At the end of the spring semester, the dean of students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year.
The average was a gain of µ = 15 pounds with a standard deviation of
σ = 6. The distribution of scores was approximately normal.
A sample of n = 4 students is selected, and the average weight change is computed for the sample.
What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p (M > 10) (four decimals)

The response is B) 5√6 in accordance with the provided assertion.

The hypotenuse of a right triangle is its longest side; its "opposite" side is the side that confronts the angle in issue; and its "adjacent" half is the side that faces it.

In a 45°-45°-90° triangle, the two legs are congruent, and the hypotenuse is equal to the leg multiplied by √2.

In this case, the leg length is given as 5√3.

Thus, the hypotenuse will have the following length:

hypotenuse = leg x √2 = 5√3 x √2 = 5√(3 x 2) = 5√6

Therefore, the answer is B) 5√6.

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The price of the watch before the discount was £25.

A percentage expresses a number as a fraction of 100. It is often used to describe a portion or share of a whole or to express a rate or proportion. Percentages can be calculated by dividing the part by the whole and multiplying by 100. Percentages are used in a wide variety of contexts, such as finance, economics, statistics, and science.

Jasοn bοught a watch and a pair οf trainers fοr a tοtal price οf £53.55.

We are given that, Jasοn received a 15% lοyalty discοunt οn the whοle price that includes nοt οnly the price οf the pair οf trainers but alsο the price οf the watch.

Nοw, the discοunted price becοmes £(100 - 15) = £85, when the οriginal price is £100.

Then, the discοunted price becοmes £1, when the οriginal price is

= [tex]$\£ \frac{100}{85}[/tex]

Then, the discοunted price becοmes £53.55, when the οriginal price is  

[tex]$\frac{100}{85} \times 53.55 = \£ 63[/tex]

Nοw, we are given that, the trainers were priced at £38.

This means that the price οf the watch befοre the discοunt is,

£(63 - 38) = £25.

Hence, the price οf the watch befοre the discοunt is £25.

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Answer:

well none of those are technically correct because A is 11, B is 7, C is 0, and D is 18

all of those answers are Mayan numerals

The statement which is correct is: If {α, β} is independent, then {w₁, w₂, w₁+ w₂} is in dependent.

In vector space theory, a set of vectors is said to be linearly independent if there is no non-trivial linear combination of vectors equal to vector zero. If such a linear combination exists, the vectors are said to be linearly dependent. These concepts are central to dimension definitions.

The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space are linearly dependent is essential to determining the dimensionality of a vector space.

According to the Question, we know that:

{w₁, w₂, w₃} are linearly independent.

Let, α₁, α₂, α₃ such that

α₁w₁ + α₂w₂+ α₃w₃ = 0

and, α₁ = α₂ = α₃ = 0

Again considering the following, we can say that:

{w₁, w₁+ w₂, w₁+w₂+w₃} such that:

β₁(w₁) + β₂(w₁+ w₂) + β₃(w₁+ w₂+ w₃) = 0

Here, the dependent variable is {α,β} and { w₁+ w₂+ w₃}

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The value of both missing angles are calculated as: ∠1 = 41° and ∠2 = 139°

We know that the sum of angles on a straight line sums up to 180 degrees.

Thus, from the given diagram, we can say that:

∠1 + ∠2 = 180

We are told that ∠2 is 16 more that 3 times ∠1.

Thus:

∠2 = 3(∠1) + 16

Thus:

3(∠1) + 16 + ∠1 = 180

4(∠1) = 180 - 16

∠1 = 164/4

∠1 = 41°

∠2 = 180 - 41

∠2 = 139°

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The total volume of the hemisphere mounted on the cuboid is 3574.76 cubic yards.

To find the volume of the hemisphere mounted on the cuboid, we need to first find the volume of the cuboid and the volume of the hemisphere separately, and then add them up.

The volume of the cuboid is given by the formula:

V_cuboid = l x w x h

where l, w, and h are the length, width, and height of the cuboid, respectively. Substituting the given values, we get:

V_cuboid = 17 yd x 14 yd x 12 yd

V_cuboid = 2856 cubic yards

Next, we need to find the volume of the hemisphere. The diameter of the hemisphere is given as 14 yd, which means that the radius is 7 yd. The volume of the hemisphere is given by the formula:

V_hemisphere = (2/3) x π x [tex]r^{3}[/tex]

V_hemisphere = (2/3) x 3.14 x [tex]7^{3}[/tex]

V_hemisphere = 718.76 cubic yards

To find the volume of the hemisphere mounted on the cuboid, we add the volumes of the cuboid and the hemisphere:

V_total = V_cuboid + V_hemisphere

V_total = 2856 + 718.76

V_total = 3574.76 cubic yards

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This should output: The value of the car in 2025 will be $11730.3 which function means that the value of the car in 2025 will be approximately $11,730.30.

A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.

To calculate the value of the car in 2025, we need to determine the value of the car after each year of depreciation from 2020 to 2025. We can represent this situation using the following function:

[tex]value = 25000 * (0.86 ** years)\\ return value\\value_2025 = car_value(5)\\print("The value of the car in 2025 will be $" + str(round(value_2025, 2)))\\[/tex]

This should output: The value of the car in 2025 will be $11730.3 which means that the value of the car in 2025 will be approximately $11,730.30.

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Answer:

average rate of change = [tex]\frac{6}{13}[/tex]

Step-by-step explanation:

the average rate of change of f(t) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ - 5, 8 ] , then

f(b) = f(8) = 6 ← point (8, 6 ) on graph

f(a) = f(- 5) = 0 ← point (- 5, 0 ) on graph

then

average rate of change = [tex]\frac{6-0}{8-(-5)}[/tex] = [tex]\frac{6}{8+5}[/tex] = [tex]\frac{6}{13}[/tex]

Dοug Smalley's weekly federal incοme tax deductiοn wοuld be $24 as a result as the table shοws that $24 in federal incοme tax.

A quantity οr sum οf sοmething is generally referred tο as a "amοunt," and it is typically quantified in units οr numbers. It can be used tο a wide range οf situatiοns, including thοse in everyday life, mathematics, and mοney. An amοunt, fοr instance, might be a sum οf mοney that is invested, οwed, οr paid. An amοunt in mathematics can be either a quantity οr a numerical value. In daily life, an amοunt may relate tο the tοtal cοst οf the prοducts in a shοpping basket οr the number οf materials required fοr a recipe.

Dοug Smalley's file status (married) and the number οf allοwances requested need us tο apply the IRS tax tables in οrder tο determine the amοunt οf federal incοme tax deducted frοm his mοnthly wages (2).

Determine the emplοyee's weekly grοss pay: $485

Remοve the amοunt οf the emplοyee's claimed weekly allοwances. The amοunt is $162.80 ($86.40 fοr the first allοwance and $76.40 fοr the secοnd allοwance) fοr twο allοwances in 2021.

$485 - $162.80 = $322.20 (adjusted grοss pay) (adjusted grοss pay)

Find the rοw fοr Dοug's adjusted grοss pay οf $322.20 and the cοlumn fοr his marital status (married) and the amοunt οf allοwances claimed using the IRS tax tables (2).

The table shοws that $24 in federal incοme tax wοuld be withheld each week.

Dοug Smalley's weekly federal incοme tax deductiοn wοuld be $24 as a result as the table shοws that $24 in federal incοme tax.

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Find the federal income tax withheld each week using the Weekly Payroll tables on pages 7-10.

Doug Smalley, a store manager, is married and earns $485 a week. He claims 2 allowances.

Answer:

D is the correct option.

Step-by-step explanation:

y = x^2 -14x + 39    

   take 1/2 of the x coefficient (-14)   square it then add it and subtract it  :

x^2 - 14x + 49    - 49    + 39        Now reduce the three Left terms

(x-7)^2   - 49 +39       simplify the R portion

y = (x-7)^2 - 10             This process is called 'completing the square'        

The approximate diameter of the pile of sand in the cone that sand was dumped in is 9.30 feet.

What is the approximate diameter?

A cone is a 3-dimensional object that consists of a ciruclar base and a vertex. The diameter is twice the length of the radius.

Radius = √[volume / (1/3 x π x height)]

=> Radius=√[136 / (1/3 x 22/7 x 6)]

=> Radius=√[136 / 6.29 = 4.65

Hence the Diameter = 4.65 x 2 = 9.30 feet

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Answer:

[tex]c=18.8389[/tex]

Step-by-step explanation:

To find hypotenuse [tex]C[/tex] use formula:

 [tex]\text{sin}(\alpha )=\frac{a}{c}[/tex]

After substituting [tex]\alpha =48^o[/tex] and [tex]a=14[/tex] we have:

[tex]\text{sin}(48^o)=\frac{14}{c}[/tex]

[tex]0.7431=\frac{14}{c}[/tex]

[tex]c=\frac{14}{0.7431}[/tex]

[tex]c=18.8389[/tex]

Answer:31

Step-by-step explanation:

14/2=7 48/2= 24 7+24=31

Answer:

X × Y

Step-by-step explanation:

Because you need do the multiplication between the time and the money

Attribution theory provides a description of how people explain the causes of their own and others' behaviors. Option d is the correct choice.

The theory referred to in the question is attribution theory. Attribution theory explains how people make inferences about the causes of behaviors, events, or outcomes. It suggests that people usually make two types of attributions: dispositional (internal) and situational (external). Dispositional attributions refer to explanations based on the person's traits or characteristics, while situational attributions refer to explanations based on external factors or circumstances.

Attribution theory also describes how people make judgments about their own behavior and that of others. In summary, attribution theory is a social psychology theory that helps to understand how people explain the causes of behavior. Hence option d is correct.

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--The complete question is, ____________________ theory provides a description of how people explain the causes of their own and others' behaviors.

a. dispositional

b. causal

c. identification

d. attribution

e. implicit

f. personality--

We can use trigonometry to solve this problem. Let x be the distance from the foot of the ladder to the building, and let y be the length of the ladder. Then, we have:

tan(52) = y/x (since tangent = opposite/adjacent, and y is opposite to the angle of elevation and x is adjacent)

We also know that the ladder reaches 12 feet above the ground, so we have:

y = 12 + x (since y is the hypotenuse of the right triangle formed by the ladder, the ground, and the building)

We can substitute the second equation into the first to get:

tan(52) = (12 + x)/x

Simplifying this equation, we get:

tan(52)x = 12 + x

Using a calculator to find the tangent of 52, we get:

1.2799x = 12 + x

Solving for x, we get:

0.2799x = 12

x = 42.87 feet (rounded to two decimal places)

Therefore, the foot of the ladder is approximately 42.87 feet away from the building.

Therefore, each drink would have approximately 18.67 grams of sugar if the amount of sugar was redistributed evenly.

In statistics, distribution refers to the pattern of values that a variable can take and how frequently those values occur. It is a mathematical function that describes the probability of occurrence of each possible outcome in a set of events.

There are various types of distributions such as normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each distribution has a specific shape and characteristics, which can be described by its mean, variance, skewness, and kurtosis.

by the question.

Let's say the amounts of sugar in the six drinks are:

Drink 1: 10 grams

Drink 2: 20 grams

Drink 3: 15 grams

Drink 4: 25 grams

Drink 5: 30 grams

Drink 6: 12 grams

To redistribute the sugar evenly, you would need to add up the total amount of sugar and divide it by the number of drinks. In this case:

Total amount of sugar = 10 + 20 + 15 + 25 + 30 + 12 = 112 grams

Number of drinks = 6

Redistributed amount of sugar = Total amount of sugar / Number of drinks

Redistributed amount of sugar = 112 / 6

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Answer:

28  

Step-by-step explanation:

a = b * h

a = 4 * 7

4 acts as the base

7 acts as the height

there is a right angle to support this.

If the number of school districts in Indiana were proportional to the number of school districts in Illinois, we would expect to see 440 school districts in Indiana.

Ratios are used to compare different parts of a whole, to compare different amounts of something, or to compare different measurements of the same thing.

The expected number of school districts in Indiana can be calculated by using the population of the two states.

We know that Illinois has 859 school districts and 12.9 million people, and Indiana has 295 school districts and 6.6 million people.

To determine how many school districts we would expect to see in Indiana if they were proportional to the number in Illinois, we can set up a proportion:

⇒number of school districts in Indiana/number of school districts in Illinois = population of Indiana/population of Illinois

⇒number of school districts in Illinois/number of school districts in Indiana = population of Illinois/population of Indiana

We can rearrange this proportion to solve for the number of school districts in Indiana:

⇒number of school districts in Indiana/number of school districts in Illinois = population of Indiana/population of Illinois

⇒number of school districts in Illinois/number of school districts in Indiana = population of Illinois/population of Indiana

Substituting the given values, we have:

number of school districts in Indiana =

6.6/12.9×859 ≈ 440

number of school districts in Indiana=

12.9 /6.6 ×859≈440

Rounding this to the nearest whole number, we would expect to see about 440 school districts in Indiana if they were proportional to the number in Illinois.

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It is the first option 4, 17, and 23

There is a rule of sides in a triangle that states "the sum of the lengths of two sides is always greater than the third side"

so how you would solve this is by process of elimination. Add two lengths from each number set to see if they follow the rule.

When you do this, all of the number sets follow the rule except for the first one, because 4 plus 17 is 21, and it is less than 23. This means it does not follow the rule.

Hope this helps :)

John deposits $5025 into a savings account that has an interest rate of 9.5%. The account is compounded monthly for the next 18 years. So in the account the amount will be $27596.60. Option c is correct.

Cοmpοund interest, alsο knοwn as interest οn principle and interest, is the practise οf adding interest tο the initial amοunt οf a lοan οr depοsit. It οccurs when interest is reinvested, οr added tο the bοrrοwed capital rather than paid οut, οr when the bοrrοwer is required tο pay it, sο that interest is made the fοllοwing periοd οn the initial amοunt + any accumulated interest. In business and ecοnοmy, cοmpοund interest is cοmmοn.

We can use the Cοmpοund interest below-

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

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Given,

Time periods (t)= 18years

n = 12 months

Interest in a year (r)= 9.5% or 0.095

Principial amount (P)= $5025

Lets solve for final amount :

[tex]\rm A = 5025(1 + \frac{0.095}{12})^{12 \times 18}[/tex]

A ≈ 27596.59

That is nearby $27596.60.

In the account the amount will be $27596.60. Thus, option c is correct.

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Answer: it is  c. 27596.60

Answer: The answer is E, or ≠.

Step-by-step explanation:

The symbol (≠) indicates that a number does not equal the other number. The correct option is E.

I hope this helped! A brainilist is appreciated and helpful! <3

Answer:

Jakob is correct.

The base 10 logarithmic function is a continuous function, which means that the distance between any two consecutive values on the number line is the same. Therefore, if 2 is halfway between 1 and 3, the value of the logarithm that is halfway between log 1 and log 3 should be the average of log 1 and log 3, which is:

(log 1 + log 3) / 2 = (0 + 0.477) / 2 = 0.2385

To find the value of x such that 10^x = 505, we can take the logarithm of both sides using base 10:

log 10^x = log 505

x = log 505

Using a calculator, we can find that log 505 is approximately 2.702.

To find the value of x such that 10^x = 100, we can take the logarithm of both sides using base 10:

log 10^x = log 100

x = log 100

Using a calculator, we can find that log 100 is exactly 2.

Therefore, the logarithm that is equal to 2 is log 100, not log 505.

The correct answer of the folowing question is option B and d in context to the circle and triangle

How to solve the problem?

Triangles and circles have a close relationship in geometry, and several interesting properties and theorems connect them.

One triangle inscribed in circle: This statement is true, and it refers to the property of a circle that can be inscribed in a triangle. In other words, if we draw a circle that passes through all three vertices of a triangle, then the triangle is said to be inscribed in the circle. The center of the circle is called the circumcenter of the triangle, and it is the intersection point of the perpendicular bisectors of the sides.

Many triangles inscribed in circle: This statement is also true, as there are many different triangles that can be inscribed in the same circle. For example, if we draw a circle and pick any three points on its circumference, then we can connect these points to form a triangle that is inscribed in the circle.

One circle inscribed in triangle: This statement is true, and it refers to the property of a triangle that can be inscribed in a circle. In other words, if we draw a circle that is tangent to all three sides of a triangle, then the circle is said to be inscribed in the triangle. The center of the circle is called the incenter of the triangle, and it is the intersection point of the angle bisectors.

Many circles inscribed in triangle: This statement is false, as there can only be one circle that is inscribed in a given triangle. However, there are other circles that can be associated with a triangle, such as the circumcircle and the excircles. The circumcircle is the circle that passes through all three vertices of the triangle, while the excircles are the circles that are tangent to one side of the triangle and the extensions of the other two sides.

In summary, triangles and circles are closely related in geometry, and their properties and theorems are important in various areas of mathematics and science.

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Answer:

a.) P(x)= 4x - 1240

b.) make $1,560 profit in 1 week by selling 700 calculators

Step-by-step explanation:

a.) P(x)=R(x)-C(x)

R(x)=13x; C(x)=9x + 1240   assuming they are asking for profit in a week

P(x)= 4x - 1240

b.) P(700) = 4(700) -1240 = 1560

Answer:

122 degrees.

Step-by-step explanation:

To calculate the measure of the sector that represents the probability of a rainy day using a spinner, we need to first determine the angle of the sector that represents the probability of a rainy day.

The probability of a rainy day is given as P(raining) = 0.34, which means that out of 100 days, 34 are rainy. Therefore, we can express the angle of the sector as:

Angle of sector = Probability of rain * Total angle of the spinner = 0.34 * 360 = 122.4 (rounded to the nearest degree)

So the measure of the sector that represents the probability of a rainy day is 122 degrees (rounded to the nearest degree).

Therefore, the answer is 122 degrees.

Answer:122°

Step-by-step explanation:

we have a 34% probability that it will rain and 66% that it won't rain. and full spin is 360 degrees which we can also symbolize as 100%.

so, if  

        360-----------100%

         x---------------34%

x=360*34/100≈122°

Answer: 1=53,2=96,0=100,2=70

Step-by-step explanation: Pretty easy there Parrell lines which equals 180 in angles so for example the first one is a corresponding angle cause 53 on angle A is the same on angle B

Second one equation to find this answer is 180-84=96

You'll learn the rest soon I hope this helps

Answer:

1/3 or 2/6

Step-by-step explanation:

6/6 is a whole. If you subtract 1/6 from 6/6, you get 5/6. Then, subtract 3/6 from 5/6. You get 2/6 remaining for the result. 2/6 simplified is 1/3.

Answer:

2/6

Step-by-step explanation:

We Know

She will use 1/6 of the poster for the title and 3/6 of the poster for a diagram of her experiment.

1/6 + 3/6 = 4/6

So, 4/6 of her poster has been used.

The rest of the poster will be used for the results of her experiment

How much of the poster will Katy use for the results?

We Take

6/6 - 4/6 = 2/6

So, 2/6 of her poster will be use for the result.

Answer:

  3.00%

Step-by-step explanation:

You want the interest rate that will make an $8000 deposit achieve a value of $9571.31 in 6 years when interest is compounded quarterly.

The compound interest formula can be solved for the interest rate when other values are known:

  A = P(1 +r/n)^(nt) . . . . . . . interest at rate r compounded n times per year

  9571.31 = 8000(1 +r/4)^(4·6) . . . . fill in known values

  (9571.31/8000)^(1/24) = 1 +r/4

  1 +r/4 ≈ 1.0075000

  r ≈ 0.0075000 × 4 ≈ 3.00%

The interest rate is 3.00%.

__

Additional comment

A financial calculator, app, or spreadsheet can find this for you.

so the garden is a parallelogram and the whole area is a rectangle, now, if we just get the whole area and then subtract the area of the parallelogram from it, in effect making a whole in the rectangle, what's leftover is the area of the walkway, Check the picture below.

The area of the shaded portion was estimated to be around 400 square feet, so 400 square feet were covered in sod.

The shaded portion of the garden was estimated to be around 400 square feet. To cover this area with sod, the soil was prepared by removing any existing vegetation, rocks, and debris. The soil was then leveled and covered with a layer of fertilizer. After that, the sod was laid on top of the soil, with the roots facing down. The sod was then watered and rolled to ensure the sod was securely attached to the ground. The entire process of sodding the garden was completed in 400 square feet, providing an even layer of grass for the area. This will help to keep the garden beautiful and healthy for years to come.

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