3 (3 – 3) = 2 ( + 3) – 30

There would be 17 lattice points lie on the hyperbola x²-y²=17

To find the lattice points on the hyperbola x²-y²=17, we can use some algebraic manipulation. First, we can rewrite the equation as y²=x²2-17, which means that both x² and y^2 must be integers.

Next, we can note that x² can only take on values that are congruent to 0 or 1 mod 4, since the only possible quadratic residues mod 4 are 0 and 1. This means that x must be an even integer or an odd integer that is ± 1 mod 4.

For each possible value of x, we can then solve for y by taking the square root of x²-17. However, we must be careful to only include the solutions where y is also an integer. This means that x²-17 must be a perfect square.

Using this method, we can check each possible value of x and find that the only lattice points on the hyperbola are (± 5, ± 2) and (± 4, ± 1). Therefore, there are a total of eight lattice points on the hyperbola x²-y²=17.

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Answer:

$550

Step-by-step explanation:

How much is the profit for 1 burrito?: $8 - ($1.50+$1) = $5.5

So, profit for 100 burritos is $5.5 x 100 = $550.

Hope this helps.

Answer:

$550

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

Cans : Dollars

6 cans : 9 dollars

DIVIDE BY 3

2 cans : 3 dollars

MULTIPLY BY 4

8 cans : 12 dollars

Hope this helps :)

Have a great day!

If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value

Proportion refers to the relationship between two quantities or numbers, indicating how they are related to each other in size or amount.

The best interpretation of a Z score of 0.47 for a sample proportion is:

b. If the null hypothesis were correct, there would be a 0.47 percent chance of getting a sample proportion that deviates from the population proportion's hypothesised value.

This interpretation is in line with the definition of a Z score, which is a measure of how many standard deviations a sample statistic (in this case, the sample proportion) is not what would be anticipated if the null hypothesis were true. A Z score of 0.47 means that the sample proportion is 0.47 standard deviations away from the expected value under the null hypothesis. Therefore, the interpretation that the probability of obtaining a sample proportion as far or farther than observed from the hypothesized value of the population proportion is 0.47, assuming the null hypothesis is true, is the most appropriate.

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To conduct a hypothesis test to analyze whether the proportion of stocks that offer dividends is different from 0.14, a two-tailed hypothesis test should be used.

To analyze whether the proportion of stocks that offer dividends is different from 0.14, the trader should use a two-tailed hypothesis test.

In a two-tailed hypothesis test, the null hypothesis states that the proportion of stocks offering dividends is equal to 0.14. The alternative hypothesis, on the other hand, is that the proportion is different from 0.14, indicating a two-sided test.

The trader wants to test whether the proportion is different, without specifying whether it is greater or smaller than 0.14. By using a two-tailed test, the trader can assess whether the proportion significantly deviates from 0.14 in either direction.

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Answer:

100

Step-by-step explanation:

0.3n - 15 = 0.2n - 5

0.3n - 0.2n = - 5 + 15

0.1n = 10

10/0.1 = n

n = 100

The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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Answer: 380 ft and 780 ft

Step-by-step explanation:

We can assume that the flag is a rectangle. If the width of the flag is w, then the length is w + 400.

The formula for the perimeter of a rectangle is \(2(l+w)\). Let's plug in the values we know.

\(P=2(l+w)\\2320=2(w+400+w)\\1160=2w+400\\760=2w\\w=380\)

We know that the length is 400 more than the width, so let's find the length.

\(l=w+400\\l=380+400=780\)

Hence, the flag's width is 380 ft and the length is 780 ft.

In the given word problem, Nevaeh's age is 7.

Given that,

Nevaeh is older than Kareem.

Their ages are consecutive integers.

The sum of the square of Nevaeh's age and twice Kareem's age is 61.

Assume Nevaeh's age as x.

Since Nevaeh is older than Kareem, Kareem's age would be x-1.

According to the problem,

The sum of the square of Nevaeh's age and twice Kareem's age is 61.

So, we can write the equation as:

x² + 2(x-1) = 61.

Expanding the equation, we get:

x² + 2x - 2 = 61.

Rearranging the terms, we have:

x² + 2x - 63 = 0.

x² + 9x - 7x - 63 = 0

x(x + 9) - 7(x + 9) = 0

(x - 7)(x+9) = 0

x = 7 or x = - 9

Since age is a positive quantity, therefore, proceed x = 7

Therefore, Nevaeh's age is 7.

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Answer:

Step-by-step explanation:

a. The area between -z and z is 0.2206, so we want to find the value of z such that P(-z < Z < z) = 0.2206.

The standard normal distribution is symmetric, so P(-z < Z < z) = 0.5 - P(Z < -z) = 0.5 - P(Z < -z) = 0.5 - 0.2206 = 0.2794

We can use a standard normal table to find the z-value such that P(Z < z) = 0.2794 which is z = 0.68.

b. The area to the left of z is 0.9951, so we want to find the value of z such that P(Z < z) = 0.9951.

We can use a standard normal table to find the z-value such that P(Z < z) = 0.9951 which is z = 2.33.

f(12) will be: substituting 12 into the expression above

The missing numbers for the respective rows are:

Row 3, column 3: -2

Row 5, column 3: -3/2

Row 1, column 1: -3/4

Row 1, column 5: -1/4

Missing number for Row 3, column 3:

8 × (-2) = -4

Missing number for Row 5, column 3:

-1/2 + (-2) = -1/2 - 2

-1/2 + (-2) = (-1 - 2)/2

-1/2 + (-2) = -3/2

Missing number for Row 1, column 1:

-6/8 = -3/4

Missing number for Row 1, column 5:

-3/4 - (-1/2) = -3/4 + 1/2

-3/4 - (-1/2) = (-3 + 2)/4

-3/4 - (-1/2) = -1/4

Therefore, Row 3, column 3 have the missing number: -2. row 5, column 3 have the missing number: -3/2. Row 1, column 1have the missing number: -3/4. Row 1, column 5 have the missing number: -1/4

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Graphing the linear functions, it is found that they will have the same height after 5 hours, of 21 inches.

A linear function is modeled by:

y = mx + b

In which:

For each function in this problem, we have that:

Hence the functions are given as follows:

The functions are graphed at the end of the answer, with A(t) in blue and B(t) in black. The intersection of the graphs is at (5,21), which means that they will have the same height after 5 hours, of 21 inches.

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Answer:

x= -11

Step-by-step explanation:

Rearrange terms

\(-1=\frac{5+x}{6} into -1=\frac{x+5}{6}\)

Multiply all terms by the same value to eliminate fraction denominators

\(-1=\frac{x+5}{6} \\6(1)=6(\frac{x+5}{6} )\)

Cancel multiplied terms that are in the denominator

\(6(-1)=6 (\frac{x+5}{6} )6(-1)=x+5\)

Multiply the numbers

\(6(-1)=x+5\\-6=x+5\)

Subtract 5 from both sides of the equation

\(-6=x+5\\-6-5=x+5-5\)

Simplify

Subtract the numbers

Subtract the numbers

Move the variable to the left

Cutting Della's hair symbolizes her mean sacrifice and desperation to provide a Christmas gift for her husband. It is a symbol of her love and devotion to him, even in the face of poverty.

Cutting Della's hair symbolizes her selfless devotion to her husband and her willingness to make a sacrifice in order to provide a Christmas gift for him. Despite lacking the money to buy a gift, she still wanted to give him something to show her love and appreciation for him. This is why she cut off her long, beautiful hair and sold it to the hairdresser for twenty dollars in order to buy her husband a platinum watch chain. Her act of cutting her hair is a powerful symbol of her love and devotion to him, even in the face of extreme poverty. Additionally, it symbolizes her strength and resilience in the face of difficult circumstances. Her sacrifice is a reminder of how far love can go in times of hardship.

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The ways in which companies can attract and retain employees are given below.

The term human resources (HR) refers to the department responsible for managing employee-related resources.

It's an essential partner in an organization's success.

Given is that to answer some ways in which companies can attract and retain employees.

The ways in which companies can attract and retain employees are -

Therefore, the ways in which companies can attract and retain employees are given above.

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Answer:

87.4°

Step-by-step explanation:

(3x + 8) + (3x + 18) + (7x + 9) = 180

3x + 8 + 3x + 18 + 7x + 9 = 180

add the common numbers

13x + 35 = 180

subtract 35

13x = 145

divide 13

x = 11.2

then plug it back in to m<3

7(11.2) + 9

78.4 + 9

= 87.4°

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer: 74.6

we draw a right triangle ABC, have: ∠ABC = 90°,  AB = 20 and ∠BAC = 75°, the height of the building is BC

we also have: tan 75° = BC/AB = BC/20

=> BC = tan 75°. 20 = 40 + 20√3 ≈ 74.6

Step-by-step explanation:

The probability steve will pass either math or history is equal to 0.94  

Probability:

Probability refers to the chances of an event will occur in random experiments. It is also defined as the ratio of the number of favorable outcomes to the total number of outcomes in a random experiment.    

Probability(Event) = Favorable Outcomes/Total Outcomes  

The Probability of an event is denoted by P(E) and P(E)' is the reciprocal of the event. In an experiment, the sum of all events will add up to 1.  

Let

Event M: Passing course Maths

Event H: Passing Course History

Here we have,

The probability of steve passing his math course, P(M) = 0.7  

then the probability of steve failing in Maths, P(M)' = 1 - 0.7 = 0.3  

The probability of steve passing his history course, P(H) = 0.8

then the probability of steve failing in History, P(H)' = 1 - 0.8 = 0.2

the probability of steve passing both courses is 0.56,    

From the above calculations,

The probability of steve failing in both = P(M)'× P(H)' =  0.3 × 0.2 = 0.06

The probability steve will pass either math or history

= 1 - (The probability of failing both courses)

= 1 - 0.06  

= 0.94    

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Answer:

Multiply the numbers inside the parenthesis with the number outside. In the case of the negative, use -1

Step-by-step explanation:

5(x-4)+3x-9x=6-(2x+5)+8x

5(x)- 5(4) +3x-9x=6 -(2x)-(5)+8x

5x-20+3x-9x=6-2x-5+8x

-x-20=6x+1

-x-6x=20+1

-7x=21

-7x/-7=21/-7

x=-3

Apply L'Hopital's rule (LHR) two times:

\(\displaystyle \lim_{x\to0} \frac{\cos^2(x) - 1}{x^2} \stackrel{LHR}= \lim_{x\to0} \frac{-2\cos(x) \sin(x)}{2x} \stackrel{LHR}= \lim_{x\to0}\frac{2\sin^2(x) - 2\cos^2(x)}{2}\)

Recall that

cos(2x) = cos²(x) - sin²(x)

So our limit is equivalent to

\(\displaystyle \lim_{x\to0}\frac{2\sin^2(x)-2\cos^2(x)}2 = \lim_{x\to0} -\cos(2x) = -\cos(0) = \boxed{-1}\)

You can also do this easily without LHR, provided that you know

\(\displaystyle \lim_{x\to0}\frac{\sin(x)}x = 1\)

We again have

\(\displaystyle \lim_{x\to0}\frac{\cos^2(x)-1}{x^2} = \lim_{x\to0}\frac{-\sin^2(x)}{x^2} = -\lim_{x\to0}\left(\frac{\sin(x)}x\right)^2 \\\\ = -\left(\lim_{x\to0}\frac{\sin(x)}x\right)^2 = -1^2 = -1\)

After a rotation of 180° counterclockwise around the origin, the points L, M and N will change to L' = (5, - 10), M' = (0, 10) and N' = (9, 6).

When rotating a point 180 degrees counterclockwise about the origin, the point changes from point A(x, y) and becomes A' (- x, - y) that is both the x and y coordinate becomes negative.

Now, we have the points:

L = (- 5, 10)

M = (0, - 10)

N = (- 9, - 6)

After rotating it 180 degrees counterclockwise about the origin, we will get the points as:

L' = (5, - 10)

M' = (0, 10)

N' = (9, 6)

Therefore, after a rotation of 180° counterclockwise around the origin, the points L, M and N will change to L' = (5, - 10), M' = (0, 10) and N' = (9, 6).

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1.746 is the critical t value that corresponds to 90% confidence.

To find the critical t-value that corresponds to 90% confidence with 16 degrees of freedom, follow these steps:
1. Determine the desired confidence level: 90%
2. Calculate the corresponding significance level (alpha) by subtracting the confidence level from 100%: 100% - 90% = 10%
3. Divide the significance level by 2 to get the value for a two-tailed test: 10% / 2 = 5%
4. Look up the critical t-value in a t-distribution table using the degrees of freedom (16) and the 5% value.

From the t-distribution table, the critical t-value for 16 degrees of freedom and 90% confidence is approximately 1.746.

So, the CRITICAL T VALUE that corresponds to a 90% CONFIDENCE level with 16 DEGREES FREEDOM is 1.746, rounded to three decimal places.

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Jamela is Distance away from her house than Yujin is, which is calculated as (4 - (2/3)t / (1 - (1/192)t).

An object's entire motion, independent of direction, is its distance. the distance that something has covered.

We can multiply the numerator and denominator of this expression by the LCD, which is 24 in order to make it simpler:

J(t) / Y(t) = [(12 - (2/3)t) * 8] / [(3 - (1/8)t) * 8]

J(t) / Y(t) = (96 - (16/3)t) / (24 - (1/8)t)

J(t) / Y(t) = (96/24 - (16/3)t/24) / (24/24 - (1/8)t/24)

J(t) / Y(t) = (4 - (2/3)t) / (1 - (1/192)t)

Jamela is farther away from her house than Yujin is, which is calculated as (4 - (2/3)t / (1 - (1/192)t).

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Answer: B. 12

Step-by-step explanation: Cause we have to subtract because let see 48+12=60 so we have to subtract each numbers with 12.

Answer:

length = 3 meters and width = 2 meters

length = 2 meters and width = 3 meters

Step-by-step explanation:

If you want to find out how big a rectangle is when you know its perimeter and area, you can use some math tricks. Here are the tricks:

Perimeter of a rectangle = 2 times (length plus width) 1

Area of a rectangle = length times width 2

Now we can use these tricks to find the length and width of the rectangle. Let's say the length is l and the width is w. Then we can write:

2 times (l plus w) = 10

l times w = 6

We can make the first trick easier by cutting both sides in half:

l plus w = 5

We can then get rid of one letter by using the other one. For example, we can write l as 5 minus w:

l = 5 - w

Then we can put this into the second trick:

(5 - w) times w = 6

This makes a puzzle that we can solve by opening up, moving around, and grouping:

5w minus w squared = 6

w squared minus 5w plus 6 = 0

(w minus 2) times (w minus 3) = 0

This means that either w minus 2 = 0 or w minus 3 = 0. Solving for w, we get two answers:

w = 2 or w = 3

We can then use these answers to find the matching answers for l:

If w = 2, then l = 5 - w = 5 - 2 = 3

If w = 3, then l = 5 - w = 5 - 3 = 2

So we have two ways to make the rectangle:

length = 3 meters and width = 2 meters

length = 2 meters and width = 3 meters

Answer:

If you use the addition property of equality, what number would you add to both sides of the equal sign to isolate the variable?

You would subtract 5/7 from both sides of the equation

What is the solution?

x = 26/7 or 3 and 5/7

Step-by-step explanation:

x + 5/7 = 31/7

Subtract 5/7 from both sides of the equation:

x + 5/7 - 5/7 = 31/7 - 5/7

x = 26/7

1: -5/7

2: 26/7

With the help of mechzewd26

Answer: a= 144. b= 67

Step-by-step explanation:

Angle b and the angle of measure 113 are same side interior angles which sum to 180 (When 2 parallel lines are cut by a transversal, special angles are formed)

113+b=180. Subtract 113 from both sides.

b= 67 degrees

Now that you have b, the interior angles of four sided figures sum to 360.

a+113+67+36=360. Combine like terms.

a+216=360. Subtract 216 from both sides.

a= 144 degrees

• Given Function A:

You need to remember that, by definition, the value of "y" is zero when the function intersects the x-axis.

Therefore, you need to set up that:

Substitute this value into the function and then solve for "x", in order to find the x-intercept:

• Given that Function B passes through these points:

You need to determine the equation of the line, in order to find the x-intercept using it.

The Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

By definition, the value of "x" is zero when the function intersects the y-axis. Therefore, knowing the first point given in the exercise (whose x-coordinate is zero), you can determine that, for this line:

Substitute "b" and the coordinates of the second point into this equation:

And then solve for "m":

Therefore, the equation of Function B in Slope-Intercept Form is:

Now you can find the x-intercept by using the procedure used for Function A:

You know that:

Hence, the answer is: Third option.