Prove that if A2 = O, then 0 is the only eigenvalue of A. STEP 1: We need to show that if there exists a nonzero vector x and a real number λ such that Ax = λx, then if A2 = O, λ must be . STEP 2: Because A2 = A · A, we can write A2x as A(Ax). STEP 3: Use the fact that Ax = λx and the properties of matrix multiplication to rewrite A2x in terms of λ and x. A2x = x STEP 4: Because A2 is a zero matrix, we can conclude that λ must be .

Answer:

$19.99

Step-by-step explanation:

Take the price for 2 pairs and divide by 2 to get the price for one pair

39.98 /2

19.99 for one pair

Answer:

Probability that the potential candidate will run for President election is 0.0096.

Step-by-step explanation:

We are given that a potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy.

To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy.

Let p = % of Americans voice support for her candidacy

The z score probability distribution for sample proportion is given by;

                               Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of Americans support her candidacy = 35%

            n = sample of Americans = 500

Now, probability that the potential candidate will obtain a p^ ≥ 0.30 and run for President is given by = P( [tex]\hat p[/tex] ≥ 0.30)

      P( [tex]\hat p[/tex] ≥ 0.30) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ≥ [tex]\frac{0.35-0.30}{\sqrt{\frac{0.35(1-0.35)}{500}} }[/tex] ) = P(Z ≥ 2.34) = 1 - P(Z [tex]\leq[/tex] 2.34)

                                                                      = 1 - 0.9904 = 0.0096

The above probability is calculated by looking at the value of x = 2.34 in the z table which has an area of 0.9904.

Hence, the required probability is 0.0096.

9514 1404 393

Answer:

  ray

Step-by-step explanation:

The dashed part of the figure is a "half-line", a line that extends in one direction from a point. Such a line is called a "ray."

Answer:

Probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.

Step-by-step explanation:

We are given that it is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8.

And we have to find the probability that the pointer will stop on an odd number or a number greater than 5.

Let the Probability that pointer will stop on an odd number = P(A)

Probability that pointer will stop on a number greater than 5 = P(B)

Probability that pointer will stop on an odd number and on a number greater than 5 =  [tex]P(A\bigcap B)[/tex]

Probability that pointer will stop on an odd number or on a number greater than 5 =  [tex]P(A\bigcup B)[/tex]

Here, Odd numbers = {1, 3, 5, 7} = 4

Numbers greater than 5 = {6, 7, 8} = 3

Also, Number which is odd and also greater than 5 = {7} = 1

Total numbers = 8

Now, Probability that pointer will stop on an odd number =  [tex]\frac{4}{8}[/tex]  = 0.5

Probability that pointer will stop on a number greater than 5 =  [tex]\frac{3}{8}[/tex]  = 0.375

Probability that pointer will stop on an odd number and on a number greater than 5 =  [tex]\frac{1}{8}[/tex]  = 0.125

Now,    [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]

                            =  0.5 + 0.375 - 0.125

                            =  0.75

Hence, probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.

The probability that the pointer will stop on an odd number or a number greater than 5 is 3/4

The sample space is:

[tex]\mathbf{S = \{1,2,3,4,5,6,7,8\}}[/tex]

Count = 8

The odd numbers are:

[tex]\mathbf{Odd = \{1,3,5,7\}}[/tex]

Count = 4

The probability of odd is:

[tex]\mathbf{P(odd) = \frac{4}{8} }[/tex]

The numbers greater than 5 are:

[tex]\mathbf{Greater= \{6,7,8\}}[/tex]

Count = 3

The probability of numbers greater than 5 is:

[tex]\mathbf{P(Greater) = \frac{3}{8}}[/tex]

Odd numbers greater than 5 are:

[tex]\mathbf{OddGreater= \{7\}}[/tex]

Count =1

The probability of odd numbers greater than 5 is:

[tex]\mathbf{P(OddGreater) = \frac{1}{8}}[/tex]

So, the probability that the pointer will stop on an odd number or a number greater than 5 is:

[tex]\mathbf{Pr = P(Odd) + P(Greater) - P(OddGreater)}[/tex]

This gives

[tex]\mathbf{Pr = \frac 48 + \frac 38 - \frac 18}[/tex]

[tex]\mathbf{Pr = \frac 68}[/tex]

Simplify

[tex]\mathbf{Pr = \frac 34}[/tex]

Hence, the required probability is 3/4

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Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4-0.25(10)+0.5(5)

Multiply -0.25 by 10 and you get -2.5

4-2.5+0.5(5)

Multiply 0.5 by 5 and you get 2.5

4-2.5+2.5

Subtract 4 minus 2.5 and you get 1.5

1.5+2.5

Add 1.5 plus 2.5 and you get 4

4

Answer:

Juan has 35 orders

Step-by-step explanation:

you subtract 40 from 75 to get 35

Juan has 35 cookie dough orders for the school fundraiser

The question involves solving a simple algebra problem related to a school fundraiser involving cookie dough orders. Juan and Rob have a total of 75 cookie dough orders together. Juan has t orders and Rob has 40 orders. The problem can be represented by the equation t + 40 = 75. To find out how many cookie dough orders Juan has, we subtract 40 from both sides of the equation, which gives us t = 35. So, Juan has 35 cookie dough orders.

Answer:

V=lwh /3

Step-by-step explanation:

Answer:

a. V=1/3(12)(8)(10)

Step-by-step explanation:

Answer:

A = $ 8,951.33

Step-by-step explanation:

A = $ 8,951.33

A = P + I where

P (principal) = $ 6,500.00

I (interest) = $ 2,451.33

Formula:

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / e^rt

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Compound Interest Equation

A = P(1 + r/n)^nt

Final answer:

Four possible solutions to the inequality X > -1 are 0, 1, 2, and 2.5, as each of these values is greater than -1. The solution set in interval notation is (-1, ∞).

Explanation:

The inequality in question is X > -1. To provide four possible solutions, we are essentially looking for any four numbers that are greater than -1. Remember, there are an infinite number of solutions since X can be any value greater than -1, but here are four specific examples:

Each of these values satisfies the inequality X > -1, because they are all greater than -1. It is important to note that solutions to inequalities like this one are often represented in interval notation, in this case, it would be (-1, ∞), meaning any number greater than -1 but less than infinity.

Answer:

40 miles

Step-by-step explanation:

Let's set x to the number of miles driven, and t to the number of hours it took to drive.

We know that 40t is equal to x.

We also know that 40t is equal to 30(t + 1/3).

Solve for t:

40t = 30(t+1/3)

40t = 30t + 10

Subtract 30t from both sides:

10t = 10

Divide 10 from both sides:

t = 1

40t = 40 x 1 = 40 miles

I drove 40 miles.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.

Suppose, I drove n number of miles and it took me x time in hours.

We know that 40x is equal to n.

Since it would take 20 more minutes, so we have the division of 20/60 = 1/3

Then, 40x is equal to 30(x+ 1/3).

Solve for t:

40x = 30(x+1/3)

40x = 30x + 10

10x = 10

Now , divide by 10 on both sides,

x = 1

40x = 40 x 1 = 40 miles

Therefore, I drove 40 miles.

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Answer:

C

Step-by-step explanation:

A. 558 m2

B. 976 m2

C. 1,680 m2

D. 1,750 m2

Answer:

1064.64

Step-by-step explanation:

Answer:

RT ≈ 7.82

Step-by-step explanation:

tan θ = opposite / adjacent

tan 41 = RT / 8

RT = tan 41 × 8

RT = 0.869 × 8

RT = 7.821

RT ≈ 7.82

Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.

To compute Jordan's total tax due, we need to apply the marginal tax rates to each income bracket. Here's the breakdown for Jordan's taxable income of $35,000:

1. Income up to $9,525: Tax rate 10%

  Tax on this bracket = $9,525 * 0.10 = $952.50

2. Income from $9,526 to $38,700: Tax rate 12%

  Taxable income in this bracket = $35,000 - $9,525 = $25,475

  Tax on this bracket = $25,475 * 0.12 = $3,057

Now, add the taxes from each bracket to find the total tax due:

Total tax due = Tax on the first bracket + Tax on the second bracket

             = $952.50 + $3,057

             = $4,009.50

Therefore, Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.

The probable question may be:

"Jordan is a single taxpayer with a taxable income of $35,000. Using the provided tax bracket table for single taxpayers, where different tax rates apply to specific income brackets, compute Jordan's total tax due. The tax rates for the respective income brackets are as follows: 10% for income up to $9,525, 12% for income between $9,526 and $38,700. Please calculate Jordan's total tax due using the marginal tax rates."

Jordan's total tax due is $4,009.48. To calculate this, we determine the tax for each income bracket Jordan falls into and add them together. Jordan's taxable income of $35,000 falls into the 12% tax bracket, so we use the 12% tax rate to calculate the tax due in that bracket. We also calculate the tax due in the 10% tax bracket for the remaining income.

To find Jordan's total tax due, we need to determine which income bracket he falls into and calculate the tax for each bracket using the corresponding tax rate. Jordan has a taxable income of $35,000, which falls into the 12% tax bracket. So, we will use the tax rate of 12% to calculate his tax due.

Step 1: Calculate the tax on the income that falls in the 12% tax bracket:

So, Jordan's tax due for the 12% tax bracket is $3,056.88.

Step 2: Calculate the tax on the income that falls in the 10% tax bracket:

So, Jordan's tax due for the 10% tax bracket is $952.60.

Step 3: Add the tax due for each bracket to get Jordan's total tax due:

Total tax due = $3,056.88 + $952.60 = $4,009.48.

Answer:

4/5 (not drawing a black marble)

3/10 (drawing a red marble)

Step-by-step explanation:

Answer:6.3

Step-by-step explanation: 6.8 +1.5 -1.2 -0.8=6.3

The amount of flour left is 6.3 kg.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total flour = 6.8 + 1.5 = 8.3 kg

Amount of flour used = 1.2 + 0.8 = 2 kg

The amount of flour left.

= 8.3 - 2

= 6.3 kg

Thus,

6.3 kg of flour is left.

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Answer:

Step-by-step explanation:

1. The basic recipe for Kool Aid makes 2 quarts. The desired amount is 20 quarts (2 multiplied by 10). The basic recipe uses 1 cup of sugar, so the desired amount of Kool Aid will use 1 cup multiplied by 10.

  10 cups of sugar are needed

__

2. The problem tells us there are 8 parts pretzels and 40 total parts, so the ratio is ...

  pretzels : total = 8 : 40

8 is a factor of both these numbers, so we can reduce this to the "basic ratio" by dividing both numbers by 8:

  8 : 40 = 1 : 5

The basic ratio is 1 : 5.

Answer:

a) Predicted value =0.5×18+6= 15

b) Predicted value =0.5×15+6= 13.5

c) Since least square equation has the tendency to regress the outcome toward mean value , as both the explanatory variable (in part a and b) are above mean value , the response variable are smaller then them.

Step-by-step explanation:

[ Find the attachments for explanation]

Final answer:

Explaining how to predict the educational level of a spouse based on correlation, and discussing why well-educated individuals may marry partners with different education levels.

Explanation:

The questions can be answered as -

(a) Predicting the educational level of a woman whose husband has completed 18 years of schooling:

Given that the correlation between the educational levels of husbands and wives is 0.50, we can use this correlation to predict the wife's educational level.

Educational level of wife = correlation * (wife's SD / husband's SD) * husband's years of schooling + wife's average years of schooling.

(b) Predicting the educational level of a man whose wife has completed 15 years of schooling:

Apply the same formula as in (a) but with the wife's years of schooling given as 15 years.

(c) Explanation of why well-educated men marry women less educated than themselves:

This can occur due to various factors such as social dynamics, career aspirations, or personal preferences.

Answer:

(a) Is not possible

(b) It is possible

(c) It is possible

(d) Is NOT possible.

Step-by-step explanation:

(a)

Is not possible, notice that for any function [tex]g[/tex]  such that

[tex]g : \mathbb{R} \rightarrow \mathbb{R}[/tex]

you would have that

[tex](g\circ f)(x) = g(f(x)) = g(|x|)[/tex]

And for, lets say -3,3 you have that

[tex]g(|-3|) = g(|3|) = g(3)[/tex] therefore is not possible to find a function that is one to one.

(b)

It is possible. Take the following function

[tex]g(x) = x\sin(x)[/tex] since [tex]\sin[/tex] is periodic it will take positive and negative numbers and if you multiply by [tex]x[/tex] each period will become bigger and bigger.

(c)

It is possible. Take the function

[tex]g(x) = \sqrt{x}[/tex]

Then

[tex](f \circ g )(x) = | \sqrt{x} | = \sqrt{x}[/tex]    and [tex]\sqrt{x}[/tex] is one to one.

(d)

It is NOT possible because   [tex](f\circ g)(x) = f(g(x)) = |g(x)|[/tex] and that will always be positive.  

Answer:

tanx·secx

Step-by-step explanation:

To simply this, you can begin by factoring sin x out of the numerator to become:

[tex]\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}[/tex]

Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:

[tex]\frac{sinx}{cos^{2}x }[/tex]

First of all, we can convert [tex]\frac{sinx}{cosx}[/tex] to tanx. However, we have a remaining [tex]\frac{1}{cosx}[/tex] which, using reciprocal identities, will become sec x.

Finally, we get our answer as tanx·secx.

Teh value of x is 23° (D)

Step-by-step explanation:

Total of angel = 360°

The value of x :

(2x + 15)° + 119° + 99° + 81° = 360°

2x + (15 + 119 + 99 + 81)° = 360°

2x + 314° = 360°

2x = 360° - 314°

2x = 46

x = 46 ÷ 2

x = 23°

So, the value of x is 23° (D)

Hope it helpful and useful :)

Answer:

The answer is digit

Step-by-step explanation:

A single number between 0 and 9 is a digit, which often makes up larger numbers.

Answer:

Alisha

Step-by-step explanation:

Speeds:

Bill:

315/7 = 45 mph

Alisha:

235/5 = 47 mph

Joanna:

414/9 = 46 mph

Answer:

The answer is Alisha.

Step-by-step explanation:

235 mph divided by 5 is equal to 47 mph.

We have been given that in the morning an iceberg weighed 380,000 pounds. It lost 0.3% of its weight during the day. We are asked to find the weight of the ice-berg at the end of the day.

The weight of the ice-berg at the end of the day would be original weight of ice-berg minus 0.3% of original weight.

[tex]\text{The weight of the ice-berg at the end of the day}=380,000-380,000\times \frac{0.3}{100}[/tex]

[tex]\text{The weight of the ice-berg at the end of the day}=380,000-3800\times 0.3[/tex]

[tex]\text{The weight of the ice-berg at the end of the day}=380,000-1140[/tex]

[tex]\text{The weight of the ice-berg at the end of the day}=378,860[/tex]

Therefore, the weight of the ice-berg at the end of the day would be 378,860 pounds.

Answer:

378860 pounds

Step-by-step explanation:

We have been given a graph. We are asked to find the values of x,y and z.

We will use parallel line's angles to solve our given problem.

We know that corresponding angles of parallel lines are equal.

We can see that angle [tex]2x+3[/tex] and 67 are corresponding angles, so we can set an equation as:

[tex]2x+3=67[/tex]

[tex]2x+3-3=67-3[/tex]

[tex]2x=64[/tex]

[tex]\frac{2x}{2}=\frac{64}{2}[/tex]

[tex]x=32[/tex]  

Therefore, the value of x is 32.

We know that interior angles on same side of transversal are supplementary.

We can see that [tex]3y+5[/tex] and 67 are interior angles, so we can set an equation as:

[tex]3y+5=67[/tex]

[tex]3y+5-5=67-5[/tex]

[tex]3y=62[/tex]

[tex]\frac{3y}{3}=\frac{62}{3}[/tex]

[tex]y=\frac{62}{3}[/tex]

Therefore, the value of y is [tex]\frac{62}{3}[/tex].

We can set an equation for angle z as:

[tex]4z+13=2x+3[/tex]

[tex]4z+13-13=2x+3-13[/tex]

[tex]4z=2x-10[/tex]

Upon substituting value of z, we will get:

[tex]4z=2(32)-10[/tex]

[tex]4z=64-10[/tex]

[tex]4z=54[/tex]

[tex]\frac{4z}{4}=\frac{54}{4}[/tex]

[tex]z=13.5[/tex]

Therefore, the value of z is 13.5.

ANSWER: The statistical procedure that should be performed is REGRESSION.

Step-by-step explanation: Regression is a statistical procedure that is used to estimate the relationship between an independent variable and a dependent variable using their mean values.

The independent variable in this case is the hours each student spend in studying, while the dependent variable is the students grade.

Since the researcher wants to determine if the hours a student spend in studying maths and science has any significant effect on their grades. The researcher should use regression, because it will show if the two variables are related and how it relates, by showing how far the points are from the trend lines of the graph.

Answer:

  0.56 mg

Step-by-step explanation:

Put 6 where t is and do the arithmetic.

  M(6) = 50(e^(-0.75·6)) = 50e^-4.5 ≈ 0.56

Olivia will have about 0.56 mg of medication remaining in her blood.

Answer:

.08

Step-by-step explanation:

Divide the percentage by 100.

8 / 100 = .08

Answer: 8% = .08

Step-by-step explanation: simple. if you use d2p. meaning decimal two percent. you take your decimal like .36 and move the dot two places forward making it 36%. same from percent to decimal by reversing it.

Answer:

We conclude that the average height of hobbit is taller than Yoda.

Step-by-step explanation:

We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.

From a sample of 7 hobbits, you find their mean height [tex]\bar X[/tex] = 80 cm with standard deviation s = 10.8 cm.

Let [tex]\mu[/tex] = average height of hobbit.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 66 cm      {means that the average height of hobbit is shorter than or equal to Yoda}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 66 cm      {means that the average height of hobbit is taller than Yoda}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

                     T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean height = 80 cm

             s = sample standard deviation = 10.8 cm

             n = sample of hobbits = 7

So, test statistics  =  [tex]\frac{80-66}{\frac{10.8}{\sqrt{7}}}[/tex]  ~ [tex]t_6[/tex]

                              =  3.429

The value of t test statistics is 3.429.

Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average height of hobbit is taller than Yoda.

Answer:

The value of x any y are "-5.29 and 0.79" and "3.79 and -2.29"

Step-by-step explanation:

Given values:

[tex]2xy =6.....(a)\\\\x-y= 3.....(b)\\\\[/tex]

After solve equation (a) we get

[tex]\ equation: \\\\2xy= 6\\\\xy =\frac{6}{2} \\\\xy = 3.....(x)\\\\[/tex]

After solve equation (b) we get

[tex]\ equation: \\\\x-y =3\\\\x= 3+y....(x1)\\[/tex]

put the value of x in to equation (x)

[tex](3+y)y = 3\\[/tex]

[tex]y^2+3y-3=0\\\\\ compare \ the \ value \ with \ ay^2+by+c=0\\a= 1\\b=3\\c=-3\\\ Formula: \\y= \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\y= \frac{-3\pm \sqrt{9+12}}{2}\\y= \frac{-3\pm \sqrt{21}}{2}\\[/tex]

The value of y is = -5.29 and 0.79, put the value of y in x1 equation so, we get: 3.79 and -2.29