Solve the system: x+y=12 x-2y=0

Answer:

Step-by-step explanation:

We can use the central limit theorem to approximate the sampling distribution of the sample means as normal with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size:

mean = 2.7 feet

standard deviation = 0.4 feet / sqrt(69) ≈ 0.048 feet

Now, we want to find the probability that the sample mean is less than 2.3 feet:

z = (2.3 - 2.7) / 0.048 ≈ -8.33

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than -8.33, which is essentially 0:

P(z < -8.33) ≈ 0

Therefore, the probability that the mean of the sample taken is less than 2.3 feet is approximately 0.

Answer: 0.3085 = 30.85% probability that an individual man's step length is less than 2.5 feet.

Step-by-step explanation:

For this, we will be using:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 2.7 feet and a standard deviation of 0.4 feet.

This means that

Find the probability that an individual man’s step length is less than 2.5 feet.

This is the p-value of Z when X = 2.5. So

has a p-value of 0.3085

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

Answer:

what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

Step-by-step explanation:

Step 2 of 2: If a sampling distribution is created using samples of the ages at which 35 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

Answer:

53

Step-by-step explanation:

7c - y ← substitute c = 7 and y = - 4 into the expression

= 7(7) - (- 4)

= 49 + 4

= 53

The volume of Joe chocolate box is 48in³

1. Volume of Joe chocolate box

Given the following dimensions:

length = 6in

height = 2in

width = 4in

Recall that,

Volume = length x width x height

Volume = 6 in x 4 in x 2 in

Volume = 48in³

2. Gift paper to wrap rectangular gift box

To calculate the amount of gift paper required to wrap the rectangular box, we need to find the surface area of the box.

Recall that,

Surface Area = 2(length x width) + 2(length x height) + 2(width x height)

Surface Area = 2(15 in x 10 in) + 2(15 in x 8 in) + 2(10 in x 8 in)

Surface Area = 300 in² + 240 in² + 160 in²

Surface Area = 700in²

3. Quantity of pasta served to Olivia

To find the quantity of pasta served to Olivia, we need to calculate the volume of the rectangular prism lunch box.

The volume of a rectangular prism can be calculated by multiplying its length, width, and height.

Given the dimensions of the lunch box, we have:

Volume = Length x Width x Height

Volume = 5 in x 4 in x 3 in

Volume = 60in³

Therefore, the quantity of pasta served to Olivia is 60in³

Learn more about Volume here:

https://brainly.com/question/27710307

#SPJ1

In this problem, we have that the graph in fact represents a function, as there are no vertically aligned points, that is, each input is mapped to a single output.

For a linear function, as is the case for this problem, both the domain and the range will always be represented by all real numbers.

More can be learned about domain and range at https://brainly.com/question/26098895

#SPJ1

Answer:

x = 4

Step-by-step explanation:

The two angles A and C added together equal 88

5x + 3 + 15x + 5 = 88  Combine like terms

20x + 8 = 88  Subtract 8 from both sides

20x + 8 - 8 = 88 - 8

20x = 80  Divide both sides by 20

x = 4

Helping in the name of Jesus.

The text is a mathematics question that asks to calculate two statistics from a given data set. The data set consists of 10 numbers that represent the number of employee absences each week over a period of 10 weeks. The mean is the average of the data set, which is found by adding up all the numbers and dividing by the number of data points. The standard deviation is a measure of how much the data varies from the mean, which is found by using a formula that involves squaring the differences between each data point and the mean, adding them up, dividing by the number of data points, and taking the square root. To answer the question, you need to use these formulas and a calculator. The answer is:

Mean = (5 + 5 + 1 + 2 + 2 + 4 + 7 + 4 + 5 + 5) / 10 = 4 Standard deviation = √[(5 - 4)² + (5 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (4 - 4)² + (7 - 4)² + (4 - 4)² + (5 - 4)² + (5 - 4)²] / 10 = √16 / 10 = √1.6 ≈ 1.26

Hopefully this helps you, so bye!

The mean, median, and mode have the same value for the normal probability distribution. Hence, option B is correct.

A probability distribution is an idealized frequency distribution. A frequency distribution describes a specific sample or dataset. It's the number of times each possible value of a variable occurs in the dataset. The number of times a value occurs in a sample is determined by its probability of occurrence

1. The mean, median, and mode have the same value for the normal probability distribution. Hence, option B is correct.

Reason for the correct option: The most widely used distribution is the normal distribution, also known as the bell curve. The normal distribution has the parameters mean (μ) and standard deviation (σ)

. Normal distributions are symmetrical about the mean value. That is why the normal distribution has equal values of mean, median, and mode. Among these three measures, the mean is considered the best measure of central tendency as it involves all the values of the data set for its computation, and any slight changes will result in a change in the mean value. This is not seen for the measures median and mode. Mean = Median = Mode =

μ

2. Reason for the wrong options:

A. In uniform distribution, only the mean and median values are same.

The mean = median for the uniform distribution is:

μ = a +b/2

Where,

a = lower limit value

b = upper limit value

And, Mode &= any value in (a, b).

C.In exponential distribution, the mean, median and mode values differ with each other.

Mean = 1/λ

Median = ln2/λ

Mode = 0

D.In Poisson distribution, the mean, median, and mode values differ from each other. The mean of the Poisson distribution is λ

Complete question The mean, median, and mode have the same value for which of the following probability distributions?

A. Uniform

B. Normal

C. Exponential

D. Poisson

Learn more about Probability distribution here

https://brainly.com/question/14210034

#SPJ1

Answer:

The probability distribution type that has a mean, median, and mode that are all equal is the constant distribution, which is represented by option (a).

In a constant distribution, all values have the same probability of occurring, and therefore, the distribution is entirely flat. Since there is only one unique value, this value is also the mean, median, and mode of the distribution.

For a symmetric distribution, the mean, median, and mode can be equal, but this is not always the case. For a positively or negatively skewed distribution, the mean, median, and mode typically differ from each other.

By answering the presented question, we may conclude that  As a result, equation the answer is Yes, because the prerequisites for inference are satisfied.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.

In this example, the requirements for inference are as follows:

The issue specifies that both samples were picked at random, hence this criterion is satisfied.

Big Counts Condition: We need to verify whether np >= 10 and n(1-p) >= 10, where n is the sample size and p is the population size, for both samples.

Independence: Because the problem does not specify whether the homes are self-sufficient, we assume that they are.

Because all three requirements have been satisfied, we can use the normal distribution to calculate a confidence interval for the difference in the percentage of households that favour starting the school year a week earlier. As a result, the answer is Yes, because the prerequisites for inference are satisfied.

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

The summing of discrete data is indicated by the integration. To determine the functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To find the area of the region between the curves, we need to integrate the difference between the upper curve and the lower curve with respect to x, over the given interval [0,2]:

Area = ∫[0,2] ([tex]e^{(-t)[/tex] - (t² + 4t + 2)) dt

We can simplify the integrand by factoring the quadratic expression inside the parentheses:

Area = ∫[0,2] ([tex]e^{(-t)[/tex] - (t + 2)(t + 2)) dt

Now we can integrate each term separately:

Area = ∫[0,2] [tex]e^{(-t)[/tex] dt - ∫[0,2] (t + 2)² dt

For the first integral, we can use the fact that the integral of e^(-t) is -e^(-t):

Area = [[tex]-e^{(-t)[/tex]]|[0,2] - ∫[0,2] (t + 2)² dt

Evaluating the first integral at the endpoints, we get:

Area = (-e⁻² + e⁰) - ∫[0,2] (t² + 4t + 4) dt

Simplifying the integrand in the second integral, we get:

Area = (-e⁻² + 1) - [[tex](t^{3/3})[/tex] + 2t² + 4t]|[0,2]

Evaluating the second integral at the endpoints, we get:

Area = (-e⁻² + 1) - [(8/3) + 8 + 8] + [(0/3) + 0 + 0]

Simplifying, we get:

Area = -e⁻² - 8/3 + 1

Area = -e⁻² - 5/3

Therefore, the area of the region between the curves is approximately -2.566 square units. Note that since the lower curve is always above the x-axis, the area is positive even though the expression we obtained for the area is negative.

Learn more about integration on:

https://brainly.com/question/2607596

#SPJ1

Answer:

The answer to your problem is, 7 friends can buy the meal on a budget of $41 which includes delivery charges of $6.

Step-by-step explanation:

We also should know what a formula is because it can explain how two expressions on each side of a sign are connected.

Example, 2x - 4 = 2.

The letter ‘ x ‘ is a preceding example.

So:

The total budget is $41.

Delivery charges are $6.

The equation is: 6 + az = 41

Z is the meal for each friend.

6 + 5z = 41

Calculate for ‘ z ‘

6 + 5z = 41

6 + 5(7) = 41

6 + 35 = 41

= 41

Thus the answer to your problem is, 7 friends can buy the meal on a budget of $41 which includes delivery charges of $6.

Answer:

The probability of drawing a black card from a deck of 52 cards is 26/52 or 1/2, since there are 26 black cards in the deck.

The probability of drawing an Ace from a deck of 52 cards is 4/52 or 1/13, since there are 4 Aces in the deck.

Since the first card is replaced before drawing the second card, the outcome of the first card does not affect the probability of drawing an Ace on the second draw. Therefore, we can multiply the probabilities of the two events to find the probability of both events happening:

Probability of drawing a black card on the first draw = 1/2

Probability of drawing an Ace on the second draw = 1/13

Probability of both events happening = (1/2) x (1/13) = 1/26

Therefore, the probability that the first card is black and the second card is an Ace is 1/26.

The calculated age that is an outlier in the dot plot is 5

From the question, we have the following parameters that can be used in our computation:

The dot plot

The outlier is the value that is far from the other values

In this case, the value 5 is far from other values

So, the outlier in the dot plot is 5

Hence, the age that is an outlier is 5

Read more about outlier at

https://brainly.com/question/27893355

#SPJ1

I = prt

interest = principal*rate*time

If we invest $x at 14% we invest $(11000-x) at 7%

816 = .06x(1) + .7(11000-x)(1)

816 = .06x + 770 - .7x

.14x - .06x = 770-1120

.-21x = -350

x = 248/.08

x = $1181 invested at 14%

11000-x = 9819 invested at 7%

There are a total of 16 possible rational roots for P(x).

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

To find the possible rational roots of a polynomial, we can use the Rational Root Theorem, which states that if a polynomial with integer coefficients has a rational root of the form p/q (where p and q are integers with no common factors), then p must be a factor of the constant term of the polynomial, and q must be a factor of the leading coefficient.

In the case of P(x) = 10x^3 + 6x^2 + 4x + 4, the constant term is 4 and the leading coefficient is 10. Therefore, the possible rational roots of P(x) must have the form p/q, where p is a factor of 4 and q is a factor of 10.

The factors of 4 are ±1, ±2, and ±4. The factors of 10 are ±1, ±2, ±5, and ±10. Therefore, the possible rational roots of P(x) are:

p/q = ±1, ±2, ±4, ±1/2, ±1/5, ±2/5, ±1/10, ±1/4

So there are a total of 16 possible rational roots for P(x).

To learn more about polynomials from the given link:

https://brainly.com/question/29073508

#SPJ1

The domains of g(-2) and the composite function hg(x) are equal to -46 and (2 - 3x⁴)/x⁴ respectively.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domains of the function g(-2) and hg(x) as follows:

g(-2) = 2 - 3(-2)⁴ {substitute -2 for x}

g(-2) = 2 - 48

g(-2) = -46

hg(x) = [3(2 - 3x⁴)]/[2 - (2 - 3x⁴)] {substitute (2 - 3x⁴) for x}

hg(x) = [3(2 - 3x⁴)]/(2 - 2 + 3x⁴)

hg(x) = [3(2 - 3x⁴)]/3x⁴

cancel out 3 we have;

hg(x) = (2 - 3x⁴)/x⁴

Therefore, the domains of g(-2) and the composite function hg(x) are equal to -46 and (2 - 3x⁴)/x⁴ respectively.

Read more about function here:https://brainly.com/question/10687170

#SPJ1

If you always reject the null hypothesis, regardless of any sample evidence, then the probability of Type II error is 0.

The statement that the chance of making Type I error when you always reject a null hypothesis is true or Yes.

This policy is a bad one because you need to aim for balance to avoid committing either type 1 or type 11 error.

A null hypothesis assumes that assumes there is no significant difference between a set of observed data and what would be expected under a certain assumption or theory. Always rejecting the null hypothesis is not a good idea because you will be making a Type I error every time you do that.

Hypothesis testing requires careful consideration of the sample evidence and the context of the problem to make a reasoned decision about the null hypothesis.

Learn more about the null hypothesis here:

https://brainly.com/question/4436370

#SPJ1

If your figure was reflected across the x-axis, the x-coordinate of the figure would remain the same while the sign of the y-coordinate would change.

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Mathematics and Geometry, a reflection over or across the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate (x-value) while the sign of the y-coordinate (y-value) changes from positive to negative or negative to positive as the case may be.

Read more on reflection here: brainly.com/question/27912791

#SPJ1

Consider the given expression is

[tex](5.23x + 3.76) - (3.67x - 6.39)[/tex]

We need to find the simplified form of the given expression.

Using distributive property we get

[tex]5.23x + 3.76 - (3.67x) - (-6.39)[/tex]

[tex]5.23x + 3.76 - 3.67x + 6.39[/tex]

On combining like terms we get

[tex](5.23x - 3.67x) + (3.76 + 6.39)[/tex]

[tex]1.56x+10.15[/tex]

Therefore, the simplified form of the given expression is [tex]\bold{1.56x+10.15}[/tex].

The points that lies on the same line are (-4, 3), (-12, 9), (16, -12) and (-20, 15).

The given coordinate points are (-8, 6) and (12, -9).

Here, slope (m)= (-9-6)/(12-(-8))

= -15/20

= -3/4

Substitute m=-3/4 and (x, y)=(-8, 6) in y=mx+c, we get

6=-3/4 (-8)+c

6=6+c

c=0

So, the equation of a line is y=-3/4 x

Now,

(-4, 3) in the given equation is 3=-3/4 (-4)

3=3

(4, 3) in the given equation is 3= -3/4 (4)

3≠ -3

(8, 6) in the given equation is 6= -3/4 (8)

6 ≠ -6

(-12, 9) in the given equation is 9= -3/4 (-12)

9=9

(16, -12) in the given equation is -12= -3/4 (16)

-12 =-12

(-20, 15) in the given equation is 15 = -3/4 (-20)

15 = 15

Therefore, the points that lies on the same line are (-4, 3), (-12, 9), (16, -12) and (-20, 15).

To learn more about the equation of a line visit:

https://brainly.com/question/2564656.

#SPJ1

Answer:

Step-by-step explanation:

length of white rectangle= 150cm = 1.5m

width of white triangle = 6 - (2 + 3) = 1m

the total area of the front of her house

= area of rectangle + area of trapezium -area of white rectangle

= (4 x 6) + ( [tex]\frac{4+6}{2}[/tex] x 1) - ( 1.5 - 1)

= 12 + 4 - 0.5

= 15.5 m²

1 can of paint covers an area of 6m²

4 can of paint = 6 x 4 = 24m²

previously, we calculated that the area of the front of her house is 15.5m². Therefore, 4 cans of paint is enough.

Thus, the length of the rectangle is 20 cm and the width of the rectangle is 6 cm.

A rectangular prism is just a three-dimensional form having six faces, two of which are lateral faces and two of which are top and bottom faces. The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its shape.

Let the width of the rectangle be 'w'.

then, the length of rectangle l = 2w + 8

Perimeter = 2(l + w)

52 = 2(l + w)

26 = 2w + 8 + w

3w = 26 - 8

w = 18/3

w = 6 cm

l = 2w + 8 = 2(6) + 8 = 20 cm

Thus, the length of the rectangle is 20 cm and the width of the rectangle is 6 cm.

Know more about the perimeter of rectangle:

https://brainly.com/question/10452031

#SPJ1

Complete question:

The rectangle shown has a perimeter of 52 cm and the given area. Its length is 8 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle.

The length of the rectangle is __ cm and the width of the rectangle is __ cm.

measure of angle 1 = 70 degrees (corresponding angle postulate)

measure of angle 3 = 60 degrees (the measure of angle BCA is 70 degrees, because the angles in a triangle add up to 180 degrees. 70 + 50 = 120, and the measure of the straight angle is 180 degrees. 180 - 120 = 60 degrees for the measure of angle 3)

measure of angle 5 = 70 degrees (angle 5 is vertical angles with angle BED, which has a measure of 70 degrees because the angles of a triangle add up to 180 degrees, and vertical angles have equal measures)

measure of angle 4 = 60 degrees (the measure of angle 5 is 70 degrees, and subtracting 70 + 50 from 180 gives you the remaining angle measure, which is 60 degrees)

measure of angle 2 = 110 degrees (angle 2 and angle BED are supplementary angles, so their measures add up to 180 degrees. 180 - 70 = 110)

Answer:

x=5

Step-by-step explanation:

4/8 = 3/6

1/2 = x/10

x= 5

The part of the restaurant that George would own after selling his share to Vince would be = 1/4. That is option H.

The quantity or part of the restaurant business that is owned by George = 3/4

The quantity of the restaurant that George sold to Vince = 1/3

That is;

= 1/3 of 3/4

= 1/3× 3/4

= 1/4

Learn more about fraction here:

https://brainly.com/question/28699958

#SPJ1

To find the perimeter of a polygon, we need to add up the lengths of all its sides.

The length of a side can be found using the distance formula, which is:

d = √[(x2 - x1)² + (y2 - y1)²]

Using this formula, we can find the lengths of the sides of triangle AMN:

d(MN) = √[(5 - 4)² + (-7 - 4)²] = √(1² + (-11)²) = √(1 + 121) = √122

d(NA) = √[(-6 - 5)² + (-6 - (-7))²] = √((-11)² + 1²) = √(121 + 1) = √122

d(AM) = √[(4 - (-6))² + (4 - (-6))²] = √(10² + 10²) = √200

So the perimeter of AMNO is:

P = d(MN) + d(NA) + d(AM) = √122 + √122 + √200 ≈ 24.3 (rounded to the nearest tenth)

Therefore, the perimeter of AMNO is approximately 24.3 units.

the polynomial function with the stated properties is:

f(x) = (11/40)x³ - (33/20)x² - (33/10)x + 55

what is  polynomial function ?

A polynomial function is a type of mathematical function that can be expressed as a sum of powers of a variable, multiplied by coefficients. The variable in a polynomial function is usually denoted by x, and the highest power of x that appears in the function is known as the degree of the polynomial.

In the given question,

A polynomial function of degree 3 with zeros of -4, -2, and 5 can be expressed in factored form as:

f(x) = a(x + 4)(x + 2)(x - 5)

where a is a constant coefficient that we need to determine, and (x + 4), (x + 2), and (x - 5) are the factors corresponding to the zeros -4, -2, and 5, respectively.

To find the value of the constant coefficient a, we can use the y-intercept of the function, which is given as -11. The y-intercept occurs when x = 0, so we can substitute x = 0 into the factored form of the function and set it equal to -11:

f(0) = a(0 + 4)(0 + 2)(0 - 5) = -11

Simplifying and solving for a, we get:

a = -11 / (42(-5)) = 11/40

Substituting this value of a back into the factored form of the function, we get:

f(x) = (11/40)(x + 4)(x + 2)(x - 5)

Expanding this expression, we get:

f(x) = (11/40)x³ - (33/20)x² - (33/10)x + 55

Therefore, the polynomial function with the stated properties is:

f(x) = (11/40)x³ - (33/20)x² - (33/10)x + 55

To know more about polynomial function , visit:

https://brainly.com/question/12976257

#SPJ1

The quotient of 6.591 × 10⁷ and 8.45 × 10² is 7.8 × 10⁴.

The result that is obtained when two numbers are divided by each other is called quotient. For example , dividing 100/ 5 , this will give 20. Here, 100 is called the dividend and 5 is called the divisor and 20 is the quotient.

Finding the quotient of 6.591 × 10⁷ and 8.45 × 10².

Using law of Indices;

(6.591/8.45) × (10⁷/10²)

= 0.78 × 10^(7-2)

= 0.78 × 10⁵

in scientific notation,

= 7.8 × 10⁴

Scientific notation is a standard way of expressing numbers as a multiple of 10.

learn more about quotient from

https://brainly.com/question/11995925

#SPJ1

The area of the shaded part is 50 in².

The area of the shaded part is calculated as follows;

Frist we need to calculate the length of the sides of the shaded area.

If we divide the length 10 in into 2, = 5 in, we will notice that it forms the leg and height and a right triangle.

The hypotenuse side of this right triangle is the length of the square of the shaded part.

L = √ (5² + 5²)

L =  √50

The area of the shaded part is calculated as;

A = L²

A = (√50)²

A = 50 in²

Learn more about area here: https://brainly.com/question/25292087

#SPJ1

Answer:

0.0277778

Step-by-step explanation:

probability to hit a 6 on each roll is 1/6, but the sum overcounts rolling 6 twice, so the actual probability of rolling 6 on either one or both roll is 1 6 + 1 6 − 1 36 = 11 36.

PLS Give BRAINLIST mean the world

happy easter:)