking about a practical application of percentages in a real-world context, which is a common subject in middle school mathematics. To find the total number of candy bars sold by the class, we need to use the information that Jillian sold 12% of the total and that this amounted to 36 candy bars. The calculation is straightforward: if 12% equals 36, we want to find 100% (the total).

To do this, we set up a simple proportion: if 12% is 36, then 1% would be 36 divided by 12, which is 3 candy bars. Since we're looking for the total, we multiply the number of candy bars representing 1% (which is 3) by 100 to find that the class sold a total of 300 candy bars before taxes.

Step-by-Step Calculation:

Find 1% of the total by dividing 36 candy bars by 12%.

1% of the total = 36 candy bars / 12 = 3 candy bars.

Multiply the value of 1% by 100 to find the total amount.

Total candy bars = 3 candy bars × 100 = 300 candy bars.

Answer:  Apply the formula for the volume of a sphere.

Step-by-step explanation:

The volume of a sphere is  

4

π

r

3

3

We just need to insert  

r

=

2

c

m

into this to get the volume.

4

π

2

3

3

=

32

3

π

The exact volume is  

32

3

π

c

m

3

The approximate volume is  

33.5103217

Answer:

Base #2

Step-by-step explanation:

For this question, we need to find the base that's volume is a factor of 60.

Base #1 Volume = 7 * 3 or 21

21 is not a factor of 60, so it cannot be the base.

Base #2 Volume = 5 * 3 or 15

15 is a factor of 60, so it is the base.

Answer: I think it's base 4. Don't rely on me, 'cause I can't understand this right now.

Using the Empirical Rule, it is found that the percent best represents the probability that any student scored between 61 and 93 on the test is of:

B. 95%.

It states that, for a normally distributed random variable:

In this problem, the mean is of 77 while the standard deviation is of 8, hence scores between 61 and 93 are exactly 2 standard deviations from the mean, hence 95% of the students scored in this range, and option B is correct.

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Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

The answer is 9x10 to the positive 16 power

The sum of the given equation in the scientific notation should be [tex]9 \times 10^{16}[/tex]

Here we Move the decimal due to this there is one non-zero digit to the left of the decimal point. In the case when the decimal is being moved to the right, so the exponent will be negative and vice versa.

So,

[tex]= (2 \times 10^{16}) + (7 \times 10^{16}) = 9 \times 10^{16}[/tex]

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