Ten out of 40 students made an A on their English test. Mr. Harris wants the same proportion of students to gen an A on his history test. If Mr. Harris has 60 students, what proportion will help determine how many students he wants to get an A on the test?

The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Answer:

C. br,rv, vb

Step-by-step explanation:

this is beacause it is from the largest to the smallest

Answer:

C. BR,RV,VB

Step-by-step explanation:

This is because it is from the largest to the smallest.

The true or false statements based on the graph on the lengths of ribbons are:

The graph shows that most common length that a ribbon has is 11²/₈ with 3 ribbons. At a simpler term, this becomes 11¹/₄.

The sum of the longest and shortest lengths is:

= 11¹/₄ + 9⁷/₈

= 21⁹/₈

The sum is therefore not 20¹/₈.

The difference between the longest and shortest lengths is:

= 11¹/₄ - 9⁷/₈

= 1³/₈

This is not 2 ¹/₈

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After 9 years with monthly compounding and no payments, Dan will owe approximately $13,189.6

Using the formula for compound interest:

A = \(P(1 + \frac{r}{n} )^{nt}\)

Where:

A = the future amount (the amount Dan will owe after 9 years)

P = the principal amount (the initial borrowed amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Given:

P = $8000

r = 18% = 0.18 (as a decimal)

n = 12 (monthly compounding)

t = 9 years

substitute the values into the formula:

A = \(8000(1 + \frac{0.18}{12} )^{12*9}\)

A = \(8000(1 + 0.015)^{108}\)

 = \(8000(1.015)^{108}\)

 = 8000(1.6487)

A = $13,189.6

Therefore, after 9 years with monthly compounding and no payments, Dan will owe approximately $13,189.6.

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Answer:

-1/2

Step-by-step explanation:

The equation for slope is (y2-y1)/(x2-x1).

Plug in the values given in the problem

(11-7)/((-2)-6)

Then simplify

4/(-8)=-1/2

Answer:

5

Step-by-step explanation:

Since y equals 200 + 10x and y also equals 5x, then

200 + 10x = 50x

Subtract 10x from both sides.

200 = 40x

Divide both sides by 40.

5 = x

Answer: He must sell 5 sculptures.

The 10th term of an arithmetic sequence is found as the 49.

As per the stated values in question.

Fifth term a5 = 24

8th term a8 = 39.

Let the first term be 'a' and the common difference be 'd'.

Then,

a5 = a + 4d

24 = a + 4d .....eq 1

a8 = a + 7d

39 = a + 7d .....eq 2

Solving eq 1 and 2.

3d = 15

d = 5

a = 4

Now,

a10 = a + 9d

a10 = 4 + (9 x 5)

a10 = 4 + 45

a10 = 49

Thus, the 10th term of an arithmetic sequence is found as the 49.

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The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.

It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5

To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.

Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).

Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).

So, the p-value for the given test is 0.067 (rounded to two significant digits).

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Answer:

48 boys

Step-by-step explanation:

Since the ratio of Boys to Girls is 4/3, set this equal to X number of boys/36. Cross multiply so 36*4=144, and 3*x= 3x. So now you have 144=3x, divide by 3 to get x=48 boys.

Answer:

48

Step-by-step explanation:

3 = 36

4 = ?

4×36 = 144÷3 = 48 boys

The number of downloads of the high quality version that was made was 600.

This is a great system of equations problem

If we call the number of standard version downloads (S)  

The high quality downloads (H).

To find S, we can rearrange the first statement to H = 910 - S,

Then we would substitute (910 - S) wherever you see an H in the second equation so that you have only S's in your equation.

Thus:

2.8(S) + 4.4(910 - S) = 3044

2.8S + 4004 - 4.4S = 3044

-1.6S = -960

s = 600

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If two variables x and y are directly proportional, then as x rises, y will rise accordingly, and as x falls, y will fall accordingly. So, y=k x can be written.

The equation for k=y/x is k=b/p.

the proportional relationship between two variables that is always constant.

Constant ratio, constant rate, constant of variation, or even changing rate are examples of proportionality constants.

When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant.

The slope is another name for the constant rate of change.

The rate of change for linear functions will be constant.

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Answer:

38

Step-by-step explanation:

This might be wrong, But to my calculations it is

-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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Answer:

16m+4

Step-by-step explanation:

Answer:

16m+4

Step-by-step explanation:

2(8m+2)

distributive property

Answer:

15 hours

Step-by-step explanation:

since 8 reports took him 3 hrs

8+8+8+8+8=60

3+3+3+3+3=15

The minimum possible number of handshakes would occur if each person only shakes hands with two other people. In this case, the first person would shake hands with the second and third person, the second person would shake hands with the first and fourth person, the third person would shake hands with the first and fifth person, and so on. This pattern would continue until the 22nd person shakes hands with the 21st and 23rd person, and the 23rd person shakes hands with the 22nd and 21st person. Therefore, the minimum possible number of handshakes would be (23-1) or 22 handshakes.
Hi! To find the minimum possible number of handshakes among the 23 people attending the party, we need to ensure that each person shakes hands with at least two other people. Here's a step-by-step explanation:

1. Have the first person shake hands with two other people. This results in 2 handshakes.
2. For each subsequent person, have them shake hands with the two people that the previous person shook hands with.

Following this pattern, the first person will have 2 handshakes, and the remaining 22 people will each contribute 1 additional handshake, making a total of 22 handshakes.

So, the minimum possible number of handshakes among the 23 people at the party is 22 handshakes.

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Answer:

Step-by-step explanation:

(-1, 6/5) = logbase4(5x^2) etc

only 5 = ln(x+5) = ln (x-1) + ln(x+1)

only 3 = log(x-1) etc.

(-1, 5) = e^x^2 = e^4x+5

Step-by-step explanation:

\(( \frac{ {6}^{5} }{ {7}^{3} })^{2} \\ = \frac{ {6}^{10} }{ {7}^{6} } \)

Hope it will help :)

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Answer:

=6

Step-by-step explanation:

50%

since 98/2 = 49

Thats it

Answer:

x+1=x *x

Step-by-step explanation:

Answer:

x+1= x*x

Step-by-step explanation:

hope this helps

The value of x if given expression as (x-1)(2-x)<0 will be 1 and 2.

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

We have been given an expression as  (x-1)(2-x)<0, then the value of x can be calculated as;

(x-1)(2-x) = 0

Therefore, Using the zero product property we get;

(x-1) = 0

x = 1

Similarly,

(2-x) = 0

2 = x

Therefore, the value of x if given expression as (x-1)(2-x)<0 will be 1 and 2.

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Answer:

\(13x - 3.4 = 17.6 + 10x\)

\( = ) \: 13x - 10x = 17.6 + 3.4\)

\( = ) \: 3x = 21\)

\( = )x = \frac{21}{3} \)

\( = ) \: x = 7\)

x = 7

13x - 3.4 = 17.6 + 10x

13x - 10x = 17.6 + 3.4

3x = 21

x = 21 : 3

x = 7

The value of the function f(−2/3) will give the value 8/3.

A function is important to show the expression that's given.

Given: f(x) = 3x^2 −5x−2.

To find f(-2/3), we substitute x = -2/3  into the equation:

f(-2/3) = 3 x (-2/3)^2  - 5(-2/3) - 2

         = 3 x 4/9 + 10/3 -2

         = 12/9 + 10/3 - 2

         = (12 + 30 - 18) / 9

         = 24 /9

        = 8/3

Therefore, f(-2/3) evaluates to 8/3.

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Answer:1700

Step-by-step explanation:

Answer:

1)C 2)B 3)B 4) D 5) B 6) A 7)B 8)C 9)A 10)B

I hope this help

Answer:

C2H2 + 3O2 ---> 2CO2 + 2H2O

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

10--2 is 12 then divided by -2 is -6

Answer:

If it is -2: the answer is -6

Step-by-step explanation:

1) do what is inside parentheses P.E.M.D.A.S

(10- (-2))/-2  ------> 12/-2 since there is a double negative it turns into a positive (+) and you add 10 + 2

2) You simply divide

12/-2 = -6  Since you are dividing a negative and a positive the result is negative

Answer:

1/3 x 1/2

Step-by-step explanation:

Answer:

-10. is the answer

Step-by-step explanation:

The equation of line p is y = 1/2x +   -10

i just answered the question on edge.

The sample mean proportion is 0.55.

The question is asking for the sample mean proportion. To find the sample mean proportion, we need to take the average of the lower and upper bounds of the confidence interval.

In this case, the lower bound of the confidence interval is 0.24 and the upper bound is 0.86. To find the sample mean proportion, we add these two values together and divide by 2:

(0.24 + 0.86) / 2 = 1.1 / 2 = 0.55

Therefore, the sample mean proportion is 0.55.

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