The ratio of 2 numbers is 3:5. The larger number is 30. What is the smaller number?​

Answer:

(x-2)^2-11

Step-by-step explanation:

Answer:

X'= (-3,6)

Y'=(7,8)

Z'=(11,2)

Step-by-step explanation:

when a point is reflected over the y axis, (x,y) becomes (-x,y). so the x value is just multiplied by -1

Answer:

X′(−3, 6), Y′(7, 8), Z′(11, 2)

Step-by-step explanation:

Imagine you are a spy who needs to infiltrate a secret base located at the origin of the coordinate plane. You have three accomplices, X, Y, and Z, who are waiting for you at different points on the plane. X is at (3, 6), Y is at (-7, 8), and Z is at (-11, 2). You have a device that can reflect any point over the y-axis, which you plan to use to confuse the enemy guards. You decide to reflect X, Y, and Z over the y-axis to create X', Y', and Z', respectively. What are the coordinates of these new points?

To find the coordinates of X', you simply change the sign of the x-coordinate of X. So, X' is at (-3, 6). Similarly, to find the coordinates of Y' and Z', you change the sign of the x-coordinates of Y and Z. So Y' is at (7, 8) and Z' is at (11, 2). Now you have three new points that are symmetric to the original ones over the y-axis.

But wait! There's a problem. The enemy guards have noticed that something is wrong. They see four points on their radar: one at the origin (you) and three on the right side of the y-axis (X', Y', and Z'). They realize that these points are reflections of some other points on the left side of the y-axis. They quickly deduce that there must be a spy among them. They start searching for you.

You need to act fast. You use your device again to reflect yourself over the y-axis. This creates a new point at (-0, 0), which is exactly the same as (0, 0). You have effectively disappeared from their radar. You sneak into the base while they are busy looking for you on the wrong side of the plane.

You have successfully completed your mission. Congratulations! You are a master of reflections.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

A)

This means in one minute, which is 1/210 of the total time, they would have ran 1/210 of the total distance.

So the runner would have ran 26.2/210 miles per minute, which is 0.12476 miles.

Rounding to the nearest hundredth of a mile,

They ran 0.12 miles per minute, so the unit rate is 0.12 miles per minute.

B)

You can work out the minutes per mile using the same concept.

For one mile, the runner would have ran 1/26.2 of the total time, so they ran 210/26.2 minutes per mile, or 8.015 minutes per mile.

Rounding to the nearest tenth, you'd round down to 8.0 minutes per mile.

So they ran 8.0 minutes per mile.

2) C)

For C, the other runner talks about the same rate as b), not a). This is because they are referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.

If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.

The weight of the glass cover is 1.225 pounds, which is less than the chain's maximum capacity of 35 pounds. Therefore, the chain can support the light cover.

To determine if the chain can support the light cover, we need to find the weight of the glass cover.

Since the cover is shaped like a square pyramid, the weight of the glass cover can be found by multiplying the area of one side of the pyramid by the thickness of glass and the weight per square foot of the glass.

Assuming that each side of the square pyramid measures 1 foot and the thickness of the glass is also 1 foot, the total weight of the glass cover can be found as follows:

Area of one side of the pyramid = (1/2) * 1 * 1 = 1/2 square feet

Weight of glass cover = (1/2) * 2.45 = 1.225 pounds

Since the weight of the glass cover is less than the chain's maximum capacity of 35 pounds, the chain can support the light cover.

So, we can say that yes, the chain can support the light cover.

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The equation of the ellipse with foci at ​(39​,0) and ​(-39​,0) and a constant difference of 30 is given as follows:

x²/39² + y²/9² = 1.

The equation of an ellipse of center (h,k) is given by the rule presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

In which:

The coordinates of the foci are given as follows:

​(39​,0) and ​(-39​,0).

The center is the midpoint of these two coordinates, hence:

The coefficient a is given as follows:

a = |39 - 0| = |0 - 39| = 0.

Considering the constant difference of 30, the constant b is given as follows:

b = a - 30 = 39 - 30 = 9.

Thus the equation of the ellipse is given as follows:

x²/39² + y²/9² = 1.

The problem asks for the equation of the ellipse with the given features.

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The orthogonal complement W⊥ of W, where W = {y : x + y - z = 0}, is spanned by the vector [1, -1, 1].

To find the orthogonal complement W⊥ of W, we need to find vectors that are orthogonal (perpendicular) to every vector in W.

The set W consists of vectors [y, x, z] that satisfy the equation x + y - z = 0.

For a vector [a, b, c] to be in W⊥, it should satisfy the condition a(y) + b(x) + c(z) = 0 for all vectors [y, x, z] in W.

Substituting the values from W into the equation, we have a(y) + b(x) + c(z) = a(x + y - z) + b(y) + c(z) = ax + ay - az + by + cz = (a + b)x + (a + b)y + (c - a)z = 0.

This gives us the following equations: a + b = 0, a + b = 0, and c - a = 0.

Solving these equations, we find that a = -b and c = a.

Therefore, the vectors in W⊥ can be written as [a, -a, a], where a is any real number

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The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

The missing image is attached with the answer below.

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If the MSbetween (Mean Square Between) is lower than the MSwithin (Mean Square Within), the F value will be less than 1.

The F value is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). It is used in analysis of variance (ANOVA) to test for significant differences among group means. The F value follows an F-distribution, and its magnitude determines the statistical significance of the differences between groups.

When the MSbetween is lower than the MSwithin, it indicates that the variability between groups is smaller compared to the variability within groups. This suggests that the differences observed among the group means are not substantial or meaningful. In other words, there is more similarity within the groups than between them.

Since the F value is calculated as the ratio of MSbetween to MSwithin, if the numerator (MSbetween) is smaller than the denominator (MSwithin), the F value will be less than 1.

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The standard deviation of the sampling distribution of the sample mean would be approximately 2.8284

To determine the standard deviation of the sampling distribution of the sample mean, we will use the formula;

σ_mean = σ / √n

where σ is the standard deviation of the population that is 20 and n is the sample size (n = 50).

So,

σ_mean = 20 / √50 = 20 / 7.07

σ_mean  = 2.8284

The standard deviation of the sampling distribution of the sample mean is approximately 2.8284 it refers to that the sample mean would typically deviate from the population mean by about 2.8284, assuming that the sample is selected randomly from the population.

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The complete question is;

Another application of the sampling distribution of the sample mean Suppose that, out of a total of 559 full-service restaurants in Delaware, the number of seats per restaurant is normally distributed with mean mu = 99.2 and standard deviation sigma = 20. The Delaware tourism board selects a simple random sample of 50 full-service restaurants located within the state and determines the mean number of seats per restaurant for the sample. The standard deviation of the sampling distribution of the sample mean is Use the tool below to answer the question that follows. There is a.25 probability that the sample mean is less than

Step-by-step explanation:

isidhxibdofeixeosgzifisvsoshzibdihddgd

Answer:

heres the square root of 20 4.47214 but i dont know what else to do for this answer. (sorry)

Step-by-step explanation:

√20 = √(4 * 5) = √4 * √5 = 2√5 ≈ 4.47214

\(\huge\text{Hey there!}\)

\(\huge\textsf{13 - (-18)}\)

\(\huge\textsf{= 13 + 18}\)

\(\huge\textsf{= \bf 31}\)

\(\boxed{\boxed{\huge\text{Therefore, your answer is most likely: \textsf{31}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\huge\text{Amphitrite1040:)}\)

Answer:

\( \displaystyle 31\)

Step-by-step explanation:

we want to simplify the following expression:

\( \displaystyle 13 - ( - 18)\)

remove parentheses and change its sign because we know that two negatives make positive Thus:

\( \displaystyle 13 + 18\)

finally simplify addition:

\( \displaystyle\bf \fbox{31}\)

hence,

\( \displaystyle 13 - ( - 18) = \boxed{31}\)

True. Marginal cost refers to the additional cost incurred by producing one more unit of output.

Since the production of one more unit requires the use of additional variable factors of production (such as labor or raw materials), marginal cost always reflects the cost of those variable factors. Fixed costs, on the other hand, do not change with changes in output and are not included in marginal cost calculations. Therefore, marginal cost only reflects the change in cost associated with variable factors of production.

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Answer:

1331 feet3

Step-by-step explanation:

Answer:

V = (1/3)(121 in^2)(11 in) = 443.7 in^3

Step-by-step explanation:

If the side length of the square base is 11 cm, then the area of that base is (11 cm)^2, or 121 cm^2.  If the height of the pyramid is 11 cm (as you seem to indicate), then the volume of the squre pyramid is

V = (1/3)(121 in^2)(11 in) = 443.7 in^3

Answer: 5 degrees

Step-by-step explanation:

The difference between -7 and -12 is 5, I don't know what you are asking for though.

This will give you the MSE value for the new model, which excludes the statistically insignificant independent variable.

To run the regression model in RStudio and calculate the Mean Squared Error (MSE), we need to perform the following steps:

1. Import the data into RStudio. Let's assume the data is stored in a data frame called "data".

```R

data <- data.frame(

 Graduate = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),

 StartingSalary = c(40, 46, 54, 39, 37, 38, 48, 52, 60, 34),

 GPA = c(3.2, 3.5, 3.6, 2.8, 2.9, 3.0, 3.4, 3.7, 3.9, 2.8),

 Activities = c(4, 5, 2, 4, 3, 4, 5, 6, 6, 1)

)

```

2. Run the regression model using the lm() function in R. We will use the StartingSalary as the dependent variable and GPA and Activities as independent variables.

```R

model <- lm(StartingSalary ~ GPA + Activities, data = data)

```

3. Calculate the Mean Squared Error (MSE) of the model. The MSE is obtained by dividing the sum of squared residuals by the number of observations.

```R

mse <- sum(model$residuals^2) / length(model$residuals)

mse

```

This will give you the MSE value of the model.

To run the regression model again without including the statistically insignificant independent variable, you would need to determine which variable is statistically insignificant. You can do this by examining the p-values of the coefficients in the model summary.

```R

summary(model)

```

Look for the p-values associated with each coefficient. If a p-value is greater than the desired significance level (e.g., 0.05), it indicates that the corresponding independent variable is not statistically significant.

Suppose, for example, the Activities variable is found to be statistically insignificant. In that case, you can run the regression model again without including it and calculate the MSE for this new model.

```R

new_model <- lm(StartingSalary ~ GPA, data = data)

mse_new <- sum(new_model$residuals^2) / length(new_model$residuals)

mse_new

```This will give you the MSE value for the new model, which excludes the statistically insignificant independent variable.

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Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

How closely a value relates to the mean of a set of values is expressed by a Z-score.

The Z-score is created using standard deviations from the mean.

A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.

So, in order to determine how far the raw score deviates from the mean, the Z score is used.

The following steps are used to determine the Z score:

z = (x - μ)/σ

We know that:  x > 550 and μ = 500, σ = 40

z = 550 - 500 / 40

z = 1.25

The graph of the normal distribution indicates:

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

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After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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Power1: Power1 will perform 3 multiplications when computing 332, and 2 multiplications when computing 319.

Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.

Power2: Power2 will perform 6 multiplications when computing 332, and 5 multiplications when computing 319.

Power3: Power3 will perform 10 multiplications when computing 332, and 9 multiplications when computing 319.

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Answer:

\(\frac{29}{50}\)

Step-by-step explanation:

\(\frac{29}{50}\) put into decimal form is 0.58 (aka 58%)

The person above me was correct but didn't have the answer in fraction form.

The probability that a randomly chosen person on the bus is an adult chaperone or a male student is 0.58.

We have the following data -

On a field trip there are 6 adult chaperones, 21 female students, and 23 male students on a bus.

We have to find the probability that a randomly chosen person on the bus is an adult chaperone or a male student.

The formula to calculate the probability of an event is -

P(A) = n (A) / n(S)

Where -

n(A) - Number of favorable outcomes.

n(S) - Number of elements in the sample space.

In the question given to us, we have -

n (A) = favorable outcomes = 23 + 6 = 29

n (S) =  Elements in the sample space 23 + 21 + 6 = 50

Hence, the probability that a randomly chosen person on the bus is an adult chaperone or a male student is -

P(A) = \(\frac{n(A)}{n(S)}\) = \(\frac{29}{50}\) = 0.58

Hence, the probability of choosing will be 0.58.

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Answer: x ≈ 6.86°

Step-by-step explanation:

Firstly, set them equal to each other:

(7x + 24) = 72°

Subtract 24 from both sides:

7x = 48°

Divide both sides by 7:

x ≈ 6.857...

This can be rounded to:

x ≈ 6.86°

The perimeter of the parallelogram with these vertices. (3, 6), (-5, 6), (6, -1), (-2, -1)  is 37.64

Let

A = (3, 6) B = (-5, 6) C = (6, -1) D = (-2, -1)

The distance between two points (x₁, y₁) and (x₂, y₂) is

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Length of AB

AB = √((-5 - 3)² + (6 - 6)²)

AB = √((-8)² + 0²)

AB = √(64 + 0) = √64

AB = 8

Length of BC

BC = √((6 - (-5))² + (-1 - 6)²)

BC = √((6 + 5)² + (-7)²)

BC = √(11² + 49) = √(121 + 49)

BC = √170

Length of CD

CD = √((-2 - 6)² + (-1 - (-1))²)

CD = √((-8)² + 0²)

CD = √(64 + 0) = √64

CD = 8

Length of DA

DA = √((3 - (-2))² + (6 - (-1))²)

DA = √((3 + 2)² + (7)²)

DA = √(5² + 49)

DA = √(25 + 49)

DA = √74

Perimeter = AB + BC + CD + DA

Perimeter = 8 + √170 + 8 + √74

Perimeter = 16 + √170 + √74

Perimeter = 37.64

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Answer:

y = 5 - ×

Step-by-step explanation:

I guessed but the numbers work

Answer:

Given:

Solving for y in steps

Multiply both sides by m:

Add 3b to both sides:

Divide both sides by 3:

Merchants from the Islamic world who traded with Europeans, innovations from ancient India.

India also gave the world chess, snakes and ladders, basmati rice, yoga, Sanskrit, Ayurveda, water on the moon, cosmetic surgery, the binary number system, ink, Fibonacci numbers, fibre optics, USB, and a host of other inventions.

As is well known, in 628 AD, Brahmagupta gave the first definition of "zero" and its use. He was a Hindu mathematician and astronomer who invented the "zero" sign, which is a dot under numerals. The Zero Project considers that the number "zero" has been there for a while without claiming to have created it.

Thus, merchants from the Islamic world who traded with Europeans, innovations from ancient India.

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Answer:

C.78%

Step-by-step explanation:

Answer:c.78%

Step-by-step explanation:

Answer:

53.658

Step-by-step explanation:

The equation of the normal plane to the surface at the point (3, 9, 27) is

ax - ty - z + (9t - 3a + 27) = 0

The equation of the normal plane to the surface defined by the equation f(x, y, z) = 0 at a given point (a, b, c), we need to find the gradient vector of the surface at that point. The gradient vector will be normal to the surface at that point.

In this case, the surface is defined by the equation f(x, y, z) = amt - yt - z = 0, and the given point is (3, 9, 27).

First, let's find the gradient vector of f(x, y, z) at the point (a, b, c):

∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Taking the partial derivatives of f(x, y, z) = amt - yt - z with respect to x, y, and z, we have:

∂f/∂x = a

∂f/∂y = -t

∂f/∂z = -1

Therefore, the gradient vector is:

∇f = (a, -t, -1)

Now, we have the normal vector to the surface at the point (a, b, c). To find the equation of the normal plane, we can use the point-normal form of the plane equation.

The equation of the normal plane is given by:

(a - x)(x - 3) + (-t)(y - 9) + (-1)(z - 27) = 0

Simplifying, we get

a(x - 3) - t(y - 9) - (z - 27) = 0

Expanding, we have

ax - 3a - ty + 9t - z + 27 = 0

So, the equation of the normal plane to the surface at the point (3, 9, 27) is

ax - ty - z + (9t - 3a + 27) = 0

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For the multisets {3 · a, 2 · b, 1 · c} and {2 · a, 3 · b, 4 · d} the solutions are  A ∪ B is {3 · a, 2 · b, 1 · c, 2 · a, 3 · b, 4 · d},A ∩ B is {2 · a, 2 · b},A − B is {1 · a, 0 · b, 1 · c} ,B − A is {0 · a, 1 · b, 4 · d} and A + B is {5 · a, 5 · b, 1 · c, 4 · d}.

We will use the given multisets A and B:

A = {3 · a, 2 · b, 1 · c}
B = {2 · a, 3 · b, 4 · d}

a) A ∪ B (union): This operation combines all elements of both multisets.
A ∪ B = {3 · a, 2 · b, 1 · c, 2 · a, 3 · b, 4 · d}

b) A ∩ B (intersection): This operation finds the common elements between both multisets.
A ∩ B = {2 · a, 2 · b} (as a and b are the common elements)

c) A − B (difference): This operation removes elements in B from A.
A − B = {1 · a, 0 · b, 1 · c}

d) B − A (difference): This operation removes elements in A from B.
B − A = {0 · a, 1 · b, 4 · d}

e) A + B (sum): This operation adds the counts of the elements in both multisets.
A + B = {5 · a, 5 · b, 1 · c, 4 · d}

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Answer:

y = 1/4x - 8

Step-by-step explanation:

Given

y + 2 = 1/4 ( x - 24 )

Arranging in slope intercept form; y = mx + c

y + 2 = 1/4x - 24 /4

y+ 2 = 1/4x - 6

y = 1/4x - 6 - 2

y = 1/4x - 8

Hope it will help :)

Answer:

y=1/4×-8

Step-by-step explanation:

say thanks if you like