A jar contains marbles that are green, red or blue,
1/6 of the marbles are red
1/3 of the marbles are blue
Given that there are 18 green marbles in the jar,
work out how many are blue,

The simplified form of the polynomial (4x² - 3x + 10) + (-9x² + 4x - 6) is -5x² + x + 4.

The constant term is the term without a variable, in this case, 4 is the constant term.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients

To simplify the polynomial, we need to combine like terms. We have:

(4x² - 3x + 10) + (-9x² + 4x - 6)

= 4x² - 3x + 10 - 9x² + 4x - 6 (distributing the negative sign)

= (4x² - 9x²) + (-3x + 4x) + (10 - 6) (grouping like terms)

= -5x² + x + 4 (combining like terms)

Therefore, the simplified form of the polynomial (4x² - 3x + 10) + (-9x² + 4x - 6) is -5x² + x + 4.

In the polynomial -5x² + x + 4, the degree is 2, the leading coefficient is -5, and the constant term is 4.

The degree of a polynomial is the highest power of the variable in the polynomial, in this case, x² has the highest power of 2.

The leading coefficient is the coefficient of the term with the highest power of the variable, in this case, -5 is the coefficient of the x² term, so it is the leading coefficient.

The constant term is the term without a variable, in this case, 4 is the constant term.

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Answer:

4.5 billion years

Step-by-step explanation:

Answer:  We can use the formula for radioactive decay:

N = N0 * (1/2)^(t/T)

where N is the current amount of the radioactive substance, N0 is the original amount, t is the time that has passed, T is the half-life.

Let's assume that the original amount of the substance in the rock was 8 units. If the current amount is 1 unit, then:

1 = 8 * (1/2)^(t/1.5 billion)

Taking the natural logarithm of both sides, we get:

ln(1) = ln(8) - (t/1.5 billion)*ln(2)

Simplifying:

0 = ln(8) - (t/1.5 billion)*ln(2)

t/1.5 billion = ln(8)/ln(2)

t = 1.5 billion * (ln(8)/ln(2))

t ≈ 3.91 billion years

Therefore, the moon rock is about 3.91 billion years old.

Step-by-step explanation:

The area of the figure is 197 square miles

To find the area of the figure, we need to first identify the shape of the figure. From the given dimensions, it appears to be an irregular quadrilateral with a triangle on top.

We can divide the figure into two parts: a rectangle with dimensions 17 mi by 10 mi, and a triangle with base 18 mi and height 3 mi.

The area of the rectangle is:

Area of rectangle = length x width = 17 mi x 10 mi = 170 mi^2

The area of the triangle is:

Area of triangle = (base x height) / 2 = (18 mi x 3 mi) / 2 = 27 mi^2

Therefore, the total area of the figure is the sum of the areas of the rectangle and triangle:

Total area = 170 mi^2 + 27 mi^2 = 197 mi^2

So the area of the figure is 197 square miles.

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Answer: To solve this problem, we need to use the central limit theorem to find the distribution of the sample means. The central limit theorem states that if we take random samples of size n from a population with a mean μ and a standard deviation σ, the distribution of the sample means approaches a normal distribution with a mean of μ and a standard deviation of σ/√n, as n gets larger.

In this case, we have a population of healthy humans with a mean temperature of μ = 98.6 degrees and a standard deviation of σ = 0.8 degrees. We want to find the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher. The sample size is large enough to use the normal distribution to approximate the distribution of the sample means.

The z-score corresponding to a sample mean of 98.25 degrees is:

z = (98.25 - 98.6) / (0.8 / sqrt(130)) = -1.91

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -1.91:

P(Z > -1.91) = 0.9719

Therefore, the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher is approximately 0.9719 or 97.19%.

Step-by-step explanation:

The measure of angle JCA is 57°

When two lines intersect, the opposite (X) angles are equal. This means ;

123° = JCY

and JCA = YCK ( verically opposite angles)

The sum of angle at a point is 360. This means the addition of all the angles above is 360°.

Representing angle JCA by x , therefore,

x+x +123+123 = 360°( angle at a point)

2x + 246 = 360

2x = 360-246

2x = 114

divide both sides by 2

x = 114/2

x = 57°

therefore the measure of angle JCA is 57°

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a.

the value of s that yields the coordinate (2, 0) is 2.

b.

the value of s that yields the coordinate (9, 1) is estimated 9.055.

we  use the distance formula between the origin and point P on the path:

d(P) = √ (x^2 + y^2) = s

For the coordinate (2, 0), we have x = 2 and y = 0. So, we can plug these values into the distance formula and solve for s:

d(P) = √(x^2 + y^2)

= √t(2^2 + 0^2) = 2

For the coordinate (9, 1), we have x = 9 and y = 1. So, we can plug these values into the distance formula and solve for s:

d(P) = √t(x^2 + y^2)

= √t(9^2 + 1^2)

= √(82)

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Answer: 48 and 32

Step-by-step explanation:

Answer:

Θ ≈ 28.07°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{17}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{8}{17}[/tex] ) ≈ 28.07° ( to the nearest hundredth )

The interval between doses should be approximately 10.4 hours to maintain a minimum concentration of 30% of the initial concentration in the body.

The interval between doses of a drug depends on its half-life and the desired minimum concentration in the body. The half-life of a drug is the time it takes for half of the initial dose to be eliminated from the body.

To determine the interval between doses, we can use the following formula

t = (t1/2 × ln(Cmin/Cmax)) / ln(2)

Where:

t1/2 is the half-life of the drug

Cmin is the desired minimum concentration in the body (expressed as a fraction of the initial concentration)

Cmax is the initial concentration of the drug

ln represents the natural logarithm function.

Substituting the given values, we get

t = (6.0h × ln(0.3)) / ln(2)

t ≈ 10.4h

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The given question is incomplete, the complete question is:

A certain drug has a half-life in the body of 6.0h. What should the interval between doses be, if the concentration of drug in the body should not fall below 30.% of its initial concentration?

Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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In the long run, new technology can have a significant impact on the long-run average total cost (LRATC) of a company.

The LRATC curve represents the lowest possible average cost at which a company can produce a particular level of output in the long run. New technology can reduce the costs of production by improving efficiency, reducing waste, and increasing productivity, leading to lower LRATC. This can lead to a shift in the LRATC curve downward, indicating that the company can now produce the same output at a lower cost than before. This can make the company more competitive and increase its profitability.

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The Central Limit Theorem is an important tool that provides the information you will need to use sample means to make inferences about a population mean.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that if we take repeated random samples of size n from any population with a finite mean and variance, then the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

This means that if we take a large enough sample size from a population, the distribution of the sample means will be approximately normal, even if the population distribution is not normal. This is important because the normal distribution is well understood and has many useful properties that make it easier to work with in statistical analyses.

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Answer:

x=27

Step-by-step explanation:

x-11=16

add 11 to both sides

x=27

The given statement "You can measure the amount of overlap of 2 data sets by comparing the distance between the medians of the IQR" is False. Because the distance between the medians can give some indication of how much overlap there is between two data sets, it is not the only factor to consider other factors are means or standard deviation.

The median is a measure of central tendency that divides the data into two halves. The interquartile range (IQR) is a measure of spread that gives the range of the middle 50% of the data.

Therefore, the distance between the medians of the IQR can give an idea of how much overlap there is between two data sets, but it is not the only measure to consider.

Other measures of overlap include comparing the means or standard deviations of the data sets, or using statistical tests such as a t-test or ANOVA to compare the groups. So, the given statement is False.

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--The given question is incomplete, the complete question is given

" You can measure the amount of overlap of 2 data sets by only comparing the distance between the medians of the IQR. True or False."--

a) The polygon has 8 sides and is called an octagon.

b) The measure of each interior angle of the octagon measures 135 degrees.

c) The measure of each exterior angle of the octagon measures 45 degrees.

a. To classify the polygon by the number of sides, we can use the formula for the sum of the interior angles of a polygon:

Sum of interior angles = (n - 2) x 180 degrees

where n is the number of sides of the polygon.

In this case, we are given that the sum of the interior angles is 1080 degrees. So we can set up an equation as follows:

(n - 2) x 180 = 1080

Simplifying this equation, we get:

n - 2 = 6

n = 8

b. To find the measure of one interior angle of the polygon, we can use the formula for the measure of each interior angle of a regular polygon:

Measure of each interior angle = (n - 2) * 180 degrees / n

Substituting n = 8 into this formula, we get:

Measure of each interior angle = (8 - 2) * 180 degrees / 8

= 135 degrees

c. To find the measure of one exterior angle of the polygon, we can use the fact that the sum of the interior and exterior angles of a polygon is 180 degrees. Therefore, the measure of each exterior angle of a regular polygon is:

Measure of each exterior angle = 360 degrees / n

Substituting n = 8 into this formula, we get:

Measure of each exterior angle = 360 degrees / 8

= 45 degrees

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Answer:

10%

Step-by-step explanation:

The claim that makes the most accurate statement regarding how many cookies the institution will require There will be 480 pupils who favour cookies at the college.

Decimals or fractions can also be used to represent percentages. Divide a percentage by 100 to turn it into a fraction.

If the sample of 225 students was truly random and not just selected from a certain group, we may calculate percentages depending on it.

As a result, "There will be roughly 640 pie-loving pupils at the college."

Thus, the claim that makes the most accurate forecast regarding how many cookies the institution will require There will be 480 pupils who favour cookies at the college.

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The number that could be expected to have ordered a medium was 64 people.

The number that could be expected to have ordered a small would be 108 people.

The number that could have been expected to have ordered a small, medium, or large was 75 people.

The number that could have been expected to have ordered a medium was :

= 16 / ( 9 + 16 + 5 + 10 ) x 160 people

= 64 people

The number that could have been expected to have ordered a small would be :

= 9 / ( 9 + 16 + 5 + 10 ) x 480 people

= 108 people

The number that could have been expected to have ordered a small, medium, or large was :

= ( 9 + 16 + 5 ) / ( 9 + 16 + 5 + 10 ) x 100

= 75 people

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The groups that describes 16% of the population of horse jockeys are option (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.

To solve this problem, we need to use the standard normal distribution, where we can find the z-score associated with the given percentages using a z-table or calculator. The z-score tells us how many standard deviations a value is from the mean.

First, we can standardize the values using the formula

z = (x - μ) / σ

where z is the z-score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

a) To find the jockeys who are shorter than 58 in., we can standardize the value as

z = (58 - 62) / 2 = -2

Using a z-table, we can find that the percentage of values below z = -2 is approximately 0.0228, which is less than 16%. Therefore, a) is not correct.

b) To find the jockeys who are taller than 64 in., we can standardize the value as

z = (64 - 62) / 2 = 1

Using a z-table, we can find that the percentage of values above z = 1 is approximately 0.1587, which is also less than 16%. Therefore, b) is not correct.

c) To find the jockeys who are shorter than 60 in., we can standardize the value as

z = (60 - 62) / 2 = -1

Using a z-table, we can find that the percentage of values below z = -1 is approximately 0.1587, which is less than 16%. Therefore, c) is correct.

d) To find the jockeys who are between 60 in. and 64 in., we can standardize the values as

z1 = (60 - 62) / 2 = -1

z2 = (64 - 62) / 2 = 1

Using a z-table, we can find the percentage between z1 and z2, which is approximately 0.6826. Therefore, d) is also correct.

Therefore, the correct answers are (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.

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The given question is incomplete, the complete question is:

Suppose the heights of professional horse jockeys are normally distributed with a mean of 62 in. and a standard deviation of 2 in.

Which group describes 16% of the population of horse jockeys?

Select each correct answer.

a) jockeys who are shorter than 58 in.

b) jockeys who are taller than 64 in.

c) jockeys who are shorter than 60 in.

d) jockeys who are between 60 in. and 64 in.

There is no solution to this system of equations. (option B).

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

There is no solution to the given graph of two linear equations or system of linear equations.

From the given graph it is clear that graph of the given two equations shows  two lines that are parallel to each other. They don't meet or intersect each other at any point.

Since no point is on both lines, there is no ordered pair that makes both equations true.

Hence, there is no solution to this system of equations.

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Answer:

Step-by-step explanation:

Given 36 books in a box with toys such that the books : toys ratio is 4 : 5, you want the initial number of toys and the number given away if the ratio becomes 12 : 11.

The number of books remains constant at 36. We can rewrite the ratios so that each shows the correct number of books:

  ratios are books : toys

  before: 4 : 5 = 36 : 45 . . . . . . . multiply by 9

  after: 12 : 11 = 36 : 33 . . . . . . . . multiply by 3

Based on the above, we see the initial number of toys is 45.

The final number of toys is 33, so the number given away is ...

  45 -33 = 12

12 toys were given away.

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The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3.

For this problem, the number of packs bought is the least common multiple of 10 and 12, which is obtained by factoring them into prime numbers as follows:

10 - 12|2

5 - 6|2

5 - 3|3

5- 1|5

1 - 1

Hence:

lcm(10, 12) = 2² x 3 x 5 = 60.

Hence:

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The chord length is approximately 1.397 centimeters where 0.7 centimeters is the separation from the center of the circle to the chord.

We can use the properties of circles to find the angle formed by the chord at the center of the circle to evaluate the length of the chord.

0.7 centimeters is the separation from the center of the circle to the chord. This remove is additionally the stature of the isosceles triangle shaped by the chord and the two radii of the circle. 

Let θ be the angle between the chord and the center of the circle. You can use trigonometry to find θ.

sin(θ/2) = 0.7/2.5

[tex]θ/2 = sin⁻¹(0.7/2.5)[/tex]

θ/2 = 0.2793

θ=2×0.2793

θ ≈ 0.5586 radians

Now that we know θ, we can use the formula for the chord length of a circle.

chord length = 2 × radius × sin(θ/2)

Chord Length = 2 × 2.5 × sin(0.2793)

String length ≈ 1.397 cm

Therefore, the chord length is approximately 1.397 centimeters.

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Answer:

natural radioactive decay, examples: postassium and carbon. Three ways to classify their physical properties mineralogical composition, grain size, and texture

Step-by-step explanation:

The equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.

Explain the term centre

A centre is a point or location that is at the middle or heart of something. It can refer to the physical centre of an object or the conceptual centre of an idea or system. Centres can be used as reference points for measurements, calculations, or decision-making processes.

According to the given information

Here we can use the distance formula:

√((x - 2)² + (y + 3)²) = r

We also know that the circle passes through the point (6, 1). Substituting these coordinates into the equation above, we get:

√((6 - 2)² + (1 + 3)²) = r

√(16 + 16) = r

r = 4√(2)

Now we can use the centre and radius to write the equation of the circle in standard form:

(x - 2)² + (y + 3)² = (4√(2))²

(x - 2)² + (y + 3)² = 32

Therefore, the equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.

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The second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.

What is the sinusoidal function?

A sinusoidal function is a mathematical function that describes a repetitive oscillation that resembles a sine or cosine wave. It can be expressed in the general form:

f(x) = A sin (Bx + C) + D

We can use the general form of a sinusoidal function to model the horizontal distance "d" of the tip of the pendulum from its vertical position at rest:

d = A sin(ωt + φ) + C

where:

A = amplitude (maximum displacement) = 7.5 inches

ω = angular frequency = (2π)/T, where T is the period = 3.1 seconds

φ = phase shift (initial horizontal displacement) = 0 (since the pendulum is at rest at t=0)

C = vertical displacement = 0 (since the pendulum is at rest at its vertical position)

Plugging in the given values, we get:

d = 7.5 sin((2π/3.1)t)

Now we can use this equation to answer the given questions:

Determine the value of d when t = 3.1 s:

We simply plug in t = 3.1 into the equation:

d = 7.5 sin((2π/3.1)(3.1))

d = 7.5 sin(2π)

d = 0 inches

Therefore, when t = 3.1 seconds, the horizontal distance of the tip of the pendulum from its vertical position is 0 inches.

Approximate the value of t when d = 4 for the second time:

To find when d = 4 for the second time, we need to find the two values of t for which the sinusoidal function equals 4. We can use the fact that the sine function repeats itself every 2π radians to solve this problem.

First, we find the period of the sinusoidal function:

T = 2π/ω = 2π/(2π/3.1) = 3.1 seconds

Next, we find the time it takes for the function to complete half a cycle, or π radians:

t1 = (π/ω) + kT, where k is an integer

t1 = (π/(2π/3.1)) + k(3.1)

t1 = (3.1/2) + 3.1k

We want to find the second time that d = 4, so we need to find the smallest integer value of k for which t2 > t1, where t2 is the time when d = 4 for the second time.

t2 = (3π/ω) + kT

t2 = (3π/(2π/3.1)) + k(3.1)

t2 = (9.3/2) + 3.1k

We want to find the smallest integer value of k such that t2 > t1 and d = 4:

7.5 sin((2π/3.1)t1) = 4

7.5 sin((2π/3.1)t2) = 4

calculating

t1 ≈ 0.604 s

t2 ≈ 2.275 s

Therefore, the second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.

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Answer:

x = 2

y = 1

Step-by-step explanation:

3y + x = 5                       y = 3 - x

3(3 - x) + x = 5

9 - 3x + x = 5

9 - 2x = 5

-2x = -4

x = 2

Now put 2 in for x and solve for y

3y + x = 5    

3y + 2 = 5

3y = 3

y = 1

Let's Check

1 = 3 - 2

1 = 1

So, x = 2 and y = 1 is the correct answer.

Answer:

4. The smaller angle is 35°.

5. AngleCAB = 40°

AngleDAC = 50°

Step-by-step explanation:

4) The 3 angles shown all together add up to 180°.

3x+10 + 90° + 2x+5 = 180°

combine like terms.

5x + 105 = 180

subtract 105

5x = 75

divide by 5

x = 15

One of the angles is 3x+10 and the other is 2x+5.

2x+5 is the smaller angle. If x=15, then 2x+5

= 2(15) + 5

= 30 + 5

= 35

The smaller angle is 35°.

5) The two angles in this question add up to 90°.

7x-16 + 6x+2 = 90°

combine like terms

13x - 14 = 90

add 14

13x = 104

divide by 13

x = 8

Angle CAB = 7x - 16

= 7(8) - 16

= 56 - 16

= 40

AngleCAB = 40°

AngleDAC = 6x + 2

= 6(8) + 2

= 48 + 2

= 50

We also could have just subtracted to find angleDAC 90 - 40 = 50.

AngleDAC = 50°