true or false: for a random sample of size 15 from a normal population with unknown variance, the test statistic with the null hypothesis of is , when is the sample mean.

Answer:

10 groups of 3, 3 groups of 10 and 5 groups of 6

Step-by-step explanation:

An inclined plane of length 8 m is used to lift the load 2 m, using the same effort.

A ramp that helps lift and lower heavy things is called an inclined plane. It is a flat surface that is positioned against a horizontal surface at an angle other than a right angle.

Work is defined as the use of force to move an object over a distance. It is derived as the product of displacement (d) and force (F). Work is given by W = F×d = 25 N×d.

When a body is lifted, we can express work as W = m×g×h where g is gravity and h is height. And the force is written as F = m×g where m is the mass of an object. Then, W = F×h

Calculating the work done to lift the load to 2 m, we get,

W = 100 N×2 m = 200 Nm.

Substitute this value in W = F×h, we get,

200 Nm = 25 N×d

Divide both sides by 25 N, and we get,

[tex]\begin{aligned}\frac{\mathrm{200\;Nm}}{\mathrm{25\;N}}&=\frac{\mathrm{25\;N\times d}}{\mathrm{25\;N}}\\d&=\mathrm{8\;m}\end{aligned}[/tex]

The value is 8 m. Therefore, the first statement is correct.

The complete question is -

To lift a load of 100 N a distance of 1 m an effort of 25 N must be applied over an inclined plane of length 4 m. What must be done to lift the load 2 m, using the same effort?

A. Use an inclined plane of length 8 m.

B. Use an inclined plane of length 2 m.

C. Use an inclined plane of length 10 m

D. Use an inclined plane of length 16 m.

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Answer:

180 degrees in a triangle

Answer:

7, 14,21 28

4,8,12,16

Step-by-step explanation:

Answer:

8, 21, 16

Step-by-step explanation:

The ratio from sugar to cups is 7:4, which is 1.75.

Divide and multiply to solve.

14 / 1.75 = 8

12 * 1.75 = 21

28 / 1.75 = 16

Step-by-step explanation:

its me ryan , 15 from michigan . Its just that i needed friends . If you want to be my good friend , please do comment below and we can be real good friends. ?

Answer:

final amount = $16512.36

Step-by-step explanation:

The question asks us to find the value of Gavin's deposit of $12,000 after 16 years, given that the interest rate of 2% is compounded quarterly.

To do this, we have to use the following formula for compound interest:

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

where:

A → amount at the end

P → principal (original) amount

r → interest rate (in decimal)

n → number of times per year that the interest is compounded

t → time (in years).

From the question, we know that the initial amount deposited is $12,000. Therefore, P = 12000. We also know that the interest rate is 2%, but the formula requires the rate to be in decimal, so r = 0.02. The time for which the money is deposited is 16 years, and therefore, t = 16. We are told that the interest is compounded quarterly, that is, every 3 months. This means that the interest is compounded 4 times yearly, so n = 4.

From the above information and formula, we can calculate the final amount:

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

⇒ [tex]A = 12000(1 + \frac{0.02}{4})^{4 \times 16}[/tex]

⇒ A = $16512.36

Therefore, the final amount after 16 years is $16512.36.

The rate of change of length of his shadow when he is 30ft away from the lamp post is  3 ft/sec .

In the question ,

it is given that ,

the length of the man is = 6 ft ,

le the distance of the man from the base of the lamp post at time "t" is = x

let the length of the shadow at time "t" = y ,

given that dx/dt = 6 ft/sec .

From the figure given ,

In triangle ABC and triangle ADE ,

AB/BC = AD/DE

that is , y/6 = (x+y)/18

after simplification ,

we get ,

2y = x .

differentiating both with respect to "t" ,

we get

2 * dy/dt = dx/dt

Substituting dx/dt = 6  ,

we get ,

dy/dt = 3 ft/sec .

Therefore , the rate of change of the length of the shadow is 3 ft/sec .

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f and g are inverses of each other and g is a reflection of y = x thus options (B) and (C) are correct.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given functions,

f(x) = [tex]2^{x}[/tex] and g(x) = [tex]log_{2} x[/tex]

It is known that the exponential function and logarithm function are inverse of each other for the same base as shown below.

It is also clear that g(x) is the reflection of x = y.

Hence "g is a reflection of y = x and f and g are inverses of one another.".

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At the end, the distance to the car will be 17 miles, and the distance that they walked is 13 miles.

We want to find the total distance at which the hikers are at the end.

Notice that each little square represents one mile. And the line ends at two little squares above the marking of 15 miles, then the distance to the car at the end is:

15mi + 2 mi = 17 miles.

We also could want to find the distance they walked on the given graph. To find that, we need to take the difference between the final distance and the initial distance.

The final distance is 17 miles, we already know this, and the initial distance is the y-intercept, which in this case is 4 miles.

Then the distance that they walked is:

D = 17mi - 4mi = 13mi

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The forward rate for the third year 3.06%

The forward rate is the interest rate applied to future financial transactions. The forward rate is calculated from the spot rate, adjusted for maintenance costs to determine future interest rates that equalize the strategy to extend short-term investments and the total return on long-term investments.

This term can also refer to interest rates charged on future financial obligations, such as interest rates on loan payments.

(n1 – n2) reservation rate calculation number. A few years later n2 no. The number of years of Forward rate = [(1 + S1)n1 / (1 + S2)n2]1/(n1-n2) – 1.

According the question:

S3 = [(1 + S₁) × (1 + F(1,2))²]¹/³ ⁻¹

= [(1 + 2.658%) × (1 + 2.340%)²]¹/³ ⁻¹

= [1.02658 × 11.1556]¹/³ ⁻¹

= (12.18)¹/³ ⁻¹

= 3.06

Therefore, calculation of spot rate for three years will be, 3.06%

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The words that fills the blank space on the method used to find the length of the diagonal AG, using Pythagorean Theorem are as follows;

Blank 1; The Pythagorean Theorem

Blank 2; Square root of 73

Blank 3; A leg

Blank 4; The hypotenuse

Blank 5; 9.4 cm

Pythagoras Theorem indicates that the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.

The diagonals from point A to point G in the cuboid can be found using Pythagoras Theorem as follows;

The diagonal of the base rectangle, ABCD, is found as follows;

AC = √(8² + 3²) = √(73)

Using the side CG as the leg of the right triangle ΔACG, with AG being the hypotenuse, we get;

CG = 4 indicated in the diagram in the question

(AG)² = (AC)² + (CG)²

(AG)² = 73 + 4² = 89

AG = √(89) ≈ 9.4

The completed statement is therefore;

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a) The expressions are given as follows:

b) The total cost for each present is of:

Hence the present that they can buy with the least amount of money is:

Jewelry.

The costs are found applying the proportions in this problem.

As a function of d, the functions are found multiplying the decimal equivalents of each discount by the cost expression.

The decimal equivalents of each discount are given as follows:

Then the actual costs are calculated replacing the instances of d in each item with the numeric value d = 79.

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according to the question,

given data in the question,

the type of rigid transformation is the equivalent of two across intersecting lines

Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.

The intersection of the two reflection lines is the center of rotation.

An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.

The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation

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The type of transformation that is equivalent to 2 reflections across intersecting lines is rotation

A slide or a shift is a translation. By executing two composite reflections along parallel lines, translations may be produced. Translations maintain orientation and are isometric.

An isometry is made up of two other isometries. The translation is equal to the combination of two reflections over two parallel lines.

according to the question,

the type of rigid transformation is the equivalent of two across intersecting lines

Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.

The intersection of the two reflection lines is the center of rotation.

An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.

The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation

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We can use the four theorems - SSS, SAS, ASA, AAS - to prove that two triangles are congruent.

To prove that the given triangles are congruent there are some rules, one of which it must satisfy to show that the two are congruent. The four theorems are stated and explained below-

SSS rule: If the 3 sides of both of the given triangles are equal, then the triangles are congruent.

SAS rule: If the 2 sides and one of the three angles of both of the given triangles are equal, then the triangles are congruent.

ASA rule: If 2 of the total three angles and a side (in the middle of the angles)of both of the given triangles are equal, then the triangles are congruent.

AAS rule: If 2 angles and a side(adjacent to the angles) of the given two triangles are equal, then the triangles are congruent.

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Answer:

6.3

Step-by-step explanation:

5% probability is there that every person ends up with the wrong suitcase.

Given,

Number of people checked in  = 5

Number of suitcases = 5

We have to find the probability that when each person taken a suitcase randomly and it ends up with the wrong suitcase;

Here,

5 people can take 5 suitcases in 5 different ways.

So,

Probability = possible outcomes / original outcome

Probability = 5 x 5 / 5

Probability = 25/5 = 5

That is,

The probability that every person ends up with the wrong suitcase is 5%

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Values are paired in the form:

(X1, Y1),.. (Xn, Yn)

(3.25, 3.2)

"Information available from the question"

In the question:

College administrators noticed that students who had higher high school GPAs tend to have higher college GPAs.

The data in the table show various high school GPAs and college GPAs for a sample of students. A 2-column table with 16 rows.

Column 1 is labeled high school g p a with entries.

3. 25, 3. 5, 3. 5, 3. 25, 2. 5, 4, 4, 3. 5, 3. 25, 3. 5, 3. 5, 4, 3, 3. 5, 2. 25, 2. 5

Column 2 is labeled college g p a with entries 3. 2, 3. 0, 2. 9, 3. 0, 3. 0, 3. 0, 3. 1, 3. 1, 3. 1, 3. 0, 3. 0, 3. 1, 3. 0, 3. 1, 2. 9, 2. 8

Now, According to the question:

Column 1 High School G P A:

3.25, 3.5, 3.5, 3.25, 2.5, 4, 4, 3.5, 3.25, 3.5, 3.5, 4, 3, 3.5, 2.25, 2.5

Column 2 College G P A :

3.2, 3.0, 2.9, 3.0, 3.0, 3.0, 3.1, 3.1, 3.1, 3.0, 3.0, 3.1, 3.0, 3.1, 2.9, 2.8.

To prepare a scatter plot ; with x - axis plotted against y - axis ;

Each point on the x - axis is paired with a corresponding point on the y - axis ;

With high school GPA on the x axis and College GPA on y :

Values are paired in the form:

(X1, Y1),.. (Xn, Yn)

(3.25, 3.2)

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Therefore the answer to following is probabilities of following problems are  (a) 0 ,(b) 1 ,(c) 0.01 and (d) 0.6 .

To investigate unpredictability, mathematicians utilize probability. It discusses the possibility (the likelihood) of an event happening. For instance, if you flip a fair coin four times, you might not get two heads and two tails each time.

Here,

(A) The event cannot happen if the probability is zero.

(b) The event is guaranteed to occur if the probability is 1.

(c) An event is very unlikely to happen if the probability is less than 0.01.

(d) The occurrence is more likely to happen if the probability is 0.6. (because the probability is greater than 0.6).

(a) 0

(b) 1

(c) 0.01

(d) 0.6

Therefore the answer to following is probabilities of following problems are  (a) 0 ,(b) 1 ,(c) 0.01 and (d) 0.6

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The number of bottles of soda is  4 and the number of bottles of juice purchased is  8.

We know that linear system of equation in two variables is required to solve the problem. Let suppose number of bottles of soda purchased by Jacob is x and number of bottles of juice purchased by Jacob is y

Since, it is given that Jacob bought 25 bottles in total, it means

=>x + y=12-----(eq1)

Also, it is given that total amount of sugar is 240grams.Now,amount of sugar present in soda bottle is 25x and amount of sugar present in juice bottles is 12y

Therefore,25x + 12y=240-----(eq2)

On solving eq1 and eq2,we get

=>x+y=12

and 25x+10y=240

Using elimination technique to solve, make x terms coefficient equal.

Multiplying eq1 by 25,we get

=>25x + 25y=25×12

=>25x +25y=300------(eq3)

Using eq3 and eq4,we get

=>25x+25y=300

and 25x+10y=240

Cancelling x terms, we get

=>15y=60

=>y=(60/15) grams

=>y=4 bottles

Now, putting value of y in eq1 ,we get

=>4+y=12

=>y=12-4

=>y=8bottles.

Hence, required value of number of bottles of soda is 4 and number of bottles of juice is 8.

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The total amount the mechanic will need in retirement savings to meet their retirement income goal is 870,000. The correct option is C.

In mathematics, an expression is a combination of numbers, symbols, and operations (such as addition, subtraction, multiplication, and division) that represents a quantity or a value.

Expressions can be very simple, such as a single number or variable, or they can be more complex, such as a combination of multiple terms with different operators.

The mechanic wants to live off 80% of their current annual gross wage, which is:

0.8 x 43,500 = $34,800 per year

The mechanic plans to draw 4% the first year from their retirement savings, which means the total retirement savings needed are:

34,800 / 0.04 = $870,000

Therefore, the answer is C) 870,000.

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Tt takes 1.5 min of time  to travel a distance of 1 km by bus

Since here we need to find the time, which basically depends on the speed of the bus, as we know the formula we refer to for calculating the time is distance/speed, here we are provided with the distance which is  1km also equal to 1000m. Now considering a normal condition where the speed of  the bus is h 40km per hour, therefore

=>Distance = Speed × Time

=?1km = 40 Km/hr × Time

Time = 1/40 hr = 0.025 hr ,Which is almost 1.5 min

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Number of games did Carly NOT play is 22.

How to calculate percentage?

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given:

Total number of games = 40

It is given that  she had played in 45 percent of the 40 games the team played.

Number of games she played = 45% of 40

                                                 = [tex]\frac{45}{100}\times 40= 18[/tex]

Number of games she did not play = 40 - 18 = 22

Therefore, number of  games did Carly NOT play is 22.

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The value of x in the regular polygon is 120 degrees.

The regular polygon is a triangle. A regular polygon has all it interior angles equal to each other. Therefore, the triangle above is an equilateral triangle.

An equilateral triangle has all its sides equal to each other and the angles are also congruent.  Each angle of an equilateral triangle is 60 degrees.

Exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore,

60 + 60 = x

Hence,

x = 120 degrees.

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The solution is, the simplified value is 2107/5 = 421.4.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

24 3/5 +4^3x(8 1/5 -2)

we have to

Simplify the Equation

With Converting 24 3/5 to a improper fraction

Calculate the Power of 4^3

Then convert 8 1/5 to a improper fraction

Subtract 41/5 and 2 to get 31/5

Then Multiple the product,

64 • 31/5 to get 1984/5

After add the fractions up

123/5 + 1984/5

=2107/5

=421.4

Hence, The solution is, the simplified value is 2107/5 = 421.4.

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Answer: 32 1/18

Step-by-step explanation: So first, I did 1/9 (-1/2) and I got 1/18. Yes although it was negative, when multiplying, it will become positive, then 1 x 1 is 1, and 9 x 2 is 18. Then, when adding it to 32, you get 32 1/18. I hoped this helped!

The summary of the ruler placement postulate is: A direct relationship exists between the set of points on the line and the collection of real numbers, where each point is matched to a single real number and   The magnitude of the gap between two points is equal to the absolute value of the subtraction of the two associated values.

The ruler placement postulate states that if two points are given, it is possible to measure the distance between them by taking the point of reference as zero. This means that any point can be chosen as an origin, and the distance between the two points can be calculated by measuring the number of units between them. This postulate also applies to curves, and the distance between two points on a curve can be measured by taking a point of reference as zero and measuring the number of units between them. This postulate is essential in the measurement of distances between points and curves in geometry.

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Answer: 537 stuffed animals

Step-by-step explanation:

Take 939 - 402 = 537

So she gave away 537 stuffed animals

Answer:

Do you have a picture of the graph?

Step-by-step explanation:

If so can you pls insert :)

The probability that at least one is type O is 0.8704.

What is a binomial distribution probability?

A value's likelihood of taking one of two independent values is summarised by the statistical distribution known as the binomial distribution.

Given,  40 % of the population has type O blood and 4 people are randomly selected to be donors

Then, binomial distribution can be given by

X ~ = Binomial(n = 4, p = 0.4)

P(at least one type O)

P[X ≥ 1]

= 1- P[X < 1]

= 1- P[X = 0]

= [tex]1 -C(4,0) * (0.4)^{0} * (1 - 0.4)^{4-0}[/tex]

=1-0.1296

=0.8704

Hence, the probability that at least one is type O is 0.8704.

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