Isla is dividing 3x3 + x2 – 12x – 4 by x + 2 using a division table.

Quotient



Divisor

3x2
– 5x
– 2
x
3x3
–5x2
–2x
+ 2
6x2
A
B

What are the missing values in the table?

Answer:

I’m not positive but I think this is what your question is asking for…. Hope this helped

Step-by-step explanation:

Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50

Step-by-step explanation:

Given the regression equation:

ŷ = -2.59 + 1.01x

We need to predict the value of ý when x (IQ score of the twin born first) is 109.

So we substitute x = 109 into the regression equation:

ŷ = -2.59 + 1.01(109)

ŷ = -2.59 + 110.09

ŷ = 107.50

Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Answer:

The area of the land can be found using the formula A = 1/2*D1*D2, where D1 and D2 are the diagonals of the parallelogram. In this case, the area is 1/2*25*12 = 150m^2.

Answer:

180m^2

Step-by-step explanation:

since you said that two sides measure 12 and 17 and the diagonal is 25 you can use herons formula to find the area of each individual triangle then multiply it by two

using heron's formula it gives us the answer of 90 m^2 for one triangle so we can multiply it by two to get the area of the whole shape and 90x2=180m^2

Remember that the rule for a dilation by a factor of k about the origin is:

Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.

Apply a dilation by a factor of 3:

Therefore, the new coordinates would be:

Answer:

7

Step-by-step explanation:

Answer: (m+7)(m+2)

Step-by-step explanation:

So, let's find two numbers that can multiply together and equal 14.

To get fourteen here are the options:

1 * 14

2 * 7

Not many options, but let's see which ones would add to equal 9.

1 + 14 = 15

2 + 7 = 9

There's our answer, 2 and 7 multiply to get 14, and add to get 9.

To write it in factored form, we would write (m+7)(m+2)

It gradually decreases as alcohol is metabolized. The function C(t)=0.135 t e^{-2.802 t}models the mean BAC measured in g/mL.

The maximum average BAC during 3 hours is 0.0001358 g/mL.

f(t) = α t e−βt --(1)

Let's rewrite this in a simple form:

f(t)= α eˡⁿ ᵗ e⁻βt = αe^(ln t −βt)

Since e^x is strictly increasing and it will be maximized exactly when its argument is maximized, so we can maximize instead:

g(t)=ln t −βt

differentiating with respect to t , and g'(t) = 0

g′(t)=1/t − β = 0

=> t =1/β

we have given a function

C(t)=0.135 t e⁻²·⁸⁰²ᵗ

if we compare it with (1) we get

β = 2.802, 0.135 = α

For it's maximized we need to check the second order condition, and that of g will differentiate again , g′′(t)= −1/t² < 0

We have to compute the derivative of C(t):

C′(t) = 0.135 t⋅(−2.802)e⁻²·⁸⁰²ᵗ + 1.35e⁻²·⁸⁰²ᵗ

For optimum at t₀ if C′(t₀)=0 and C′′(t₀)≠0. Here, we have

C′(t₀) = 0.135t₀⋅(−2.802)e⁻²·⁸⁰²ᵗ₀+ 0.135e⁻²·⁸⁰²ᵗ₀ =e⁻²·⁸⁰²ᵗ₀(−0.135* 2.802t₀+ 0.135)=0

It is clear that e⁻²·⁸⁰²ᵗ₀ not equal to zero for all t₀∈R, so that

=> −0.135* 2.802t₀+0.135=0

=> t₀ = 1/2.802 ≈0.36

let us consider t is in hours, so that it makes t₀ =0.36h≈21.41min. This is the only optimum and one should verify it is indeed a maximum, i.e. C′′(t₀)<0.

Now, easily compute the maximum average BAC, which is C(t₀)=C(0.36) = 0.135 (0.36)e⁻²·⁸⁰²⁽⁰·³⁶⁾

= 0.0486(0.3678) = 0.01787508

Hence, the maximum average BAC, is 0.017 g/dL.

Maximum average BAC during the first 3 hours,

t = 3 , C(t)=C(3) = 0.135 (3)e⁻²·⁸⁰²⁽³⁾ = 0.0001358 g/mL

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Answer:

(x + 7)/(x + 1)

Step-by-step explanation:

Simplify the following:

(x^2 + 11 x + 28)/(x^2 + 5 x + 4)

The factors of 4 that sum to 5 are 4 and 1. So, x^2 + 5 x + 4 = (x + 4) (x + 1):

(x^2 + 11 x + 28)/((x + 1) (x + 4))

The factors of 28 that sum to 11 are 7 and 4. So, x^2 + 11 x + 28 = (x + 7) (x + 4):

((x + 4) (x + 7))/((x + 4) (x + 1))

((x + 7) (x + 4))/((x + 4) (x + 1)) = (x + 4)/(x + 4)×(x + 7)/(x + 1) = (x + 7)/(x + 1):

Answer: (x + 7)/(x + 1)

Next time write the expression how it needs to be, the way you wrote it woould have given a toally different result.

x^2 + 11 x + 28/x^2 + 5 x + 4

Answer:

solving this as you would in algebra 2:

x2+11x+28 / x2+5x+4 = x+7 / x+1

Step-by-step explanation:

solving this as you would in algebra 2:

x2+11x+28 / x2+5x+4

1. on both the top and the bottom you have to find a factor of the last number (in this case 28 and 4) that multiplys to be the number but adds to be the 2nd term (11x and 5x)

2. for the top the two terms would be (x+7) and (x+4). on thebottom half it would be (x+4) and (x+1)

** 7 times 4 equals 28, 7 plus 4 equals 11; 4 times 1 equals 4, 4 plus 1 equals

3. x+4 is common term on both the top side and the bottom half so you cross it out. this leaves us with our answer of: x+7 over x+1

hope this helps:)

Answer:

x = -18

y = 4

Step-by-step explanation:

x + y = 4

2x + 3y = 30

You can do any math operation to each side of the equal sign as long as you do the same operation to both sides.

change x + y = 4       to        x = 4 - y  

Now substitute (4 - y) into the second equation, in place of x.

2(4-y) + 3y = 30

multiply the 2(4-y) part:

8 -2y + 3y = 30

simplify:

8 + y = 30

subtract 8 from each side:

y = 22

now substitute the value of y back into the first equation to solve for x:

x + 22 = 4

subtract 22 from both sides:

x = -18

Check:

x + y = 4

22 -18 = 4  

4 = 4       (this checks)

2(-18) + 3(22) = 30

-36 + 66 = 30

30 =30     (this checks also)

PS: you could have solved for y first if you had wanted to. The results would be the same.

Answer:

(0,2)

Step-by-step explanation:

The equations must be derived from the graph:

First, find the slope of f(x):

\(m=\frac{y_2-y_1}{x_2-x_1}\) let \((x_1,y_1)=(-3,3)\) and \((x_2,y_2)=(3,1)\)

\(m=\frac{(1)-(3)}{(3)-(-3)}\\m=\frac{-2}{6}\\m=-\frac{1}{3}\)

Then use \(y-y_1=m(x-x_1)\)

\(y-3=-\frac{1}{3}[x-(-3)]\\y-3=-\frac{1}{3}x-1\\y=-\frac{1}{3}x+2\\f(x)=-\frac{1}{3}x+2\)

For g(x), let:

\((x_1,y_1)=(-3,0)\\(x_2,y_2)=(0,2)\)

\(m=\frac{(2)-(0)}{(0)-(-3)}\\m=\frac{2}{3}\)

\(y-0=\frac{2}{3}[x-(-3)]\\y=\frac{2}{3}x+2\\g(x)=\frac{2}{3}x+2\)

Now, to solve for x, allow the two expressions written in terms of x equal each other.

\(-\frac{1}{3}x+2=\frac{2}{3}x+2\\(-\frac{1}{3}x+2)+\frac{1}{3}x=(\frac{2}{3}x+2)+\frac{1}{3}x\\2=x+2\\(2)-2=(x+2)-2\\x=0\)

To solve for y, substitute 0 for x in f(x):

\(y=-\frac{1}{3}x+2\\y=-\frac{1}{3}(0)+2\\y=0+2\\y=2\)

So, the solution to this system of equations would be the ordered pair (0,2).  This solution is seen on the graph as the intersection of the two lines.

Answer:

Step-by-step explanation:

we are expected to solve for the final velocity

using

V^2=U^2+2as we have

s=1m

U=0m/s

a=9.81m/s^2

substituting we have

V^2=U^2+2as

V^2=0+2*9.81*1

V^2=19.62

squaring both sides we have

V=√19.62

V=4.4m/s

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Answer:

A

Step-by-step explanation:

x= -2

Answer:

f = -3 , 5/2

Step-by-step explanation:

8f² + 4f - 60 = 0

Divide the entire equation by 4

2f² + f  - 15 = 0

Product = -30

Sum = 1

Factors = -5 , 6      {(-5)*6 = -30  and -5 +6 = 1}

2f² + f -15 = 0        {Rewrite the middle term using the factors}

2f² + 6f - 5f -15 = 0

2f(f + 3) - 5(f + 3) = 0

(f +3) (2f - 5) = 0

f +3  = 0    ; 2f -5 = 0

f = -3         ; 2f = 5

                    f = 5/2

ok

1.- Calcualte the total price for 19 sticks

price = 19 x 26

= $494

2.- Conclusion

there is not enough money to buy the sticks the total cost is

$494 and he only has $480.

3.- He needs 494 - 480 = $14 more money

Answer:

16 : 28

Step-by-step explanation:

If 12 out of the 28 pupils are female, we can calculate the number of males by subtracting the number of females from the total number of pupils.

28 - 12 = 16

So, there are 16 males in the class. Now, we know that the ratio of males : total is 16 : 28.

I hope this helps! Have a lovely day!! :)

(brainliest is much appreciated!!)

Answer:

give they guy brainliest

Step-by-step explanation:

because hes right

The probability of at least one of the next four randomly selected births being a boy can be calculated as approximately 0.992.

To find the probability of at least one boy, we can calculate the probability of the complementary event, which is the probability of all four births being girls.

The probability of a single birth being a girl is 0.473, so the probability of all four births being girls is :

\((0.473)^4 = 0.049\)

Therefore, the probability of at least one boy is 1 - 0.049 = 0.951. However, this probability represents the chance for any of the four births to be a boy. Since there are four opportunities for a boy to be born, we need to consider the complement of no boy being born in any of the four births, which is \((1 - 0.951)^4\)≈ \(0.992\\\). Hence, the probability that at least one of the next four births is a boy is approximately 0.992.

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Answer:

Difference Difference

1. 85 - 32 = 53 42 - 15 = 27

2. 76 + 21 = 97 65 + 12 = 77

3. 77 - 20 = 57 66 + 21 = 87

4. 72 + 25 = 97 62 + 25 = 87

5. 76 + 21 = 97 59 - 2 = 57

6. 63 + 14 = 77 48 + 11 = 59

7. 68 - 11 = 57 47 - 10 = 37

Answer:

The dotted line is 4.9

Step-by-step explanation:

The lower triangle is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

2^2 + 4^2 = c^2

4+16 = c^2

20 =c^2

Taking the square root of each side

sqrt(20) = c

The upper rectangle has a length of sqrt(20) and a height of 2

We can use the  Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse  to find the  diagonal

2^2 + (sqrt(20))^2 = c^2

4+20 = c^2

24 = c^2

Taking the square root of each side

sqrt(24) = c

4.898979486=c

Rounding to the nearest tenth

4.9 =c

Type II error occurs when the test incorrectly fails to reject an actually false null hypothesis.

In hypothesis testing, we have the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the status quo or the assumption that there is no significant difference or effect, while the alternative hypothesis suggests otherwise.

When conducting a statistical test, we aim to gather evidence to either reject or fail to reject the null hypothesis based on the available data.

Type II error specifically refers to the situation where we fail to reject the null hypothesis even though it is actually false. In other words, we miss detecting a true effect or difference that exists in the population.

This error can occur due to various reasons, such as limited sample size, inadequate statistical power, or variability in the data.

It means that we do not have enough evidence to conclude that the null hypothesis is false, even though it may be false in reality.

The consequence of a Type II error is that we may overlook important findings or fail to make accurate conclusions.

It is important to consider the potential for Type II errors when interpreting the results of a statistical test, and researchers often perform power calculations to determine an adequate sample size to minimize the risk of this error.

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There are major difference between them on the basis principles each method uses, the accuracy or precision, the complexity of the techniques, and any sources of error.

Relative Dating :-

Radiometric Dating :-

Difference between Relative Dating and Radiometric Dating are :

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The risk in the unexposed group over 21 years of follow-up is approximately 0.2562%.None of the provided options match the calculated value exactly.

To calculate the risk in the unexposed group, we need to divide the number of cases by the total person-years of follow-up.

Given information:

Unexposed group:

Individuals (n1): 18,842

Person-years (PY1): 351,551

Cases of smoking cessation (C1): 9

Risk in the unexposed group is calculated as:

Risk1 = (C1 / PY1) * 100%

Risk1 = (9 / 351,551) * 100%

Calculating the risk:

Risk1 ≈ 0.0025621 * 100%

Risk1 ≈ 0.2562%

Therefore, the risk in the unexposed group over 21 years of follow-up is approximately 0.2562%.

None of the provided options match the calculated value exactly.

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Using linear function to solve this problem, for every 1 gallon of gas, Francisco travelled 27.9 miles

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. where m is slope of the line and b is the y - intercept

We can use the data given in writing out our equation

390.6 = 14x

If 14 gallons = 390.6 miles

 1 gallon = x miles

x = 390.6 / 14

x = 27.9 miles

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Answer:            23,187 x 2/3 < 23187     is the answer

Step-by-step explanation:  

the growth rate, k, is approximately 1.98%.

To find the growth rate, k, we can use the formula for continuous compound interest:

A = P * \(e^{(rt)}\)

Where:

A = final amount (twice the initial investment)

P = initial investment

r = growth rate (in decimal form)

t = time (in years)

Given that the initial investment, P, is $61738 and the doubling time is 35 years, we can set up the equation as follows:

2P = P *\(e^{(r * 35)}\)

Divide both sides of the equation by P:

2 = \(e^{(35r)}\)

To solve for r, take the natural logarithm (ln) of both sides:

ln(2) = ln(\(e^{(35r)}\))

Using the property l\(n(e^x)\) = x:

ln(2) = 35r

Now, divide both sides by 35:

r = ln(2) / 35

Using a calculator, we can evaluate this :

r ≈ 0.0198

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The equation x + 8a - b = 8(x + a) - (2a - b) can be solved for the vector x in terms of the vectors a and b.

To find the solution, we can simplify the equation by expanding and rearranging the terms:

x + 8a - b = 8x + 8a - 2a + b

Combining like terms, we get:

x - 8x = -2a + b - 8a + 8a - b

Simplifying further:

-7x = -2a

Dividing both sides by -7:

x = (2/7)a

Therefore, the solution for the vector x in terms of the vectors a and b is x = (2/7)a. This means that x is a scalar multiple of the vector a, where the scalar is 2/7.

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If 5 pounds of raspberries costs 22.50, 1 pound will cost 4.50.

To put it simply, we can take 22.50 and divide it by 5. We do this because we are trying to solve for the price of 1, not 5.

22.50 ÷ 5 = 4.50

Therefore, 1 pound of raspberries costs 4.50.

Answer:

4.50$

Hope this helps!

Step-by-step explanation:

1 pound = $?

5 pounds = $22.50

1 pound * 5 = 5 pounds

$? * 5 = $22.50

$? = $22.50 ÷ 5

$? = 4.50

Answer:

5x²-7x+2

step by step explanation:

(f•g)(x) = f(x)•g(x)

(x-1)•(5x-2)

x×5x-2x-5x-1×(-2)

5x²-2x-5x+2

=5x²-7x+2