IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Out of a randomly selected 1450 people from the population, how many of them would have an IQ between 106 and 125, to the nearest whole number?

The cost of four points is:4 x $1,370 = $5,480Thus, the four points will cost the homebuyers $5,480.

Points can help lower mortgage rates on fixed-rate loans. The concept of points, which are basically prepaid interest, is a little complicated.

Each point is worth one percent of the loan amount, and paying points can lower your interest rate by a certain amount, typically about one-eighth to one-quarter of a percentage point.

The cost of points in the given scenario can be found using the following steps:

The loan amount to purchase a condominium is $137,000. The homebuyers obtained a 15-year fixed-rate loan with a rate of 5.05%.

If the homebuyers opt for four points, their loan rate will decrease to 4.81%.

To figure out how much the points will cost the homebuyers, we must first determine the cost of one point. Since one point is equal to 1% of the loan amount, one point on a $137,000 loan is:1% of $137,000 = $1,370

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a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

We have,

To find the mean and standard deviation for the first year of the contract, we can use the given information and the properties of the normal distribution.

Given:

The mean salary for professors in the previous year = $62,000

Standard deviation in the previous year = $2,000

Raise in the first year = $1,500

Mean for the first year of the contract:

The mean salary for the first year can be obtained by adding the raise to the previous mean:

Mean = Previous Mean + Raise

Mean = $62,000 + $1,500

Mean = $63,500

The standard deviation for the first year of the contract:

Since each professor receives the same raise, the standard deviation remains the same:

Standard Deviation = $2,000

Therefore, for the first year of the contract, the mean salary is $63,500, and the standard deviation remains $2,000.

Now,

In the second year of the contract, each professor receives a 3% raise based on their salary during the first year of the contract.

To find the mean and standard deviation for the second year, we can use the given information and the properties of the normal distribution.

Mean for the second year of the contract:

To calculate the mean for the second year, we need to add a 3% raise to the mean salary of the first year:

Mean = Mean of the first year + (3% * Mean of the first year)

Mean = $63,500 + (0.03 * $63,500)

Mean = $63,500 + $1,905

Mean = $65,405

The standard deviation for the second year of the contract:

Since each professor receives a raise based on their salary from the first year, the standard deviation also increases. To calculate the standard deviation, we multiply the standard deviation from the first year by the percentage increase:

Standard Deviation = Standard Deviation of the first year * (Percentage Increase / 100)

Standard Deviation = $2,000 * (3 / 100)

Standard Deviation = $2,000 * 0.03

Standard Deviation = $60

Therefore, for the second year of the contract, the mean salary is $65,405, and the standard deviation is $60.

Thus,

a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

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The center of mass of the system is approximately (3.7, 2.6).

The center of mass of a system of objects is the point where all the weight of the system appears to be concentrated. It can be defined as the average location of the weighted parts of the system.

The center of mass of a system is dependent on the mass of the objects in the system and their positions.

Let's determine the center of mass of the system with masses of 2, 3, and 5 at the points (-1, 2), (1, 1), and (3, 3), respectively. Let's name the masses m1, m2, and m3, respectively, and the coordinates (x1, y1), (x2, y2), and (x3, y3).

The x-component of the center of mass is given by the formula:

x= (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)

The y-component of the center of mass is given by the formula:

y= (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)

By using the given values, let's calculate the x and y components of the center of mass:

x = (2 x -1 + 3 x 1 + 5 x 3) / (2 + 3 + 5) = 37/10 ≈ 3.7y

= (2 x 2 + 3 x 1 + 5 x 3) / (2 + 3 + 5)

= 26/10 = 2.6

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Answer: 8C3

Step-by-step explanation: You need to use Combinations for this. Out of 8, you need to select 3, so answer is 8C3.

Multiply three consecutive digits backwards starting from 8, and divide by 3 factorial

(8*7*6)/(3*2*1)

=56

Answer:

195

Step-by-step explanation:

a = 3/2

According to the formula tn= a + (n-1)d

81/2= 3/2 + (13 - 1)d

81/2= 3/2 + 12d

81/3 = 12d

Therefore 27/12 = d

Sn= n/2 [2a + (n-1)d]

[tex]S_{13}[/tex] = 13/2 [2(3/2) + (13-1)(27/12)]

     = 13/2 (3 + 27)

     = 39/2 + 351/2

     = 390/2

     = 195

Blue Jelly beans are 0.1764 part of total .

Given,

Total beans = 17

Blue = 3

Red =2

White =4

Green =8

Now,

Out of total , green jelly beans = 8/17

Out of total , red jelly beans = 2/17

Out of total , white jelly beans = 4/17

Out of total , blue jelly beans = 3/17

Hence the blue jelly beans are 0.1764 part of total jelly beans .

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Answer:

total annual cost: 49313

cost per mile: 14 cents

Step-by-step explanation:

find total annual cost by adding everything up

find cost per mile by doing 4897/34500

cost/ miles

we use variable cost since the only thing that might change each year is the amount of miles they drive

fixed costs are fixed and don't change

Answer:

The lengths are equal so the triangle is equilateral

Step-by-step explanation:

We can write the points as follows,

(2,0), (-1,[tex]\sqrt{3}[/tex]) (-1,-[tex]\sqrt{3}[/tex])

now if it is an equilateral triangle, all side lengths must be equal

first we compute the sides(vectors)

(2-(-1),-[tex]\sqrt{3}[/tex]) = (3,-[tex]\sqrt{3}[/tex]) = side 1

(2-(-1),[tex]\sqrt{3}[/tex]) = (3,[tex]\sqrt{3}[/tex]) = side 2

(-1+1,[tex]\sqrt{3}[/tex]+[tex]\sqrt{3}[/tex]) = (0,2[tex]\sqrt{3}[/tex]) = side 3

now we compute the lengths of the sides using pythagoras theorem

(3)^2 + (-[tex]\sqrt{3}[/tex])^2 = (length of side 1)^2 = 9 + 3 = 12

similarly, (3)^2 + ([tex]\sqrt{3}[/tex])^2 = 12 = Length of side 2 squared

and,( 2[tex]\sqrt{3}[/tex])^2 = length of side 3 squared = 12

since the squares are equal, so the lengths must also be equal

so the triangle is equilateral

this is just a quick addition to the superb posting by "hamza0100" above

well, indeed, in the argand or imaginary plane, for those values above we have the coordinates of A(2 , 0) , B(-1 √3) and C(-1 , -√3), let' use the distance formula for those fellows

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{\sqrt{3}}) ~\hfill AB=\sqrt{(~~ -1- 2~~)^2 + (~~ \sqrt{3}- 0~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( \sqrt{3})^2} \implies \boxed{AB=\sqrt{ 12 }}[/tex]

[tex]B(\stackrel{x_1}{-1}~,~\stackrel{y_1}{\sqrt{3}})\qquad C(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-\sqrt{3}}) \\\\\\ BC=\sqrt{(~~ -1- (-1)~~)^2 + (~~ -\sqrt{3}- \sqrt{3}~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 0)^2 + ( -2\sqrt{3})^2} \implies \boxed{BC=\sqrt{ 12 }}[/tex]

[tex]C(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-\sqrt{3}})\qquad A(\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill CA=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 0- (-\sqrt{3})~~)^2} \\\\\\ ~\hfill CA=\sqrt{( 3)^2 + (-\sqrt{3})^2} \implies \boxed{CA=\sqrt{ 12 }} \\\\[-0.35em] ~\dotfill\\\\ AB=BC=CA=\sqrt{12}\implies 2\sqrt{3}\hspace{5em}\qquad equilateral\textit{\LARGE \checkmark}[/tex]

Answer: 2

Step-by-step explanation: 10 divided by 5 equals 2

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Based on the functions given, it should be noted that the values will be 2, -2x and -8x.

Using the definition of the derivative, we have:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

= lim(h->0) [2(x + h) - 2x] / h

= lim(h->0) 2h / h

= lim(h->0) 2

= 2

Therefore, f'(x) = 2.

For f(x) = 9 - x²:

Using the definition of the derivative, we have:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

= lim(h->0) [9 - (x + h)² - (9 - x²)] / h

= lim(h->0) [9 - (x² + 2xh + h²) - 9 + x²] / h

= lim(h->0) [-2xh - h²] / h

= lim(h->0) (-2x - h)

= -2x

Therefore, f'(x) = -2x.

For f(x) = -4x²:

Using the definition of the derivative, we have:

f'(x) = lim(h->0) [f(x + h) - f(x)] / h

= lim(h->0) [-4(x + h)² - (-4x²)] / h

= lim(h->0) [-4(x² + 2xh + h²) + 4x²] / h

= lim(h->0) [-4x² - 8xh - 4h² + 4x²] / h

= lim(h->0) [-8xh - 4h²] / h

= lim(h->0) (-8x - 4h)

= -8x

Therefore, f'(x) = -8x.

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Answer:

y = -x + 8

Step-by-step explanation:

Let's break down the equation step by step to understand it better.

The equation in point-slope form is given as:

y - y1 = m(x - x1)

In this case, we have:

y - 0 = -1(x - 8)

The point-slope form uses a specific point (x1, y1) on the line and the slope (m) of the line.

Here, the point (x1, y1) is (8, 0), which represents a point on the line. This means that when x = 8, y = 0. The graph has a point at (8, 0), which confirms this information.

The slope (m) is -1 in this equation. The slope represents the rate at which y changes with respect to x. In this case, since the slope is -1, it means that for every unit increase in x, y decreases by 1. The negative sign indicates that the line has a downward slope.

By substituting the values into the equation, we get:

y - 0 = -1(x - 8)

Simplifying further:

y = -x + 8

This is the final equation of the line in slope-intercept form. It tells us that y is equal to -x plus 8. In other words, the line decreases by 1 unit in the y-direction for every 1 unit increase in the x-direction, and it intersects the y-axis at the point (0, 8).

If the graph has points at (0, 8) and (8, 0), the equation y = -x + 8 accurately represents that line.

Step-by-step explanation:

triangle EFG is an isosceles triangle

angle G

= 180°-58°

= 122° (adj. angles on a str. line)

angle F

= (180°-122°)÷2

= 29° (angles in a triangle)

(a) The null hypothesis is that the mean birth weight of babies born at full term is 7.2 pounds. The alternative hypothesis is that the mean birth weight of babies born at full term is greater than 7.2 pounds.

(b) If the scientist decides to reject the null hypothesis, she might be making a Type I error.

(c) A Type II error occurs when the null hypothesis is false, but the scientist fails to reject it.

a A Type I error occurs when the null hypothesis is true, but the scientist rejects it. In this case, the null hypothesis is that the mean birth weight of babies born at full term is 7.2 pounds. If the scientist rejects this hypothesis, she is saying that she believes that the mean birth weight is greater than 7.2 pounds. However, if the null hypothesis is true, then the mean birth weight is actually 7.2 pounds, and the scientist has made a mistake.

b In this case, the scientist would fail to reject the null hypothesis and conclude that the mean birth weight of babies born at full term is 7.2 pounds. However, the true mean birth weight is 7.7 pounds, so the scientist would be making a Type II error.

c In the context of a Type II error, suppose the null hypothesis is false, meaning there is indeed a significant difference or relationship. However, due to various factors such as insufficient sample size, low statistical power, or other limitations, the scientist fails to reject the null hypothesis. Consequently, they accept the null hypothesis even though it is false, leading to a Type II error.

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The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer:

.35x = 140(.15)

.35x = 21

x = 60 oz of 35% salt.

The scientist will need 60 oz of the 35% salt solution and 80 oz of water.

1

Because the number 97 is a prime number

Answer:

The greatest common factor (GCF) of two numbers is the largest number that divides evenly into both numbers. Since 97 is a prime number and 24 is not divisible by 97, the GCF of 97 and 24 is 1.

To determine the number of light bulbs expected to last between 2030 hours and 2060 hours, we need to calculate the z-scores corresponding to these values and then use the z-score formula to find the proportion of light bulbs within this range.

The z-score formula is given by:

z = (x - μ) / σ

where:

x = value

μ = mean

σ = standard deviation

For 2030 hours:

z1 = (2030 - 2000) / 25

For 2060 hours:

z2 = (2060 - 2000) / 25

Now, we can use the z-scores to find the proportions associated with each value using a standard normal distribution table or calculator. The table or calculator will provide the area/proportion under the normal curve between the mean and each z-score.

Let's calculate the z-scores and find the proportions:

z1 = (2030 - 2000) / 25 = 1.2

z2 = (2060 - 2000) / 25 = 2.4

Using a standard normal distribution table or calculator, we can find the proportions corresponding to these z-scores:

P(z < 1.2) ≈ 0.8849

P(z < 2.4) ≈ 0.9918

To find the proportion of light bulbs expected to last between 2030 hours and 2060 hours, we subtract the cumulative probabilities:

P(2030 < x < 2060) = P(z1 < z < z2) = P(z < z2) - P(z < z1)

P(2030 < x < 2060) ≈ 0.9918 - 0.8849

Finally, we multiply this proportion by the total number of light bulbs (665) to get the estimated number of light bulbs expected to last between 2030 hours and 2060 hours:

Number of light bulbs ≈ (0.9918 - 0.8849) * 665

Rounding to the nearest whole number, the expected number of light bulbs that would last between 2030 hours and 2060 hours is approximately 71.[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

Because we are adding 2/5, we would be moving in the positive direction, which is to the right.

To find the number that corresponds to 22% of a given value, you can divide the given value by 22% (or 0.22).

Let's use this approach to find the number:

3300 ÷ 0.22 = 15,000

So, 22% of 15,000 is equal to 3300.

Answer:

x = 15000

Step-by-step explanation:

If you are using a calculator, simply enter 3300×100÷22, which will give you the answer.

There are 14 Geometry problems in Vardan's homework assignment.

The number of geometry problems in Vardan's homework assignment, we need to calculate 58 1/3 percent of the total number of problems.

First, let's convert 58 1/3 percent to a decimal by dividing it by 100:

58 1/3 percent = 58.33/100 = 0.5833

Next, we multiply the decimal by the total number of problems:

Number of geometry problems = 0.5833 * 24

To calculate this, we can multiply 0.5833 by 24:

Number of geometry problems = 0.5833 * 24 = 14

Therefore, there are 14 geometry problems in Vardan's homework assignment.

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As of December 31, Deloitte should recognize $15,000 as revenue for the advisory services completed.

To solve the given question, we need to determine the amount of revenue that Deloitte should recognize as of December 31, based on the percentage of services completed.

Here's how we can calculate it:

Calculate the total revenue for the contract:

Total revenue = $20,000

Determine the percentage of services completed:

Percentage of services completed = 75%

Calculate the revenue recognized as of December 31:

Revenue recognized = Percentage of services completed × Total revenue

= 75% × $20,000

= $15,000

Therefore, as of December 31, Deloitte should recognize $15,000 as revenue for the advisory services completed.

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Answer:-2

Step-by-step explanation:

x(4)+16=8

Answer:

2.5

Step-by-step explanation:

The explanation is attached below.

The measure of angle 1 and angle 4 are equal, that is 62°, by vertical angle theorem.

Given that, m∠1=62° and lines t and l intersect.

From the given figure,

m∠1 and m∠4 are vertically opposite angles.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

Here, m∠1 =m∠4=62°

Hence, it is proved.

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Answer:

See below

Step-by-step explanation:

Since the spinner has the numbers 1, 2, and 3 on it, and we want to find the probability of spinning a number less than 2, there is only one possible outcome that satisfies this condition, which is spinning a 1. Therefore, the probability of spinning a number less than 2 is:

P(less than 2) = P(1) = 1/3

So the probability of spinning a number less than 2 is 1/3.