1+1+1+1+1+1 to the power of 9.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

Answer:

7

Step-by-step explanation:

7/12 of 12

7/12 × 12

7/1 × 1

= 7

Answer:

He has a lot of money

Step-by-step explanation:

The probability density function of EX + (1 - §)Y is given by f(x) * p + g(x) * (1 - p), where f(x) and g(x) are the density functions of X and Y, respectively, and p is the probability of success for the Bernoulli distributed random variable §.

To compute the probability density function (pdf) of EX + (1 - §)Y, we can make use of the properties of expected value and independence. The expected value of a random variable is essentially the average value it takes over all possible outcomes. In this case, we have two random variables, X and Y, with their respective density functions f(x) and g(x).

The expression EX + (1 - §)Y represents a linear combination of X and Y, where the weight for X is the probability of success p and the weight for Y is (1 - p). Since the Bernoulli random variable § is independent of X and Y, we can treat p as a constant in the context of this calculation.

To find the pdf of EX + (1 - §)Y, we need to consider the probability that the combined random variable takes on a particular value x. This probability can be expressed as the sum of two components. The first component, f(x) * p, represents the contribution from X, where f(x) is the density function of X. The second component, g(x) * (1 - p), represents the contribution from Y, where g(x) is the density function of Y.

By combining these two components, we obtain the pdf of EX + (1 - §)Y as f(x) * p + g(x) * (1 - p).

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The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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The z-score corresponding to a sample mean of 69 is approximately -0.286.

The z-score corresponding to a sample mean of m = 69 can be calculated using the formula:
z = (m - µ) / (σ / √n)
Plugging in the given values, we get:
z = (69 - 71) / (21 / √9)
z = -0.86
Therefore, the z-score corresponding to a sample mean of m = 69 is -0.86.
To calculate the z-score for a sample mean (m) of 69, given a population mean (µ) of 71, standard deviation (σ) of 21, and sample size (n) of 9, use the formula:
z = (m - µ) / (σ / √n)
Plug in the values:
z = (69 - 71) / (21 / √9)
z = -2 / (21 / 3)
z = -2 / 7
z = -0.286
The z-score corresponding to a sample mean of 69 is approximately -0.286.

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Answer: x = 38

116

38

28

Step-by-step explanation:

2x + 40 + x + x - 12 = 180

Simplify.

4x + 28 = 180

Subtract 28 on both sides.

4x = 152

Divide by 4 on both sides.

x = 38



Answer:

-35

Step-by-step explanation:

PEMDAS

Answer:

-35

Step-by-step explanation:

PEMDAS

solve for 3+4=7

-5*7=-35

The y-intercept of the line passes through (12,-4) and (-6,10) is 32/6

Let (x1, y1) = (12, -4)

and (x2, y2) = (-6, 10)

Using the formula of the two-point form of equation of line,

(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)

(y + 4)/(10 + 4) = (x - 12)/(-6 - 12)

(y + 4)/14 = (x - 12)/(-18)

-18y -72= 14x - 168

-18y = 14x - 168 + 72

-18y = 14x - 96

y = -(14/18)x + 96/18

y = -7/9 x + 32/6

Comparing with slope-intercept form of line y = mx + b

y-intercept(b) = 32/6

Therefore, the y-intercept of the line passes through (12,-4) and (-6,10) is 32/6

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We should use Multiple regression to predict an indivdual's weight change.

To determine if we can use sugar intake and hours of exercise to predict an individual's weight change, the test that we should use is

Multiple regression is a type of regression analysis in which multiple independent variables are studied to evaluate their effect on a dependent variable.

The dependent variable is also referred to as the response, target or criterion variable, while the independent variables are referred to as predictors, covariates, or explanatory variables.

Therefore, option A (Multiple Regression) is the correct answer for this question.

Pearson's correlation is a statistical technique that is used to establish the strength and direction of the relationship between two continuous variables.

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Simplify the expression and express in standard form.

So answer is,

The best choice to display the numbers which are outliers as well as the mean for the given data [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32] would be a Box-and-Whisker Plot.

In a Box-and-Whisker Plot, the central box represents the interquartile range (IQR), which contains the middle 50% of the data. The line within the box represents the median. Outliers, which are values that lie significantly outside the range of the rest of the data, are depicted as individual points outside the box.

By using a Box-and-Whisker Plot, we can visually identify the outliers in the data set and observe how they deviate from the rest of the values. Additionally, the plot displays the median, which represents the central tendency of the data. This allows us to simultaneously analyze both the outliers and the mean (through the median) in a concise and informative manner.

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Answer:

x=-5400/5323

Step-by-step explanation:

Answer:

  false

Step-by-step explanation:

They will be scaled copies of each other where the scale factor is 1. The claim is false.

Solution a needed 70 ounces and solution b needed 50 ounces

What does "1 ounce" mean?

One ounce weighs 437.5 grains or 28.349 grams and is a sixteenth of a pound (avoirdupois) of weight.

One ounce, abbreviated "oz," equals 480 grains, or 31.103 grams, and is one-twelfth of a Troy or Apothecaries' pound in weight. abbreviation for fluid ounce. a tiny amount or percentage.

So, let x=the of ounces of the 50% acid solution. The total volume after both are mixed is 100 ounces so the amount of the 20% solution will be 120-X. The equation will therefore be:

50% * x + 20% * (100-x) = 41% * 100

Dropping the ‘%’ we get

50x + 2000 - 20x = 4100

30x = 2100

x = 2100/30 = 70

Hence 70 ounces will be needed

Solution a = 70 ounces

Solution b = 50 ounces

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Thus, the expected number of calls in one hour is 15.

To find the expected number of calls in one hour, we need to convert the rate of one call every four minutes into calls per hour.

There are 60 minutes in an hour, so we divide 60 by 4 to find the number of four-minute intervals in one hour.

60 minutes / 4 minutes = 15 intervals

Therefore, the rate of one call every four minutes translates to 15 calls per hour.

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Answer:

When f or g are equivalent to a number you are solving for x. For example b, d, e, f. In the equation g(x) =2x2-5 I assumed 2 was a typo. So, if it's incorrect, please use same steps and just adjust the solution.

Step-by-step explanation:

\(f(x)=-\frac{2}{3x}+3\)

a) \(f(3)=-\frac{2}{2(3)} +3\)

           \(=-\frac{1}{3}+3\) \(=\frac{-1+6}{3}\) \(=\frac{5}{3}\)

b) \(f(x)=-5\)

      \(-5=-\frac{2}{3x}+3\)

      \(-8=-\frac{2}{3x}\)

  \(-24x=-2\)

        \(x=\frac{1}{12}\)

\(g(x)=2x-5\)

c) \(g(-3)=2(-3)-5\)

               \(=-6-5\)

               \(=-11\)

d) \(g(x)=-7\)

      \(-7=2x-5\)

      \(-2=2x\)

        \(x=-1\)

e) \(g(x)=8\)

        \(8=2x-5\)

       \(12=2x\)

        \(x=6\)

f)  \(g(x)=9\)

         \(9=2x-5\)

        \(11=2x\)

         \(x=\frac{11}{2}\)

As per the proportion the reason behind equal amounts of each color in every bag has the proportion less than the other colors.

The term called proportion is defined as  an equation that defines that the two given ratios are equivalent to each other

Here we know that they may not put equal amount of colors because they put the 2 most popular colors in the bag.

Because of the the popular colors of bag were Blue and Orange. Here as per the proportion of other color bags are less than that of blue and orange.

This is the real reason behind the Mars put more amount in more popular colors and less amount in less popular colors.

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The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.

The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-

To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.

34/9 = 3(⁷/₉)

43/9 = 4(⁷/₉)

32/5 = 6(²/₅)

Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.

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Answer:First one is first step. 2 is Last step. 3 is fourth step. 4 is second step. 5 is Third step

Step-by-step explanation:

I went down the column

Answer:

the answer i got is 2 (x+1) (2x^2-2x+1) / x :)

Answer:

\(\frac{2x}{x-1}\)

Step-by-step explanation:

\(\frac{4x^2+4x}{2x^2-2}\) ← factor numerator and denominator

= \(\frac{4x(x+1)}{2(x^2-1)}\) ← cancel 4 and 2 on numerator/denominator by 2

= \(\frac{2x(x+1)}{x^2-1}\) ← x² - 1 is a difference of squares

= \(\frac{2x(x+1)}{(x-1)(x+1)}\) ← cancel (x + 1) on numerator and denominator

= \(\frac{2x}{x-1}\)

Answer:

Increase of 9.3%

Step-by-step explanation:

Hence, the percent increase in salary did Jerry receive is \(4.68\)%.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Here given that,

Jerry’s monthly salary was $\(3,050\) last year. This year his monthly salary is $\(3,350\).

His monthly salary in last year is $ \(3050\).

In this year his salary is $\(3350\).

So, the increase in salary is

\(3350-3050=300\)

And the overal salary is $ \(3050+3350=6400\)

So, the percent increase in salary did Jerry receive is

\(\frac{300}{6400}\) × \(100=4.68\)

Hence, the percent increase in salary did Jerry receive is \(4.68\)%.

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Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

The residual if you know the actual number is 3 and the predicted value is 1.6l is 1.4.

The residual is a measure of the difference between the predicted value and the actual value. In this case, the actual number is 3, and the predicted value is 1.6. To find the residual, we subtract the predicted value from the actual value:

Residual = Actual Value - Predicted Value

= 3 - 1.6

= 1.4

Therefore, the residual in this case is 1.4.

The residual represents the error or the amount by which the predicted value differs from the actual value.

A positive residual indicates that the predicted value is lower than the actual value, while a negative residual indicates that the predicted value is higher than the actual value.

In this case, the positive residual of 1.4 indicates that the predicted value of 1.6 underestimates the actual value of 3 by 1.4.

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The profit percentage for the given cost price and the selling price is 25 percent.

The money that remains after paying your business expenses is your profit. Gross profit, operating profit, and net profit are the three primary types of profit. The largest profit is gross. The amount left over after paying for the sold goods and services is displayed.

Given that, a cupboard was bought for Rs.2000 and sold for Rs. 2500.

Profit = Selling price - Cost price

Here, profit = 2500-2000= ₹500

We know that, Profit percentage (%) = Profit/Cost price ×100

So, Profit percentage (%) =500/2000 ×100

= 1/4×100= 25%

Therefore, the profit percentage is 25 percent.

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Your question is incomplete, probably the complete question/missing part is:

A cupboard was bought for Rs.2000 and sold for Rs. 2500. Find the profit or loss percent.