Find the functional value.
f(0) if f(x) = x - 3x^2

Answer:

Step-by-step explanation:

14!=8.71782912x10^10

14!=14x13x12x11x10x9x8x7x6x5x4x3x2x1

So we want to evaluate:

For this, we might convert 2pi/3 to degrees.

This, is to make the graph more understandable.

Remember that:

So we could make the following ratio:

Solving for x:

Therefore, x=120°. Now, we could graph:

So,

The multiple of 2, 5, and 7, such that the sum of the 3 digits is 10 is:

630

We want to find a number that is a multiple of 2, 5 and 7, such that the sum of the 3 digits is 10. (such that the number is not 280)

So our number N is of the form:

N = a*(2*5*7)

Where a is an integer.

N = a*70

Here we just need to find the value of a such that the sum of the 3 digits of the outcome is equal to 10.

For example, if a = 2 then:

N = 2*70 = 140

The sum gives 1 + 4 + 0 = 5

Now we jut need to keep trying values of a.

Eventually, we will get to:

if a = 9 then:

N = 9*70 = 630

The sum gives: 6 + 3 + 0 = 10

So this is our number.

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Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

Answer:

m=2

Step-by-step explanation:

use points (2,2) and (6,10)

(find y of slope)10-2=8

(find x of slope)6-2=4

8/4=2

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μemployed(μ1) be the sample mean of students who are employed and μnot employed(μ2) be the sample mean of students who are not employed

The random variable is μ1 - μ2 = difference in the mean of the employed and unemployed students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(μ1 - μ2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 3.22

μ2 = 3.33

s1 = 0.475

s2 = 0.524

n1 = 172

n2 = 116

t = (3.22 - 3.33)/√(0.475²/172 + 0.524²/116)

t = - 1.81

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.475²/172 + 0.524²/116]²/[(1/172 - 1)(0.475²/172)² + (1/116 - 1)(0.524²/116)²] = 0.00001353363/0.00000005878

df = 230

We would determine the probability value from the t test calculator. It becomes

p value = 0.036

Since alpha, 0.05 > than the p value, 0.036, then we would reject the null hypothesis.

Therefore, at a 5% significant level, this information support the hypothesis that for students at this university, those who are not employed have a higher mean GPA than those who are employed

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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The z-score for the lowest final grade for a freshmen is given as follows:

Z = -1.83.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 74.38, \sigma = 4.445, X = 66.25\)

Hence the z-score for the lowest final grade for a freshmen is obtained as follows:

Z = (66.25 - 74.38)/4.445

Z = -1.83.

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Answer:

9.4

Step-by-step explanation:

85/9=9.4...

I put ... at end because it continues forever the 4s I hoped I helped

Answer:

2) 8x^2 -6x-7 hope this helps

Answer:

5 degrees every hour.

Step-by-step explanation:

35/7=5

Answer: 5

Step-by-step explanation:

35 degrees / 7 hours = 5 degrees per hour

Answer:

-$35.00

Step-by-step explanation: I think

The exact value of x is √1156 and it follows the Pythagorean triple

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

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Convert the problem to standard form and write the initial tableau with slack variables:

Maximize

\(Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6\)

Subject to:

\(x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000\)

All variables are non-negative.

Tableau

 x1  x2  x3  x4  x5  x6  s1  s2   b

Z -3 -3 7 6 18 14 0 0 0

s1 1 1 0 0 0 0 1 0 4000

s2 3 3 3 3 3 2 0 1 6000

x5 0 0 1 0 1/3 0 0 0 0

x6 0 0 0 1 0 1/2 0 0 0

The basic variables are s1, s2, x5, and x6.

Step 1: Choose  entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.

Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,

corresponding to s1. s1 leaves the basis.

Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.

 x1    x2    x3    x4     x5     x6   s1    s2       b

Z -3 -3 7 6 18 14 0 0 0

x5 0 0 1 0 1/3 0 0 0 0

s2 3 3 3 3 2 2/3 2/3 0 1/3 24000

x3 1 0 1/3 0 1/3 0 -1/3 0 0

x4 0 1 0 1/3 0 1/2 -1/6 0 0

The basic variables are x5, x3, x4, and s2.

Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.

Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.

As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.

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Answer:

1/3

Step-by-step explanation:

Probability of getting a marble is 0.3.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Two boxes Probability of selecting either of the box = 0.5

Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,

let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )

Box contains : 3 blue and 5 red marbles,

let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )

So, the final probability of getting a blue ball is 0.3.

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Probability of getting a marble is 0.3.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Two boxes Probability of selecting either of the box = 0.5

Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,

let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )

Box contains : 3 blue and 5 red marbles,

let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )

So, the final probability of getting a blue ball is 0.3.

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Using the concept of ratio, the rate at which questions were answered correctly is 0.867 which is option B

Rate can be defined as comparing two or more ratio with a standard value.

The rate of correct answer can be calculated using the ratio between the number of correct answers to numbers of questions answered.

The rate is given as;

rate = 65 / 75

rate = 0.867

The rate of correct answers is 0.867

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Answer:

x = 7; y = 3

Step-by-step explanation:

I used the Trial and Error Method and found that x = 7 and y = 3

=> 7 + 3 = 10

=> 10 = 10. ✔

=> 7 - 3 = 4

=> 4 = 4. ✔

Therefore, x = 7 and y = 3

Hoped this helped.

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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Using the z-distribution for the margin of error, it is found that 355 samples should be taken.

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which  z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The estimate is of 18%, hence \(\pi = 0.18\).

95% confidence, hence \(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so \(z = 1.96\).  

The minimum sample size is n for which M = 0.04, hence:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 1.96\sqrt{\frac{0.18(0.82)}{n}}\)

\(0.04\sqrt{n} = 1.96\sqrt{0.18(0.82)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.18(0.82)}}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.18(0.82)}}{0.04}\right)^2\)

\(n = 354.4\)

Rounding up, 355 samples should be taken.

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Answer:

A)  P(Z > 5000) = 0.0322

B)  P( Y = 2 or 3) ≅  0.9032

Step-by-step explanation:

From the given information;

Suppose the sales for the first week are denoted by X and the sales for the second week are denoted by Y.

Then;

X & Y are independent and they follow a normal distribution.

i.e.

\(XY \sim N(\mu,\sigma^2)\)

\(XY \sim N(2200,230^2)\)

If we set Z to be equal to X+Y

Then, \(Z \sim N(2 \times 2200,2 \times 230^2)\) since two normal distribution appears normal

\(Z \sim N(4400,105800)\)

So;

\(P(Z > 5000) = 1 - P( Z< \dfrac{x = \mu}{\sqrt{\sigma}})\)

\(P(Z > 5000) = 1 - P( Z< \dfrac{5000-4400}{\sqrt{105800}})\)

\(P(Z > 5000) = 1 - P( Z< \dfrac{600}{325.2691})\)

\(P(Z > 5000) = 1 - P( Z< 1.844626495)\)

\(P(Z > 5000) = 1 - P( Z< 1.85)\)

From the Z - tables;

P(Z > 5000) = 1 - 0.9678

P(Z > 5000) = 0.0322

B)

Let Y be the random variable that obeys the Binomial distribution.

Y represents the numbers of weeks in the next 3 weeks where the gross weekly sales exceed $2000

Thus;

\(Y \sim Bin(3,p)\)

where;

\(p = 1 - P( Z < \dfrac{2000-2200}{230})\)

\(p = 1 - P( Z < \dfrac{-200}{230})\)

p = 1 - P( Z < - 0.869565)

From the Z - tables;

p = 1 - 0.1924

p = 0.8076

Now;

P(Y ≥ 2) = P(Y = 2) + P( Y =3 )

Using the formula

\(P(X = r ) = ^nC_r \times p^r \times q ^{n-r}\)

\(P( Y = 2 \ or \ 3) =^ 3C_2 \times 0.8076^2 \times ( 1- 0.8076) ^ {3-2} + ^ 3C_3 \times 0.8076^3 \times ( 1- 0.8076) ^ {3-3}\)

\(P( Y = 2 \ or \ 3) =\dfrac{3!}{2!(3-2)!} \times 0.8076^2 \times ( 0.1924) ^ 1 + \dfrac{3!}{3!(3-3)!}\times 0.8076^3 \times ( 0.1924) ^ {0}\)

\(P( Y = 2 \ or \ 3) =0.3764600911 +0.526731063\)

P( Y = 2 or 3) = 0.9031911541

P( Y = 2 or 3) ≅  0.9032

Answer:

The probability that the number of free throws he makes exceeds 80 is approximately 0.50

Step-by-step explanation:

According to the given data we have the following:

P(Make a Throw) = 0.80%

n=100

Binomial distribution:

mean:   np = 0.80*100= 80

hence, standard deviation=√np(1-p)=√80*0.20=4

Therefore, to calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:

P(X>80)= 1- P(X<80)

You could calculate this value via a normal distributionapproximation:

P(Z<(80-80)/4)=1-P(Z<0)=1-50=0.50

The probability that the number of free throws he makes exceeds 80 is approximately 0.50

The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.

Given that,

A college basketball player makes 80% of his free throws.

Over the course of the season, he will attempt 100 free throws.

Assuming free throw attempts are independent.

We have to determine,

The probability that the number of free throws he makes exceeds 80 is.

According to the question,

P(Make a Throw) = 80% = 0.80

number of free throws n = 100

Binomial distribution:

Mean: \(n \times p = 0.80 \times 100 = 80\)

Then, The standard deviation is determined by using the formula;

\(= \sqrt{np(1-p)} \\\\=\sqrt{80\times (1-0.80)}\\\\= \sqrt{80 \times 0.20 } \\\\= \sqrt{16} \\\\= 4\)

Therefore,

To calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:

\(P(X>80)= 1- P(X<80)\)

To calculate this value via a normal distribution approximation:

\(P(Z<\dfrac{80-80}{4})=1-P(Z<0)=1-0.50=0.5000\)

Hence, The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.

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Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

Answer:

11,200

Step-by-step explanation:

You can look up "Meters to Centimeters" and that should help you in the future

Answer:

11,200

Step-by-step explanation:

Answer:

the rule is scientific notation. if you are multiplying, move the decimal point over the amount of zeros to the right. if dividing, move the decimal point over to the left for the number of zeros there are.

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

180=35+90+m∠3

If 6 is an element in the domain of f(x) = (8x - 16)/2, the corresponding element in the range include the following: [16].

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Based on the information provided, we have the following function rule:

Function, f(x) = y = (8x - 16)/2

When the domain x = 6, the range (y) of this function is given by;

Range, y = (8(6) - 16)/2

Range, y = (48 - 16)/2

Range, y = 32/2

Range, y = 16.

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Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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9514 1404 393

Answer:

  c.  1/x^2

Step-by-step explanation:

You want to solve for a:

  1/√a = x

  1/a = x^2 . . . . . square both sides

  1/x^2 = a . . . . . multiply both sides by a/x^2

Answer:

14743

Step-by-step explanation:

B. the business world and its industries control those in poverty

C. that the place is polluted and depressing

In this prooof, we need to complete the 8th step to simplify the expression.

We are given:

Combining like terms on the left-hand side, we get

Subtracting the d squared term from each side, we have:

Next, we subtract the e squared term from each side:

Finally, we divide by -2 on each side:

Since d represents the slope of line AB and e represents the lope of line BC, we show that the slopes multiplied together give us -1.