14
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the f
If p-1 is a factor of p*+p²+p-k, the value of kis
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Answer:

145.68

Step-by-step explanation:

When rounding 145.678 to the nearest hundred, we look at the digit in the tens column, which is 4. Since 4 is less than 5, we round down to the nearest hundred. Therefore, 145.678 rounded to the nearest hundred is 100.

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Mean = \dfrac{Sum\: of \: Observations }{No.\:of \:Observations }}\\[/tex]

As per question, we are given -

[tex] \:\:\:\:\:\:\star\:\sf Sum \:of \:observations \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 9+4+8+8+7+x \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 36+x \\[/tex]

Now that, we are given all the values which are required for solving this problem, so we can substitute the values and solve for the sixth datum -

[tex] \:\:\:\:\:\:\longrightarrow \sf Mean = \dfrac{Sum\: of \: Observation }{No.\:of \:Observation }\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 7 = \dfrac{36+x}{6}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 7\times 6 = 36+x \\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf 42 -36 =x\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{x = 6}\\[/tex]

Answer:

Step-by-step explanation:

height x is in the wrong spot of the triangle -90 x 100 then divide sum like that.. (:

Based on the given data, it is expected that approximately 4 of the next 15 drinks sold will be espressos.

To find the expected number of espressos out of the next 15 drinks sold, we can use the proportion of espressos in the recorded drinks as an estimate.

The proportion of espressos in the recorded drinks is 4 out of a total of 20 drinks, or 4/20 = 0.2. This means that about 20% of the recorded drinks were espressos.

To estimate how many of the next 15 drinks sold would be espressos, we can use the proportion of espressos in the current data.

Out of a total of 20 drinks (1 mocha + 3 macchiatos + 5 Americanos + 7 lattes + 4 espressos), the proportion of espressos is 4/20 = 0.2.

Therefore, we can expect that approximately 0.2 * 15 = 3 of the next 15 drinks sold will be espressos.

So we can expect that three of the next 15 drinks sold will be espressos.

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Answer:

Step-by-step explanation:

Middle right = 3

Bottom left = 15t

Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

3 * ( 5t + 4 )

3 * 5t + 3 * 4

15t + 12

Answer:

Step-by-step explanation:

112

Answer:

y = -x² + 5

Step-by-step explanation:

If x = -1

y = -(-1²) + 5

y = 4

If x = 0

y = 0 + 5

y = 5

If x = 1

y = -1² + 5

y = 4

If x = 2

y = -2² + 5

y = 1

If x = 3

y = -3² + 5

y = -4

Hope this helps!

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Answer: It would be 8 tickets to break even.

Step-by-step explanation: 8×6.75=54

Using the given information, the drama club must sell 50 tickets to break even.

From the question we are to determine the number of tickets that must be sold to at least break even

From the given information,

The drama club has $1262.50 from fund raising

and

They estimated that the entire production will cost $1600.00

Thus,

They need to raise $1600.00 - $1262.50 to break even

$1600.00 - $1262.50 = $337.5

Also from the given information,

Each ticket cost $6.75

Therefore,

The must sell $337.5/$6.75 tickets to break even

$337.5/$6.75 = 50

Hence, the must sell 50 tickets

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The speed of the air current is 22.36 mph(rounded to two decimal places).

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.

Let's assume the speed of the air current as x mph.

When the plane is traveling from Los Angeles to New York, it flies with a tailwind, so its effective speed will be the sum of its cruising speed and the speed of the air current, which is 505 + x mph.

When the plane is traveling from New York to Los Angeles, it flies against the headwind, so its effective speed will be the difference between its cruising speed and the speed of the air current, which is 505 - x mph.

We can use the formula:

time = distance / speed

to set up an equation based on the given information:

2500 / (505 + x) + 2500 / (505 - x) = 10

Multiplying both sides by (505 + x) * (505 - x), we get:

2500(505 - x) + 2500(505 + x) = 10(505 + x)(505 - x)

Simplifying the equation, we get:

Simplifying further, we get:

10x² = 5000

x² = 500

x = 22.36 (rounded to two decimal places)

Therefore, the speed of the air current is 22.36 mph.

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The 11th term in the arithmetic sequence 13, 19, 25, 31 is 73.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed number called the common difference (d) to the preceding term.

To find the 11th term in the arithmetic sequence 13, 19, 25, 31, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where:

an is the nth term

a1 is the first term

n is the number of the term we want to find

d is the common difference

In this sequence, the first term (a1) is 13 and the common difference (d) is 6 (we can see that by subtracting each term from the one before it). So we can plug in the values we know:

a11 = 13 + (11 - 1)6

a11 = 13 + 60

a11 = 73

Therefore, the 11th term in the sequence 13, 19, 25, 31 is 73.

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The probability of getting a head with her lucky coin is 0.46 and the margin of error for Melissa's estimated probability is 0.218.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. The range of probability is 0 to 1, with 0 representing impossibility and 1 denoting certainty.

Let X be the "number of heads" in a n=13 trial.

The observed percentage of fortunate coins with heads is,

X= 6

The estimated probability of Josue ‘flipping a head’ with his lucky coin is,

p = X/n

p = 6/13

p = 0.46

A statistic called the margin of error measures the degree of random sampling error in a survey's findings. It indicates a likelihood that the results of a sample will be quite close to the findings that one would arrive at if the full population had been surveyed. The margin of error is obtained by multiplying the critical value by the standard deviation.

The estimated probability calculated using Josue's margin of error (ME) assuming,

α = 1 - 0.95= 0.05 is,

ME= Zc x [tex]\sqrt{{p^(1-p^)/n[/tex]

Here, p = 0.46, Zc= z(0.05/2)= 1.96

ME = 1.96 x √0.46⨉0.55/20

ME = 1.96 x √0.01238

ME = 0.21808≅ 0.218

The margin of error is 0.218.

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[tex]p = 5a[/tex]

Answer

P=60

Step by step explanation

a= 12

so according to the formula

p=5(12)

p=60

The perimeter of a pentagon with sides that are each 12 inches long is 60 inches.

The perimeter of a form is the space surrounding its edge.

The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline. Depending on the size, the perimeter of several figures can be the same.

We have,

Sides of Pentagon = 12 inches

We know that Pentagon have 5 sides.

So, Perimeter of Pentagon

= 5 x side

= 5 x 12

= 60 inches

Thus, the Perimeter is 60 inches.

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2.38 km is equivalent to 2,380,000 millimeters.

A method for measuring temperature, length, volume, weight, and distance is known as the metric system. It is founded on three fundamental units that allow us to measure almost anything in the universe.

M- meter, used to measure the length

Kg- kilogram, used to measure the mass

S- second, used to measure time

To convert 2.38 km into mm,

We know 1 km = 1000 m

And 1 m = 1000 mm

So, 2.38 km is equivalent to 2,380,000 millimeters. (rounded to the nearest thousandth)

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The probability that a person did not see the ad given that they did not purchase the game is 0.146.

Let A be the event that a person has seen the advertisement, and let B be the event that a person has not purchased the game. We are asked to find the probability P(A' | B), which is the probability that a person did not see the ad given that they did not purchase the game.

We can use Bayes' theorem to calculate this probability:

P(A' | B) = P(B | A') * P(A') / P(B)

Where

We know that 47% of the market has seen the ad, so the probability of not seeing the ad is 1 - 0.47 = 0.53. We also know that 48% of those who see the ad purchase the game, so 52% of those who see the ad do not purchase the game. Finally, we know that 86% of those who have not seen the ad have not purchased the game.

Putting all of this information together, we can calculate:

P(B | A') = 86%

P(A') = 53%

P(B) = P(B | A') * P(A') + P(B | A) * P(A) = 0.52 * 0.47 + 0.14 * 0.53 = 0.3111

Substituting these values into Bayes' theorem, we get:

P(A' | B) = (0.86 * 0.53) / 0.3111 = 0.146 (rounded to three decimal places)

Therefore, the probability that a person did not see the ad given that they did not purchase the game is 0.146.

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Answer:

Step-by-step explanation:

The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side.

What is the bisector about?

A bisector is known to be a kind of straight line that cut or divide an angle or a line segment.

Note that The next step in the construction is Aaron should Use the compass to find the perpendicular bisector for side as it is the right step to take.

The correct answer to this question is letter b.There are only three steps in constructing a circle circumscribed by a triangle. He is done with the first step.  Use the compass to find the perpendicular bisector for side DF. I hope I have helped you.

18/99 simplified is 2/11 by dividing the numerator and denominator by 9.

A mathematical expression can be simplified by replacing it with an equivalent one that is easier (typically shorter), for example. In computer algebra, formulas of algebra are simplified. Boolean equation simplification is also known as logic optimization.

To simplify 18/99

We need to simplify the denominator and numerator by the greatest common factor.

In 18 and 99, 9 is the greatest common factor so, we can divide the numerator and denominator by 9 .

[tex]\frac{18}{99} = \frac{18/9}{99/9} \\\frac{18}{99} = \frac{2}{11}[/tex]

Therefore 18/99 simplified is 2/11

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Answer: 24 meters

Step-by-step explanation:

15/45 = 8/x

15x = 360

x = 24

The length of the bell tower's shadow is 24 meters. This can be answered by the concept of similar triangles.

To determine the length of the bell tower's shadow, we can use the concept of similar triangles. The height of the crane, the length of its shadow, and the height of the bell tower form one set of similar triangles. We can write the proportion:

height of crane / length of crane's shadow = height of bell tower / length of bell tower's shadow

Plugging in the given values, we get:

15 / 8 = 45 / x

Solving for x, we get x = 24.

Therefore, the length of the bell tower's shadow is 24 meters.

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The study is investigating the relationship between the exposure to the suspected drug during pregnancy and the risk

of delivering a malformed infant. This study design is a case-control study design.

The resultant data are: forty mothers have taken the suspected drug during their pregnancies. Of these mothers, 35

have delivered malformed infants. In addition, 10 other infants are born with malfunctions," then the answer would be

as follows:

The type of study design that is described in this scenario is a case-control study design.

A case-control study design is a type of observational study design that compares people with a particular condition

(cases) to people without that condition (controls) to determine whether there is a relationship between the exposure

to a suspected risk factor and the development of the condition.

In this scenario, the cases are the 35 mothers who delivered malformed infants, and the controls are the 5 mothers

who did not deliver malformed infants. The study is investigating the relationship between the exposure to the

suspected drug during pregnancy and the risk of delivering a malformed infant. Therefore, this study design is a case

control study design.

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Jacki's estimates are reasonable because they make the total of the five winning basketball scores equal to 500 points.

The correct answer is D. It is reasonable because all the scores equal 500.

First, we know that the five winning scores totaled 500 points.
Three of the scores (81, 112, and 97) are already recorded in the team log. We can add these three scores together to find out how many points we need to reach 500:

81 + 112 + 97 = 290 points.

To find the remaining points needed, we can subtract the sum of the known scores (290 points) from the total points (500 points):

500 - 290 = 210 points.
Jacki estimated that the other two scores were 100 and 110 points.

We can add these two scores together to check if they equal the remaining points needed (210 points):

100 + 110 = 210 points.

Since Jacki's estimates add up to the remaining points needed (210 points), we can conclude that her estimates are reasonable.

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Number of business owners in the survey planned to provide a holiday gift to their employees this year is 27

We are given that 30% of business owners planned to provide a holiday gift to their employees this year. We can use this percentage to estimate the number of business owners in the sample who planned to provide a gift.

To do this, we can multiply the percentage by the total number of business owners in the sample

30% of 90 business owners = 0.30 x 90 = 27 business owners

Rounding to the nearest whole number, we get:

Approximately 27 business owners planned to provide a holiday gift to their employees this year.

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The given question is incomplete, the complete question is:

Last year 44% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 30% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 90 business owners.

How many business owners in the survey planned to provide a holiday gift to their employees this year? Round your answer to the nearest whole number.

Answer: x = 50, y = 25

Step-by-step explanation:

Use your trigonometric identities. Sin = Opposite over hypotenuse. Sin(60) = [tex]25\sqrt{3}/x[/tex]. Therefore, [tex]25\sqrt{3}/sin(60) = x[/tex]. Sin(60) = 0.866, so your answer is 50.0014667312, or x = 50. Do the same for the other one, just with tan (Opposite over adjacent). Your answer is 25.  

A delivery from a particular year at the hospital is randomly choose. The probability that the baby is a girl is equals to the 0.4897.

We have provide a data of girl and boy born babies in a particular year.

At hospital, total born boy baby = 796

born baby girls in hospital = 764

total babies in hospital = 796 + 764

= 1560

We have to determine the probability that the baby is a girl. Let the event E be the choose baby is girl. Probability is defined as the ratio of favourable outcomes to the possible outcomes of an event .

So, favourable outcomes for event E

= 764

Total possible outcomes = 1560

So, the probability that the baby is a girl, P( E) = 764/1560

= 0.4897

Hence, required probability value is 0.4897.

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The percentage increase in the cost of building the bridge was approximately 57.08%.

Percentage increase is a measure of the amount of increase or growth expressed as a percentage of the original value. It is calculated by subtracting the original value from the new value, then dividing the result by the original value, and finally multiplying the quotient by 100.

To find the percentage increase, we need to calculate the difference between the final cost and the initial cost, and then divide that difference by the initial cost and multiply by 100 to get the percentage increase.

The formula for percentage increase is:

Percentage increase = (New value - Old value) / Old value x 100

Difference = Final cost - Initial cost

Difference = £37.7 million - £24 million

Difference = £13.7 million

Percentage increase = (Difference / Initial cost) x 100

Percentage increase = (13.7 / 24) x 100

Percentage increase = 57.08%

Therefore, the percentage increase in the cost of building the bridge was approximately 57.08%.

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A marketing company is testing eight different page designs for its new catalogue of clothing. The analysis is most appropriate is ANOVA

The best analysis to use to determine whether there is a noticeable difference in sales amounts between the eight various page designs in the marketing company's new clothing catalogue is Analysis of Variance. In this instance, the averages of the sales figures for each of the eight page designs were compared using the statistical technique known as an ANOVA.

If there is a statistically significant difference between the group means, then at least one of the patterns may be linked to a higher degree of revenue than the others. This can be determined using an ANOVA. The marketing firm can use this data to identify the page designs that are most successful at driving purchases and change their catalogue as necessary to maximise income.

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Normal distribution is symmetric distribution so mean, median and mode are the same. The tails are the same length.

The left tail of such a distribution is longer than the right tail in negative type of asymmetric distribution. The “extremities” of a distribution are precisely what their name suggests - the extensions on either side of a distribution. While this term can be applied to a set of data, it is more easily observable when the data is represented graphically, as the extremities become readily apparent.

The extension on the left is referred to as the left-extremity, and likewise, the one on the right is called the right-extremity. It's not essential for a distribution to have both of these; it can have just one on either side.

Upper and Lower Extremities: Although it's more common to denote the extremities as being on the "left" or "right," this can be problematic if you're not examining a graph. In other words, if you're dealing with a set of data, it may not be immediately clear which data should be placed on the left or right of a graph. The alternative names for the right and left extremities, which address this problem, are upper extremity and lower extremity.

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Thus, by the property of side side side congruence of triangle, ΔRST ≅ ΔUTS .

Both triangles are considered congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

Given :

The statements are-

RS ≅ UT              Given

RT ≅ US              Given

St  ≅ TS            Common

ΔRST ≅ ΔUTS   By side side side congruence

Thus, by the property of  side side side congruence of triangle, ΔRST ≅ ΔUTS .

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The required probability of the given exponential distribution with mean of 10 minutes is equal to 0.39 rounded to two decimal places.

The amount of time spent at a bank follows an exponential distribution with a mean of 10 minutes,

The probability density function (PDF) of the time spent at the bank is given by,

f(x) = (1/10)e^(-x/10), where x ≥ 0

The probability of spending less than 5 minutes at the bank,

Evaluate the cumulative distribution function (CDF) of the exponential distribution up to x=5 minutes,

P(X < 5) = [tex]\int_{0}^{5}[/tex] f(x) dx

=[tex]\int_{0}^{5}[/tex](1/10)e^(-x/10) dx

= [-e^(-x/10)][tex]|_{0}^{5}[/tex]

= -e^(-1/2) + 1

≈ 0.393

Therefore, the probability of spending less than 5 minutes at the bank is approximately 0.39, rounded to two decimal places.

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By answering the presented question, we may conclude that So Christian  equation spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry. Let's start by defining some variables to represent the number of words each student spelled correctly:

Let x be the number of words Christian spelled.

x + (3x - 2) + (2x + 1) = 95

6x - 1 = 95

6x = 96

x = 16

So Christian spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

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the equation for K is K(x) = -20x⁵+ 260x³ - 800x.

How to solve the question?

Since K is a degree 5 polynomial with zeros i and 8-i, it also has two other complex zeros that are conjugates of each other, namely -i and 8+i. Thus, we can express K in factored form as:

K(x) = a(x-i)(x+i)(x-(8-i))(x-(8+i))(x-0)

where a is some constant coefficient. Simplifying the above expression, we get:

K(x) = a(x²+ 1)(x² - 16x + 65)x

Now we can use the fact that K(-4) = -49300 to solve for the coefficient a. Plugging in -4 for x, we get:

K(-4) = a((-4)²+ 1)((-4)²- 16(-4) + 65)(-4) = -49300

Simplifying the expression above, we get:

a(17)(129) = -49300

a = -20

Thus, the equation for K(x) is:

K(x) = -20(x² + 1)(x²- 16x + 65)x

Expanding and simplifying the expression above, we get:

K(x) = -20x⁵ + 260x³ - 800x

Therefore, the equation for K is K(x) = -20x⁵+ 260x³ - 800x.

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We need to find the initial horizontal component of the vector that represents the velocity of the ball. Let us represent that initial horizontal component by, [tex]\bold{v_x}[/tex].

Now, since basketball player shoots the ball with an initial velocity, [tex]\bold{v}[/tex], of 17.0 ft./sec at an angle of 34.1 degrees with the horizontal, we can find the initial horizontal component by, [tex]\bold{v_x}[/tex] using the following formula:

[tex]\bold{v_x}=\bold{v}\text{cos}(\theta)=17.0\times\text{cos}(34.1^\circ)\thickapprox14.1[/tex] ft./sec