In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance. Find the critical value(s).
Select one:
a. Both -1.96 and 1.96
b. Only 1.699
c. Only -1.699
d. Only -1.645
e. Both -2.045 and 2.045
f. Only 1.645

The number 240 is a composite number and can be written as the product of prime factors 2 x 2 x 2 x 2 x 3 x 5.

The number 240 is a composite number. This is because it can be divided by numbers other than 1 and itself.

To write 240 as the product of prime factors, we can use the factor tree method:

240
/  \
2   120
  /  \
 2    60
     /  \
    2    30
        /  \
       2    15
           /  \
          3    5

So, the prime factors of 240 are 2, 2, 2, 2, 3, and 5.

We can write this as:

240 = 2 x 2 x 2 x 2 x 3 x 5

Therefore, the number 240 is a composite number and can be written as the product of prime factors 2 x 2 x 2 x 2 x 3 x 5.

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Answer: 12.124355653

Step-by-step explanation: I did the math on a calculator

The perimeter of the base is 32 cm.

The area of the base is 48 cm².

The total surface area of the triangular prism is 1184 cm².

The diagram above is a triangular prism. Therefore, let's find the perimeter of the base, area of the base and surface area of the triangular prism.

Hence,

perimeter of the base = 10 + 10 + 12

perimeter of the base = 20 + 12

perimeter of the base = 32 cm

Area of the base = 1 / 2 bh

where

Therefore,

Area of the base = 1 / 2 × 12 × 8

Area of the base = 48 cm²

Hence,

total surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)

total surface area of the triangular prism = 12(8) + 34(10 + 10 + 12)

total surface area of the triangular prism = 96 + 34(32)

total surface area of the triangular prism =96 + 1088

total surface area of the triangular prism = 1184 cm²

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If Lindsay he mows the lawn in 10 hours and with his brother Grant he does it in 2 hours, Grant would mow the lawn alone in 2.5 hours.

To find out how long it would take Grant to mow the lawn alone, we can use the formula for combined work:

1/t₁ + 1/t₂ = 1/ttotal

Where t₁ is the time it takes Lindsay to mow the lawn alone, t₂ is the time it takes Grant to mow the lawn alone, and ttotal is the time it takes both of them to mow the lawn together.

Plugging in the given values:

1/10 + 1/t₂ = 1/2

Multiplying both sides by 20t₂ to clear the fractions:

2t₂ + 20 = 10t₂

Rearranging and simplifying:
8t₂ = 20
t₂ = 20/8
t₂ = 2.5

So it would take Grant 2.5 hours to mow the lawn alone.

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The simplified expression is 45°, which is closest to option a. 38°.

Lines are one-dimensional geometrical objects that extend infinitely in both directions. Angles are formed when two lines intersect, and they measure the amount of rotation between the lines.

We can use the formula:

arctan(x) + arctan(y) = arctan[(x + y) / (1 - xy)]

to simplify the expression.

Setting x = 1/3 and y = 2/3, we have:

arctan(1/3) + arctan(2/3) = arctan[(1/3) + (2/3) / (1 - (1/3)(2/3))]

= arctan(1)

= 45°

Therefore, the simplified expression is 45°, which is closest to option

a. 38°.

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The final answer is:

4C+2D = [28 28]
       [14 26]

To find 4C+2D, we first need to multiply the matrices C and D by their respective scalars, 4 and 2. Then, we add the resulting matrices together.

First, let's multiply matrix C by 4:

4C = 4[5 3] = [20 12]
   [1 2]   [ 4  8]

Next, let's multiply matrix D by 2:

2D = 2[4 8] = [ 8 16]
   [5 9]   [10 18]

Now, we can add the resulting matrices together:

4C+2D = [20 12] + [ 8 16] = [28 28]
       [ 4  8]   [10 18]   [14 26]

So, the final answer is:

4C+2D = [28 28]
       [14 26]

I hope this helps! Let me know if you have any further questions.

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Answer:

A) 59°

Step-by-step explanation:

m<ADC is a right angle, therefore it is 90°

so that means you can now subtract the angle that you already know [31°] from it to get the angle that is left over, m<ADB

90°-31°= 59° (subtracting m<ADC [90°] from m<BDC [31°] leaves your remaining angle m<ADB [59°]

The solution to the system of linear equations -1.2x+0.3y=-8.4 -1.4x+0.2y=10.6, is x = -27 and y = -136.

The given system of linear equations is:

-1.2x+0.3y=-8.4
-1.4x+0.2y=10.6

To determine whether the system has a solution, we can use the method of elimination. First, we need to multiply each equation by a constant to make the coefficients of one of the variables the same in both equations. In this case, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same:

-2.4x+0.6y=-16.8
-4.2x+0.6y=31.8

Next, we can subtract the second equation from the first equation to eliminate the y variable:

1.8x=-48.6

Finally, we can solve for x:

x=-27

Now we can plug this value of x back into one of the original equations to solve for y:

-1.2(-27)+0.3y=-8.4
32.4+0.3y=-8.4
0.3y=-40.8
y=-136

So the solution to the system of linear equations is x=-27 and y=-136. Therefore, the given system of linear equations does have a solution.

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The answer of this question is -4,298,008. We solve this question by taking the LCM of denominators.

The smallest multiple that two or more numbers share is known as the least common multiple. Least Common Multiple short form is LCM.

We can find LCM of these number by taking least common multiple.

LCM of 3, 3, 17, 13 is 663 .

(a) [tex]-\frac{22}{3} *663 = -22*221[/tex]

[tex]= -4862[/tex]

(b) [tex]\frac{4}{3} * 663 = 4 * 221[/tex]

[tex]= 884[/tex]

(c) [tex]\frac{6}{17} *663 = 6 * 17[/tex]

[tex]= 102[/tex]

(d) [tex]\frac{2}{13}*663 = 2*51[/tex]

[tex]=102[/tex]

So, the answer is -4,298,008 .

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let's convert the mixed fraction to improper fraction first.

[tex]\stackrel{mixed}{3\frac{5}{6}}\implies \cfrac{3\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{23}{6}} \\\\[-0.35em] ~\dotfill\\\\ 3\frac{5}{6}\times 12\implies \cfrac{23}{6}\times 12\implies \cfrac{23}{6}\times \cfrac{12}{1}\implies \cfrac{23}{1}\times \cfrac{12}{6}\implies 23\times 2\implies \text{\LARGE 46}[/tex]

Answer:

True

Step-by-step explanation:

Plug in x = 1 into the function expression. You should get  f(xx) = 4

Plug in x = 2 and you will get f(x) = 13

So the function value has increased from 4 at x = 1 to 13 at x = 2

or, just plot it and see it visually

The rule that could be used to prove that the two triangles are congruent is given as follows:

A. Side - Side - Side.

The Side-Side-Side congruence theorem states that if all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.

For this problem, we have that the two congruent sides are given as follows:

If the third sides are congruent, then the Side-Side-Side congruence theorem can be used.

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To find out how many minutes it would take Teresa to run 9 miles at the same rate, we can use a proportion.

We know that Teresa took 44 minutes to run 6 miles. This means she was running at a rate of 6 miles per 44 minutes. To solve for how long it would take to run 9 miles, we can set up a proportion with this information.

Let x = the number of minutes it would take Teresa to run 9 miles.

6/44 = 9/x

Cross-multiply to solve for x: 44x = 54

Divide both sides by 44 to find the solution: x = 54/44 = 1.227 minutes

Therefore, it would take Teresa 1.227 minutes to run 9 miles at the same rate.

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A store has three sizes of cans of nuts. The large size contains 2 pounds of peanuts and 1 pound of cashews. The mammoth size contains 1 pound of walnuts, 6 pounds of peanuts, and 2 pounds of cashews.

The giant size contains 1 pound of walnuts, 4 pounds of peanuts, and 2 pounds of enehews. Suppose that the store recelives be filled with the given sizes of cans?

To solve this problem, let's assign variables to the unknowns. Let G represent the number of giant cans, M represent the number of mammoth cans, and L represent the number of large cans.

We can then write out the system of linear equations:

2L + 1M + 4G = 2 lbs. of peanuts
1L + 6M + 1G = 1 lbs. of walnuts
1L + 2M + 2G = 2 lbs. of cashews

Solving this system of equations can be done with any method, such as substitution, elimination, or graphing.

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The velocity of the bird is approximately 40.04 km/hour.

What is velocity ?

Velocity is a measure of the rate at which an object changes its position in a particular direction. It is a vector quantity, which means that it has both a magnitude (speed) and a direction.

To find the velocity of the bird, we can use the formula:

velocity = distance/time

Given that the bird flies 961 km in 24 hours, we can substitute these values into the formula:\

velocity = 961 km / 24 hours

Simplifying this expression, we get:

velocity = 40.04 km/hour (rounded to two decimal places)

Therefore, the velocity of the bird is approximately 40.04 km/hour.

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The number of home-runs LA Dodgers hit is  35.

Given,

Total home runs in Major league = 583

Home - runs accounted by LA Dodgers = 6 %

Number of home-runs by LA Dodgers

                = 6% of 583

                = 6/100 * (583)

                = 0.06 * 585

                = 34.98

                = 35 approximately

Hence, the total number of homeruns that did the LA Dodgers hit are 35 approximately.

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1) The sale price on the painting is $1,235.

2) The regular price of the mechanic's tool set is $340.

3) The regular price of the battery is $111.84.

1) To find the sale price on a painting that has a regular price of $1,900 and is on sale for 35% off the regular price, we can use the formula: sale price = regular price - (regular price * discount rate).
In this case, the sale price would be $1,900 - ($1,900 * 0.35) = $1,900 - $665 = $1,235.
So the sale price of the painting is $1,235.

2) To find the regular price of a mechanic's tool set that is on sale for $204 after a markdown of 40% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $204 / (1 - 0.40) = $204 / 0.60 = $340.
So the regular price of the mechanic's tool set is $340.

3) To find the regular price of a battery that has a discount price of $85 and is on sale for 24% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $85 / (1 - 0.24) = $85 / 0.76 = $111.84.
So the regular price of the battery is $111.84.

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The probability that a person is randomly assigned a seat in rows A,B,C, E is 4/15.

The probability that a person is randomly assigned a seat in rows A,B,C, E can be calculated by dividing the number of desired outcomes by the total number of possible outcomes.

In this case, the desired outcomes are the rows A,B,C, and E, which is a total of 4 rows. The total number of possible outcomes are the 15 rows of bleachers in the school gym, labeled A through O.

So, the probability is calculated as follows:

P(A,B,C, or E) = 4/15

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The measure of angle KYC, considering the concept of vertical angles, is given as follows:

m < KYC = 69º.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles for this problem are given as follows:

<KYC and 69º.

As they are opposite by the vertex at the crossing of the two diagonal segments for this problem.

Hence the measure of angle KYC is given as follows:

m < KYC = 69º.

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Answer:

x=36

y=6

system of equations

The area of the circle is 63.62 square meters

To work out the area of a circle, we need to use the formula A = πr^2, where A is the area of the circle, π is a mathematical constant approximately equal to 3.142, and r is the radius of the circle.

In this problem, we are given the diameter of the circle, which is the distance across the circle passing through its center. The radius is half of the diameter, so we can find it by dividing the diameter by 2.

In this case, the diameter is 9 meters, so the radius is 9/2 = 4.5 meters. We then substitute this value into the formula:

A = πr^2

A = 3.142 x (4.5)^2

A = 3.142 x 20.25

A = 63.6175

A ≈ 63.62 square meters

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The given question is incomplete, the complete question is:

Work out the area of the circle where diameter is 9 meter

Take π it to be 3.142 and give your answer to 2 decimal places.

The area of the shaded diagonal plane is  17.5 square units.

The area of the shaded diagonal plane is calculated as follows:

Using Pythagoras' theorem, let the hypotenuse formed by the diagonal be x

x² = 3² + 5²

x² = 9 + 25

x² = 34

x = √34

The shape of the shaded plane is a rectangle.

The area of the rectangle will be:

Area = length * width

Area = √34 * 3

Area do the shaded plane = 17.5 square units

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Answer:

We know that cot A = adjacent side / opposite side = 21/20.

Let x be the length of the adjacent side and y be the length of the opposite side.

Using the Pythagorean theorem, we have:

x^2 + y^2 = (20k)^2, where k is some positive constant.

Since angle A is in Quadrant I, x is positive and y is positive. Thus, we can take the square root of both sides to get:

x + y = 20k.

Now, we can use the fact that cot A = adjacent side / opposite side = 21/20 to get:

x/y = 21/20.

Multiplying both sides by y, we get:

x = (21/20)y.

Substituting this into x + y = 20k, we get:

(21/20)y + y = 20k

Simplifying, we get:

(41/20)y = 20k

y = (20k)/(41/20) = (400k)/41

Now, we can use the Pythagorean theorem to find x:

x^2 + y^2 = (20k)^2

(21/20)y^2 + y^2 = (20k)^2

(441/400)y^2 = (20k)^2

y^2 = (400/441)(20k)^2

y = (20k/441)sqrt(441 x 20)

y = (20k/21)sqrt(20)

Therefore, angle A in simplest radical form using a rational denominator is given by:

tan A = y/x = [(20k/21)sqrt(20)] / [(21/20)y] = sqrt(20)/21

A = arctan(sqrt(20)/21)

By answering the above question, we may state that Without having both  expressions the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.  

If Megan and Mindy both depicted the entire playground, then their pictures ought to match. Their designs ought to depict the remaining 4/6 of the playground if the plan they viewed only showed 2/6 of it.

You may assess a drawing's accuracy by contrasting it with the first design that Megan and Mindy viewed. They are correct if their designs depict the remaining 4/6 of the playground and the original plan matches. Their drawings are incorrect if they do not reflect the original design or do not depict the remaining 4/6 of the playground.

Without having both the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.

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By adding the rectangle, the shaded area is [tex]53 in^2[/tex], rοunded tο the nearest whole figure.

The entire area οf a three-dimensional οbject's surface is known as surface area. It is a measurement of an οbject's expοsed surface. Indicating an οbject's surface area typically involves using square measurements like square inches οr square meters. The surface area οf a cube, fοr instance, is equal to the tοtal οf the areas οf each οf its six faces. The calculatiοn fοr a cube's surface area is: Surface Area Equals 6*[tex]side^2[/tex] where "side" denοtes the cube's extent οn οne side.

given:

The bigger semicircle has a radius οf 5 inches and a diameter οf 10 inches. Consequently, the bigger semicircle's area is:

(5 in) * (1/2) * π  = 39.27 in (rοunded tο twο decimal places)

The smaller semicircle has a radius of οf 2 inches and a width of οf 4 inches. Consequently, the smaller semicircle's size is:

(2 in) * (1/2) * π * 6.28 in (rοunded tο twο decimal places)

The rectangle's area is: because it is 10 inches long and 2 inches wide.

10 in + 2 in equals [tex]20 in ^2.[/tex]

We can add the area οf the rectangle tο the area οf the larger semicircle after subtracting the areas οf the smaller and larger semicircles tο determine the area οf the shaded regiοn:

[tex]39.27 in^2 - 6.28 in^2+ 20 in^2 = 52.99 in^2.[/tex]

By adding the rectangle, the shaded area is 53 in2, rοunded tο the nearest whole figure.

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Answer: :)

Step-by-step explanation:

To classify the triangle as acute, right, or obtuse, we need to determine the measure of the largest angle in the triangle. We can use the Law of Cosines to find the angles of the triangle:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

For this triangle, we have:

c = 12

a = 6

b = 9

Using these values in the Law of Cosines, we get:

12^2 = 6^2 + 9^2 - 2(6)(9)cos(C)

144 = 117 - 108cos(C)

27 = 108cos(C)

cos(C) = 0.25

To find angle C, we can take the inverse cosine (cos^-1) of both sides:

C = cos^-1(0.25)

C ≈ 75.5°

Now we can classify the triangle based on its largest angle:

- If C is less than 90 degrees, then the triangle is acute.

- If C is exactly 90 degrees, then the triangle is right.

- If C is greater than 90 degrees, then the triangle is obtuse.

In this case, since C ≈ 75.5°, which is less than 90 degrees, we know that this triangle is an acute triangle.