x^4-5x^3+7x^2-5x+6=0

The approximate probability that "x" will be within 0.5 of population mean is (c) 0.3026.

We use "Central-limit-theorem" to find probability that "x" will be within 0.5 of population mean. According to the central limit theorem, the distribution of sample means approaches a "Normal-Distribution" with mean μ and standard deviation σ/√(n), where μ = population mean, σ = population standard deviation, and n = sample size,

In this case, we have, sample-size of (n) = 49, population mean (μ) = 43, and population "standard-deviation" of (σ) = 9.

So, standard-deviation of sample mean distribution is:

standard deviation = σ/√(n) = 9/√(49) = 1.2857,

To find the probability that x will be within 0.5 of the population mean, we need to standardize the interval using the standard deviation of the sample mean distribution,

z = (x - μ)/(σ/√n) = (43 + 0.5 - 43)/(1.2857) = 0.3892,

The probability that "x" will be within 0.5 of the population mean is the area under the standard normal distribution curve between z = -0.3892 and z = 0.3892.

P(-0.3892 < Z < 0.3892) = P(Z < 0.3892) - P(Z < -0.3892)

= 0.6513 - 0.3487

= 0.3026

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Suppose that a random sample of size 49 is to be selected from a population with mean 43 and standard-deviation 9. What is the approximate probability that "x" will be within 0.5 of the population mean?

(a) 0.5026

(b) 0.6974

(c) 0.3026

(d) 0.6053

Check the picture below.

Answer:

y= 32

Step-by-step explanation:

Answer:

The answer for y is 32

Step-by-step explanation:

-3=-11+√2y

-3+11=√2y

8=√2y

square both sides

8²=√2y²

64=2y

divide both sides by 2

2y/2=64/2

y=32

Answer:

The RN should set up the infusion pump to deliver 125 mL/hour.

To calculate the infusion rate, we can use the following formula:

Infusion rate = Volume / Time

In this case, the volume is 1000 mL and the time is 8 hours. Plugging these values into the formula, we get the following:

Infusion rate = 1000 mL / 8 hours

Infusion rate = 125 mL/hour

Therefore, the RN should set up the infusion pump to deliver 125 mL/hour.

It is important to note that this is just the calculated rate. The actual rate may vary slightly depending on the type of infusion pump and the settings that are used.

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

You could multiply every number but that would take too much time

Instead you have to logic through the problem

Numbers in multiplication follow cyclical sets. i.e. the ones place in the multiples of 3 goes 3,6,9,2,5,8,1,4,7,0,3 forever. (That is why 3 is a "mod 10" number there are 10 possible 1s place values)

The helpful number here is 5

5 is mod 2 because any multiple ends in a 5 or a 0. Given that you are doing all of the odd numbers, five times any odd number will end in a 5, and any odd number ending in 5 times another odd number will also end in 5 so the ones place for all odd numbers multiplied from 1 to 2023 is 5.

When multiplying all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5. This is based on the pattern observed in the last digits of the products of odd numbers.

In mathematics, specifically in number theory, we often make use of patterns to solve problems. When you're asked to find the last digit of the product when you multiply all the odd numbers from 1 to 2023, inclusive, it is helpful to look for a pattern in the last digits of the products of odd numbers.

Let's start small. The first five odd numbers are 1, 3, 5, 7, and 9. The product of these numbers is 945, and the last digit, or unit digit, is 5. Let's add another odd number to the product, 11. The product becomes 10395, and again, the unit's digit is 5. As you can see, the pattern is that no matter how many odd numbers you multiply together, the unit's digit (or the last digit) of the product is always 5.

Therefore, when you multiply all the odd numbers from 1 to 2023, inclusive, the last digit of the product will be 5.

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The length of the tangent x is 11.2 units.

Given is circle with radius 8.4 units and a tangent with x units, we need to find the length of the tangent,

Since we know that the tangents are perpendicular to the circle, so to find the length,

Using Pythagoras theorem,

Hypotenuse is 5.6+8.4 = 14 units,

So,

14² = 8.4² + x²

x = √196 - 70.56

x = 11.2

Hence the length of the tangent x is 11.2 units.

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The tax allowance for a person with two kids and no dependent relative earning 180,000 naira per month before tax is 34,375 naira.

The tax allowance is calculated by first determining the individual's annual income before tax, which in this case is 2,160,000 naira (180,000 x 12 months). Next, the individual's personal allowance of 1,500,000 naira is subtracted from their annual income.

The resulting figure is 660,000 naira, which is then multiplied by 5% to give a tax allowance of 33,000 naira. An additional 375 naira is added to this figure for each child, resulting in a total tax allowance of 34,375 naira for an individual with two kids and no dependent relative earning 180,000 naira per month before tax. This tax allowance reduces the individual's taxable income, thereby reducing the amount of tax they would be required to pay.

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Possible committees contain at least one member of each class is 5235.

Number of freshman = 3

Number of sophomores = 4

Number of juniors = 4

Number of seniors = 5

Total = 3 + 4+ 4 + 5 = 16

Number of committees of five members of the council would contain at least one member of each class is given by = total - Number of possibility without freshmen - Number of possibility without sophomores - Number of possibility without juniors - Number of possibility without seniors

= [tex](\left \116 \atop 5\right. ) - (\left \413 \atop 5\right. ) -(\left \112 \atop 5\right. )-(\left \112 \atop 5\right. )-(\left \111 \atop 5\right. )[/tex]

= 8568 - 1287 - 792 - 792 - 462

= 5235

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Answer:

48%

Step-by-step explanation:

Let x equal the percent

25x = 12

25x/25 = 12/25

x =0.48

0.48 = 48%

The proportion of students that choose nachos is given as follows:

0.3333.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The proportion of students choosing nachos is the probability that a single student choose nachos.

Out of 33 students, 11 choose nachos, hence the proportion is given as follows:

11/33 = 1/3 = 0.3333.

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The probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

What is probability?

Probability is a way to gauge how likely or unlikely something is to happen. It measures the degree of ambiguity surrounding the result of a single event or a series of related occurrences. Typically, probability is stated as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certain or guaranteed event.

To determine the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, we need information about the distribution of baseball weights. Without specific information about the distribution, it is challenging to provide an exact probability.

However, assuming the weights of baseballs follow a normal distribution with a known mean and standard deviation, we can provide a general guideline for calculating the probability using the Central Limit Theorem.

Let's assume the mean weight of a baseball is μ grams, and the standard deviation is σ grams. Since we don't have the exact values, we'll need to make some assumptions. Let's say the mean weight of a baseball is 150 grams, and the standard deviation is 5 grams.

The average weight of the 16 baseballs follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ/[tex]\sqrt[1]{n}[/tex]).

In this case, the mean is 150 grams, and the standard deviation is 5 grams divided by the square root of 16 (since we have 16 baseballs). The square root of 16 is 4.

The standard deviation of the average weight is 5 grams / 4 = 1.25 grams.

Now, we want to calculate the probability that the average weight is more than 147 grams. To do this, we can convert it into a standard normal distribution by subtracting the mean (150 grams) and dividing by the standard deviation (1.25 grams).

The z-score for 147 grams is (147 - 150) / 1.25 = -2.4.

Using a standard normal distribution table or calculator, we can find the probability associated with a z-score of -2.4. Let's assume it is P(Z < -2.4) = 0.0082.

However, since we are interested in the probability that the average weight is more than 147 grams, we need to consider the area to the right of the z-score (-2.4). This is equal to 1 - P(Z < -2.4).

Therefore, the probability that a pack of 16 baseballs would have an average weight of more than 147 grams, given our assumptions, is approximately 1 - 0.0082 = 0.9918, or 99.18%.

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Answer:

=62/63

=[tex]\frac{62}{63}[/tex]

Step-by-step explanation:

Convert everything to a denominator 63

=[tex]=\frac{3*9}{63} +-\frac{2*7}{63} +\frac{7*7}{63}[/tex]

=[tex]\frac{27}{63} +\frac{-14}{63} +\frac{49}{63}\\[/tex]

Add up the numerators

= [tex]\frac{62}{63}[/tex]

The distance between two opposite corners of the intersection is, 15 meters.

We have to given that;

Hillsdale Street and Salem Avenue intersect.

And,  Hillsdale Street is 12 meters wide and Salem Avenue is 9 meters wide,

Since, WE know that;

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Now, Let us assume that,  distance between two opposite corners of the intersection is, x

Hence, We can formulate for the given condition,

⇒ Hypotenuse² = Base² + Opposite²

⇒ x² = 12² + 9²

⇒ x² = 144 + 81

⇒ x² = 225

Taking square root on both side,

⇒ x = √225

⇒ x = 15

Therefore, We get;

The distance of two opposite corners of the intersection is,

⇒ 15 meters.

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After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.

First, find the value of the investment when it is compounded periodically, 12 times a year.

The formula is:

= Amount invested x ( 1 + rate ) ^ number of periods

= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰

= $ 53, 678. 16

If compounded annually, the value would be :

= 9, 000 x ( 1 + 9 % ) ²⁰

= $ 50, 439. 69

The difference is :

= 53, 678. 16 - 50, 439. 69

= $ 3, 238. 47

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Answer:

Here are the correct answers:

B. gram

C. milligram

Based on the results of the 40 trials, the estimated probability of randomly choosing a red cube from the bag is 2/5 in its simplified form.

     To arrive at this answer, we can use the formula for probability: Probability of an event = Number of favorable outcomes / Total number of outcomes. In this case, the favorable outcome is selecting a red cube, and the total number of outcomes is 40 (since a cube is selected and put back in the bag before each trial). We know that a red cube was selected 16 times out of 40 trials, so the number of favorable outcomes is 16. Thus, the probability of selecting a red cube is 16/40, which simplifies to 2/5. Therefore, based on the results of the 40 trials, the estimated probability of randomly choosing a red cube from the bag is 2/5.

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Answer: Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).

Step-by-step explanation:

Let's first find the coordinates of the midpoint of AC, which will be the coordinates of point B if AB:BC is 1:2.

The x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of C) / 2 = (-5 + 4) / 2 = -0.5

The y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of C) / 2 = (4 - 5) / 2 = -0.5

So the midpoint of AC is B(-0.5, -0.5).

Now we can find the coordinates of A by using the midpoint formula:

The x-coordinate of A = (2 * x-coordinate of B + x-coordinate of C) / 3 = (2 * (-0.5) + 4) / 3 = 1.17

The y-coordinate of A = (2 * y-coordinate of B + y-coordinate of C) / 3 = (2 * (-0.5) - 5) / 3 = -2.17

So the coordinates of point A are (1.17, -2.17).

Therefore, the coordinates of point B that partitions the segment AC such that AB:BC is 1:2 are (1.17, -2.17).

Answer:

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

The angle formed by two secants is half the difference of the intercepted arc measures:

Substitute values and solve for x:

We need to look at the coefficients of the x and y terms in the equation. The lengths of the transverse and conjugate axes are 10 and 14, respectively.

The standard form of the equation for a hyperbola with a horizontal transverse axis is (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) is the center of the hyperbola. In this case, the equation given is already in standard form with (h,k) = (0,0).

Comparing the given equation to the standard form, we see that a^2 = 25 and b^2 = 49. Therefore, a = 5 and b = 7.

The transverse axis is the longer axis and is parallel to the x-axis, so its length is 2a = 10. The conjugate axis is the shorter axis and is perpendicular to the transverse axis, so its length is 2b = 14.

Therefore, the lengths of the transverse and conjugate axes are 10 and 14, respectively.

The equation of the hyperbola you provided is x^2/25 - y^2/49 = 1. In this equation, we can identify the terms a^2 and b^2:

a^2 = 25
b^2 = 49

To find the lengths of the transverse and conjugate axes, we need to first find the values of a and b:

a = √25 = 5
b = √49 = 7

The length of the transverse axis is 2a, and the length of the conjugate axis is 2b. Therefore:

Length of transverse axis = 2a = 2(5) = 10
Length of conjugate axis = 2b = 2(7) = 14

So, the lengths of the transverse and conjugate axes are 10 and 14, respectively.

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The area of the carpet is 108 sq. ft.

To find the area of the carpet, we first need to multiply the length and width of the carpet. Therefore, 9 ft. x 12 ft. = 108 sq. ft.

The Smiths need to buy a 108 sq. ft. carpet to center it in their 15 ft. by 20 ft. room.

The area of the carpet is 108 sq. ft.


To find the area of the carpet, you need to multiply its length by its width. In this case, the dimensions of the carpet are 9 ft. by 12 ft.

Area = length × width
Area = 9 ft × 12 ft


The area of the 9 ft. by 12 ft. carpet that the Smiths want to buy and center in their 15 ft. by 20 ft. room is 108 sq. ft.

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Answer:

Variance is a measure of variability which describes the average degree of spread in the data about the mean.

Step-by-step explanation:

The value of x and y are 10 and 10√3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Here the hypotenuse is 20 and the opposite to angle 30 is x and the adjacent is y

Therefore;

sin30 = x/20

1/2 = x/20

2x = 20

x = 20/2 = 10

cos 30 = y/20

√3/2 = y/20

2y = 20√3

y = 20√3/2

y = 10√3

therefore the value of x and y are 10 and 10√3

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Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

<95141404393>

The 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

To calculate the 95.44% confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's determine the critical value. Since the confidence level is 95.44%, we need to find the z-score that corresponds to a tail probability of (1 - 0.9544)/2 = 0.0228. Looking up this value in the standard normal distribution table or using a statistical calculator, we find that the z-score is approximately 2.17.

Next, we need to determine the standard deviation of the population. Since we don't have that information, we'll use the sample standard deviation as an estimate. Let's assume the sample standard deviation is 5 minutes.

Now we can calculate the confidence interval:

Confidence Interval = 22.3 ± (2.17) * (5 / sqrt(20))

Calculating the expression inside the parentheses:

= 22.3 ± (2.17) * (5 / sqrt(20))

= 22.3 ± 2.17 * (5 / 4.472)

= 22.3 ± 2.17 * 1.118

Calculating the confidence interval:

Lower Limit = 22.3 - (2.17 * 1.118)

Upper Limit = 22.3 + (2.17 * 1.118)

Lower Limit = 22.3 - 2.42706 ≈ 19.87294

Upper Limit = 22.3 + 2.42706 ≈ 24.72706

Therefore, the 95.44% confidence interval for the population mean is approximately (19.87 minutes, 24.73 minutes).

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The equation of the parabola that opens up or down, with a vertex at (0, 5) and passing through (-6, 4), is y = (-1/36)x^2 + 5

To find the equation of a parabola that opens up or down given the vertex and a point, we can use the standard form of the equation:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola. In this case, the vertex is (0, 5), so we have h = 0 and k = 5.

Now, we can substitute the given point (-6, 4) into the equation to determine the value of a:

4 = a(-6 - 0)^2 + 5

4 = 36a + 5

36a = -1

a = -1/36

Substituting the value of a back into the equation, we have:

y = (-1/36)(x - 0)^2 + 5

y = (-1/36)x^2 + 5

Therefore, the equation of the parabola that opens up or down, with a vertex at (0, 5) and passing through (-6, 4), is y = (-1/36)x^2 + 5.

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Answer:

4 days

Step-by-step explanation:

first, figure out how many cars are produced in a day. since there are 7 days in a week, and 1400 cars are produced in a week, divide 1400 by 7. 1400/7 equals 200. so, if 200 cars produced each day, then:

200x= 800 (x = days)

200x/200 = 800/200

So, 4 days.

The volume of the cylinder is 29.78 inches cube.

The volume of the cone is  9.93 inches cube.

The figure above is a sphere, cylinder and a cone. The volume of the figure can be represented as follows:

volume of a sphere = 4 / 3πr³

where

20 = 4 / 3 × π × r³

cross multiply

4r³π = 60

r³π = 15

r = ∛15 / π

r = ∛4.78

r = 1.68 inches

volume of a cylinder = πr²h

where

volume of a cone = 1 / 3 πr²h

where

Therefore, let's find the volume of the cylinder and cone with the following information.

Hence,

volume of the cylinder = π × (r)² × 2r

volume of the cylinder = 2(1.68)³π

volume of the cylinder = 29.78 inches cube

Therefore,

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × 3.14 × r² × 2r

volume of the cone = 1 / 3 × 3.14 × 2(1.68)³

volume of the cone = 29.77744896 / 3

volume of the cone = 9.93 inches cube

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Answer: 50 1/3

Step-by-step explanation: (30 X 5 +4) divided by 3 = 50 1/3