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17. Find the value of x.
(5x + 4)
(7x + 4)
(4x + 9)
(4x + 1)
(9x-6)

Answer:

2

Step-by-step explanation:

The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.

In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.

By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.

Therefore, a left-tailed hypothesis test is appropriate in this scenario.

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Answer:

option 2

Step-by-step explanation:

The problem can be solved using Pythagoras' identity for a right triangle.

The angle between due East and due North is 90°

The solution here involves using the Cosine rule.

let x be the direct distance between house and office, then

x² = 17² + 21² - 2(17)(21)cos90° → option 2

Note that since cos90° = 0 the equation reduces to

x² = 17² + 21² ← Pythagoras' identity

Vectors, a = (-3, -2, 10) and b = (-7, 5, -2).(A) Scalar Projection:The scalar projection of b onto a is given as follows Where |b| is the magnitude of b, θ is the angle between the vectors a and b.

Based on the above formula, the magnitude of vector b, |b| can be calculated as:

|b| = √((-7)² + 5² + (-2)²) = √74

The angle between the vectors a and b, θ can be calculated as:cos(θ) = a.b/|a||b|where, Now,cos(θ) = 41/(√113 × √74) = 0.684The scalar projection of b onto a can be calculated by multiplying |b| by cos(θ).Hence,Scalar projection = S = |b| cos(θ) = √74 × 0.684 ≈ 6.47 (rounded off to two decimal places)(B) Component decomposition:

Let the parallel component of b be represented as bₐ and the orthogonal component of b be represented as b⊥.Thus Therefore,Parallel component Orthogonal Component

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Answer:

x=7

Step-by-step explanation:

Start with the left side

-5x+7x+8

combine like terms

2x+8=1+3x

subtract 2x from both sides to get 8=1+x

subtract 1 from both sides to get 7

put the variable on the left

x=7

Hope this helps :-)

There are 715 ways to select 9 players for the starting lineup.

Permutation is used whenever there is arrangement or where order is important . denoted by \(P(n,r)=\frac{n!}{(n-r)!}\)

n= no of item  , r = no of items to be arranged.

Combination is used when there is selection . denoted by\(C(n,r)=\frac{n!}{r!(n-r)!}\)

n=no of item  , r= no of item to be selected.

Part (a)

In the given question

we have to select 9 players out of 13 player , combination will be used

\(C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}\)=715 ways.

Part(b)

In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.

Since the batting order is important , permutation will be used.

\(P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5\)

=259459200 ways.

Part(c)

In this part we have to do selection of  3 left-handed outfielders and have all other 6 positions occupied by right-handed players.

Since order is not important Combination  will be used.

To select 3 left handers from total 6 left handers = C(6,3)

& to select 6 positions of left handers from remaining 7 right handers=C(7,6)

No of ways of selection = C(6,3)*C(7,6)

\(=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\\)

On solving further we get

\(= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways\)

Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.

(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .

(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.

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If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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Answer:

8y + 10

Step-by-step explanation:

3 + (7 + 8y) =

Apply the associative property:

= (3 + 7) + 8y

= 10 + 8y

Apply the commutative property:

= 8y + 10

x is the third side of the triangle, we have:

7 + 10 > x > 10 - 7

<=> 3 < x < 17

so the answer is C. III and IV only

Answer:

C

Step-by-step explanation:

given 2 sides of a triangle, then the third side, x , is in the range

difference of 2 sides < x < sum of 2 sides , that is

10 - 7 < x < 10 + 7

3 < x < 17

The only values in the list between 3 and 17 are 4 and 16.

That is III and IV only → C

Hey there!

1/10 = 10/k

FIRST you have to CROSS MULTIPLY

1 • k = 10 • 10

1 • k = 1k ➡️ k

10 • 10 = 100

k = 100

Therefore, your answer is: k = 100

Good luck on your assignment and enjoy your day!

~Amphitrite1040

Answer:

E

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

Answer:

more ... The same shape and size, but we are allowed to flip, slide or turn. In this example the shapes are congruent (you only need to flip one over and move it a little). Angles are congruent when they are the same size (in degrees or radians). Sides are congruent when they are the same length.

Step-by-step explanation:

happy to help ya:)

Answer:

Congruent means two or more objects that are the same. All angles and sides have to be the same length and measure.

Step-by-step explanation:

congruent means equal two

Answer:

A) y=0.5x+10 C) 17.5 dollars (don't forget your units)

Step-by-step explanation:

a) 0.5 is the price paid per song, or x, and 10 is the price that does not change for a month, so we can say that y=0.5x+10

c) to download 15 songs, we substitute x by 15

y=0.5(15)+10

y=7.5 + 10

y=17.5

and for b, im sorry but I cannot graph here.

Solution:

Given that;

The price of a house decreased from $400, 000 to $300, 000 in one year

The difference is

The percentage decrease will be

Hence, the percentage decrease is 25%

There are 56 different ways to choose 5 books from this collection.

In this case, we have 8 subjects from which we need to choose 5 books. Since there are at least 5 copies of each book, we can assume that we have enough copies of each subject to choose from. The formula for combinations is nCr = n! / (r!(n-r)!), where n represents the total number of subjects and r represents the number of books to be chosen.  

In our case, n = 8 and r = 5.

Plugging these values into the formula, we get 8! / (5!(8-5)!) = 8! / (5!3!).

Simplifying further, we get (8 * 7 * 6) / (3 * 2 * 1) = 56.

Therefore, there are 56 different ways to choose 5 books from this collection.

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Answer:Red

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 blue out of 15 chips

Answer:

\(y = 2\)

Step-by-step explanation:

1) Simplify 5y/9 - y/9 to 4y/9.

\( \frac{4y}{9} = \frac{8}{9} \)

2) Multiply both sides by 9.

\(4y = \frac{8}{9} \times 9\)

3) Cancle 9.

\(4y = 8\)

4) Divide both sides by 4.

\(y = \frac{8}{4} \)

4) Simplify 8/4 to 2.

\(y = 2\)

Hence, the answer is y = 2.

\( \frac{x}{3° } + 49° = 180° \\ \)

Cross multiply

\(x + 147° = 180°\)

simplify

x = 180° - 147°

answer : x = 33°

Answer:

The probability that he doesn’t win is 6/(n + 6)

Step-by-step explanation:

Mathematically, the probability that an event occur is 1 minus the probability that the event doe not occur.

Thus, what we are saying here is that the sum of the probabilities that Paul wins the raffle draw and he doesn’t win the raffle draw is 1

This can be mathematically expressed as;

probability that he doesn’t win = 1 - probability that he wins

Thus we have;

1- n/(n+ 6)

= [(n+ 6) -(n)]/(n+6) = 6/n+ 6

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Answer:

x=49.0

Step-by-step explanation:

Hi there!

In this right triangle, we're given an angle and the opposing side, and we're trying to solve for the length of the hypotenuse.

In this situation, we can use the sine ratio:

\(sin\theta=\frac{opp}{hyp}\)

Plug in the known information

\(sin(28)=\frac{23}{x}\\x=\frac{23}{sin(28)}\\x=49.0\)

Therefore, the length of the missing side is 49.0 units when rounded to the nearest tenth.

I hope this helps!

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

P(X=k) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

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Answer:

Intensity = 2500/x^2

6.25 lumem

5 Feets

Step-by-step explanation:

Given the following :

Area (A) = 0.1x^2

Intensity, Energy and Area are related by the formular :

Intensity = power / Area

A) If 250 lumens of light energy is produced :

Intensity (I) = 250 / 0.1x^2

Intensity = 2500/x^2

x = distance

B) USING THE EQUATION :

1) What is the intensity of light on an object that is 20 feet from the spotlight source?

x = 20

Intensity = 2500/x^2

Intensity = 2500/20^2

Intensity = 2500/400

Intensity = 6.25 lumen

11) How far from the spotlight is an object that recieves 100 lumens of light per square foot?

Intensity = 100

100 = 2500 / x^2

100x^2 = 2500

x^2 = 2500/ 100

x^2 = 25

x = 5 Feets

The Jacobi method and Gauss-Seidel method converge to the solution is x₁ = -1.999, x₂  -2.001 and x₃ = 1.000

Given system of equations:

4x₁ + 2x₂ - 2x₃ = 0

x₁ - 3x₂x₃ = 7

3x₁ - x₂ + 4x₃ = 5

Rearranging the equations to isolate each variable on the left side:

x₁ = (3x₂ - 4x₃) / 4

x₂ = (x₁ - 7) / (3x₃)

x₃ = (5 - 3x₁ + x₂) / 4

Let's start with initial approximations:

x₁₀ = 0

x₂₀ = 0

x₃₀ = 0

Performing iterations using Jacobi method:

Iteration 1:

x₁₁ = (3(0) - 4(0)) / 4 = 0

x₂₁ = (0 - 7) / (3(0)) = -∞ (undefined)

x₃₁ = (5 - 3(0) + 0) / 4 = 1.25

Iteration 2:

x₁₂ = (3(0) - 4(1.25)) / 4 = -1.25

x₂₂ = (-1.25 - 7) / (3(1.25)) = -1.267

x₃₂ = (5 - 3(-1.25) + (-1.267)) / 4 =1.017

Iteration 3:

x₁₃ = (3(-1.267) - 4(1.017)) / 4 = -1.144

x₂₃ = (-1.144 - 7) / (3(1.017)) = -1.038

x₃₃ = (5 - 3(-1.144) + (-1.038)) / 4 = 1.004

Iteration 4:

x₁₄ = -1.026

x₂₄ = -1.005

x₃₄ = 1.000

Iteration 5:

x₁₅ = -1.001

x₂₅ = -1.000

x₃₅ = 1.000

After five iterations, the successive approximations for x₁, x₂, and x₃ are identical when rounded to three significant digits.

Now let's perform the Gauss-Seidel method:

Using the updated values from the Jacobi method as initial approximations:

x₁₀ = -1.001

x₂₀ = -1.000

x₃₀ = 1.000

Performing iterations using Gauss-Seidel method:

Iteration 1:

x₁₁ = (3(-1.000) - 4(1.000)) / 4= -1.750

x₂₁ = (-1.750 - 7) / (3(1.000)) = -2.250

x₃₁ = (5 - 3(-1.750) + (-2.250)) / 4 = 0.875

Iteration 2:

x₁₂ = (3(-2.250) - 4(0.875)) / 4 = -2.000

x₂₂ = (-2.000 - 7) / (3(0.875)) = -2.095

x₃₂ = (5 - 3(-2.000) + (-2.095)) / 4 = 1.024

Iteration 3:

x₁₃ = -1.997

x₂₃ = -2.016

x₃₃ = 1.003

Iteration 4:

x₁₄ = -1.999

x₂₄ = -2.001

x₃₄ = 1.000

After four iterations, the successive approximations for x₁, x₂, and x₃ are identical.

Therefore, both the Jacobi method and Gauss-Seidel method converge to the solution:

x₁ = -1.999

x₂  -2.001

x₃ = 1.000

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Answer: the perimeter of the garden is 24 and the area of the garden is 32

Step-by-step explanation:

Perimeter: 4 + 4 + 8 + 8 = 24

Area: 4 x 8 = 32

Answer:

125000

Step-by-step explanation:

106250/85=1250

1250*100=125000

The calculated value of x in the circle is 59

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

The circle

The measure of angle at the center of the circle is calculated as

Center = 2 * 31

So, we have

Center = 62

The sum of angles in a triangle is 180

So, we have

x + x + 62 = 180

This gives

2x = 118

Divide by 2

x = 59

Hence, the value of x is 59

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Answer:

median = 4

Step-by-step explanation:

On the box plot the median is represented by the vertical line inside the box.

That is the median = 4

Answer:

Terry had £780 initially and Faye had £1300

Step-by-step explanation:

System of Equations

We'll call the following variables:

x = Terry's balance in his bank account

y = Faye's balance in her bank account

The initial relation between them is:

\(\frac{x}{y}=\frac{3}{5}\)

Cross-multiplying:

5x = 3y        [1]

If Terry put £220 in his account he had x+220 and if Faye withdrew £300 from her account, she had y-300. Both quantities are equal, thus

x + 220 = y - 300

Subtracting 220:

x = y - 520         [2]

Substituting in [1]

5(y - 520) = 3y

Multiplying:

5y - 2600 = 3y

Adding 2600 and subtracting 3y:

2y = 2600

Dividing by 2:

y = 1300

From [2]:

x = 1300 - 520

x = 780

Terry had £780 initially and Faye had £1300