Find the closest point to y in the subspace W spanned by Bold v 1 and Bold v 2. yequals[Start 4 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 1 3rd Row 1st Column 1 4st Row 1st Column 13 EndMatrix ]​, Bold v 1equals[Start 4 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 2 3rd Row 1st Column negative 1 4st Row 1st Column 2 EndMatrix ]​, Bold v 2equals[Start 4 By 1 Matrix 1st Row 1st Column negative 4 2nd Row 1st Column 1 3rd Row 1st Column 0 4st Row 1st Column 3 EndMatrix ]The closest point to y in W is the vector [Start 4 By 1 Matrix 1st Row 1st Column nothing 2nd Row 1st Column nothing 3rd Row 1st Column nothing 4st Row 1st Column nothing EndMatrix ].

Answer:

A square

Step-by-step explanation: A square is a parallelogram. This is always true. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides.

Answer:

I think it is the parallelograms and square

Step-by-step explanation:

because they never intersect they stay the length apart

Answer:

The answer is  " [tex]C= \frac{5}{2x^2}+ 4xy - 2y^4.[/tex]"

Step-by-step explanation:

It given that, [tex]\frac {\partial(5x + 4y)}{\partial y} = \frac{\partial(4x- 8y^3)} {\partial x} \\\\[/tex] it is the differential equation.

Solve the above equation.

[tex]\frac {\partial M (x, y)}{\partial y} = (5x+ 4y)[/tex]

So, [tex]M (x, y) = \frac{5}{2x^2}+4xy +\varphi (y).[/tex]

[tex]\frac{\partial M (x, y)}{ \partial y }= 4x- 8y^3 \ and \ \ 4x + \varphi ' (y) = 4x- 8y^3 \\\\\ so, \ \\varphi ' (y) = -8y^3[/tex]

or [tex]\varphi (y) = -2y^4+c[/tex]

To find the general solution

[tex]M(x, y )= c \\C= \frac{5}{2x^2}+ 4xy - 2y^4.[/tex]

Answer:

16% of the apples have diameters that are less than 6.82cm

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 7.25cm

Standard deviation = 0.43cm

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Using the empirical rule, what percentage of the apples have diameters that are less than 6.82cm?

6.82 = 7.25 - 1*0.43

So 6.82 is one standard deviation below the mean.

Of the 50% of the diameters below the mean, 68% are within 1 standard deviation of the mean.

So 100-68 = 32% are not within 1 standard deviation of the mean.

0.5*0.32 = 0.16

16% of the apples have diameters that are less than 6.82cm

Answer:

range: {4, 10, 16}

Step-by-step explanation:

Find the range of the function y = 3x - 2

for the domain (2, 4, 6).

There are only 3 domain values here.

so  3 range values.

y = 3*2 - 2 =  6 - 2 = 4

y = 3*4 - 2 = 12 - 2 = 10

y = 3*6 - 2 = 18 -2 = 16

range: 4, 10, 16

Answer:

-855

Step-by-step explanation:

Find the 54th term of the arithmetic sequence -7,-23,-39

The first term is a_1 = -7

we see that the common difference = d = -23 - (-7) = -16

so the formula:  a_n = (n- 1)*d + a_1

a_54 = (54 - 1)* (-16) + (-7)

a_54 = 53 *(-16) - 7 = -848 - 7 =  -855

Answer:

$150

Step-by-step explanation:

Annual Real Estate Tax Rate =1.8%

Value of Bonnie's House = $100,000

Annual Tax= 1.8 % × $100,000 =0.018 × $100,000 = $1,800

Therefore, tax payment on a monthly basis

= $1,800÷12 Months

= $150 per month.

Real estate tax will add $150 per month to Bonnie's mortgage payment.

Final answer:

The real estate taxes on Bonnie's $100,000 house at a 1.8 percent tax rate add $150 to her monthly mortgage payment, after calculating the annual tax and dividing by 12 months.

Explanation:

To calculate the real estate taxes that will add to Bonnie's monthly mortgage payment, we need to apply the tax rate to the value of the home and then divide by 12 to find the monthly amount.

The annual real estate taxes would be calculated as follows:

Therefore, the real estate taxes will add $150 to Bonnie's monthly mortgage payment.

Answer:

The students have eaten 72 ounces of fruit snacks.

X = 72 ounces

Step-by-step explanation:

There are total 20 packs of fruit snacks

The weight of each pack is 6 ounces.

Let us first find the total weight of the snacks.

Total weight = 6*20

Total weight = 120 ounces

Let X represents the ounces of fruit snacks that students have eaten.

Let Y represents the 48 ounces of fruit snacks left in the box

Total weight = X + Y

120 = X + 48

X = 120 - 48

X = 72 ounces

Therefore, the students have eaten 72 ounces of fruit snacks.

Answer:

x = 72 ounces

The number of ounces of fruit snacks the students ate is 72 ounces

Step-by-step explanation:

Given;

Let x represent the number of ounces of fruit the students ate;

The total number of ounces of fruit initially in the box is;

20 packs × 6 ounces/pack = 120 ounces

The remaining ounces of fruit is;

48 ounces

Therefore;

120 - x = 48

Solving for x;

x = 120 - 48

x = 72 ounces

The number of ounces of fruit snacks the students ate is 72 ounces

Answer:

A

Step-by-step explanation:

because there will be a vertical line at x= -2

The equation of a line parallel to the y-axis is of the form x = constant. Thus, among the provided options, option A: x = -2 is the correct answer.

In Mathematics, a line that is parallel to the y-axis represents an equation where x equals a constant. The y values can change, but the x value will always remain constant. This is because parallel lines to the y-axis don't slope, they are vertical lines. In the provided options, the equation that fits this description is x = -2. Therefore, the answer to your question, 'Choose the equation of the line that is parallel to the y-axis' is option A: x = -2.

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Answer:

C - 7

Step-by-step explanation:

A^2-B^2

Let A = 3 and B=-4

(3)^2 - (-4)^2

9 - 16

-7

Answer:

The 90% confidence interval to estimate the mean breaking weight for this type cable is between 751.38 lb and 803.42 lb.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the student t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 47 - 1 = 46

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 46 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.6787

The margin of error is:

M = T*s = 1.6787*15.5 = 26.02 lb

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 777.4 - 26.02 = 751.38

The upper end of the interval is the sample mean added to M. So it is 777.4 + 26.02 = 803.42

The 90% confidence interval to estimate the mean breaking weight for this type cable is between 751.38 lb and 803.42 lb.

Answer:

[tex]777.4-1.679\frac{15.5}{\sqrt{47}}=773.60[/tex]    

[tex]777.4+1.679\frac{15.5}{\sqrt{47}}=781.20[/tex]    

We are 90% confident that the true mean for the breaking weigth for this typpe of cable is between 773.60 and 781.20

Step-by-step explanation:

Data provided from the problem

[tex]\bar X=777.4[/tex] represent the sample mean for the breaking weights

[tex]\mu[/tex] population mean

s=15.5 lb represent the sample standard deviation

n=47 represent the sample size  

Confidence interval

The confidence interval for the true population mean is given by:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom, given by:

[tex]df=n-1=47-1=46[/tex]

The Confidence level is 0.90 or 90%, the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2 =0.05[/tex] and the critical value for this case is [tex]t_{\alpha/2}=1.679[/tex]

Replacing into the confidence formula we got:

[tex]777.4-1.679\frac{15.5}{\sqrt{47}}=773.60[/tex]    

[tex]777.4+1.679\frac{15.5}{\sqrt{47}}=781.20[/tex]    

We are 90% confident that the true mean for the breaking weigth for this typpe of cable is between 773.60 and 781.20

Answer:

Volume, [tex]V=96.79\ \text{feet}^3[/tex]

Step-by-step explanation:

An artist creates a cone shaped sculpture for an art exhibit.

Height of sculpture is 8 feets

The circumference of base of the cone is 21.352 feet.

The base of a con is circular shaped. So,

[tex]2\pi r= 21.352[/tex]

r is radius of cone

[tex]r= \dfrac{21.352}{2\times 3.14} \\\\r=3.4\ ft[/tex]

The volume of cone shaped sculpture is given by :

[tex]V=\dfrac{1}{3}\pi r^2 h\\\\V=\dfrac{1}{3}\times 3.14\times (3.4)^2 \times 8\\\\V=96.79\ \text{feet}^3[/tex]

So, the volume of the sculpture is [tex]96.79\ \text{feet}^3[/tex].

Fractions not equivalent to 7/8 are those that do not share the same 7 to 8 ratio when simplified. Multiplying by the reciprocal is key to understanding fraction division, and it is important to comprehend fraction operations for proficiency in mathematics. Educational systems need to improve the teaching of fractions, as evidenced by standardized test results.

The fractions that are not equivalent to 7/8 are any fractions where the numerator and denominator do not have the same ratio as 7 to 8. For example, the fraction 14/16 is equivalent to 7/8 because if you divide both 14 and 16 by the same number, which is 2, you will get 7/8. However, fractions like 1/2, 6/8, or 9/10 are not equivalent to 7/8. To determine if fractions are equivalent, you can simplify them to their lowest terms or cross-multiply to compare ratios.

Turning to common misconceptions about fractions, remember that multiplication and division are intimately linked: dividing by 8 is the same as multiplying by its reciprocal (1/8), and vice versa. Understanding this concept helps to build a strong foundation for working with fractions. Furthermore, not all fractions of a total are equal, and understanding the mechanics of adding, subtracting, multiplying, and dividing fractions is essential for developing proficiency in mathematics.

As illustrated in the example with 1,000 and 1/8, recognizing the patterns and relationships between fractions and other numbers aids in solving problems quickly and accurately. Educational systems evidently need to better equip students with these essential skills for handling fractions and percentages, as highlighted by the results of the High School Exit Exam.

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Fractions that are not equivalent to 7/8 include 3/4, 1/2, 2/3, 1/3, and 1/5. These fractions represent different values when simplified.

To determine which fractions are not equivalent to 7/8, we need to understand the concept of equivalent fractions. Two fractions are equivalent if they represent the same part of a whole even if their numerators and denominators are different.

For example, 14/16 is an equivalent fraction to 7/8 because if you simplify 14/16, you divide both the numerator and the denominator by 2, which equals 7/8. However, some fractions that are not equivalent to 7/8 include:

These fractions do not simplify to 7/8 and therefore represent different values.

Answer:

a) [tex] P(X>10) =1-P(X<10) = 1-F(10) = 1-\frac{10-6}{12-6} = 0.333[/tex]

b) [tex] P(X<11)= F(11) = \frac{11-6}{12-6}= 0.833[/tex]

c) [tex] P(6.5<X<8)= F(8) -F(6.5) = \frac{8-6}{12-6}-\frac{6.5-6}{12-6}= 0.333-0.0833 = 0.250[/tex]

In the figure attached we have the illustration for the probability for each part.

Step-by-step explanation:

For this case we define the random variable X as the voltages in a circuit  and the distribution for X is given by:

[tex]X \sim Unif (a= 6, b=12) [/tex]

Part a

we want this probability:

[tex] P(X>10)[/tex]

We can use the cumulative distirbution function given by:

[tex] F(x) = \frac{x-a}{b-a}, a\leq X \leq b[/tex]

And using the complement rule we have this:

[tex] P(X>10) =1-P(X<10) = 1-F(10) = 1-\frac{10-6}{12-6} = 0.333[/tex]

Part b

We want this probability:

[tex] P(X<11)[/tex]

And using the cumulative distirbution function we got:

[tex] P(X<11)= F(11) = \frac{11-6}{12-6}= 0.833[/tex]

Part c

We want this probability:

[tex] P(6.5<X<8)[/tex]

And using the cumulative distirbution function we got:

[tex] P(6.5<X<8)= F(8) -F(6.5) = \frac{8-6}{12-6}-\frac{6.5-6}{12-6}= 0.333-0.0833 = 0.250[/tex]

In the figure attached we have the illustration for the probability for each part.

To find the probability of a given range of voltage levels in a circuit, we need to determine the proportion of voltages that fall within that range. In this case, the range of voltages varies between 6 volts and 12 volts, and they are spread evenly. The probability of the voltage being greater than 10 volts is 1/3, the probability of the voltage being less than 11 volts is 5/6, and the probability of the voltage being between 6.5 volts and 8 volts is 1/4.

To find the probability of a given range of voltage levels, we need to determine the percentage of voltage values that fall within that range. In this case, the range of voltages varies between 6 volts and 12 volts. Since the voltages are spread evenly, we can calculate the probability by finding the proportion of the range compared to the total range of possibilities.

Answer:

6 días (6 days)

Step-by-step explanation:

El número de horas-hombre es directamente proporcional a la cantidad de sillas producidas. Entonces: (The number of man-hours is inversely proportional to the quantity of manufactured chairs. Then:)

[tex]\frac{(16\,p)\cdot \left(9\,\frac{h}{d\cdot p} \right)\cdot \left(12\,d\right)}{60\,c} = \frac{(40\,p)\cdot \left(8\,\frac{h}{d\cdot p} \right)\cdot x}{60\,c}[/tex]

La cantidad de sillas producidas es (The quantity of manufactures chairs is):

[tex]x = \frac{\left(16\,p\right)\cdot \left(9\,\frac{h}{d\cdot p} \right)\cdot \left(12\,d\right)}{(40\,p)\cdot \left(8\,\frac{h}{d\cdot p} \right)}[/tex]

[tex]x = 5.4\,days[/tex]

Lo cual significa que se necesitan 6 días (Which mean that 6 days are needed).

Answer:

Step-by-step explanation:

Hello!

To study time perception, 8 students measured one minute (counted to 60), the given data show the actual time (in seconds) it took each student to measure one minute:

53, 52, 75, 62, 68, 58, 49, 49

8 observations make this sample, n=8

You can summarize the observed data using descriptive statistics:

Central tendency measures:

Median (Me):

The median is the value that separates the sample in a half ( the bottom 50% from the top 50%). To calculate it you have to calculate its position:

(for even samples) PosMe: n/2= 8/2= 4

Then you arrange the data from least to greatest and identify the 4th value:

49, 49, 52, 53, 58, 62, 68, 75

Me= 53s

Mode (Md):

The mode is the most observed value, i.e. the value with the most absolute frequency:

In this data set, the only value that was observed more than once is 49, so that is the value of the mode

Md= 49s

Mean (X[bar]):

Is the average or expected value of the data set, it is always within the range of definition of the variable but it doesn't necessarily correspond to and observation. You calculate it as:

X[bar]= ∑X/n= (53+52+75+62+68+58+49+49)/8= 466/8= 58.25s

Measures of dispersion:

Range (R):

The is the difference between the minimum and maximum observations of the sample.

R= max - min = 75 - 49= 26s

Standard deviation (S):

It shows the variability between the values of the sample. A low standard deviation tells that the observations are close to the meanwhile a high standard deviation show that the values are further away from the mean.

∑X= 466

∑X²= 27772

[tex]S= \sqrt{(\frac{1}{n-1})[sumX^2-\frac{(sumX)^2}{n} ]= \sqrt{(\frac{1}{7} )[27772-\frac{(466)^2}{8} ]} = \sqrt{\frac{1255}{14} } = 9.47s[/tex]

S= 9.47s

I hope this helps!

Answer:

Complex and imaginary

Step-by-step explanation:

I had this same exact question on my test! It is both complex and imaginary

The value of 3n-(2+n) is 6 for n=4. This is obtained by applying simple algebraic operations such as adding like terms to the given expression.

An expression consists of coefficients, variables, and constants.

Given expression is 3n - (2+n) and it has a solution 6 for a value of n.

So, it can be written as 3n - (2+n) = 6

Expanding the obtained equation:

3n-2-n=6

Adding like terms

(3n - n) - 2 = 6

2n=6+2

2n=8

⇒ n=4

Therefore, for n=4 the value of the given expression is equal to 6.

Learn more about expressions here:

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Answer: 412.310 miles

Step-by-step explanation:

The diagram representing the scenario is shown in the attached photo. The bearing is taken with respect to the northern direction. The angles at B are determined by applying the concept of alternate angles with respect to parallel lines.

A right angle triangle ABC is formed. The starting point is A and the end point is C. The distance, x between A and C represents the hypotenuse of the triangle.

We would determine x by applying Pythagoras theorem which us expressed as

Hypotenuse² = opposite side² + adjacent side²

x² = 400² + 100² = 170000

x = √170000

x = 412.310 miles

Answer:

1/4

Step-by-step explanation:

Answer:

This study is an experiment.

Step-by-step explanation:

This is a case of experiment, as the visitors are assigned randomly to one of the two advertisements. The researcher intervene introducing a variable (the type of advertisement) and then study the results.

If it was an observational study, the researcher would observe, for example, the behaviour of the visitor without defining or controlling the exposure to one of the advertisement for a group of visitors.

Answer:

B)18

Step-by-step explanation:

3z-3

Let z=7

3*7 -3

Multiply first

21-3

Then subtract

18

Answer:

B

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

3.66+.72+1.77+2.17=8.32×6%=8.8192 =8.82

Answer:

C Yes, the total of her purchase after sales tax is $8.82.

Step-by-step explanation:

3.66+0.72+1.77+2.17= $8.32

8.32*.06 =0.4992

0.4992+8.32= $8.82

Hope this helps!

Answer:

Check the explanation

Step-by-step explanation:

The margin of error does not take into account any problems with the wording of the survey question, interview errors, bias from sequence of questions, and so forth.

The margin of error reflects the difference between p(sample proportion) and P(Population proportion).

The margin of error addresses sampling variability and does not cover errors from survey design or administration flaws. Issues like question wording or interviewer bias are separate from sampling error. These design-related problems are not included in the margin of error.

The margin of error in a poll typically accounts for the natural variability that comes from sampling a subset of the population, rather than the entire population. This means it does not include errors that may arise from problems such as the wording of the survey question, interview errors, or bias from the sequence of questions. These issues are related to the design and administration of the survey and not the sampling process, so they are not reflected in the reported margin of error.

Answer:

Parameter because the value is a numerical measurement describing a characteristic of a population.

Step-by-step explanation:

key word is, the study of all 4548 employees

The underlined number, 45%, is a parameter because it's a numerical measurement that describes a characteristic of an entire population (in this case, all 4548 employees at a college). If the data was from a subset of the population or a sample, then it would be a statistic.

The underlined number 45% is a parameter because the value is a numerical measurement describing a characteristic of a population. In statistics, a parameter refers to a numerical characteristic of a population. In this case, the whole population under study is all 4548 employees at a college, and the underlined number represents the proportion of this entire population that owns computers.

To illustrate this concept further, consider a situation where you are studying a smaller group or sample from the entire population of employees. A statistic, on the other hand, would be a numerical measurement that describes a characteristic of this sample. If you were to evaluate a subset of 1000 employees from this college and found that 40% of them own computers, that would be a statistic because the value is describing a characteristic of a sample, not the entire population.

In summary, a parameter is a numerical characteristic of a whole population while a statistic is a numerical characteristic of a sample taken from that population.

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Answer: 4) 50 minutes walking , 50 minutes basketball and 6) 70 minutes walking, 60 minutes basketball

Joshua can distribute his time among walking and basketball in a variety of ways.

Without any constraints on total time spent, all provided options, from 40 minutes each for walking and basketball to 70 minutes walking and 60 minutes basketball, are considered valid solutions.

The problem seems to deal with the way Joshua divides his time between two activities, which are walking and basketball. As the question does not state a limit to the total time Joshau can spend on activities, we can assume each mentioned time division can be considered a possible solution.

Therefore, under this assumption, all provided options are valid as Joshua can spend:

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Answer:

By the Empirical Rule, the approximate percentage of cars that remain in service between 69 and 74 months is 13.5%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed(bell-shaped) random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 64

Standard deviation = 5.

Using the empirical rule, what is the approximate percentage of cars that remain in service between 69 and 74 months?

69 = 64 + 1*5

So 69 is one standard deviation above the mean.

74 = 64 + 2*5

So 74 is two standard deviations above the mean.

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

This means that:

95 - 68 = 27% between 1 and 2 standard deviations of the mean.

The normal distribution is symmetric, which means that 27/2 = 13.5% of those are below the mean(within 1 and 2 standard deviations below the mean) and 13.5% of those are above the mean(between 69 and 74).

So

By the Empirical Rule, the approximate percentage of cars that remain in service between 69 and 74 months is 13.5%.

Answer:

14.1 u^2

Step-by-step explanation:

A=pi*6^2*45/360=3.14*36*45/360=3.14*45/10≈14.1

Answer:

19

Step-by-step explanation:

We'll begin by calculating the mean of the data. This is illustrated below:

Mean = summation of data / number of data

Data from the question: 9, 13, 43, 55

Mean = (9 + 13 + 43 + 55)/4

Mean = 120/4

Mean = 30.

Now, we can calculate the mean absolute deviation (MAD) as follow:

MAD = summation of the absolute deviation from the mean / number of data.

MAD = [ |9–30| + |13–30| + |43–30| + |55–30| ] /4

MAD = [ 21 + 17 + 13 + 25] /4

MAD = 76/4

MAD = 19.

Therefore, the mea absolute deviation (MAD) of their ages is 19

Answer:

19

Step-by-step explanation: