Find the solution to this system:
Equation 1: 5x – 2y = -11 (2)
Equation 2: -2x + 5y = 17
Step #2
Multiplying Equation 2 by will create additive
inverses for the x-coefficients.

When a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

A double-napped cone is formed by rotating a straight line around another straight line that is parallel to it.

The intersection of a plane with a double-napped cone is referred to as a conic section. A degenerate conic section is formed when a plane intersects a double-napped cone at the vertex.

Thus, when a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

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Answer: Volume of a sphere = 4/3 * pi * r^3       r = radius of sphere      pi~ 3.14

Step-by-step explanation: If you use the radius in inches, your result will be in cubic inches (in^3)

The amount of water in cubic inches, that Mya's exercise ball will hold is 904.779 in³.

The volume of a sphere is the volume of space occupied by a sphere.  It is given by the formula:

\(\text{Volume of Sphere} = \dfrac{4}{3}\pi r^3\)

As it is given that the diameter of Mya's ball is 12 inches, also we know that the volume of a sphere is given by the formula,

\(\text{Volume of Sphere} = \dfrac{4}{3}\pi r^3\)

As we know that the diameter of Mya's ball is 12 inches, therefore, the radius of Mya's ball can be written as,

\(\rm Radius = \dfrac{Diameter}{2} = \dfrac{12\ in}{2} = 6\ in.\)

Now, if we substitute the value of the radius of Mya's ball in the formula of the volume of the ball,

\(\rm \text{Volume of Ball} = \dfrac{4}{3}\times \pi \times 6^3 = 904.779\ in^3\)

Hence, the amount of water in cubic inches, that Mya's exercise ball will hold is 904.779 in³.

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The unit vector that has the same direction as -5i + 9j is (-5/106)i + (9/106)j.

To find a unit vector with the same direction as a given vector, we need to:

To find a unit vector with the same direction as -5i + 9j, we need to divide this vector by its magnitude:

For the vector -5i + 9j, the magnitude is:

\(| -5i + 9j | = sqrt((-5)^2 + 9^2) = sqrt(106)\)

To find a unit vector in the same direction, we divide the vector by its magnitude:

\((-5i + 9j) / | -5i + 9j | = (-5/106)i + (9/106)j\)

So, the unit vector that has the same direction as -5i + 9j is (-5/106)i + (9/106)j.

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Answer: (3,8)

5 + 2 (-1) = 3

10 + 2 (-1) = 8

Answer:

1/10th

Step-by-step explanation:

You multiply,

1/2 x 1/5 = 1/10

You can also picture it. Cut half a sheet of paper into 5 pieces. that means the other half would have 5 pieces too you cut it. That means there would be 10 pieces in total. He uses one of those pieces.

Answer:

-11q+1

Step by Step Explanation:

7-6-2q-9q

1-2q-9q

1-11q= -11q+1

Answer:

6.73E-8 I think

Step-by-step explanation:

Answer:

\(7.4 \times {10}^{ - 8} - 6.7 \times {10}^{ - 9} \\ = (7.4 - 6.7) {10}^{ - 8 + ( - 9)} \\ = 0.7 \times {10}^{-17} \)

Answer:

173

Step-by-step explanation:

130+18=148

148+25=173

if they are optional

all are correct

Correct option is

D

All are correct

the equation of a given progressive wave is

y=5sin(100πt−0.4πx) ......(i)

The standard equation of a progressive wave is

y=asin(ωt−Kx) ...(ii)

Comparing (i) and (ii), we get

a=5m,ω=100π rad s

−1

,k=o.4πm

−1

도움이 되기를 바랍니다. :)

좋은 하루 되세요 :)

가장 똑똑한 것으로 표시 :)

For a population with mean μ, if c=0.90, x=15.2,o=3.0, and n=95, then the 90% confidence interval for μ is (14.5,15.9)

To find the 90% confidence interval for μ, follow these steps:

Therefore, the 90% confidence interval for μ is (14.5, 15.9)

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(a) The conditional probability mass function of X₁ given X₂ = 1 is P(X₁ = 1 | X₂ = 1) = 7/18.

(b) The conditional probability mass function of X₁ given X₂ = 0 is P(X₁ = 1 | X₂ = 0) = 2/18 = 1/9.

(c) Assuming balls are selected with replacement, the conditional probability mass function of X₁ given X₂ = 1 is P(X₁ = 1 | X₂ = 1) = 12/19.

(d) Assuming balls are selected with replacement, the conditional probability mass function of X₁ given X₂ = 0 is P(X₁ = 1 | X₂ = 0) = 7/19.

(a) When the balls are selected without replacement and X₂ is known to be 1 (black), there are 12 black balls left out of 18 remaining balls. Therefore, the probability of X₁ being 1 (black) is 12/18 = 7/18.

(b) When the balls are selected without replacement and X₂ is known to be 0 (white), there are still 7 black balls left out of 18 remaining balls. Therefore, the probability of X₁ being 1 (black) is 7/18.

(c) When the balls are selected with replacement, the probability of selecting a black ball remains constant at 12/19, regardless of the outcome of the second draw. Therefore, P(X₁ = 1 | X₂ = 1) = 12/19.

(d) When the balls are selected with replacement, the probability of selecting a black ball remains constant at 12/19, regardless of the outcome of the second draw. Therefore, P(X₁ = 1 | X₂ = 0) = 12/19.

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Answer:

n 1 hour Dylan can paint 1/4 of the wall, and Brett can paint 1/3 of the wall.

Therefore together they can paint 1/4+1/3 = 7/12 of wall

Therefore they can paint entire wall in 12/7 hours

Step-by-step explanation:

you ' re welcome grandma loves youu ! < 33 ; )

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Complete question is;

The lengths of two sides of a right triangle ABC are given.

Find the length of the missing side.

b = 16 ft and c = 30 ft

Answer:

25.377 ft

Step-by-step explanation:

From online sources, c is the hypotenuse of the triangle.

Thus, we can use pythagoras theorem to solve for the other side of the right angle triangle.

c² = a² + b²

Where a is the length of the missing side.

Thus;

30² = a² + 16²

a² + 256 = 900

a² = 900 - 256

a² = 644

a = √644

a = 25.377 ft

Answer:

Below

Step-by-step explanation:

Front = 3 x 4 = 12 cm^2

Back = 3 x 4 = 12 cm^2

Right = 3 x 4 = 12 cm^2

Left = 3 x 4 = 12 cm^2

top = 3 x 3 = 9 cm^2

Add em all up : 57 cm^2

Hope this helped!

Answer: 57 cm^2

Step-by-step explanation:

4(3)(4)+(3)(3) = 57

Answer:

2.22

Step-by-step explanation:

\(\sqrt[3]{11} =2.223980091\)

Rounded to hundredths: 2.22

Answer

The height of the plane at that time is 1.1 miles

The distance of the plane's path is 10.1 miles

Explanation

The situation models a right angle triangle as shown below

Using trigonometric ratio,

tan 6° = opposite / adjacent

The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,

The height of the plane at that time ≈ 1.1 miles

The hypotenuse of the triangle formed is the distance of the plane path.

Therefore, this distance can be calculated using Pythagoras rule as follows:

The distance of the plane's path = 10.1 miles

Value of p is 0.5.

Given

Mean of a binomial distribution np = 12

Sample n = 60

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

To calculate the mean of a binomial distribution B(n, p) we need to multiply the number of trials n by the probability of successes p,

mean = n × p .

Value of p:

np = 12

(60) p = 12

p = 12/60

p = 1/2

p = 0.5

Value of p is 0.5.

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The distance of the point (-7,-4) from x axis is 7 units.

If we put the point (-7,-4) in the cartesian plan then it will lays in the third quadrant . Since the x point is given is -7 which is negative so we have to step forward 7 points to the left side from the origin of the plan. Then the y point is given  -4 which is also negative so after moving 7 steps in the negative x direction we have to step 4 points to negative y direction whic means in the downward direction.

The distance from the x axis is 7 units.

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The number of patients served per day that minimizes the cost per patient per day of running the hospital is 100.

To determine the number of patients served per day that minimizes the cost per patient per day, we need to find the value of x that minimizes the cost function. The cost per day of running the hospital is given by 300,000 * (1 + 0.75\(x^2\)) dollars, where x represents the number of patients served per day.As the hospital's capacity increases in increments of 25, the optimal number of patients served per day remains constant at 100.

To find the minimum cost per patient per day, we divide the total cost by the number of patients served per day. So the cost per patient per day is (300,000 * (1 + 0.75\(x^2\))) / x dollars.

To find the value of x that minimizes this cost per patient per day, we can take the derivative of the cost function with respect to x and set it equal to zero. However, since the cost function is quadratic, we can observe that the cost per patient per day is minimized when the numerator is minimized.

Since the numerator is a constant value, the minimum cost per patient per day occurs when \(x^2\) is minimized. The only positive integer value of x that satisfies this condition is x = 100. Therefore, the optimal number of patients served per day that minimizes the cost per patient per day is 100.

As the hospital's capacity increases from 200 to 500 in increments of 25, the optimal number of patients served per day remains constant at 100. This means that regardless of the increase in capacity, the hospital should aim to serve 100 patients per day to minimize the cost per patient per day of running the hospital.

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Answer:

slope = \(\frac{2}{3}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (15, 18 ) and (x₂, y₂ ) = (6, 12 )

m = \(\frac{12-18}{6-15}\) = \(\frac{-6}{-9}\) = \(\frac{2}{3}\)

Remember, when finding the slope, use this formula: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1} }\)

We can start by labeling (15, 18) as \(x_{1}\) and \(y_{1}\) and (6, 12) as \(x_{2}\) and \(y_{2}\). Now, we can plug these number into the formula: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1} }=\frac{12-18}{6-15}=\frac{-6}{-9} =\frac{2}{3}\)

Thus, the slope of the line is \(\frac{2}{3}\). Hope this helps! Let me know if you have any questions related to this problem.

Answer:

67 mph

Step-by-step explanation

A method you'd want to remember is r = d/t, or rate equals distance divided by time.

Since the Morris family drove 368.5 miles in 5.5 hours, you'd divide the distance by 5.5.

(368.5/5.5) = 67 miles per hour.

So their average rate is 67 miles per hour.

Approximately 32% of students scored above 86 on the university exam.

To determine the percentage of students who score above 86, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.

According to this rule, in a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 78 and the standard deviation is 8, we can calculate the z-score for 86 using the formula:

z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (86 - 78) / 8 = 1

Since 86 is one standard deviation above the mean, we know that approximately 68% of students scored below 86. Therefore, the percentage of students who score above 86 can be estimated as 100% - 68% = 32%.

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△CMN is equilateral because CM = CN (midpoint property) and ∠CMN = ∠CNM = ∠MNC (corresponding angles).

To prove that △CMN is an equilateral triangle, we need to show that all three sides are equal in length and that all three angles are equal.

Let's start by analyzing the given information and the properties of the figure.

△ABC is an equilateral triangle, meaning all three sides (AB, BC, and CA) are equal in length.

△CDE is an equilateral triangle, implying that all three sides (CD, DE, and EC) are equal in length.

Point M is the midpoint of AD, so AM = MD.

Point N is the midpoint of BE, so BN = NE.

Now, let's proceed with the proof:

Show that CM = CN.

Since M is the midpoint of AD and N is the midpoint of BE, we can write:

AM = MD (definition of M being the midpoint)

BN = NE (definition of N being the midpoint)

By adding these two equations, we get:

AM + BN = MD + NE

Now, let's examine the left-hand side of the equation. The sum AM + BN represents the length of AB, as AM and BN are the midpoints of AD and BE respectively. Since AB is a side of the equilateral triangle △ABC, it is equal in length to BC and CA. Therefore, we can rewrite the equation as:

AB = MD + NE

Next, let's consider the right-hand side of the equation. MD + NE represents the length of DE, which is a side of the equilateral triangle △CDE. As mentioned earlier, all sides of △CDE are equal in length. Therefore, we can rewrite the equation as:

AB = DE

Since AB = BC = CA (because △ABC is equilateral), and DE = CD = EC (because △CDE is equilateral), we can conclude that:

BC = DE

This implies that the line segments BC and DE have the same length. Moreover, since BC is parallel to DE, the line segments BC and DE are congruent (have equal length) according to the properties of parallel lines. Therefore, we have:

BC = DE = CM + MN + NE

Now, let's examine the right-hand side of the equation. CM + MN + NE represents the length of CN. We've just established that BC = DE, so we can substitute these equal lengths in the equation:

BC = CM + MN + NE

Simplifying the equation, we have:

BC = CN

Therefore, we've shown that CM = CN, meaning that two sides of △CMN are equal.

Show that ∠CMN = ∠CNM = ∠MNC.

To prove that all three angles of △CMN are equal, we need to show that ∠CMN = ∠CNM = ∠MNC.

First, let's consider △CME. Since △CDE is equilateral, the angle ∠CME is 60 degrees. As MN is parallel to CD, we can conclude that ∠CMN is congruent to ∠CME (corresponding angles). Therefore, ∠CMN = ∠CME = 60 degrees.

Next, let's consider △CNB. Since △ABC is equilateral, the angle ∠ACB is 60 degrees. As MN is parallel to AB, we can conclude that ∠CNM is congruent to ∠CNB (corresponding angles). Therefore, ∠CNM = ∠CNB = 60 degrees.

Since ∠CMN = ∠CME = 60 degrees and ∠CNM

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Answer:

dunno

Step-by-step explanation:

Answer:2.25

Step-by-step explanation:

3/4 is equal to 0.75 and 0.75*3=2.25

The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.

An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.

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