if a vector coincides with its orthogonal projection onto a subspace, then the vector must be in the subspace.

90 minutes

Step-by-step explanation:

1/2 an hour = 30 minutes

1/4 an hour = 15 minutes

45+15=60

60+30=90

The value of 'b' obtained for the given exponential function is 0.055.

The stated exponential function is-

y = 5832(b)ˣ

This, function contains the point (3, 1).

Put the value in the r function;

1 = 5832(b)³

(b)³ = 1/5832

b = ∛1/5832

b = 0.055

Thus, the value of 'b' obtained for the given exponential function is 0.055.

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Answer:

0

Step-by-step explanation:

8  twin-size blanket , y = 1 queen-size blankets will be the fabric used

According to the given information

let

x = number of yards of fabric required to make a twin-size blanket.

y = the number of yards of fabric required to make a queen-size blanket

This week, they used 441 yards of cloth to create 49 twin-size blankets and 49 queen-size blankets:

49x + 49y = 441

The group members finished 21 queen-size blankets and 48 twin-size blankets last week, using 405 yards of cloth altogether:

48x + 21y = 405

Solving the two equations

1029x + 1029y = 9261

2352x + 1029y = 19845

hence

Solving the above two equations

We get

1323x = 10584

x = 8

Putting the value of x in above one equation

y = 1

8  twin-size blanket , y = 1 queen-size blankets will be the fabric used

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The coordinates of B' are (14, 19) when coordinate of B are (4, 15)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

Translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Given that after translation the point A(-4,7) to the point A'(6,11)

(x,y)---->(x+10, y+4)

A(-4,7)---->(-4+10, 7+4)=A'(6, 11)

Now we need to find coordinates of B' when B is (4, 15)

(4,15)--->(4+10, 15+4)=(14, 19)

Hence, the coordinates of B' are (14, 19) when coordinate of B are (4, 15)

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Answer:

Solution of the given equation by elimination method is x=0.5 and y=5.

Step-by-step explanation:

8x + 7y = 39 --------------(1)

4x - 14y = -68 ------------(2)

Multiply the equation 2 by -2, then add the equations along.

Equation (2) multiply by -2 :  -8x +28y = 136

8x + 7y = 39 --------------(1)

-8x +28y = 136-----------(2)

Add these equations to eliminate x:

0x+35y=175

35y=175

y=5

Substitute y=5 in 8x+7y=39:

8x+(7)(5) =39

8x+35=39

8x=39-35

8x=4

X=8/4

x=0.5

Solution of the given equation by elimination method is x=0.5 and y=5.

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The equation that represents the employee’s salary, S, after t years since the employee began working with the company is S(t) = 35400 * (1.08)^t

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

Initial salary = 35400

Raise = 8%

Number of years = t

The equation that represents the employee’s salary is calculated as

Salary = Initial salary * (1 + raise)^Number of years

Substitute the known values in the above equation, so, we have the following representation

Salary = 35400 * (1 + 8%)^t

So, we have

S(t) = 35400 * (1.08)^t

Hence, the equation is S(t) = 35400 * (1.08)^t

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Answer: $1,184,537.217

Step-by-step explanation:

You just multiply the number by 1.22 every year.

For example: year 1 (60,000 * 1.22)= 73,200

Year 2: (73,200 *1.22) =89,304

and so on until year 15 is reached.

The statement nine more than the product of 5 times the number of tires t can be written as, 9 + 5t, so option A is correct.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given statement:

nine more than the product of 5 times the number of tires t

The above statement can be written as

= 9 + 5 × t

= 9 + 5t

Therefore, the statement nine more than the product of 5 times the number of tires t can be written as, 9 + 5t.

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The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.

Given that,

There is a line of unassembled furniture produced by The Mean Corporation. The customer care manager is aware that 0.63 of customers have had no issues putting together their furniture at home based on past data.

The null and alternative hypotheses are:

H₀: π = 0.63

H₁: π > 0.63

We have to find

(a) Calculate the test statistic (z).

(b) Calculate the P-value.

We know that,

a) z = p - π / √(π(1-π)/n)

      = 0.67 - 0.63 / √(0.63×0.37/102)

      = 0.04 / 0.0478

      = 0.84

b) p value(one tailed) is 0.2005.

Therefore, The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.

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Answer:

you forgot the sentences dude

As per the given confidence interval, the population mean remodeling costs for the two types of projects is -1.6

Confidence interval

The  range of values that's likely to include a population value with a certain degree of confidence is known as confidence interval.

Given,

A certain association provided data on the cost of the most popular home remodeling projects.

Here we need to find the the population mean remodeling costs for the two types of projects.

Here we will find the point estimate of the difference between the population mean remodeling costs for the two types of projects using an equation,

=> X1​ − X2​

In order to calculate the sample mean we will use equation,

=> X = ∑x/n

Now, we have to substitute values we get,

=> X1 ​= 21.2

=> X2 ​= 22.8

Here X1 refers the sample mean remodeling costs for the kitchen and X2​refers the sample mean remodeling cost for the master bedroom.

Therefore, the point estimate of the difference between the population mean remodeling costs for the two types of projects are,

=> X1 ​− X2​ ​= −1.6

Therefore, we estimate that the remodeling master bedroom has the mean costs of 1.6 greater than mean remodeling costs for the kitchen.

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Answer:

as you can see on the picture, they both have same rectangle

1st figure is i divide it by 2 and shade 1 to get 1/2

2nd figure is I divide it by 5 and shade 2 to get 2/5

if we use LCD:

1/2 will become 5/10

2/5 will become 4/10

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, then we have to explain what she can:

decrease the sample size.

increase the confidence level.

increase the sample size.

increase the sample size.

As we know that;

The formula of Margin of Error is;

ME = Z(α)× √σ^2/n

where; ME = margin of error

α = confidence level

z(α) = quantile

σ = standard deviation

n = sample size

So as we can see that Margin of Error is inversely proportion to sample size.

So, if a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

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Answer:

The answer is b!

Step-by-step explanation:

the answer is A .

the open end of the arrow points to the bigger variable. When the variable is included there will be a line under the arrow

The probability that all the marbles are red is 0.0156 and The probability that none of the marbles are red is 0.2109.

Given ,

bag contains 8 red marbles

7 - white marbles

8 - blue marbles.

a.The probability that every marble is red is

8/23 * 7/22 * 6/21

= 0.0156.

b.The likelihood that no red marbles are present is

15/23 * 14/22 * 13/21

= 0.2109.

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The reasonable 95% confidence intervals for the population mean difference is (7.83, 12.13) , the correct option is (a) .

In the question ,

it is given that ,

90% confidence interval is given as (8.21 , 11.75)

using this interval , we have to find the 95% confidence interval .

Now, [tex]x_{d}[/tex]  - E = 8.21

[tex]x_{d}[/tex] + E = 11.75 , where E is the margin of Error .

Solving the equations ,

we get ,

E = 1.77  and [tex]x_{d}[/tex] = 9.98

So , the margin of error E is given as

E = [tex]t_{\frac{0.10}{2},15 } \times \frac{S.D.}{\sqrt{n} }[/tex]

we have to find standard deviation from this ;

given n = 16 and [tex]t_{\frac{0.10}{2},15 }[/tex] = 1.7531

Substituting in the margin of error equation ,

we get ,

S.D. = (1.77 × 4)/1.7531

= 4.0386

So , the 95% confidence interval is given as [tex]x_{d}[/tex]  ± [tex]t_{\frac{0.10}{2},14 } \times \frac{S.D.}{\sqrt{n} }[/tex] .

from t table , [tex]t_{\frac{0.10}{2},14 }[/tex] = 2.1314

Substituting ,

we get ,

CI = (9.98 ± 2.1314×4.0386/√16)

= (9.98 ± 2.1519)

= ( 9.98 - 2.1519 , 9.98 + 2.1519)

= (7.83 , 12.13)

Therefore , the correct option is (a) (7.83 , 12.13)    .

The given question is incomplete , the complete question is

Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply:

(a) (7.83, 12.13)  

(b) (7.53, 11.83)

(c) (8.45, 11.51)

(d) (8.63, 11.33)

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f(5) = 7 is another to say a point at (5 , 7)

f(2) = 0 is another to say a point of (2 , 0)

to get the equation of any straight line, we simply need two points off of it, let's use those two above

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -3 } \implies \cfrac{ 7 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 7 }{ 3 }}(x-\stackrel{x_1}{5}) \\\\\\ y-7=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }\implies y=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }+7\implies {\Large \begin{array}{llll} y=\cfrac{ 7 }{ 3 }x-\cfrac{14}{3} \end{array}}[/tex]

Hence, [tex]x=16[/tex] when [tex]y=48[/tex].

What is the direct variation?

A direct variation, also called direct proportion is a relationship between two variables [tex]x[/tex] and [tex]y[/tex] that can be written as [tex]y = kx[/tex], [tex]k\neq 0[/tex].

Here given that,

The direct variation and [tex]y=75[/tex] when [tex]x=25[/tex],

As we know that,

[tex]y[/tex]α[tex]x[/tex]

[tex]y=kx[/tex]

[tex]75=k(25)\\\\k=\frac{75}{25}\\\\k=3[/tex]

So, when [tex]y=48[/tex]

[tex]y=kx\\\\48=3x\\\\x=\frac{48}{3}\\\\x=16[/tex]

Hence, [tex]x=16[/tex] when [tex]y=48[/tex].

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The change she should receive is $50.50 and we can find it by using simple cost and price calculations.

What is selling price?

Selling price is the amount of money that a seller charges for a product or service. It is the amount of money that a buyer pays for a product or service. The selling price is determined by a variety of factors, such as the cost of production, the perceived value of the product or service, the market demand for the product or service, competitive pricing in the market, and the profit desired by the seller. The selling price may also be affected by the availability of financing options for buyers, taxes, and other applicable fees. The selling price is an important factor in marketing and promoting a product or service. It must be set at the right level to attract buyers and ensure that the seller can make a profit.

Selling price for a shirt = $31.18

Selling price for a hat = $18.32

Total amount she have = $100

Total selling price (for both) = $49.50

So, the remaining amount = $100 - $49.50

                                            = $50.50

So, the change she should receive = $50.50

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The range is the set of all possible y-values that could come from the equation y = |x|.

Since the absolute value only results in 0 or positive numbers, the range cannot include any negative real numbers.  

    |3| = 3

    |0| = 0

    |-3| = 3

Therefore the range is not all real numbers, since all negative real numbers are excluded from the range.

The range is y ≥ 0.

A function is a rule that for each input has at most one output.

Describe a function. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (the domain) and their outputs (the codomain), where each input has exactly one output and the output can be traced back to the original input.

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(a) The area of the shaded region is 0.2709.

(b) The area of the shaded region is 0.3520.

(c) The area of the shaded region is 0.5555.

(d) The area of the shaded region is 0.6197

What is standard normal curve?

The horizontal axis is approached but never touched by the standard normal curve as it extends indefinitely in both directions. The center of the bell-shaped standard normal curve, which has a z=0 slope, is. Nearly all of the standard normal curve's area lies between z = 3 and z = 3.

The shaded area under the standard normal curve are,

1) Find,  P[Z > 0.61 ]

= P[Z > 0.50]

= 1 - P[Z < -0.50]

= 1 - 0.7291 ( use z table)

=   0.2709

The area of the shaded region is 0.2709.

2) Find,  P[Z < -0.38 ]

= P[Z < -0.38 ]

= 0.3520 ... ( use z table)

The area of the shaded region is 0.3520.

3) Find,  P( -0.58 < Z < 0.98 )

= P(Z < 0.98 ) - P(Z < -0.58 )

= 0.8365 - 0.2810 ......(using z-table)

= 0.5555

The area of the shaded region is 0.5555.

4) Find ,  P( -0.11 < Z > 0.98 )

= 1 - P(Z < 0.98 ) - P(Z < -0.11 )

= 1 - ( 0.8365 - 0.4562 ) ......(using z-table)

= 1 - 0.3803

= 0.6197

Hence, the area of the shaded region is 0.6197.

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The sixth term of the sequence 9, 16,23,30,37 is 44

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 2, 4, 6, 8, 10, 12.. . is an arithmetic progression with a common difference of 2.

The nth term of an arithmetic sequence is given as a+(n-1)d. Where d is the common difference and a is the first term.

fourth term = 30

second term = 16

third term = (30+16)/2 = 46/2 = 23

therefore d= 30-23 = 7

a = 16-7 = 9

therefore the sixth term = 9+(6-1)7= 9+5×7 = 9+35= 44.

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The answers of given statements are

a) option (A) i.e Net income.

b) The funds grow faster in case of compund interest.

c) Establish a theory of probable cause is third step

d) Gas and insurance

e) It is the rate for each day that is worked.

f) The production factors are labour, land etc.

g) Three basic questions related to economy are

What will be produced?how will it be produced?

how will the output society produces be distributed?

We have given some statements,

a) Saving should treated as an another type -->

Net income

After all sales-related expenses have been taken out, the remaining earnings are referred to as net income. Savings is the act of holding money for use in the future; it does not include paying for an item or service up front. The saving reffered as net income, or income after all expenses.

b) Compound interest is usually better than simple interest because it pays -->or allows funds to grow at a faster rate than they would in an account with a simple interest rate.

c) Third step in troubleshooting a computer problem is :

Step 3. Establish a theory of probable cause. Eliminate the simple and obvious possible causes.

d) Gas and insurance is expenditure will be the same whether you lease or buy a new vehicle.

e) Hourly pay is the rate for each day that is worked and is often calculated upon the number of hours the labor has been given to the factory.

f)The factors of production are

g) An economic system is any system of allocating scarce resources. Economic systems answer three basic questions:

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The similarities between matrix factorization and content-based filtering and/or collaborative filtering are given below.

What is matrix factorization and collaborative filtering?

A group of cooperative filtering algorithms used in recommender systems is called matrix factorization. The user-item interaction matrix is broken down into the product of two rectangular matrices with lower dimensions by matrix factorization algorithms.

Collaborative filtering makes recommendations by simultaneously comparing similarities between users and items, addressing some of the drawbacks of content-based filtering.

collaborative filtering: user-based for example, CF calculates users' similarities in the item space. Then taking similar users's interest to do a recommendation for the target user. CF is one case of neighborhood methods.

matrix factorization amounts to mapping features of user and item via linear combination to latent factor space respectively.

Then calculating the similarity via inner-product of latent user factor and latent item factor.

CF covers local information of target user for the sake of neighborhood methods, while MF covers global information.

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Answer:

Step-by-step explanation:het