Use synthetic division to find the result when 4x^4-7x^3+7x^2-12x+15 is divided by x-1. If there is a remainder, express the result in the form q(x)+r(x)/b(x)

a) The sampling distribution of p can be approximated as a normal distribution with mean μp = .17 and standard deviation σp = .0203.

b) The probability that the sample proportion will be within ±.02 of the population proportion is 0.6778

In statistics, sampling distribution plays a crucial role in estimating the parameters of a population. The sampling distribution helps us to understand the probability distribution of sample statistics that we obtain by taking random samples from a population.

a) In this case, we are interested in the proportion of households that spend more than $100 per week on groceries, denoted by p. We know that the population proportion is p = .17, and a sample of 800 households will be selected from the population.

The central limit theorem states that if the sample size is large enough (in this case, n = 800), then the sampling distribution of p will be approximately normal with a mean of p and a standard deviation of:

σp = √(p(1-p)/n)

where p is the population proportion, and n is the sample size. Plugging in the values, we get:

σp = √(.17(1-.17)/800) = .0203

b) Now, we want to find the probability that the sample proportion will be within ±.02 of the population proportion. That is, we want to find P(.15 ≤ p ≤ .19).

To calculate this probability, we need to standardize the distribution using the z-score formula:

z = (p - μp) / σp

Plugging in the values, we get:

z = (.15 - .17) / .0203 = -0.9867

z = (.19 - .17) / .0203 = 0.9867

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(z ≤ -0.9867) = 0.1611

P(z ≤ 0.9867) = 0.8389

Therefore, the probability that the sample proportion will be within ±.02 of the population proportion is:

P(.15 ≤ p ≤ .19) = P(z ≤ 0.9867) - P(z ≤ -0.9867) = 0.8389 - 0.1611 = 0.6778

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Complete Question:

The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population.

a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.

b. What is the probability that the sample proportion will be within ±.02 of the population proportion?

Answer: 167.55 cm.

Step-by-step explanation:

Cone volume formula is V=1/3hπr².

Substitute...

V= 1/3 (10) (π) (4)^2

V= 53 1/3 π

V= 167.55 cm

Hope this helps!

MM

Answer:

35 m

Step-by-step explanation:

I will assume the goal is not to waste any wood.  We need to find a common length that will allow each piece of wood to be divided into whole pieces with nothing left over.  The shortest plank is 70 m, but that length will cause a loss of 35 m on the 105m plank, and also 35m on the 175m plank after two 70m sections have been cut off (175 - 140 = 35).

Looking at the actual lengths, one might spot that they are all evenly divisible by 35.  See the table below.  The numbers under "35" are the result of the length divided by 35.  They are all whole numbers.  We can cut each plank into 35m sections and have none left over.

Length (m) 35 (factor)

  70                  2 planks

  105          3 planks

  175          5 planks

This will result in 10 35m planks.  

No need to plank me.

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.

In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ

where, μ--> population mean,

σ --> population standard deviation and

x --> the raw-score.

Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.

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The length of the third side of the triangle will be 2 feet. Then the correct option is F.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Any two parts of a triangle can be added together to have a length larger than the third side.

A triangle has two side lengths of 3 feet. Let 'x' be the third side.

By the theorem, the inequality is given as,

x < 3

The length of the third side of the triangle will be 2 feet. Then the correct option is F.

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Answer:

 No

Step-by-step explanation:

You want to know if the set of even integers has the density property.

The density property states that for any two elements of a set, there are additional elements of the set between them.

There are no even integers between any two consecutive even integers, so the set of even integers does not have the density property.

The required probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The total number of ways to choose any 2 students from a group of 12 is given by the combination formula:

C(12,2) = 12! / (2! * 10!) = 66

This means there are 66 total ways for Mr. Mackinson to choose any 2 students from the class.

To calculate the probability of choosing 2 girls, we need to count the number of ways to choose 2 girls from the group of 6 girls. We can use the combination formula again:

C(6,2) = 6! / (2! * 4!) = 15

This means there are 15 ways for Mr. Mackinson to choose any 2 girls from the class.

So the probability of Mr. Mackinson choosing 2 girls is:

P(2 girls) = number of ways to choose 2 girls / total number of ways to choose 2 students

= C(6,2) / C(12,2)

= 15 / 66

= 0.2273

Therefore, the probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

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Answer:

The value of x is 12.

Greetings!!!

Firstly, recall the Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'. The hypotenuse is the longest side and it's always opposite the right angle. In this triangle a² = b²+ c² and angle is a right angle.

a, b, and c represent the lengths of sides of a triangle, then: a2+b2=c2 if and only if the triangle is a right triangle.

Thus, on this question

the hypotenuse is a= 20

the value of b= 16

so the required value is c

[tex]a {}^{2} = b {}^{2} + c {}^{2} [/tex]

substitute known variables into the equation

[tex](20 ){}^{2} = (16) {}^{2} +( c) {}^{2} [/tex]

evaluate both sides

[tex]400 = 256 +( c) {}^{2} [/tex]

minus 256 from both sides

[tex]400 - 256 = (c) {}^{2} [/tex]

[tex]144 = (c) \frac{2}{} [/tex]

write bothe sides under radical in order to erase the square

[tex] \sqrt{144} = \sqrt{c {}^{2} } [/tex]

solve for c

[tex]c = 12[/tex]

Hope it helps

Answer:

x = 12

Step-by-step explanation:

Pythagoras Theorem

= Hypotenuse² = adjacent² + opposite²

From the question

Hypotenuse = 20

Adjacent = x

Opposite = 16.

The value for x

= 20² = x² + 16²

= 400 = x² + 256

= 400-256 = x²

= 144 = x²

[tex] \sqrt{144} = { \sqrt{x} }^{2} \\ \sqrt{144} = x \\ 12 = x[/tex]

Therefore adjacent (X) = 12

Answer:

Step-by-step explanation:

chicken

The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.

Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.

Let's call the height of AB "x". We can use the tangent function to solve for x:

tan(55) = x/20

Multiplying both sides by 20:

x = 20 tan(55)

Using a calculator, we get:

x ≈ 27.8 feet

Therefore,

The height of the portion AB of the lamppost is approximately 27.8 feet.

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Answer: 20 tan 55

Step-by-step explanation:

took test and got it right

4.1. The boys' masses range from a minimum of 32 kg to a maximum of 82 kg.

4.2. The girls' masses range from a minimum of 35 kg to a maximum of 67 kg.

5: To create the frequency table, we need to tally the number of male and female learners in each mass interval. Here are the tallies:

Mass interval Tally

40 - 49,9 kg |||| (4 females)

50 - 59,9 kg ||||||| (7 females)

60 - 69,9 kg ||||| (5 females)

70-79,9 kg || (2 males)

80 - 89,9 kg || (2 males)

Note: The vertical lines represent the tallies, with each line representing one learner.

6: By looking at the frequency table, we can compare the number of male and female learners in each mass interval. We can see that there are more female learners in the lower mass intervals (40-49.9 kg, 50-59.9 kg, and 60-69.9 kg) compared to male learners. On the other hand, there are more male learners in the higher mass intervals (70-79.9 kg and 80-89.9 kg) compared to female learners

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The temperature inside the building when the heat was turned on at 6 am was approximately 57.4 F

To solve this problem, we can use the formula for heat transfer:

Q = mcΔT

where Q is the amount of heat transferred, m is the mass of the air, c is the specific heat of air, and ΔT is the change in temperature.

First, we can calculate the amount of heat lost from the building between 10 pm and 2 am. Assuming the building is a closed system, the amount of heat lost must be equal to the amount of heat gained by the outside environment. We can assume that the mass of air in the building remains constant, and use the specific heat of air at constant volume, which is approximately 0.718 J/g·K.

Q = mcΔT = (m)(0.718)(65-70) = -3.59m

Next, we can calculate the amount of heat gained by the building between 2 am and 6 am. Again, assuming the building is a closed system, the amount of heat gained must be equal to the amount of heat lost by the outside environment. We can assume that the mass of air in the building remains constant, and use the same specific heat of air at constant volume.

Q = mcΔT = (m)(0.718)(T-65)

where T is the temperature inside the building at 6 am. We can set this equal to the heat lost by the outside environment:

Q = -3.59m

Using the average temperature of 45 f for the outside environment, we can calculate the change in temperature between 10 pm and 6 am:

ΔT = (45-70) = -25

So the amount of heat lost by the outside environment is:

Q = mcΔT = (m)(0.718)(-25) = -17.95m

Setting this equal to the heat gained by the building:

(m)(0.718)(T-65) = -17.95m

Simplifying and solving for T, we get:

T = 57.4 F

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If p and q vary inversely and p = 14 when a = 4, then the work is  q = 8, p = 7.

What is inverse proportionality?

Inverse proportionality occurs when x increases and y decreases, and when x decreases and y increases.

If p and q vary inversely, this means that their product is constant:

p * q = k

where k is a constant. We can use this relationship to solve the problem.

We are given that when a = 4, p = 14. This means that:

p * a = k

14 * 4 = k

56 = k

So we know that the product of p and a is 56.

To find p when q = 8, we can use the fact that p and q vary inversely. This means that:

p * q = k

We know that k = 56, so we can substitute:

p * q = 56

We are given that q = 8, so we can substitute this as well:

p * 8 = 56

Solving for p, we get:

p = 56 / 8 = 7

Therefore, when q = 8, p = 7.

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The correct statement regarding the probabilities is given as follows:

c. The experimental probability is 4% higher than the theoretical probability.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the theoretical probability, we have that the coin is equally as likely to fall heads or tails, hence:

p = 1/2

p = 0.5 = 50%.

For the experimental probability, we have that on 100 trials, 54 resulted in heads, hence:

p = 54/100

p = 0.54 = 54%.

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By using shipping volume, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift.

To solve this problem, we need to work backwards from the shipping volume and use the given processing rates to determine the required processing volumes for each stage of the process.

First, we can calculate the total number of hours of packing and shipping required to process 168,000 units:

168,000 units ÷ 175 units per person per hour = 960 hours

Next, we can determine the volume of items that need to be packed by Group B in order to ship this total volume. Since Group B processes 65% of the volume, we can set up the following equation:

0.65x = 168,000 units

where x is the total volume of items processed by all packing groups. Solving for x, we get:

x = 168,000 units ÷ 0.65 = 258,461.54 units

So the total volume of items processed by all packing groups is approximately 258,461.54 units. We can now use the given processing rates to determine the required processing volumes for each stage:

Picking: 100% of 258,461.54 units = 258,461.54 units

Packing Group A: 35% of 258,461.54 units = 90,461.54 units

Packing Group B: 65% of 258,461.54 units = 168,000 units

Therefore, Packing Group B needs to process 168,000 units in order to ship a total of 168,000 units for the shift. The answer is 168,000.

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____The given question is incorrect, the correct question is given below:

Team % of Volume Items processed per person per hour Picking 100% 150 Packing Group A 35% 105 Packing Group B 65% 70 Shipping 100% 175 How many items will be processed by Packing Group B in order to ship a total of 168,000 units for the shift?

46,  

70,  

84,000,  

109,200,  

168,000

The probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours is 0.835.

In the question Justin has a bird feeder which gets visited by an average of 18 birds every 2 hours during daylight hours and we have to find what is the probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours.

This can be calculated using the Poisson distribution formula, P(X > 5) = 1 - P(X ≤ 5).

P(X > 5) = 1 - P(X ≤ 5)

= 1 - (P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5))

= 1 - (0.0022 + 0.0133 + 0.0514 + 0.1245 + 0.2141 + 0.2769)

= 0.8351

Therefore, the probability that the bird feeder will be visited by more than 5 birds in a 40 minute period during daylight hours is 0.835.

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Answer:

Helena can paint approximately 32 of these cylinders complete

Step-by-step explanation:

The surface area of a cylinder can be found using the formula:

Surface Area = 2πr(r + h), where r is the radius and h is the height (or length) of the cylinder.

For a cylinder with a radius of 5 cm and a length of 3 cm, the surface area is:

Surface Area = 2π x 5 x (5 + 3) = 2π x 5 x 8 = 80π cm²

So, the surface area of one cylinder is 80π cm². To find the number of cylinders that Helena can paint, we can divide her total paint coverage by the surface area of one cylinder:

2500 cm² ÷ 80π cm² = 31.83 (approximately 32 cylinders).

So, Helena can paint approximately 32 of these cylinders completel

Answer:

  (b)  area = 29 units²

Step-by-step explanation:

You want the area of the irregular shape shown in the figure.

The area of a rectangular shape is the product of its length and width:

  A = LW

The given shape can be considered to be a 6 unit square with some pieces removed. The area of the remaining shape is the area of that square less the areas of the removed pieces.

The piece removed from the upper left corner is a 2-unit square. Its area is ...

  A = (2 units)(2 units) = 4 units²

The piece removed from the lower right side is 3 units by 1 unit, so its area is ...

  A = (3 units)(1 units) = 3 units²

The area of the square before those pieces were removed was ...

  A = (6 units)(6 units) = 36 units²

Then the area of the remaining shape after the pieces are removed is ...

  Area = 36 units² -4 units² -3 units² = (36 -7) units² = 29 units²

The area of the figure is 29 units².

__

Additional comment

Quite often, the area of an irregular shape is more easily found by subtracting missing areas than by dividing up the existing shape into pieces whose area formulas you know.

The second attachment shows division of the area into smaller rectangles. Working clockwise from upper left, their areas are 1×2, 3×4, 3×1, 3×4, for a total of 2+12+3+12 = 29 square units.

Answer:

it's simple 4 that is 100% the correct answer

120% is equivalent to the fraction 11/5.

Fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin.  

If 1/5 = 20%, then we can convert 120% to a fraction by first dividing by 100 to get the decimal equivalent, and then adding 1 to get the fractional equivalent:

120% = 120/100 = 1.2

1.2 + 1 = 2.2

Therefore, 120% is equivalent to the fraction 11/5.

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Answer:

A - Decrease a number by 30% is the same as multiplying by 70%.

Step-by-step explanation:

This statement is incorrect. Decreasing a number by 30% means that the number will be reduced by 30% of its original value. For example, if the original number is 100, decreasing it by 30% would give you 100 - 30% * 100 = 100 - 30 = 70. On the other hand, multiplying a number by 70% would increase it by 70% of its original value, which is a different operation.

C - Decrease a number by 0.30 is the same as multiplying by 0.70.

This statement is also incorrect. Decreasing a number by 0.30 means subtracting 0.30 from the original number, while multiplying by 0.70 means multiplying the original number by 0.70. These are two different operations that will result in different results.

The number of days until recovery is noted for each patient is option d) Experimental group the half in yellow rooms

Health psychologists are interested in understanding the factors that can impact a patient's recovery time following a surgical procedure. One hypothesis that they may want to test is whether the color of the hospital room can influence recovery time.

In experimental research, we often manipulate one variable to see if it has an effect on another variable. The variable that is being manipulated is called the independent variable, while the variable that is being measured is called the dependent variable. In this case, the independent variable is the color of the hospital room, and the dependent variable is the length of recovery time.

To test the hypothesis that yellow hospital rooms will shorten recovery time, the researchers randomly assign half of the patients to yellow rooms and the other half to white rooms. By randomly assigning the patients to the different conditions, the researchers can be sure that any differences in recovery time between the two groups are not due to pre-existing differences between the patients.

In order to make sure that the color of the room is the only thing that is different between the two groups, the researchers use a control group. The control group is the group of patients who are placed in white rooms. By comparing the recovery time of the patients in the yellow room group to the recovery time of the patients in the white room group, the researchers can determine whether the color of the room had an effect on recovery time.

Finally, the group of patients who are placed in the yellow rooms is called the experimental group. This is because they are the group that is being exposed to the independent variable (the yellow color of the room). By comparing the recovery time of the experimental group to the recovery time of the control group, the researchers can determine whether the yellow color of the room had an effect on recovery time.

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Complete Question:

A health psychologist wants to test the hypothesis that yellow hospital rooms will shorten the recovery time for surgical patients when compared to recovery times of patients in standard white hospital rooms. Half of the patients are randomly assigned to yellow rooms, the other half to white rooms. The number of days until recovery is noted for each patient.

1a) Independent variable color of the walls

1b) Dependent variable the length of recovery time

1c) Control group the half in white rooms

1d) Experimental group the half in yellow rooms

For the given system of equations, the answers are of the given choices (A), (B) and (D).

A group of two or more equations with shared variables is referred to as a system of linear equations. Finding the value of the unknown variables employed in the equations that must satisfy both equations is necessary to solve a system of equations.

Given equations are -

y - 10 = 2x ⇒ y = 2x + 10

1/2y = x + 5 ⇒ y = 2x + 10

We can observe from the equation, that both the lines are same,

So any pair of values (x, y) that satisfy the equation y = 2x + 10 is a solution to the system. For example:

(0, 10) is a solution, since y = 2(0) + 10 = 10 and (1/2).10 = 0 + 5 =

(1, 12) is a solution, since y = 2(1) + 10 = 12 and (1/2).12 = 6 = 1 + 5

(2, -6) is a not solution, since y = 2(2) + 10 = 14 and (1/2)(-6) = 7 = 2 + 5

(-5, 0) is a solution, since y = 2(-5) + 10 = 0 and (1/2)(0) = 0

Therefore, the answer is of the given choices are (A), (B), (D).

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Answer:

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

Given function:

This is the vertex form and the standard form is:

Convert the given equation into standard form:

Answer:

The standard form of the given quadratic function is:

[tex]g(x)=-2x^2+20x-33[/tex]

Step-by-step explanation:

The standard form of a quadratic function is f(x) = ax² + bx + c.

To write the given function in standard form, expand the brackets:

[tex]\implies g(x)=-2(x-5)(x-5)+17[/tex]

[tex]\implies g(x)=-2(x^2-10x+25)+17[/tex]

Apply the distributive law:  m(a + b + c) = ma + mb + mc

[tex]\implies g(x)=-2x^2+20x-50+17[/tex]

Add the numbers:  -50 + 17 = -33

[tex]\implies g(x)=-2x^2+20x-33[/tex]

The possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as: b ≤ 4.5

Let's denote the height of Natasha as "n" and the height of her little brother as "b".

We know that Natasha is one foot taller than her little brother, so we can write:

n = b + 1

We also know that Natasha's height is no more than 5-1/2 feet, so we can write:

n ≤ 5.5

Now we can substitute the first equation into the second equation and get:

b + 1 ≤ 5.5

Simplifying this inequality, we get:

b ≤ 4.5

Therefore, the possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as:

b ≤ 4.5

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The line plot is attached based on the information given.

A line plot is a graph that shows data as dots or checkmarks above a number line to indicate how frequently each value occurs. Only numerical, discrete data, not continuous data, is shown using line graphs. Line plots categorize the data by showing how often each value appears on a number line. Small data sets make these graphs easy to make, and the revealed frequency patterns allow for interpretation.

Each mark on the line plot represents one of the distances Tomas rode. The number on the horizontal axis represents the day of the week and the vertical axis represents the distance in miles. The line plot shows that on most days, Tomas rode between 3 and 5 1/2 miles.

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The length of CF is given as 45 cm

Since AE is the altitude of the parallelogram ABCD, it is perpendicular to the base DC. Similarly, CF is the altitude of the triangle ACD, and it is perpendicular to the base AD.

Let's use the properties of parallelograms and triangles to solve for the area and length of CF.

Since ABCD is a parallelogram, we know that opposite sides are parallel and equal in length. Therefore, BC = AD = 6 cm.

To find the area of the parallelogram, we can use the formula:

ar(ABCD) = base × height

We can choose any base and height, as long as they form a right angle. Since we know AE is the altitude of the parallelogram, we can use it as the height. Let's choose base AB, which is perpendicular to AE. Therefore,

ar(ABCD) = AB × AE = 12 cm × 7.5 cm = 90 cm²

So, the area of the parallelogram ABCD is 90 cm².

Now, let's find the length of CF. Since CF is the altitude of the triangle ACD, we can use the formula for the area of a triangle:

ar(ACD) = 1/2 × base × height

where the base is AD and the height is CF. We know the area of the triangle ACD is half the area of the parallelogram ABCD, which is 90/2 = 45 cm². Therefore,

45 cm² = 1/2 × 6 cm × CF

Simplifying this equation, we get:

CF = (45 cm² × 2) / (6 cm) = 15 cm

So, the length of CF is 15 cm.

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