9. 12 points for the linear operator 2.r т y - on R2 and the ordered bases B:= {[+1 0) : and B' := - {:0} 0 (a) find the matrix representation (TB of T relative to B: (b) find the matrix representation (Tle of T relative to B' directly and then by the change of matriz representation formula.

Answer:

5 is rounded to 5.0

Step-by-step explanation:

Answer: i think c but it might not be right

Step-by-step explanation:

Answer:

it's c

Step-by-step explanation:

This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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The 90% confidence interval estimate for the population mean is (67.325, 72.675).

To construct a confidence interval estimate for the population mean, we can use the formula:

CI = x ± z * (σ/√n)

where CI is the confidence interval, x is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Given the values x = 70, σ = 15, and n = 65, we need to determine the z-score for a 90% confidence level. Using a standard normal distribution table or calculator, the z-score for a 90% confidence level is approximately 1.645.

Substituting the values into the formula, we have:

CI = 70 ± 1.645 * (15/√65)

Simplifying the expression, we get:

CI = (70 - 1.645 * (15/√65), 70 + 1.645 * (15/√65))

Calculating the values, we find:

CI ≈ (67.325, 72.675)

Therefore, the 90% confidence interval estimate for the population mean is (67.325, 72.675). This means that we can be 90% confident that the true population mean falls within this interval.

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Required:

We need to fill the given diagram with suitable words.

Explanation:

Consider the first line.

There is a choice of fish-bottled water is coming from fish and bottled water.

Consider the second like there is Chicken-bottled water and we have bottled water.

There must be chicken under food.

There are only three types of drink that are Bottled water, Soft drink, and juice.

In drinks for fish, there are already two drinks Bottled water and juice so the remaining is Soft drinks.

Chicken and juice give a choice of Chicken-Juice.

Vegetable and Juice give a choice of Vegetable- Juice.

Answer:

\(\theta = \frac{\pi}{6}\)

Step-by-step explanation:

\(tan^ 2 \theta - ( \sqrt 3 + \frac{1}{\sqrt3}}) tan \theta + 1 = 0\\\\tan \theta - ( \sqrt 3 + \frac{1}{\sqrt3}}) +\frac{1}{ tan \theta } = 0\\\\\)          \([ \ divide \ by \ tan \theta \ on \ both \ sides \ ]\)

\(tan\theta + \frac{1}{ tan \theta }- ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\frac{tan^2 \theta + 1}{ tan \theta } - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\frac{sec ^2 \theta}{ \frac{sin \theta }{cos \theta}} - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\)              \([ \tan ^ 2\theta + 1 = sec ^2 \theta \ , \ tan \theta = \frac{sin \theta }{cos \theta } \ ]\)

\(\frac{sec^2 \theta }{sin \theta \times sec \theta } - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\)                  \([\ \frac{sin \theta }{cos \theta } = sin \theta \times sec \theta \ ]\)

\(\frac{sec \theta }{sin \theta } - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\)

\(sec \theta \ cosec \theta - ( \sqrt 3 + \frac{1}{\sqrt3}}) = 0\\\\\)              \([ \ \frac{1}{sin \theta } = cosec \theta \ , \ \frac{ sec \theta }{sin \theta } = sec \theta cosec \theta \ ]\)

\(sec \theta \ cosec \theta - \sqrt 3 - \frac{1}{\sqrt3}} = 0\\\\\frac{\sqrt 3\ sec \theta \ cosec \theta - 3 - 1}{\sqrt3} = 0\\\\\sqrt 3 sec \theta cosec \theta - 4 = 0\\\\\)              

\(\sqrt3 \frac{1}{cos \theta } \frac{1}{sin \theta } - 4 = 0\\\\\frac{\sqrt3 - 4sin \theta cos \theta} { sin \theta cos \theta } = 0\)                      

\(\sqrt 3 - 2sin 2\theta = 0\)                                  \([ \ sin 2 \theta = 2 sin \theta cos \theta \ ]\)

\(2sin 2 \theta = \sqrt3\\\\sin 2 \theta = \frac{\sqrt3 }{2} \\\\2 \theta = sin^{-1} (\frac{\sqrt3}{2})\\\\2 \theta = 60^{ \circ} = \frac{ \pi}{3}\\\\\theta = \frac{\pi} {6}\)

To convert a mass value from grams to nanograms, we need to multiply the given value by a conversion factor. In this case, we can convert 0.00000000572 grams to nanograms by multiplying it by 1,000,000,000.

To convert grams to nanograms, we use the conversion factor that 1 gram is equal to 1,000,000,000 nanograms. Therefore, to convert the mass of 0.00000000572 grams to nanograms, we multiply it by the conversion factor:

0.00000000572 g × 1,000,000,000 ng/g = 5.72 ng

Hence, the mass of 0.00000000572 grams is equivalent to 5.72 nanograms.

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To convert a mass of 0.00000000572 g to ng (nanograms), we can multiply the given mass by a conversion factor.

The prefix "nano-" represents a factor of 10^-9. Therefore, to convert grams to nanograms, we need to multiply the given mass by 10^9.

0.00000000572 g × 10^9 ng/g = 5.72 ng

By multiplying the mass in grams by the conversion factor, we find that the mass of 0.00000000572 g is equivalent to 5.72 ng.

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The base and exponent of −2^4 are

Base: -2

Exponent: 4

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

-2^4

In the expression -2^4, -2 is the base and 4 is the exponent.

The base is the number that is being multiplied by itself and the exponent is the number of times the base is being multiplied by itself.

In this case the base is -2 and the exponent is 4.

So the expression -2^4 means -2 multiplied by itself 4 times.

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Answer:

It means that the quantities have the same relative size. In other words they have the same ratio.

Step-by-step explanation:

For example look at the attached files

Answer: 1. 452.39

2. 28.54

3.50.27

4. 60.28

Step-by-step explanation:

area=\(\pi r^{2}\)

12*12=144

144*3.14=452.39

25*3.14=28.54

circumference=\(2\pi r\)

2*3.14*8=50.27

2*3.14*10=62.83

Answer:

4/5 is the slope

Step-by-step explanation:

The line is written in the form

y = mx+b where m is the slope and b is the y intercept

y = 4/5x -3

4/5 is the slope and -3 is the y intercept

Answer:

8,000 pounds

Step-by-step explanation:

1 US ton = 2,000 pounds

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

1 ton is 2000 pounds

4 tons = 8000 pounds

Answer:

i.x=1      (x,y)=(1,3)

y=3

ii.x=2      (x,y)=(2,4)

y=4

iii.x=3      (x,y)=(3,5)

y=5

iv.x=4       (x,y)=(4,6)

y=6

v.x=5        (x,y)=(5,7)

y=7

Step-by-step explanation:

To differentiate the expression Y(X) = 2V*-1, we can use the power rule of differentiation. First, we need to consider that V* is a variable and treat it as a constant when differentiating with respect to X.

So, differentiating the expression Y(X) = 2V*-1 with respect to X, we get:

dY/dX = d/dX (2V*-1)
= 2dV*/dX

We can simplify this expression by storing the result in a variable called "firstder":

import sympy as sp
Vstar = sp.Symbol('V*')
X = sp.Symbol('X')

firstder = 2*sp.diff(Vstar,X)

Now, the variable "firstder" contains the symbolic expression for the derivative of Y with respect to X.

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The  insect population that is growing at a faster rate is; A. The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week.

From the graph attached, we see that he ants have an exponential growth because the equation is; y = 3.8ˣ.

Now after each week, the colony multiplies by 3.8.

First week is; y = 3.8¹ = 3.8

Second week would have; y = 3.8² = 14.44.

Third week would have; y = 3.8³ = 54.9.

However, the second graph which is a linear function shows that bee hive growth adds 3.8 after each week. This means that;

The second week would have; 2 * 3.8 = 7.6

The 3rd week would have; 3 * 3.6 = 11.4.

Thus, we conclude that the ant colony is growing faster

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Answer:

The answer is D

Step-by-step explanation:

The person who saked this question will find this useless but this is for all the other ppl to come here for the answer

We have shown that:  lim (n → ∞) ∑[(x²+1)Δx] = 14/3  and we have calculated the definite integral of f(x) over the interval [0, 2].

A definite integral is a mathematical concept that represents the area under the curve of a function between two specific points on the x-axis.

It is denoted by ∫f(x)dx, where f(x) is the function being integrated, and dx represents an infinitely small change in x

This problem requires us to recognize the limit as a Riemann sum for a function and calculate the definite integral of the function.

Given: Ax=2, xᵢ= iAx = 2i, n → ∞, f(x) = x² + 1.

First, we can express the Riemann sum as:

∑[f(xᵢ)Δx] = ∑(2i)² + 1 = 4∑(i²) + 2n

Next, we can recognize the limit as the definite integral of f(x) over the interval [a, b]:

lim (n → ∞) ∑[f(xᵢ)Δx] = ∫[a, b] f(x) dx = ∫[0, 2] (x² + 1) dx = [x³/3 + x] [0, 2] = 8/3 + 2 = 14/3

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Answer:

100

Step-by-step explanation:

a triangle is 180, so 180-58-22 is your answer

The difference quotient of the function f(x) = 4x² - 5x is 8x + 4h - 5.

The formula for difference quotient is expressed as:

\(\frac{f(x+h)-f(x)}{h}\)

Given the function in the question:

f(x) = 4x² - 5x

To solve for the difference quotient, we evaluate the function at x = x+h:

First;

f(x + h) = 4(x + h)² - 5(x + h)

Simplifying, we gt:

f(x + h) = 4x² + 8hx + 4h² - 5x - 5h

f(x + h) = 4h² + 8hx + 4x² - 5h - 5x

Next, plug in the components into the difference quotient formula:

\(\frac{f(x+h)-f(x)}{h}\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - (4x^2 - 5x)}{h}\\\\Simplify\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - 4x^2 + 5x)}{h}\\\\\frac{(4h^2 + 8hx - 5h)}{h}\\\\\frac{h(4h + 8x - 5)}{h}\\\\8x + 4h -5\)

Therefore, the difference quotient is 8x + 4h - 5.

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Step-by-step explanation:

here ! I used the formula area = length × width

and just some algrbric expressions solving

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

The expression that shows how many pears Christina picked is 15 - p.

The problem states that Philip picked 15 pears. Let's call the number of pears that Christina picked "x". We know that Christina picked fewer pears than Philip, so we can express that relationship as:

x = 15 - p

The reason for this expression is that if Philip picked 15 pears and Christina picked "p fewer pears than Philip", we can subtract "p" from the 15 pears that Philip picked to get the number of pears that Christina picked. That is, Christina's number of pears (x) equals 15 minus the number of pears that Philip picked (p).

For example, if Philip picked 10 pears, then Christina picked p fewer pears, which is 10 - p. If Philip picked 15 pears, then Christina picked 15 - p. This expression allows us to calculate the number of pears that Christina picked based on the number of pears that Philip picked (represented by "p").

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Therefore, the expression \(t^{(-3/4)}\) in rational form is:

\(B. 1/^4 \sqrt {t^3}\)

What is the exponential function?

An exponential function is a mathematical function of the form:

f(x) = aˣ

where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.

To write the expression \(t^{(-3/4)}\) in rational form, we need to eliminate the negative exponent.

Recall that a negative exponent can be rewritten as the reciprocal of the positive exponent. In this case,  \(t^{(-3/4)}\) can be written as 1/ \(t^{(-3/4)}\).

Therefore, the expression \(t^{(-3/4)}\)in rational form is:

\(B. 1/^4 \sqrt {t^3}\)

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There are 57 different ways a person can vote for the regional judges.

To determine the number of different ways a person can vote for regional judges, we can use the concept of combinations. In this case, we want to find the number of ways to choose a certain number of judges from a total of 6 candidates.

Since voters can choose to vote for 0, 1, 2, 3, or 4 judges, we need to find the sum of all the possible combinations for each number of judges.

For choosing 0 judges, there is only one possible combination (choosing none).

For choosing 1 judge, there are 6 possible combinations (choosing one out of the six candidates).

For choosing 2 judges, there are \(C(6, 2) = 15\) possible combinations. This is calculated using the combination formula, which  \(C(n, r)\)represents the number of combinations of choosing r items from a set of n items.

For choosing 3 judges, there are \(C(6, 3) = 20\) possible combinations.

For choosing 4 judges, there are \(C(6, 4) = 15\) possible combinations.

To find the total number of different ways a person can vote, we sum up the number of combinations for each scenario:

\(1 + 6 + 15 + 20 + 15 = 57\)

Therefore, there are 57 different ways a person can vote for the regional judges.

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Answer:

The estimate size of the crowd is 52800 people

Step-by-step explanation:

The given information are;

The number of people that fit comfortably in a 2 by 2 foot area = 5

Therefore, we have;

The area occupied by the 5 people = 2 × 2

The crowd ratio = 5/(2 × 2) = 5/4

The area occupied by the crowd = 4 feet deep, and 1 mile long on both sides of the street

By conversion factors, 1 mile = 5,280 feet

Therefore, the area occupied by the crowd = 4 × 5280 × 2 = 42240 ft²

The number of people in the crowd = Crowd ratio × The area occupied by the crowd

The number of people in the crowd = 5/4 × 42240 = 52800 people

Therefore, The estimated size of the crowd = 52800 people.

Answer:  3/4

Step-by-step explanation:

The slope = (y2-y1)/(x2-x1) for two points (x1,y1) and (x2,y2).

In this image, the two points are (-3,-2) and (1,1)

We can plug this into the equation.

Slope = (1-(-2))/(1-(-3))

Slope = 3/4

Answer:

slope = \(\frac{3}{4}\)

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 ) = (- 3, - 2) and (x₂, y₂ ) = (1, 1) ← 2 points on the line

m = \(\frac{1-(-2)}{1-(-3)}\) = \(\frac{1+2}{1+3}\) = \(\frac{3}{4}\)

During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Answer:

Step-by-step explanation:

What you are testing is a distribution of means, because you have a sample of eleven individuals (N=11), a population mean, and the population variance. Basically, the problem is asking: what is the likelihood that the sample mean (153.45 lbs) could have been obtained from a population where (M=149) if the null hypothesis is true?

p1: 15 year old boys with a mean weight of 153.45 lbs from City "Unknown".

p2: 15 year old boys with a mean weight of 149.00 lbs from the population.

H1: The sample of boys from City "Unknown" was not drawn from a population where the average weight of 15 year old boys = 149lbs.

H0: The sample of boys from City "Unknown" was drawn from a population where the average weight of 15 year old boys = 149lbs.

Mean = 149 [μM = μ = 149]

Variance = 16.2squared/11 = 262.44/11 = 23.86 [σM2 = σ2/N]

Standard Deviation = 4.88 [σM = √σM2 = √(σ2/N)]

Shape = normal

Using .01 level of significance for a two-tailed test, the cutoff sample score is +/- 2.575

Z = (M-µ) / σM = (153.45 - 149) / 4.88 = .91

.91 < 2.575

σM or the Standard Error of the Mean is 4.88 so...

for 99% confidence interval,

lower limit = 153.45 + (-2.575)(4.88) = 140.88

upper limit = 153.45 + (2.575)(4.88) = 166.02

the 99% confidence interval = 140.88 — 166.02 (lbs)

the population mean (µ=149.00) is included in the interval, which confirms results of Z test.

Conclusion: retain null, there is <.01 probability that the sample from City "Unknown" was drawn from a population where the mean weight is NOT = 149.00lbs.

Answer:

a. -5

b. 6254

c. - 1881

d. -1200

Step-by-step explanation:

Sorry,I think you can use your calculator to solve your problem but remember don't forget to follow the rules of numeral operation.

CMIIW

\(( - 32) \div 8 \times 2 + 2 - ( - 1) \\ = ( - 32) \div 8 \times 2 + 2 + 1 \\ = - 4 \times 2 + 2 + 1 \\ = - 8 + 2 + 1 \\ = - 8 + 3 \\ = - 5\)

\(53 \times ( - 9) - ( - 109) \times 53 \\ = 53 \times ( - 9) + 109 \times 53 \\ = 53( - 9 + 109) \\ = 53 \times 100 \\ = 5300\)

\( - 19 \times 99 \\ = - 1881\)

\(( - 63) \times 12 + 12 \times ( - 37) \\ = 12( - 63 - 37) \\ = 12 \times ( - 100) \\ = - 1200\)

Hope you could understand.

If you have any query feel free to ask.