What is the most common measuring system in the world?
English
Metric
Apothecary
None of the above

For f(1) = 0 the statement is true that (x - 1) is the factor of the function.

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given a function,

f(x) = x⁶ - x⁴ + 2x² - 2

and f(1) = 0

substitute the values,

f(x) = x⁶ - x⁴ + 2x² - 2

f(1) = 1⁶ - 1⁴ + 2(1)² - 2

f(1) = 0

so when x = 1 function is zero,

so x - 1 = 0 and (x - 1) is one of the factor of function f(x).

Hence the statement is true.

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The value of k is given as follows:

k = 2.

The polynomial for this problem is defined as follows:

P(p) = p^4 + p² + p - k.

We have that p - 1 is a factor of the polynomial, meaning that according to the Factor Theorem, P(1) = 0.

Hence, considering that when p = 1, P = 0, the value of k is obtained as follows:

1^4 + 1² + 1 - k = 1

3 - k = 1

k = 3 - 1

k = 2.

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The required number would be -23 for the given statement.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

Let the required number would be x.

As per the question, we can write the algebraic form would be as:

-7(x + 7) = 16

Using the distributive property,

-7x - 49 = 16

-7x = 16 + 49

-7x = 65

x = -65/7

x = -23

Thus, the required number would be -23.

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The question seems incomplete, the complete question would be as:

The product of a number and -7 increased by 9, is at most 16. Find the number.

The potential energy of an object is given by the equation:

PE = mgh

where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height.

Rearranging this equation, we get:

h = PE / (mg)

Substituting the given values, we get:

h = 16800 J / (68.0 kg x 9.81 m/s^2)

h = 24.8 meters

Therefore, the cliff-jumper is standing 24.8 meters above the base of the cliff.

Answer:

h

Step-by-step explanation:

The ball will be 864 feet above the ground after 7 seconds. The equation for calculating the height of an object after a certain amount of time given a certain initial velocity is: h = v_0 * t - 0.5 * g * t^2

The equation for calculating the height of an object after a certain amount of time given a certain initial velocity is:

h = v_0 * t - 0.5 * g * t^2

where h is the height, v_0 is the initial velocity, t is the time, and g is the acceleration due to gravity (9.81 m/s^2).

In this case, h = 112 feet/sec * 7 sec - 0.5 * 9.81 m/s^2 * (7 sec)^2

h = 864 feet

The ball will be 864 feet above the ground after 7 seconds.

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The value of P(greater than 4 or less than 5) is 66.7%

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

Spinner = 3 4 5

Using the above as a guide, we have the following:

4 or 5 = 2

Total = 3

So, we have

P(greater than 4 or less than 5) = 2/3

Evaluate

P(greater than 4 or less than 5) = 66.7%

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A confusion interval of 99 percent between  -0.020 and 0.120 for the difference in the true percentage of the population that say "Yes".

What does confidence interval mean?

If you repeat your experiment or resample the population in the same manner, the confidence interval is the range of values you expect your estimate to fall within a specific proportion of the time.

In point a:

The confidence interval will not provide convincing proof that only the two population prolongations differentiate because a 99 percent confidence interval for both the difference throughout the true promotion around -0.020 and 0.120 is included 0.

In point b:

This confidence interval gives strong evidence also that two population proportions were identical because there is a confusion interval of 99 percent between  -0.020 and 0.120 for the difference in the true percentage of the population that say "Yes".

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The complete question is -

A CBS News poll asked 606 randomly selected women and 442 randomly selected men, "Do you think putting a special tax on junk food would encourage more people to lose weight?" 170 of the women and 102 of the men said "Yes." A 99% confidence interval for the difference (Women – Men) in the true proportion of people in each population who would say "Yes" is –0.020 to 0.120.

a. Does the confidence interval provide convincing evidence that the two population proportions are different? Explain your answer.

b. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

If a cell phone tower is 24 meters tall and casts a shadow 45 meters long, then 15 m long of a shadow will be cast by a nearby marble column that is 8 meters tall.

A Cell phone tower is 24 meters tall.

Casts of a shadow is 45 meters long.

A nearby marble column that is 8 meters tall.

We have to determine the how long of a shadow will be cast by a nearby marble column.

Since, the triangle △PQR∼△MNO

So from the diagram

MN/PQ = ON/RQ

8/24 = x/45

Multiply by 45 on both side, we get

x = 8/24 × 45

x = 360/24

x = 15

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Answer:

2 in

Step-by-step explanation:

Hope it helps.

On math thing

a. the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.

b. the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.

A) The probability of finding exactly 6 defects in a carpet roll can be calculated using the Poisson probability formula:

P(X = 6) = (e^-λ) * (λ^6) / 6!

where λ = 2.0 (the average number of defects per roll), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the values, we get:

P(X = 6) = (e^-2) * (2^6) / 6! = 0.0403

So the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.

B) To find the probability of finding 3 or fewer defects in a carpet roll, we need to calculate the cumulative probability:

P(X ≤ 3) = Σ_{i=0}^3 P(X = i) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

where P(X = i) is the probability of finding exactly i defects, which can be calculated using the Poisson probability formula.

Plugging in the values and adding the probabilities, we get:

P(X ≤ 3) = (e^-2) + (e^-2) * (2^1) / 1! + (e^-2) * (2^2) / 2! + (e^-2) * (2^3) / 3!

P(X ≤ 3) = 0.135

So the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.

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Complete question:

The World Carpet and Rug Company buys medium grade carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution,

A) What is the probability of finding exactly 6 defects in a carpet roll chosen at random?

b) What is the probability of finding 3 or fewer defects in a carpet roll?

The solution is 5/4.

A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

here, we have,

√150/√96

=√6√25/√6√16

=5√6/4√6

=5/4

Hence, The solution is 5/4.

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Answer:

.99

Step-by-step explanation:

345/353 =0.98

cube root =0 .99

so each edge is 0.99 m

The volume of the wood sample is calculated using the given density and mass. Given that this sample is a cube, the volume is also equal to the cube of the edge length. Therefore, finding the cube root of the volume gives us the edge length, which is about 0.99 meters.

The density of a material is defined by the ratio of its mass to its volume, expressed by the formula density = mass/volume. Given that the mass of the sample is 345 kg and the density is 353 kg/m³, you can calculate the volume by rearranging the formula to volume = mass/density. So, the volume comes out to be approximately 0.977 cubic meters. Now, since the sample is a cube, all sides are equal. The volume of a cube is given by the formula volume = edge ^ 3 (edge length cubed). You are hence looking to find the cube root of the volume, which is approximately 0.99 meters. Therefore, the length of one edge of the wood sample is approximately 0.99 meters to the nearest hundredth of a meter.

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There are no such pairs. The sum of the reciprocals of any two positive integers is always greater than[tex]$\frac14$[/tex].

The sum of the reciprocals of any two positive integers is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex], which is always greater than [tex]$\frac14$[/tex]. Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex]

For any two positive integers m and n, the sum of their reciprocals is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex] which is always greater than [tex]$\frac14$[/tex] This is because [tex]\frac{1}{m}$ ,$\frac{1}{n}[/tex] are both positive numbers, and so their sum must be greater than [tex]$\frac14$[/tex]Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex].

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If there is no line in the box to indicate the median, it is possible that the median has not been calculated or that the data set is too small to provide an accurate representation of the median.

A boxplot is a visual representation of the distribution of a set of data, and it typically consists of a box, two whiskers, and possibly some outliers. The box represents the interquartile range (IQR), which is the range between the first and third quartiles of the data. The median (or second quartile) is usually represented by a line within the box.

If there is no line in the box to indicate the median, it is possible that the median has not been calculated or that the data set is too small to provide an accurate representation of the median. With only 20 students, it is possible that the median may not be a meaningful representation of the central tendency of the data, especially if there are extreme outliers or skewed distributions. In such cases, it is best to consult other measures of central tendency, such as the mean or mode, to get a better understanding of the data.

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Answer:

100 dimes.

Step-by-step explanation:

Two equations.

First modeling the total money with x as nickels and y as dimes.

0.05x + 0.1y = 12.50

Second, modeling the amount of coins.

x + y = 150

Which you can alter to substitute for in the first equation.

x = 150 - y

Subsitute.

0.05(150 - y) + 0.1y = 12.50

7.5 - 0.05y + 0.1y = 12.50

0.05y = 5

y = 100

Paul has 100 dimes and 50 nickels.

These polygons have the following areas:

Case 9: 67

Case 10: 72

Case 11: 84

Case 12: 87.5

Case 13: 90

The walkway seal has a cost of $ 774.

In this question we need to determine the areas of irregular polygons and polygonal sections, these areas can be obtained in terms of sums and triangles and rectangles, whose formulas are introduced below:

Triangles

A = 0.5 · w · l

Rectangles

A = w · l

Where:

Now we proceed to determine the areas of each polygon:

Case 9

A = 0.5 · 3 · 4 + 0.5 · 6 · 4 + 0.5 · 2 · 7 + 0.5 · 2 · 7 + 5 · 7

A = 6 + 12 + 7 + 7 + 35

A = 67

Case 10

A = 4 · 0.5 · 3² + 9 · 6

A = 18 + 54

A = 72

Case 11

A = 0.5 · 3 · 12 + 3 · 12 + 0.5 · 3 · 12 + 0.5 · 1 · 4 + 0.5 · 5 · 4

A = 18 + 36 + 18 + 2 + 10

A = 84

Case 12

A = 0.5 · 7 · 3 + 7² + 0.5 · 3 · 4 + 0.5 · 3 · 4 + 4²

A = 10.5 + 49 + 6 + 6 + 16

A = 87.5

Case 13

A = 0.5 · 5 · 3 + 0.5 · 1 · 5 + 10 · 8

A = 7.5 + 2.5 + 80

A = 90

Case 14

A = 4 · 0.5 · (12 ft) · (10 ft) + 2 · (18 ft) · (12 ft) + 2 · (10 ft) · (18 ft)

A = 240 ft² + 432 ft² + 360 ft²

A = 1032 ft²

And the seal cost is:

C = (0.75 $ / ft²) · (1032 ft²)

C = $ 774

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The probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer is 5/45, or approximately 0.11.

To calculate the probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer, we need to consider the number of possible combinations of socks that result in a match and divide that by the total number of possible combinations of two socks.

The man has a total of 5 pairs of socks, or 10 socks, so there are 10 choose 2, or 45, possible combinations of two socks. Out of these, 5 of them result in a match, because there are 5 pairs of matching socks in the drawer.

Therefore, the probability of getting a matched pair of socks is 5/45, or approximately 0.11. This means that there is an 11% chance that the man will select a matched pair of socks if he randomly selects two socks from the drawer.

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The new check register balance of $131.35 now matches the bank statement balance of $161.96.

A bank balance is the amount of money a person or organization has in their account at a financial institution such as a bank. It reflects the amount of money that is available for spending or withdrawal, taking into account any transactions that have been made or are pending. The bank balance is an important aspect of managing finances, and individuals and businesses monitor their balances regularly to ensure that they have enough money to cover their expenses and to make sure that their accounts are in good standing.

To reconcile the checking account, you need to find out the reason for the difference between the check register balance ($107.87) and the bank statement balance ($161.96).

Add the interest earned of $0.43 to the check register balance: $107.87 + $0.43 = $108.30

Add the ATM deposit of $56 to the check register balance: $108.30 + $56 = $164.30

Subtract the incorrect amount of Check 307 ($32.95 instead of $35.29) from the check register balance: $164.30 - $32.95 = $131.35

The new check register balance of $131.35 now matches the bank statement balance of $161.96. This means the checking account has been reconciled.

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The correct way to write the ratio using fractional notation is [tex]\frac{2}{9}[/tex]  (two-ninths).

In math, a fraction is a mathematical expression that shows pars in a whole. Due to this, fractions include a numerator (number placed above) and a denominator (number placed below).

Ratios and fractions are equivalent, which means you just need to make sure the first number is the numerator and the second number is the denominator. Moreover, the fraction should be simplified if possible. Based on this, the fraction is:

[tex]\frac{2}{9}[/tex]

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Nevaeh would have $54 more in her account than Jonathan, to the nearest dollar.

Let's denote the amount of money Nevaeh has in her account after t years as A, and the amount of money Jonathan has in his account after t years as B.

We can use the formula for continuously compounded interest:

Compound interest finds its usage in most of the transactions in the banking and finance sectors and other areas.

And for monthly compounded interest:

We can plug in t = 14 to get the amounts for each person after 14 years:

The difference between these amounts is the amount by which Nevaeh would have more money in her account than Jonathan, to the nearest dollar:

difference = A - B

difference = round(difference)

Using a calculator, we find that:

difference = 977.78 - 923.61 = 54.17

So, Nevaeh would have $54 more in her account than Jonathan, to the nearest dollar.

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Answer: 4

Step-by-step explanation:

The median is the value in the middle of a data set. When rearranging the data, it should be:

2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10

4 is directly in the middle since there is 10 numbers exactly to the left and right of it

Hope this helps!

The median of the histogram is M = 5

A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable. Histograms frequently divide data into different "bins" or "range groups" and count how many points are in each bin.

A histogram displays the frequency distribution of a set of continuous data. It is useful for visualizing the shape of the data distribution, such as whether it is symmetrical or skewed, and identifying any outliers or gaps in the data.

One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data.

Given data ,

Let the histogram be represented as A

Now , the value of A is

The frequency of 1 = 0

The frequency of 2 = 1

The frequency of 3 = 5

The frequency of 4 = 5

The frequency of 5 = 4

The frequency of 6 = 2

The frequency of 7 = 1

The frequency of 8 = 1

The frequency of 9 = 1

The frequency of 10 = 1

So , the midpoint of the distribution is M = 10/2 = 5

Hence , the median of the histogram is M = 5

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Ans: 55°

Let's draw two parallel line intersecting angle x° and 45° as shown in the photo.

i) a=25° [Being Alternative Angle]

ii) d=15° [Being Alternative Angle]

iii) c= 45°-d[45°=c+d]

=45°-15°

=30°

iv)b=c[Being Alternative Angle]

v)x=a+b[Combining Angle a & b]

=25°+30°

=55°

The amount of paper used to create the label was approximately 201.06 cm². This was calculated by multiplying the diameter of 16 cm by the height of 8 cm and then multiplying the result by 3.14 (T).

The amount of paper used to create the label for an 8 cm tall cylinder can with a diameter of 16 cm can be calculated by using the formula for the lateral surface area of a cylinder (T*r*h). T is the constant pi, which is equal to 3.14. r is the radius of the cylinder, which is equal to half of the diameter (16 cm/2 = 8 cm). h is the height of the cylinder, 8 cm. Therefore, the lateral surface area of the cylinder can is calculated by multiplying 3.14 by 8 cm (radius) by 8 cm (height). This results in 201.06 cm² of paper needed to create the label. The label can be wrapped around the cylinder, covering the whole surface area of the can.

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Examining the driving information between Roger and Rita we can say that

Since the Roger and Rita drive at constant speed we check their speed at 1 hour

Roger = in 1 hour covers a distance of 65 miles

Rita = in 1 hour covers a distance of 93 miles

Hence we can say that Rita has a head start,

solving for the head start

= 93 miles - 65 miles

= 22 miles

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The area of the given figure is 66 square miles.

As we can see in the figure, we have 2 different rectangles attached to one another. So the total area of the figure will be the area of the vertical rectangle plus the area of the horizontal rectangle.

Area of the horizontal rectangle = L₁ × W₁

L₁ = 9 mi

W₁ = 2 mi

∴ Area = 9 mi × 2 mi

= 18 square miles

Area of the vertical rectangle = L₂ × W₂

L₂ = 12 mi

W₂ = 4 mi

∴Area = 12 mi × 4 mi

= 48 square miles

Now, the total area of the figure = the area of the vertical rectangle + the area of the horizontal rectangle.

= 48 square miles + 18 square miles

= 66 square miles.

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Let assume the probability of the three events as P(A), P(B), and P(C), respectively. Then:

(a) The probability that at least one of the three events occurs is given by:

P (A or B or C) = 1 - P (not A and not B and not C) = 1 - P (not A) * P (not B) * P (not C)

where P (not A) is the complement of P (A), and similarly for P (not B) and P (not C).

(b) The probability that exactly one of the three events occurs can be calculated by adding the probabilities of each event occurring individually and then subtracting the probability that two events occur simultaneously.

P (exactly one) = P(A) + P(B) + P(C) - 2 * P (A and B) - 2 * P (A and C) - 2 * P(B and C) + 3 * P (A and B and C)

Note that the above formulas assume that the events are mutually exclusive and exhaustive, meaning that one and only one of the events must occur and the sum of the probabilities of the individual events is equal to 1.

If this is not the case, the probabilities need to be adjusted accordingly.

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Answer:

  x²/9 +y²/64 = 1

Step-by-step explanation:

You want the figure defined by x = 3sin(θ) and y = 8cos(θ) to be described by an equation in rectangular form.

The trig identity sin(x)² +cos(x)² = 1 is helpful here.

  x = 3sin(θ)   ⇒   x/3 = sin(θ)

  y = 8cos(θ)   ⇒   y/8 = cos(θ)

Combining these using the above identity, we have ...

  (x/3)² +(y/8)² = 1 . . . . . . the equation of an ellipse

We can simplify the denominators to ...

  x²/9 +y²/64 = 1

__

Additional comment

The attached graph uses different colors and textures to show the two forms of expressing the graph result in the same figure.

Step-by-step explanation:

above is the explanation of the question

Since LMNO is a parallelogram, opposite angles are congruent, which means that angle L is congruent to angle N and angle M is congruent to angle O.

Since angles L and M are adjacent angles in a parallelogram, they are supplementary, which means that their sum is 180 degrees. Therefore, the sum of the measures of angles L and M is:

L + M = 180 degrees.

Answer: 180 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So and L and M add up to 180 degrees.