What do all products of the square of binomial have in common?

The expression for the area of the triangle is given as follows:

A = 1.5x^4 + x³ - 0.5x².

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5(3x² - x)(x² + x)

A = 0.5(3x^4 + 3x³ - x³ - x²)

A = 0.5(3x^4 + 2x³ - x²)

A = 1.5x^4 + x³ - 0.5x².

More can be learned about the area of a triangle at https://brainly.com/question/21735282

#SPJ1

Yes, the sample size of 4,706 is large enough to justify the use of the z formula.

To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.

One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.

In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.

Learn more about central limit theorem here

brainly.com/question/18403552

#SPJ4

The function f(x) that has a local minimum at (0,0) and a local maximum at (1,3) is f(x) = 2x³ - 3x².

From the information, we can set up a system of equations as follows:

f'(x) = 3ax² + 2bx + c = 0 (at x=0)

f'(x) = 3ax² + 2bx + c = 0 (at x=1)

Plugging in x=0, we get:

f'(0) = c = 0

Plugging in x=1, we get:

f'(1) = 3a + 2b + c = 0

3a + 2b = -c = 0

3a + 2b = 0 (since c=0)

Solving the system of equations, we get:

a = 2

b = -3

c = 0

d = 0

The function is f(x) = 2x³ - 3x²

Learn more about functions on

https://brainly.com/question/11624077

#SPJ4

Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be (c) 11.

The dot-plot displays a unimodal distribution with a moderate to large spread of the data.

The spread of the data is roughly from 0 to 40, with most of the dots being between 10 to 30.

The spread of the dots, it is unlikely that the standard deviation of the data is as small as 5 or 8.

Similarly.

It is unlikely that the standard deviation is as large as 20 or 15 as there are a significant number of data points that lie within the 20-30 range.

Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be around 11.

For similar questions on Standard Deviation

https://brainly.com/question/24298037

#SPJ11

The quarterly dividend payment per share based on the question above will be: $0.02.

The close price for the week will be: $5.45.

For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:

Close price = Total cost / Number of shares

                    = $2,790.40 / 512

                    = $5.45

To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:

Annual dividend per share = Total annual dividend / Number of shares

                                              = $40.96 / 512

                                                = $0.08

From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:

Quarterly dividend per share = Annual dividend per share / 4

                                                  = $0.08 / 4

                                                   = $0.02

Hence the quarterly dividend payment per share will be: $0.02.

Learn more about dividend from

https://brainly.com/question/2960815

#SPJ1

See text below

Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)

EARNINGS

52-WEEK

TICK

VOL.

WEEK'S

LATEST

THIS NEXT DIV

High Low

Name

Sym.

100s

Yld.

P/E Last Chg.

Year

Year

Year

Amt

8.50

3.20

Targa Resources

TRGP

412574 1.8

PO

dd

+0.41

0.25

0.18

0.12

Answer:

Okay, let's solve this step-by-step:

   There is a spinner with 14 equal areas, numbered 1 through 14

   We want to find the probability that the result is a multiple of 3 or a multiple of 4

   There are 14 possible outcomes (numbers 1 through 14) when the spinner is spun.

   Of these 14 numbers:

   4 are multiples of 3: 3, 6, 9, 12

   4 are multiples of 4: 4, 8, 12, 16

   However, 12 is also a multiple of both 3 and 4, so we have counted it twice.

   We need to subtract 1 from each to account for this:

   Multiples of 3: 3

   Multiples of 4: 4

   So there are 3 possible multiples of 3 and 3 possible multiples of 4.

   In total, there are 3 + 3 = 6 possible multiples of 3 or 4.

   To calculate probability:

   Probability = (Number of favorable outcomes) / (Total possible outcomes)

   = 6 / 14

   = 3/7

   Converting to a percent: 3/7 = 42.9%

   Rounded to the nearest whole percent: 43%

Therefore, the probability that the result is a multiple of 3 or a multiple of 4 is 43%.

Step-by-step explanation:

To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185

b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:

P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)

We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,

P(painted | curvilinear) = 14/183 ≈ 0.0765

We are moreover given that there are 837 pieces in add up, of which 183 are painted.

P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765

P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266

thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.

To learn about probability visit:

https://brainly.com/question/31120123

#SPJ4

Answer:$2.7 would be saved

Step-by-step explanation:

Multiply 18 by .15 which gives you 2.7 which is the answer.

If you know that a girl plays soccer, then the probability that she also plays basketball = 0.23

The correct answer is an option (c)

Let's assume that event S: a girl plays soccer

event B: a girl plays basketball

Here, the probability that the girl plays soccer would be,

P(S) = P(SB) + P(SB')

where B' means a girl does not play basketball

here, P(SB) = 0.075 and P(SB') = 0.250

So, P(S) = 0.075 + 0.250

P(S) = 0.325

We need to find the probability that a girl plays basketball knowing that she plays a soccer.

i.e., the conditional probability P(B|S)

Using formula for the conditional probability,

P(B|S) = P(BS) / P(S)

           = 0.075 / 0.325

           = 0.23

Therefore, the correct answer is an option (c)

Learn more about the probability here:

https://brainly.com/question/15124899

#SPJ4

Find the complete question below.

If one zero of the polynomial 3x^2 + 8x + k is  the reciprocal of the

other, then k = 3 by applying product of roots formula.

The quadratic polynomial is 3x^2 + 8x + k.

Let the roots of  3x^2 + 8x + k be m and n where m and n are reciprocal of each other. Therefore, n = 1/m

Thus, the product of roots is = m*n = m*(1/m) = 1 ____(1)

The general equation of a quadratic equation can be written as,

ax^2 + bx + c = 0

where a and b are coefficients of x^2 and x respectively and c is a constant term.

From product of roots formula we know that,

Product of roots =constant term/ coefficient of x^2 = c/a

Therefore, for polynomial is 3x^2 + 8x + k we get,

Product of roots = k/3 ____(2)

From equating equation (1) and (2) we get,

k/3 = 1

⇒ k = 3

To know more about product of roots here

https://brainly.com/question/10719430

#SPJ4

The given question is incomplete, the complete question is

"If one zero of the polynomial 3x^2+8x+k is the reciprocal of the other, then find the value of k."

The volume of the cheese head is 192 cubic inches.

Explain the term volume

Volume refers to the amount of space that an object or substance occupies in three dimensions. It is typically measured in units such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas, depending on its shape and dimensions.

According to the given information

The volume V of a triangular prism is given by the formula:

V = (1/2) * b * h * L

In this case, the base of the triangle is 12 inches, the height of the triangle is 8 inches, and the length of the prism (depth of the 3D shape) is 4 inches. Substituting these values into the formula, we get:

V = (1/2) * 12 * 8 * 4

V = 192 cubic inches

To know more about volume visit

brainly.com/question/1578538

#SPJ1

Trigonometric ratios allow us to determine the value of Cos²θ to be = 5/9. As a result, choice D is the best one.

Triangle side ratios are known as ratios of trigonometry. These ratios demonstrate how a right triangle's edges to angles ratio functions in mathematics. The sine, cosine, and tangent trigonometric ratios are the fundamental three. The sin, cos, and tan functions can be used for calculating the other significant trig ratios, cosec, sec, and cot.

Here in the question,

Sinθ = 2/3

Now,

Cos²θ = 1 - Sin²θ

= 1- (2/3) ²

= 1 - 4/9

= (9-4)/9

= 5/9

Therefore, the value of Cos²θ = 5/9.

Option D is the correct option.

To know more about trigonometric ratios, visit:

brainly.com/question/25122825

#SPJ1

The complete question is:

Given: sinθ = 2/3 and is in the second quadrant; evaluate the following expression: cos²θ

a). -7/9

b). -1/9

c). 1/9

d). 5/9

Answer:

1300 milliliters

Step-by-step explanation:

There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.

Answer:

[tex]y = {1.5}^{x} [/tex]

[tex] ln(y) = ln( {1.5}^{x} ) [/tex]

[tex] ln(y) = x ln(1.5) [/tex]

[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]

[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]

Answer:

[tex] {21}^{2} + {x}^{2} = {35}^{2} [/tex]

[tex] {x}^{2} =784[/tex]

[tex]x = 28[/tex]

[tex] {y}^{2} + {32}^{2} = {35}^{2} [/tex]

[tex] {y}^{2} = 201[/tex]

[tex]y = \sqrt{201} = 14.18[/tex]

The ladder will reach about 14.2 feet up the side of the house.

Answer:

Step-by-step explanation:

18

(a) The probability that both missiles will hit the target is 1/10.

(b) The probability that at least one missile will hit the target is 11/20.

To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting

P(both missiles hit) = P(first missile hits) × P(second missile hits)

P(both missiles hit) = (1/4) × (2/5)

P(both missiles hit) = 2/20

P(both missiles hit) = 1/10

So the probability that both missiles will hit the target is 1/10.

(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)

P(at least one missile hits) = 1 - P(both missiles miss)

P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)

P(at least one missile hits) = 1 - (3/4) × (3/5)

P(at least one missile hits) = 1 - 9/20

P(at least one missile hits) = 11/20

Learn more about probability here

brainly.com/question/11234923

#SPJ4

It will take approximately 268.08 cubic feet of air to fill the giant beach ball.

A sphere is a three-dimensional geometric shape that is perfectly round in shape, with every point on its surface equidistant from its center. It is a type of round solid figure that has no edges or vertices. The surface of a sphere is continuous, and it encloses a fixed volume of space.

The formula for the volume of a sphere is:

V = (4/3) × π × r³

where r is the radius of the sphere.

In this case, the radius of the beach ball is 4 feet, so we can substitute this value into the formula:

V = (4/3) ×π × (4)³

V = (4/3) × π × 64

V = 268.08 cubic feet (rounded to two decimal places)

Therefore, it will take approximately 268.08 cubic feet of air to fill the giant beach ball.

To know more about volume, visit:

https://brainly.com/question/1578538

#SPJ1

a) The linear equation is:

y = 25 + x

b) When the daughter's is one third of her mother's age​ we will have x = 12.5

We know that the mother is 25 years older than the daughter, so, if the daughter's age is x, the mother's age can be defined as the linear equation:

y = 25 + x

b) When the daughter's age is one third of her mother's, we have:

x = (1/3)*y

3x = y

Replacing that in the equation above we will get:

3x = 25 + x

3x - x = 25

2x = 25

x = 25/2 = 12.5

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

Answer:

Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.

Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.

The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.

Step-by-step explanation:

The tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass cutting process.

The tank has four vertical rectangular sides, a bottom, and no top. Since there is no top, we do not need to include the area of any glass for the top of the tank.

The area of each rectangular side is given by multiplying the height by the width. The area of the bottom is given by multiplying the length by the width. Therefore, the total area of glass used to make the tank is:

Area = 2(height x width) + 2(height x length) + (length x width)

Substituting the given values, we get:

Area = 2(23 x 18) + 2(23 x 12) + (18 x 12)

Area = 1,656 + 1,656 + 216

Area = 3,528

Therefore, the tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass-cutting process.

Learn more about area here:

https://brainly.com/question/11580351

#SPJ1

Answer:

$14,766.00

Step-by-step explanation:

Interest = principle x rate x time

I = 13800 (.14)(.5)

I = 966

Total:

Principle plus interest

13800 + 966 = 14,766

Helping in the name of Jesus.

Answer:22x121=2662

Step-by-step explanation:

The multiplicand is 22, the multiplier is 121 and the product is 2662.

Answer: 0.5

Step-by-step explanation:

1/2% is equal to 50 out of 100, or 50/100.

So you turn that into a decimal (fifty one hundredths).

0.50

You can get rid of the 0 at the end.

0.5

Hope this helps!!! :)

The true statements are:

A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.

C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.

Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.

Learn about mean here https://brainly.com/question/1136789

#SPJ1

Answer:

1E+30

Step-by-step explanation:

The probability of rolling a 5 when playing a game with a die is an example of empirical probability.

Empirical probability is determined through observation and experimentation, by counting the number of times an event occurs and dividing it by the total number of trials. In this case, the children have likely rolled the die multiple times and recorded the number of times a 5 was rolled.

They then calculated the probability of rolling a 5 by dividing the number of times a 5 was rolled by the total number of rolls. Empirical probability is commonly used in fields such as science and statistics, where data is gathered through experimentation and observation.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

(a) The point estimate is 92/160 = 0.575 or 57.5%.

(b) Using the salt program, the 90% confidence interval is [0.502, 0.648].

(c) Using the salt program, the 95% confidence interval is [0.476, 0.674].

(d) The 95% confidence interval is wider than the 90% confidence interval.

(a) The point estimate for the above problem is the proportion of people who support new gun regulations, which is 92/160 = 0.575 or 57.5%.

(b) To find the 90% confidence interval, we can use the following formula:

[tex]CI = p ± z*(sqrt(p*(1-p)/n))[/tex]

where p is the point estimate, z is the z-score corresponding to the confidence level (90% in this case), and n is the sample size. Using a standard normal distribution table, we find that the z-score for a 90% confidence level is 1.645. Substituting the values, we get:

[tex]CI = 0.575 ± 1.645*(sqrt(0.575*(1-0.575)/160)) = (0.500, 0.650)[/tex]

Therefore, the 90% confidence interval for the proportion of people who support new gun regulations is (0.500, 0.650).

(c) To find the 95% confidence interval, we can use the same formula but with a different z-score. The z-score for a 95% confidence level is 1.96. Substituting the values, we get:

[tex]CI = 0.575 ± 1.96*(sqrt(0.575*(1-0.575)/160)) = (0.480, 0.670)[/tex]

Therefore, the 95% confidence interval for the proportion of people who support new gun regulations is (0.480, 0.670).

(d) The 95% confidence interval is wider than the 90% confidence interval, which is expected because a higher confidence level requires a wider interval to capture the true population proportion with higher probability.

Learn more about   z-score

https://brainly.com/question/15016913

#SPJ4

The evaluated solution for the  given  question comprises of sample point of a that are  {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4  below under the condition of a fair coin is tossed three times, and the events a and b are defined.

a)  Points sample  for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points  sample  for event b: {HTT, THT, TTH, HHH}
Points  sample  for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
  Points  sample for event ac: {TTT}
  Points  sample for event a c: {TTT, HHHH}

b)  Event a probability= 7/8 = 0.875
  Event b probability= 1/2 = 0.5
  Event ab probability = 3/8 = 0.375
  Event ac probability   = 1/8 = 0.125
  Event a c probability  = 1/16 + 1/8 = 0.1875

c) Probability of a b implementing additive rule
    P(a b) = P(a) + P(b) - P(a ∩ b)
     P(a ∩ b) = P(a) + P(b) - P(a b)
     P(a ∩ b) = (7/8) + (1/2) - (3/8)
     P(a ∩ b) = 9/8 - 3/8
     P(a ∩ b) = 6/8
     P(a ∩ b) = 3/4

d)  Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.


To learn more about probability,
https://brainly.com/question/13604758
#SPJ4