Question 6 A test of hypothesis was performed to determine, at 5% level of significance, if the majority of the engineering graduates pass the PE exam in their first try. If the computed value of the test statistic Z based on the sample information is z = 2.10, then the p-value for this test is: 0.00895 O 0.05 0.9821 None of these O 0.0179 N • Previous Not saved S

The range of projectile =21556.122 m

The maximum height of the projectile will be = 5280.03 m

The speed at which the projectile hits will be 650 m/s.

Initial speed [tex]v_0=650 \:m/s[/tex]

Angle of elevation [tex]\theta=30^{\circ}[/tex]

Acceleration due to gravity [tex]=9.8 m/s^2[/tex]

i) Range of the Projectile:

[tex]$$\begin{aligned}& R=\frac{v_0^2 \sin (2 \theta)}{g}=\frac{(650)^2 \sin (30)}{9.8} \\& R=21556.122 m\end{aligned}$$[/tex]

ii) Maximum Height of the projectile.

[tex]$$\begin{aligned}& H=\frac{v_0{ }^2 \sin ^2 \theta}{2 g}=\frac{(650)^2 \sin ^2(30)}{2 \times 9.8} \\& H=5389.03 m\end{aligned}$$[/tex]

iii) The speed at which the projectile hits the ground is the same as the initial speed.

i.e. speed [tex]$=650 \mathrm{~m} / \mathrm{s}$[/tex]

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If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.

How to solve word problems?

Recognize the issue, including all the terminology used to describe it. Recognize what we need to look for, Recognize the issue's context.

Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.

Put the strategy into action and find a solution.

Given:

Elephants at the Norfolk zoo are fed = 1/2 of the barrel

Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed

= 7/10 * 1/2

= 7/20

Therefore, If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.

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Answer:

55 degrees

Step-by-step explanation:

Sum of ALL three angles of a triangle ALWAYS equal 180

rule is 6x+5 will equal the sum of the 2 known angles because of this

6x+5=3x+x+45

6x+5=4x+45

-4x.    -4x

2x+5=45

    -5. -5

2x=40

/2. /2

x=20

6(20)+5

120+5

125

180-125

55

hopes this helps please mark brainliest

The simplified form of the expression is 123/20 x - 228

From the question, we have the following parameters that can be used in our computation:

three 7/5 X +4-232 -5/4 X

Rewrite the above expression properly

So, we have the following representation

37/5 x + 4 - 232 - 5/4 x

Collect the like terms in the above expression

So, we have the following representation

37/5 x - 5/4 x + 4 - 232

Evaluate the like terms in the above expression

So, we have the following representation

123/20 x + 4 - 232

Solving further, we have

123/20 x - 228

Hence, the solution is  123/20 x - 228

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The development made to the Judaism is mentioned below;

Action as Leader;

Abraham;

Abraham's care for others is one of his leadership strengths. Abraham expressed his sorrow for Sodom and Gomorrah when the Lord informed him that they would be destroyed. He "stick his neck out for his people," as one who cares for others. He pleaded with God on their behalf.

Moses;

Early on, Moses realized he didn't have to handle everything by himself. He eventually succeeded as a leader by using delegation.

David;

As a man of God, David had learned to wait on the Lord, but he also had to learn how to be patient with those around him.

Solomon;

His name in Hebrew means peace and he used his wisdom to bring about peace in the world through deeds rather than conquest.

Contribution to Judaism

Abraham;

Before Abraham, people believed in multiple gods; Abraham was the first to preach that there is only one God. Ironically, Terach, Abraham's father, had made a fortune by selling idols of several deities.

Moses;

The Jews were delivered from slavery in Egypt by Moses, who also guided them to the Holy Land that God had promised.

David;

Many of the Old Testament Psalms are attributed to him; they were probably penned on his renowned lyre, upon which he was reputed to be a master.

Solomon;

As the Israelite monarch who constructed the first Temple in Jerusalem, Solomon is well-known. He was also the second and final king of a united Israel, which was at the height of its power during his rule (after his father, David).

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A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.

Given a line with equation y = mx + c, the slope is denoted by m.

Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:

m₁ x m₂ = -1

The given line equation is:  y = 2x+1

Hence,

m₁ = 2

Compute the slope from 2 points: (4, 2) and (-1, k)

m₂ = (k - 2) / (-1 - 4)

m₂ = (-1/5) (k - 2)

Use the condition for perpendicular lines:

m₁ x m₂ = -1

2 x (-1/5) (k - 2) = -1

2k - 4 = 5

2k = 9

k = 9/2

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On solving the provided question, we can say that In lexicographic order, the following variation will be (5,6,7,4,3,2,1).

It is known as permuting the set in mathematics to rearrange the components of a set that is already ordered or, if the set is not already ordered, to place its members in a linear or sequential order. In this sense, "permutation" refers to the process of changing the linear order of an ordered set.It should be mentioned that a permutation is a mathematical concept that describes several potential arrangements of numbers or other objects.

The ascending numerical order is the lexicographic order when it comes to numbers. From left to right, the numbers are growing. The permutations of "1,2,3," for instance, are 123, 132, 213, 231, 312, and 321 in lexicographic order.

In lexicographic order, the following variation will be (5,6,7,4,3,2,1).

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The Equation of parabola  ( y + 8 )² = 12( x - 2 )

In math, what is a parabola?

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.

                 All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.

Given,

Directrix is known as x=a Directrix=a=3 Equation of parabola

(Y-y1)²= 4a(X-x1)

Vertex (X1,Y1) = (2,-8)

Directrix=a=3

Equation of parabola

       ( y - y₁ )² = 4a( x - x₁)

        ( y - ( -8))² = 4 * 3(x - 2 )

          ( y + 8 )² = 12( x - 2 )

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The percentage of students who owns either a television or stereo is given by the set formula P ( A ∪ B ) = 23 %

What is Set Theory Formula?

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

The equation is n(A∪B) = n(A) + n(B) - n(A⋂B)

Given data ,

Percentage of college students who owns a television or stereo be represented as = P ( A ∪ B )

Percentage of college students who owns a television is P ( A ) = 15 %

Percentage of college students who owns a stereo is P ( B ) = 10 %

Let the percentage of college students who owns a television and stereo  is P ( A ∩ B ) = 2 %

So , the value of P ( A ∪ B ) is calculated as

P (A∪B) = P ( A ) + P ( B ) - P ( A ⋂ B )

Substituting the values in the equation , we get

P (A∪B) = 15 + 10 - 2

On simplifying the equation , we get

P (A∪B) = 25 - 2

P (A∪B) = 23 %

Therefore , the value of P (A∪B) is 23 %

Hence , the percentage of students is 23 %

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The weight of the baseball equipment in the container is 7(4/5) pounds.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Container weight = 23(2/5) pounds

Baseball equipment.

= 1/3 of 23(2/5) pounds

= 1/3 x 117/5

= 39/5

= 7(4/5) pounds

= 7.8 pounds

Thus,

The weight of the baseball is 7.8 pounds.

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If t is less than s and s is less than r then the relationship between the values t and r is - t is less than r.

We are given that-

t is less than s i.e. t < s

and

s is less than r i.e. s < r

Now, let us find the relationship between the values of t and r.

t < s and s < r

this implies that -  t < s < r

Hence, we get t < r.

Thus, we get that if t is less than s and s is less than r then the relationship between the values t and r is - t is less than r i.e. t < r.

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Answer:

D.) No solution

Step-by-step explanation:

Not exactly sure what the question is, not quite sure what it's asking but based on what I see on the graph, I'd say that it's D.) no solution, because both lines are parallel meaning that there is no solution to the system of equation. If there were to be a solution to the equation you would have to see an intersection which is where both lines meet/touch at a certain point. If both lines have the same point and are on top of one another that means that it has infinitely many solutions...

(If wrong, I'm sorry)

Answer:

10

Step-by-step explanation:

2 1/2 divided by 1/4

1. Make improper

5/2 divided by 1/4

2. Keep Change Flip (Multiply by reciprocals)

5/2x4/1

3. Solve!

20/2

4. Simplify

10/1=10

Answer:

h - (3/h)

Step-by-step explanation:

The expression for the sequence of operations described is h - (3/h).

To evaluate this expression, we would first need to divide 3 by h to find the quotient, and then subtract that quotient from h. This would give us the final result of the sequence of operations.

For example, if h = 10, we would first divide 3 by 10 to get 0.3. We would then subtract 0.3 from 10 to get 9.7. This would be the final result of the sequence of operations.

In general, the expression h - (3/h) can be used to represent any sequence of operations that involves subtracting the quotient of 3 from h. The value of h can be any number, and the final result of the sequence of operations will depend on the specific value of h that is used.

The probability of the area hit by the dart between the bigger square and the smaller square is equal to 0.7656.

As given in the question,

Total number of squares present = 2

Side length of the bigger square = 16 units

Side length of the smaller square = 14 units

Area of the bigger square = ( side length )²

                                           = ( 16 )²

                                           = 256 square units

Area of the smaller square = ( side length )²

                                           = ( 14 )²

                                           = 196 square units

Here favorable outcome is represented by small square and total outcome is represented by bigger square

Probability that the given dart hit the area between the square is

= 196 / 256

= 49/64

= 0.765625

≈ 0.7656

Therefore, the probability of the dart hitting the area formed by bigger square and smaller square is equal to 0.7656.

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The different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour include 11 cups of 1/4 or 3.67 cups of 3/4.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.

The combination will be:.

= 2 3/4 ÷ 1/4.

= 11

The second combination will be:

= 2 3/4 ÷ 3/4

= 3.67

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As per the given standard deviation, the Lana hypothesis is not equal to 25 point and the alternative hypothesis is greater.

The term standard deviation refers the measure of how dispersed the data is in relation to the mean.

Here we have given that the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection.

And we need to find if  the mean social marginality scores are not the same for all four age groups

While we looking into the given the alternate hypothesis for this problem is μ greater than 115 point.

And here we have to find the test statistics which are equal to x, power, minus μ, divided by 10 point.

And the bar is 125 points in the x bar and 25.2 points in the me.

Then it can be written as,

=> x² = 125.2

Where as 1.5 and sigma equal to 30 and then equal to 25.

Now, we have to do the Minus 115 and then divided into 30 by root 5 and 25 by root.

Then we will get it as 1.70

Now we have to simplify it.

Which is, is that greater than 1.70, which is equal to 1 minus p p, is less than 1.70, which is equal to 1 minus 0.9554, which is equal to 0.0446.

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Answer:

  14.7

Step-by-step explanation:

You want the side opposite the 60° angle in a right triangle with hypotenuse 17.

The sine relation is ...

  Sin = Opposite/Hypotenuse

Solving for the opposite side gives ...

  Opposite = Hypotenuse × Sin

  x = 17·sin(60°) ≈ 14.7

The missing side is about 14.7.

As per the given distribution, the mean of the sampling distribution is Pa - Pb

The term mean in distribution refers adding all numbers in the data set and then dividing by the number of values in the set.

Here we have given that the proportions of flowers that are blue are papa and pbpb , respectively.

And we need to find the mean of the sampling distribution

While we looking into the given question the mean of a sampling distribution is the population mean from which values are sampled.

Here for a population of mean µ, then the mean of the sampling distribution is μx

=> μα = μ

Here from the given parameters, let us consider that then independent random samples of 50 species-a flowers and 100 species-b flowers are selected

Then it can be written as Pa refers sample proportion of blue specie - a and Pb refers sample proportion of blue specie - b

Therefore, the resulting mean is Pa - Pb

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Answer:

To solve the given trigonometric equation, we can start by isolating the cos(theta) term on one side of the equation. We can do this by dividing both sides of the equation by csc(theta):cos(theta) * csc(theta) - 2cos(theta) = 0

cos(theta) * csc(theta) / csc(theta) - 2cos(theta) / csc(theta) = 0 / csc(theta)

cos(theta) - 2cos(theta) / csc(theta) = 0Next, we can combine like terms on the left side of the equation:cos(theta) - 2cos(theta) / csc(theta) = 0

-2cos(theta) / csc(theta) + cos(theta) = 0

(1 - 2 / csc(theta)) cos(theta) = 0Since cos(theta) cannot be equal to 0 (because the angle theta is between 0 and 2pi), the only solution to this equation is:1 - 2 / csc(theta) = 0

1 = 2 / csc(theta)

csc(theta) = 2This means that the value of csc(theta) is equal to 2. To find the value of theta, we can use the inverse cosecant function (arcsec) to solve for theta:theta = arcsec(2)The value of arcsec(2) is approximately 1.047198, which is the solution to the given equation for theta.Note that this is just one solution to the equation, as there may be other solutions for theta depending on the values of the trigonometric functions. It is important to check that the solution falls within the given range of 0 < theta < 2pi.

I don't see the picture. Can you send it in the message.

suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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The magnitude of the vector having the initial point P and the terminal point Q is 17.

What is magnitude ?

Simply said, "distance or amount" is the definition of size. In terms of motion, it shows the absolute or relative size, direction, or movement of an item. It is used to describe something's size or scope. Magnitude in physics often refers to a size or amount.

Given: p (- 3,2) , q (5,17)

vector  = (17-2)i + (5+3)j

= 15i + 8j

Magnitude = [tex]\sqrt{(15^{2}+8^{2} ) }[/tex]

magnitude =17

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Answer: -26=2(3p-5) is false

Step-by-step explanation:

The solution is 4

Substitute in 4 in place of the variables to prove whether its false or true

1/4(4)+17=18

18=18 true

5=4(4)-11

5=16-11

5=5 true

-26=2(3(4)-5)

-26=2(7)

-26[tex]\neq[/tex]14

3(4+4)=24

3(8)=24

24=24 true

-26=2(3p-5) is false

Answer:

The third option is false, because when you plug in 4 for p, you get 14, and 14 is not equal to -26.

Hope this helps! :D

Step-by-step explanation:

Answer:

44.44 %

Step-by-step explanation:

16 000 / 36 000 = .4444   = 44.44%

The volume of the given cylinder is V = 1809.56 in³ and the volume of the NBA basketball is V = 448.92 in³.

The formula for the volume of a cylinder is V = π × r² × h cubic units.

Where the radius of the cylinder is represented by 'r' and the height of the cylinder is represented by 'h'.

The formula for the volume of the sphere is V = 4/3 × π × r³ cubic units.

Where the radius of the sphere is represented by 'r'.

The given cylinder has a diameter is of 16 inches and a height of 9 inches.

I.e., d = 2r = 16 in and h = 9 in

Then the volume of the cylinder is

V = π × (d/2)² × h

  = π × (16/2)² × 9

  = π × 64 × 9

  = 1809.56 in³

The shape of the NBA basketball is a sphere. The given sphere has a diameter of 9.5 inches.

I.e., d = 2r = 9.5 in

Then the volume of the sphere is

V = 4/3 × π × (d/2)³

  = 4/3 × π × (9.5/2)³

  = 4/3 × π × (4.75)³

  = 4/3 × π × 107.172

  = 448.92 in³

Therefore, the volume of the cylinder and the basketball are 1809.56 in³ and 448.92 in³ respectively.

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To answer this question, we first need to determine the objective and constraint equations.

The objective is to maximize the area of the rectangular garden, which is given by the equation $A = xy$.

The constraint is that the total cost of the fencing must not exceed $320. In other words, we have the equation $6x + 2(y+x) \le 320$.

To express the quantity to be maximized as a function of $x$, we can simply plug in the equation for the area of the rectangular garden into the objective equation. This gives us the function $f(x) = xy = x^2y$.

To find the optimal values of $x$ and $y$, we can use the method of Lagrange multipliers. Let $\lambda$ be the Lagrange multiplier. The Lagrange function is given by

$$L(x,y,\lambda) = x^2y + \lambda(6x + 2(y+x) - 320)$$

To find the optimal values of $x$ and $y$, we need to find the values of $x$ and $y$ that maximize $L(x,y,\lambda)$. To do this, we take the partial derivatives of $L(x,y,\lambda)$ with respect to $x$ and $y$ and set them equal to 0. This gives us the equations

$$\frac{\partial L}{\partial x} = 2xy + 6\lambda = 0 \quad \text{and} \quad \frac{\partial L}{\partial y} = x^2 + 2\lambda = 0$$

We can solve these equations simultaneously to find the optimal values of $x$ and $y$. First, we can solve for $y$ in the second equation to get

$$y = -\frac{x^2}{2\lambda}$$

Substituting this expression for $y$ into the first equation, we get

$$2x \left(-\frac{x^2}{2\lambda}\right) + 6\lambda = 0 \quad \Rightarrow \quad -x^3 + 12\lambda^2 = 0$$

Since $\lambda$ cannot be 0, we can divide both sides of this equation by $-12\lambda^2$ to get

$$x^3 = 12\lambda^2 \quad \Rightarrow \quad x = \sqrt[3]{12\lambda^2}$$

Substituting this expression for $x$ into the expression for $y$, we get

$$y = -\frac{\sqrt[3]{12\lambda^2}}{2\lambda}$$

Now we need to find the value of $\lambda$ that satisfies the constraint $6x + 2(y+x) \le 320$. Substituting the expressions for $x$ and $y$ into this equation, we get

$$6\sqrt[3]{12\lambda^2} + 2\left(-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + \sqrt[3]{12\lambda^2}\right) \le 320$$

Simplifying, we get

$$-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + 10\sqrt[3]{12\lambda^2} \le 320$$

Dividing both sides by $10\sqrt[3]{12\lambda^

Balinese metallophones have thicker metal keys than Javanese ones so   they produce a brighter sound. therefore correct answer is B.

A metallophone is any musical instrument in which the sound- producing body is a piece of metal( other than a substance string), conforming of tuned essence bars, tubes, rods, coliseums, or plates. ultimate repeatedly the metal body is struck to produce sound, generally with a mallet, but may likewise be triggered by discordance, keyboard action, or other means.

Metallophones have been used in music in Asia for thousands of spells. There are several different types used in Balinese and Javanese gamelan ensembles, containing the gender, gangsa and saron. These devices have a single row of bars, tuned to the distinctive pelog or slendro scales, or a subset of them.

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