​Greg's age is 6 less than 5 times​ Rachel's age. In four years the sum of their ages will be 20. How old is each person​ now?

Answer:

Here's the completed input-output table for the function f(x) = 3x²+2:

X f(X)

-2 14

-1 5

0 2

1 5

2 14

Step-by-step explanation:

w = amount of wagon stamps

b = amount of sailboat stamps

so hmm we know Megan bought 4 stamps, so whatever "w" and "b" are, we know that w + b = 4.

we also know that Megan spent 16 cents on all, and that the wagon ones cost 1c, so for "w" amount that's a total of 1*w or 1w.  Now, the sailboat stamps cost 5c, that will give us a total of 5*b or 5b for those.

[tex]w+b=4\implies b=4-w \\\\[-0.35em] ~\dotfill\\\\ 1w+5b=16\implies \stackrel{\textit{substituting from the 1st equation}}{1w+5(4-w)=16} \implies w+20-5w=16 \\\\\\ 20-4w=16\implies 20=4w+16\implies 4=4w\implies \cfrac{4}{4}=w\implies \boxed{1=w} \\\\\\ \stackrel{\textit{since we know that}}{b=4-w}\implies b=4-1\implies \boxed{b=3}[/tex]

From the set a, b, c, d, e, f, g, we can derive 15 3-element subsets having the letter "a".

We can select 2 more elements from the set's remaining 6 components to create a 3-element subgroup that includes the letter "a": a, b, c, d, e, f, g.

The binomial coefficient indicates the number of possible methods to select 2 elements from a set of 6:

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

The positive numbers that appear as coefficients in the binomial theorem are known as binomial coefficients in mathematics. A binomial coefficient is frequently written as ( ) and is indexed by the pair of numbers n k 0.displaystyle "tbinom" nk. It is the multiplicative formula that can be used to calculate the coefficient of the xk component in the polynomial expansion of the binomial power (1 + x)n.

Thus, from the set a, b, c, d, e, f, g, we can derive 15 3-element subsets having the letter "a".

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The equation that gives the number of bacteria in the population after 2 hours is -

P{ 2 }  = 260 + (1/4 x 260)

The exponential function is given by -

y = eˣ

Given is that in a lab experiment, a population of 200 bacteria is able to quadruple every hour.

The population of the bacteria after the first hour is -

P{ 1 }  = 200 + (1/4 x 200) = 200 + 60 = 260 bacterias.

The population of the bacteria after the second hour is -

P{ 2 }  = 260 + (1/4 x 260) = 260 + 65 = 325 bacterias

After the second hour, the population of the bacteria would be -

P{ 2 }  = 260 + (1/4 x 260)

Therefore, the equation that gives the number of bacteria in the population after 2 hours is -

P{ 2 }  = 260 + (1/4 x 260)

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Answer:

if my calculation is correct the answer is 16 3/8-9 5/8 - fraction calculator. The result is 27/4 = 6 3/4 = 6.75 = twenty-seven quarters (or six and three quarters)

Step-by-step explanation:

The statement that ; "Null A is the set of all solutions of the equation Ax = 0" , is True because null space is the set of solutions of equation Ax = 0 .

The Dimensions of the matrix A is written as m × n ;

The Null Space of a matrix A, is denoted by null(A), and

The Null Space is defined as the set of all solutions to the homogeneous linear equation Ax = 0, where x is an n-dimensional column vector.

In other words, we say that  null(A) consists of all vectors x that make the  Ax = 0 that is the Zero vector.

Therefore , we can conclude that Null A is the set of all solutions of the equation Ax = 0  .

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The given question is incomplete , the complete question is

Let A be an m×n matrix.  The statement is True or False ?

Null A is the set of all solutions of the equation Ax = 0  .

1/4  is the probability of drawing a blue marble .

What does math probability mean?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences. It is predicated on the likelihood that something will occur. The logic underpinning probability serves as the foundation for theoretical probability.

                         For instance, the theoretical chance of receiving a head while tossing a coin is 12. There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.

total red balls = 5

total green balls = 3

total blue balls = 2

The probability of drawing a blue marble is now = 1/4.

The probability of drawing a red marble = 2/5.

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Answer:

121 3

Step-by-step explanation:

The population size varies in several ways. The sample size was insufficient, which is the best explanation for why the simulation of the sampling distribution is not roughly normal.

A person's or a researcher's choice of sample size will limit the study's statistical power if it is too small or inadequate for the alpha level and the analyses they have decided to do.

Because of the aforementioned, it is much harder to determine from one's sample whether a statistical effect is existent in the population.

A sample size that is either too small or too large can affect the ability to extrapolate the results, with the latter increasing the detection of differences and accentuating statistical differences that are not clinically significant.

The complete question is:-

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

A. The samples were not selected at random.

B . The sample size was not sufficiently large.

C. The population distribution was approximately normal.

D. The samples were selected without replacement.

E. The sample means were less than the population mean.

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(a) The answer is 3. To solve 4610 mod 7, we start by dividing 4610 by 7, which gives us 658 with a remainder of 4. Next, we divide 658 by 7, which gives us 93 with a remainder of 5. We keep dividing by 7 until we reach a number below 7. This gives us a remainder of 3, so the answer is 3.

(b) The answer is 6. To solve 345 mod 9, we start by dividing 345 by 9, which gives us 38 with a remainder of 3. Next, we divide 38 by 9, which gives us 4 with a remainder of 2.

We keep dividing by 9 until we reach a number below 9. This gives us a remainder of 6, so the answer is 6.

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The solar radius R² from its luminosity and effective temperature is R ≈ 695586.468 km.

We can find solar radius by direct substitution of values into Eqn 1.3

See the pic below,

Given L = 4πR²σT⁴

where,

L is the Luminosity

R solar radius

T the effective temperature

σ is the Stefan Boltman's constant

From 1 solar radius can be written as,

R² = L/4πσT⁴

L = 3.846 x 10²⁶

R² = 3.846x10²⁶/4x3.14x5.6703x10⁻⁸ x 5780⁴

R ≈ 695586.468 km

Therefore, the solar radius is R ≈ 695586.468 km

g = GM/r²

g = 6.67x10⁻¹¹ x 1.99 x 10³⁰/(6.95x10⁸)²

g = 274.13m/s² about 30 times that of earth.

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Answer: the number is 12.

Step-by-step explanation:

Let's call the two-digit number "x". We know that the sum of its digits is 7, so we can represent the number as 10a + b, where a and b are the digits of the number and a is the tens digit and b is the units digit.

The statement that "reversing its digits increases the number by 9" means that the number obtained by reversing the digits is x + 9. We can represent this reversed number as 10b + a.

So, we have two equations:

10a + b = x

10b + a = x + 9

Now, we can substitute the value of x from the first equation into the second equation:

10b + a = 10a + b + 9

Expanding both sides, we get:

10b + a = 10a + b + 9

9b = 9a + 9

b = a + 1

We know that 0 < a < 9, since the number is a two-digit number. So, we can conclude that 0 < b < 10.

We can now substitute the value of b into the first equation:

10a + (a + 1) = x

11a + 1 = x

11a = x - 1

a = (x - 1) / 11

Since a is the tens digit of the number, it must be an integer. We can test different values of x to find the value that satisfies this condition.

If x = 20, then a = (20 - 1) / 11 = 1. This gives us b = a + 1 = 2. The original number is 10a + b = 10 + 2 = 12, which satisfies all the conditions.

So, the number is 12.

The solution for the given equation is 6. Therefore, option A is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is |2x+3=15.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 2x=15-3

2x=12

x=6

Therefore, option A is the correct answer.

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(a) Descriptive statistics from the survey are 44%, 11.8%.

(b)  All investment managers is estimated to have an average expected 12-month return on equities of 11.8%.

(c)  Based on the sample, we can estimate that it will take an average of 2.9 years for technology and telecom stocks

Descriptive statistics from the survey are: (i) 44% of managers classified themselves as bullish or very bullish on the stock market, and (ii) the average expected return over the next 12 months for equities was 11.8%.

Based on the sample, we can infer that the population of all investment managers is estimated to have an average expected 12-month return on equities of 11.8%.

Based on the sample, we can estimate that it will take an average of 2.9 years for technology and telecom stocks to resume sustainable growth according to the population of all investment managers.

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The color of a mixture that is 3/5 red is given as follows:

Purple.

To obtain the color, we must look at the proportions in the context of the problem.

The proportion of red of each mixture is obtained dividing the number of red drops by the total number of drops, hence:

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3(x + 16)< 27 is the expression for three times the sum of a number and 16 is a least 27.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that three times the sum of a number and 16 is a least 27

Here we can see that  three times the sum of a number and 16 means

3(x + 16)

Therefore, 3(x + 16)< 27

Hence, 3(x + 16)< 27 is the expression.

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Using percentages we know that the water that will drain in the 2nd hour will be 25% of the remaining water.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

Convert both percentages to fractions of 100 or decimals, multiply them, then use the result to calculate the percentage of the %.

Calculating 50% of 40%, for instance, yields (50/100) x (40/100) = 0.50 x 0.40 = 0.20, which equals 20/100 or 20%.

NOTE: Using the percent sign and a division by 100 at the same time is improper.

So, in the first hour:

The drained water is 20%.

Remaining left: 80%

Then, 20% of 80 would be:

20/80 * 100 = 25%

Therefore, using percentages we know that the water that will drain in the 2nd hour will be 25% of the remaining water.

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The area of the given figure will be 145.13 m².

The area of a rectangle is calculated as length multiplied by width, while the area of a semi-circle is half the area of a circle with the same radius. We can calculate the combined area of the rectangle and semi-circle as follows:

Area of rectangle = length x width = 15 m x 8 m = 120 m^2

Area of semi-circle = 1/2 x pi x radius^2 = 1/2 x pi x 4^2 = 8 pi m^2

To find the total combined area, we add the area of the rectangle to the area of the semi-circle:

Total combined area = Area of rectangle + Area of the semi-circle

= 120 m² + 8π m²

= 120 m² + 25.13 m² (using π= 3.14159)

= 145.13 m

Therefore, the combined area of the rectangle and semi-circle is 145.13 square meters (rounded to two decimal places).

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So, one serving of Kind bars, which is two bars, contributes for roughly 13.8% of a 2,000 calorie diet's daily fat consumption.

An equation is a mathematical statement that shows that two expressions are equal. Equations can be used to represent relationships between variables, or to solve problems. Equations use mathematical symbols, such as the equal sign (=), to show the equality between the two expressions. For example, the equation 2x + 3 = 7 represents the relationship between the variable x and the constants 2 and 3. The equation can be solved for x to find its value. In this case, solving for x would give us x = 2.

Here,

The calculation for determining the percentage of daily fat intake in a serving of Kind bars is based on the Recommended Dietary Allowance (RDA) for fat. The RDA is a guideline for the average daily amount of a nutrient that is considered sufficient to meet the needs of most people.

For a 2,000 calorie diet, the RDA for total fat is about 65 grams per day. To calculate the percentage of daily fat intake in a serving of Kind bars, you divide the total amount of fat in the serving by the RDA for daily fat and multiply by 100.

For example, if one serving of Kind bars contains 9 grams of fat, you would perform the following calculation:

9 grams fat ÷ 65 grams RDA for daily fat x 100 = 13.8% daily fat intake

So, one serving of Kind bars, which is two bars, accounts for approximately 13.8% of a person's daily fat intake for a 2,000 calorie diet.

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Step-by-step explanation:

JKLM to J'K'L'M -

Reflection, over the line y=x

J'K'L'M to J"K"L"M -

Dilation of 1/2

Hope this helps :)

To assume that the sampling distribution of the sample mean is approximately normal -  A random sample of 10 taken from a population distribution that is skewed to the right.

There are several conditions that must be met for the sampling distribution of the sample mean to be approximately normal, including:

In these cases, the central limit theorem may not apply and the sampling distribution may not be approximately normal.

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The following question may be like this:

For which conditions is not appropriate to assume that the sampling distribution of the sample mean is approximately normal?

Answer:

Below

Step-by-step explanation:

DE is   MID segment.....so it cuts AC in half....then x = 6

The value of the probability p(s2) is 1.36, p(s3) is 1/18, p(s4) is 1/12, p(s5) is 1/9, p(s6) is 5/36, p(s7) is 1/6, and p(s8) 5/36

The sample space for this problem can be represented as all the possible outcomes when two dice are thrown.

Each die has six sides with numbers 1 through 6, so there are 6 x 6 = 36 possible outcomes. We can represent each outcome as a pair of numbers (i, j) where i is the number on the first die and j is the number on the second die.

Now, we want to find the probability of getting a certain total when the two dice are thrown. We can define an event Sj as the event where the total of the values on the dice is j.

To calculate the probability of each event, we need to count the number of outcomes that belong to each event, and divide by the total number of outcomes (which is 36).

Let's start with S2. The only outcome that belongs to this event is (1, 1), so the probability of getting a total of 2 is 1/36.

For S3, we can get a total of 3 in two ways: (1, 2) and (2, 1). So the probability of getting a total of 3 is 2/36 or 1/18.

For S4, we can get a total of 4 in three ways: (1, 3), (2, 2), and (3, 1). So the probability of getting a total of 4 is 3/36 or 1/12.

For S5, we can get a total of 5 in four ways: (1, 4), (2, 3), (3, 2), and (4, 1). So the probability of getting a total of 5 is 4/36 or 1/9.

For S6, we can get a total of 6 in five ways: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1). So the probability of getting a total of 6 is 5/36.

For S7, we can get a total of 7 in six ways: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So the probability of getting a total of 7 is 6/36 or 1/6.

Finally, for S8, we can get a total of 8 in five ways: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). So the probability of getting a total of 8 is 5/36.

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Heron's formula states that the area of a triangle can be found using the following formula:[tex]A = √s(s-a)(s-b)(s-c)[/tex] where s is the semiperimeter of the triangle [tex](s = (a + b + c)/2)[/tex].

In the case of an equilateral triangle, all three sides (a, b, and c) are the same length. So, if we set x = y = z in the formula, we get [tex]A = √s(s-x)(s-x)(s-x).[/tex] Simplifying this expression yields [tex]A = (√s/4) * x^2[/tex].

We can also write the perimeter of the triangle as P = 3x. Substituting this into the area formula, we get [tex]A = [(P/3)*√3/4] * (P/3)^2[/tex]. This expression can be simplified to [tex]A = (1/12) * P^2 * √3.[/tex]

This shows that for a fixed perimeter, the area of an equilateral triangle is maximized. This is due to the fact that the area is proportional to the square of the sides, and in an  equilateral triangle all sides are equal, thus maximizing the area. Heron's formula states that the area of a triangle can be found using the following formula: A = √s(s-a)(s-b)(s-c) where s is the semiperimeter of the triangle (s = (a + b + c)/2).

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The height of the building is given as follows:

205 feet.

The three trigonometric ratios are defined as follows:

Regarding the angle of 64º, we have that:

Hence the height is obtained applying the tangent of 64º, as follows:

tan(64º) = h/100

h = 100 x tangent of 64 degrees

h = 205 feet.

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The options that are true with respect to the lengths of the sides of the triangle and the included angle between sides a and b are;

The triangle is not a right triangle

cos(θ) < 0

The angle θ is an obtuse angle

A triangle is a polygon that has three sides and three interior angles.

The specified sides of the triangle are; a, b, and c

The relationship between the squares of the lengths of the sides, obtained from a similar question is presented as follows; a² + b² < c²

The specified measure of the angle opposite the side c = θ

According to Pythagorean Theorem, a triangle is a right triangle, if in the triangle, we can get; a² + b² = c²

The specified inequality, relating the squares of the lengths of the sides, a² + b² < c², which therefore, indicates;

According to cosine rule, we get;

c² = a² + b² - 2·a·b·cos(θ)

However; a² + b² < c²

c² - (a² + b²) = -2·a·b·cos(θ)

a² + b² < c²

0 < c² - (a² + b²)

0 < c² - (a² + b²) = -2·a·b·cos(θ)

0 < -2·a·b·cos(θ)

Dividing both sides by -1, the inequality sign is reversed, and we get;

0/(-1) > -2·a·b·cos(θ)/(-1) = 2·a·b·cos(θ)

0 > 2·a·b·cos(θ)

Therefore; 2·a·b·cos(θ) < 0

2·a·b·cos(θ)/(2·a·b) = cos(θ)  < 0/(2·a·b) = 0

cos(θ) is therefore, negative, which indicates that θ is in the second quadrant, with the solution, obtained using an online tool which can be expressed as follows;

(π/2) + 2·π·n < θ < (3·π/2) + 2·π·n

Where n = 0, we get;

(π/2) < θ < (3·π/2); The angle θ is therefore larger than π/2 = 90° and less than (3·π/2) = 270°, which in a triangle the maximum angle is 180°, indicating that the angle θ is an obtuse angle.

Part of the question includes to select the options that are true from the following;

cos(θ) < 0

The angle θ is an obtuse angle

The specified triangle is a right triangle

The triangle is not a right triangle

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The density of the object is 3.4 × 10¹² mg/kL.

Density of an object is defined as the mass of the object per unit volume.

The formula to calculate the density of an object is,

D = M / V

Here D is the density, M is the mass and V is the volume of the object.

Given that,

M = 850.0 kg = 850 × 1,000,000 mg = 85 × 10⁷ mg

V = 25 cL = 25 × 10⁻⁵ kL

Substituting the values,

Density = (85 × 10⁷ mg) / (25 × 10⁻⁵ kL)

             = 3.4 × 10⁷⁻⁻⁵

             = 3.4 × 10¹² mg/kL

Hence the density of the given object is 3.4 × 10¹² mg/kL.

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The probability that outmost 15 calls will be received is 0.2

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability of receiving more than 15 calls is 0.8 i.ep( > 15) = 0.8

The total probability is 1

Therefore ,

the probability of receiving at most 15 calls is 0.2

i.e p( ≤15 ) = 1-0.8

= 0.2

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