Add.
(7v–4)+(–4v3–v2–8v–5)

The two positive numbers that satisfy the given requirements are √17 and 34

Given the sum of the first number squared and the second number

is 51.

Let's assume first number is x.

second number is y.

Square of first number is [tex]x^2[/tex].

sum of the first number squared and the second number = [tex]x^2 + y[/tex].

[tex]x^2 + y = 51[/tex]

subtract [tex]x^2[/tex] from both side of equal sign.

[tex]x^2 + y- x^2 = 51 - x^2[/tex]

[tex]y = 51 - x^2[/tex]

Product of both numbers p  = x*y.

[tex]p = x*(51 - x^2)[/tex]

[tex]p = 51*x - x^3.[/tex]

Given the product is a maximum.

so derivative of p with respect to x  will be = 0.

derivative of p with respect to x is  [tex]51-3*x^2[/tex]

[tex]51-3*x^2 = 0[/tex]

[tex]3*x^2=51[/tex]

[tex]x^2 = 17[/tex]

x = √17.

put value of x in [tex]y = 51 - x^2[/tex]

[tex]y = 51 - (\sqrt17)^2[/tex] = 51 - 17 = 34

So the value of x and y is √17 and 34 respectively.

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The best guess for the mean score for all the Georgia students would be 1050 number here.

Given that:

The mean score for a random sample of Georgia students is 1050.

Assuming,

1) X-bar = 42; µ = 44; standard deviation (sigma) = 10; N = 64. Calculate the standard error.

1) The standard error is computed as:

[tex]\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{64}} = 1.25[/tex]

2) You know that X-bar = 42, mu = 44, sigma-sub-X = 10, and N = 64, Calculate z-obtained.

2) The Z-value is computed as:

[tex]Z = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{N}}} = \frac{42- 44}{\frac{10}{\sqrt{64}}} = -1.6[/tex]

3) The mean score on most IQ tests is 100 with a standard deviation of 15. If Sally has a score of 110 on an IQ test, what is her z-score.

3) The Z -score here is computed as:

[tex]Z = \frac{X -\mu}{\sigma} = \frac{110-100}{15} = 0.6667[/tex]

The best point estimate for the population mean score is equal to the sample mean which is 1050 in this case. Therefore the best guess for the mean score for all the Georgia students would be 1050 here.

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Answer:

x=36

Step-by-step explanation:

There isn't a ton of information regarding exactly what you are looking for to answer this question. However, if you are trying to simply convert the following word phrase to an expression, here you go:

Hence, the final expression would be written as:

[tex](3x+4) < 4(x+1)[/tex]

Hope this helps!

The p-value is greater than the significance level, so we do not reject the null hypothesis for the significance level is 0.01 (1%)

What is significance level?

"Significance" in statistics refers to something that is "not by chance" or "likely true." We can infer that when a statistician claims that a finding is "very significant," he or she is implying that it may very well be true. It does not imply that the finding is very significant, but it does imply that it is highly likely. The fixed likelihood of incorrectly eliminating the null hypothesis when it is, in fact, true is what is referred to as the level of significance. The probability of type I error is defined as the degree of significance, and the researcher sets it based on the results of the error. The statistical significance is measured by its level of significance. It specifies whether the null hypothesis is thought to be accepted or rejected.

The p-value for ACT is 0.0286

The significance level is 0.01 (1%)

Hence, the p-value is greater than the significance level, so we do not reject the null hypothesis. We conclude that there is insufficient evidence to conclude that there is any linear relationship at a 1% level of significance between GPA and ACT scores.

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The probability that no two teams win the same number of games is 742.

The number of powers of 2 in 40! is

= (40/2) + (40/4) + (40/8) + (40/16) + (40/32)

= 20 + 10 + 5 + 2 + 1

= 38.

780-38 = 742.

Hence, the probability that no two teams win the same number of games is 742.

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98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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The probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Given:

The probability that a person who makes reservations on a certain flight and does not show up for the flight is p=0.05.

The probability that a person who makes reservations on a certain flight and does show up for the flight is 1-p=1-0.05=0.95.

The airlines sell 160 tickets for a flight with only 155 seats.

Let X be a random variable that denotes the number of persons who show up for the flight and it follows a binomial distribution with parameters n = 160 and p = 0.95.

Hence, X~ Binom (n = 160, p = 0.95).

Here,

np=160×0.95=152>5

n(1-p)=160×0.05 = 8.1>5

Hence, both np and n(1-p) are greater than 5, the binomial distribution can be approximated to normal distribution.

The probability that a seat will be available for every person holding a reservation and planning to fly is calculated as follows:

P(X ≤ 155) = (P < 155 + 0.5)

                 [tex]=P(x < 155.5)\\\\=P(\frac{X-np}{\sqrt{np(1-p)}} < \frac{155.5 - (160 \times 0.95}{\sqrt{160\times 0.95 \times 0.05}})\\\\=P(Z < \frac{155.5-152}{2.7568})\\\\=P(Z < 1.27)\\\\=0.8980[/tex]

Hence the probability that a seat will be available for every person holding a reservation and planning to fly is 0.8980.

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The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.

When two rays are linked at their ends, they create an angle in geometry.

The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.

Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

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The probability that a randomly chosen mango of this type won't be deemed to be large in size is 26.43%.

For the stated question;

The formula for the z-score is;

z = (x - μ)/σ

x < 425 gram

mean  μ = 400,

standard deviation σ = 40:

Thus,

z = (425 - 400)/40

z = 0.625

P(X < 425) = 1 - P(z = 0.625)

P(X < 425) = 1 - 0.7357

P(X < 425) = 0.2643

Thus, there is a 26.43% chance that a randomly chosen mango of this sort will not be regarded as being huge in size.

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Answer:0.8413

Step-by-step explanation:

0.8413

The mean is μ=400, and the standard deviation is σ=25.

Open Excel.  Click on an empty cell.  Type =NORMDIST(425,400,25,1) and press ENTER.

The probability, rounded to four decimal places, is P(X<425)≈0.8413.

4300 km to miles:

[tex]{ \red{ \tt{2671.896}}}[/tex]

2671.896 in nearest whole number :

[tex]{ \blue{\boxed{ \tt{2672}}}}[/tex]

The percent of increase on the truck was 375%.

The equation representing the situation is written as

the number of customers Olaf had originally is 80

From the given information the following is deduced

Olaf has 11 more than triple the amount of customers as when he started selling newspapers

let the amount be x

3x + 11 = ?

He now has 71 customers

3x + 11 = 71

solving the equation

3x = 71 - 11

3x = 60

x = 20

Olaf had 80 customers

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The numerical side length of length AD is 44 units

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

AD= 4x + 8

CD = 5x - 1

Also, from the complete question (added at the end of the solution), we understand that

The lengths AD and CD are congruent

These parameters and statements above mean that

AD = CD

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

4x + 8 = 5x - 1

Collect the like terms

5x - 4x = 1 + 8

Evaluate the like terms

x = 9

Substitute x = 9 in AD= 4x + 8

AD= 4 x 9 + 8

Evaluate

AD= 44

Hence, the length is 44 units

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Complete question

Given that lengths AD and CD are congruent.

Find AD

CD = 5x-1 and AD = 4x+8

Answer:

H

Step-by-step explanation:

Answer:

Commutative Property of Multiplication

Step-by-step explanation:

Hope it helps!

The coefficient of determination is 0.588 and the percentage of the total variation is 58.8%.

The coefficient of determination (r^2) refers to a measurement used to explain how much variability of one variable can be caused by its relationship to another related variable. It is the fit of goodness and measures how well a statistical model fits the observed data and is a number between 0 and 1. When the value of linear correlation coefficient r is known, the coefficient of determination can be computed simply by squaring r.

Hence if r = 0.767, then the coefficient of determination = r^2 = 0.588

As percentage of the total variation is same as the coefficient of determination (given in percentage) and is given by the R² value = 58.8%. Hence, about 58.8% of variation is explained by the linear relationship between the two variables.

Note: The question is incomplete. The complete question probably is: Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. r = 0.767.

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It will take 3 years for the value of the computer of initial value $1000 to reach $512.

Given, Timothy purchased a computer for $1,000.

The value of the computer depreciates by 20% every year.

we have to find the number of years value of computer will take to reach $512.

Let, the function representing this situation be,

V(t) = AB^t

where, A is the initial value of the computer and B is the depreciating rate.

So, V(t) = (1000)(1 - 20/100)^t

V(t) = (1000)(0.8)^t

Now, the value will be, 512

512 = 1000(0.8)^t

0.512 = (0.8)^t

t = 3

So, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

Hence, it will take 3 years for the value of the computer of initial value $1000 to reach $512.

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Using proportions and ratios, the cost of 1.4lbs is $10.96

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

This is basically the process of comparing two ratios with one another.

In this problem, we will compare the two ratios and solve for the unknown cost of 1.4lbs

0.6 / 4.71 = 1.4 / x

Cross multiply both sides

x = (4.71 * 1.4) / 0.6

x = 10.96

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The regression equation is y = 0.9x+ 7.5

given that

xi:  2   6    9    13    20

Yi : 7   18   9    26   23  

from the given data we have:

∑x = 2+6+9+13+20 = 50

∑y = 7+18+9+26+23 = 83

Also, we need to calculate:

∑xy = 2 × 7+ 6 × 18+ 9× 9+ 13 × 26+ 20×23 = 1001

∑[tex]x^{2}[/tex] = [tex]2^{2}[/tex] + [tex]6^{2}[/tex] + [tex]9^{2}[/tex] + [tex]13^{2}[/tex] + [tex]20^{2}[/tex] = 690

∑[tex]y^{2}[/tex]= [tex]7^{2}[/tex] +  [tex]18^{2}[/tex] + [tex]9^{2}[/tex] + [tex]26^{2}[/tex] + [tex]23^{2}[/tex] = 1659

the slope b is calculated:

b = ∑xy - ∑x × ∑y/n ÷ ∑[tex]x^{2}[/tex] - (∑x)^2 /n

now we need to substitute above values in the equation:

b = 1001 - 50×83 /5 ÷ 690 - (50)^2/5

b= 0.9

the y-intercept (a) is :

a = y - bx

where

y = ∑y/n = 83/5 = 16.6

x = ∑x/n = 50/5 = 10

now substitute these values

a = 16.5 - 0.9 × 10

a = 7.5

the regression equation:

y = bx + a

now ,

y = 0.9x+ 7.5

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The expected value of distribution A is 1 and distribution B is 3. The standard deviation for both distributions is the same which is 1.225. In conclusion, distribution B is better than distribution A.

Events with countable or finite outcomes are counted in a discrete probability distribution. This includes the probability values for the discrete random variable. The expected value for this type of distribution is calculated by E(X)=μ=ΣxP(x). And the standard deviation is calculated by σ=√(E(X²)-(E(X))²).

a) Expected value for the distributions A and B is calculated as follows,

The expected value for distribution A,

[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.50)+(1\times0.20)+(2\times0.15)+(3\times0.10)+(4\times0.05)\\&=1\end{aligned}[/tex]

The expected value for distribution B,

[tex]\begin{aligned}E(X)&=\sum x P(x)\\&= (0\times0.05)+(1\times0.10)+(2\times0.15)+(3\times0.20)+(4\times0.50)\\&=3\end{aligned}[/tex]

b) The standard deviation for the distributions A and B is calculated as follows,

First, find E(X²) for distribution A and B to substitute in the standard deviation formula.

The  E(X²) for distribution A is,

[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.50)+(1^2\times0.20)+(2^2\times0.15)+(3^2\times0.10)+(4^2\times0.05)\\&=2.5\end{aligned}[/tex]

The  E(X²) for distribution B is,

[tex]\begin{aligned}E(X^2)&=\sum x^2P(x)\\&=(0^2\times0.05)+(1^2\times0.10)+(2^2\times0.15)+(3^2\times0.20)+(4^2\times0.50)\\&=10.5\end{aligned}[/tex]

Then, the standard deviation for distribution A is,

[tex]\begin{aligned}\sigma_A&=\sqrt{2.5-1^2}\\&=1.225\end{aligned}[/tex]

The standard deviation for distribution B is,

[tex]\begin{aligned}\sigma_B&=\sqrt{10.5-3^2}\\&=1.225\end{aligned}[/tex]

Distribution A and B have the same standard deviation.

c) The standard deviation values are the same for both distributions.  But the expected value of distribution A is lesser than the expected value of distribution B. So distribution B looks better than distribution A.

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The hypotheses for [tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)

Given:

Nationwide scores as  n1=1000, [tex]x_{1}[/tex]` = 21.4 ,σ1 = 3

Carolina scores as n2=500,  [tex]x_{2}[/tex]` = 21.2 ,σ2 = 3

So from here we can say

µ represents population mean.

[tex]u_{1}[/tex] represent population mean for nationwide scores.

[tex]u_{2}[/tex] represents population mean for Carolina scores.

[tex]H_{0}[/tex] is [tex]\µ_{1}[/tex] = [tex]\µ_{2}[/tex] and for [tex]H_{1}[/tex] [tex]\µ_{1} > \µ_{2}[/tex] (claim)

Given Question is incomplete, Complete Question here,

a survey of 1000 students nationwide showed a mean act score of 21.4. a survey of 500 south Carolina scores showed a mean of 21.2. if the population standard deviation in each case is 3, can we conclude the national average is greater than the south Carolina average?

use α=0.01 and [tex]\µ_{1}[/tex] for the nationwide mean act score.

State the hypotheses and identify the claim.

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The change in rate of length of shadow is 2.692 ft/sec.

Given,

Height of tall person =7 ft

Height of tall lamp post = 20 ft

Rate at which tall person walks = 5 ft/sec

Let,

Distance between tall person and lamp post be x ft

the length of shadow be y ft

From similar triangles,

[tex]\frac{x+y}{20}=\frac{y}{7}\\\\7(x+y)=20y\\\\7x+7y=20y\\\\13y=7x\\\\y=\frac{7x}{13}[/tex]

Differentiating on both sides with respect to time 't'

[tex]\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}[/tex]

here, [tex]\frac{dx}{dt}[/tex] is nothing but the change in distance between tall person and lamppost it means rate at which tall person walks=5 ft/sec

[tex]\frac{dy}{dt}=\frac{7}{13}*5\\\\\frac{dy}{dt}=\frac{35}{13}=2.692\ ft/sec[/tex]

Thus, the change in rate of length of shadow is 2.692 ft/sec.

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When the population standard deviation is much greater than 5.

What is the standard deviation?

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Here, we have

The circumstance is a score that is 5 points above the mean considered a central value.

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

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Answer:

by dividing by 100

Step-by-step explanation:

630 ÷ 100 = 6.3

Answer:

see solution

Step-by-step explanation:

equation: y = 1 - 3x

when x is -2:
y = 1 -3 * -2  = y = 1+6 = y = 7
coordinates = (x,y) = (-2,7)

when x is -1:
y = 1-3*-1 = y = 1+3 = y = 4
coordinates = (x,y) = (-1,4)

when x is 0:
y = 1 - 3 * 0 = y = 1-0 = y =1
coordinates = (x,y) = (0,1)

when x is 1
y = 1-3*1 = y = 1-3 = y = -2
coordinates = (x,y) = (1,-2)

When x is 2
y = 1-3*2 = y = 1-6 = y = -5
coordinates = (x,y) = (2,-5)

when x is 3
y = 1-3*3 = y = 1-9 = y = -8
coordinates = (x,y) = (3,-8)

Plot these points on the graph and join up the dots to see the line.

bye

The summary of the percent of times each and every category appears for the entire sample is called the frequency distribution , the correct option is (d) .

In the question ,

it is asked about what is The summary of the percent of times each and every category appears for the entire sample is called ,

it is called frequency distribution ,

Frequency distribution : it lists all categories of data and number of occurrences for each data category and

it  is also the summary of percent of times each and every category appears for entire sample .

Therefore , the correct option is (d) .

The given question is incomplete , the complete question is

The summary of the percent of times each and every category appears for the entire sample is called the ,

(a) mode

(b) categorical percentage rate

(c) percentage distribution

(d) frequency distribution

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Carrying out the operations on the polynomials shows that

A + B - polynomial

A - B - polynomial

A * B - polynomial

The given polynomials are  

A = 3x²( x − 1 )

B = -3x³ + 4x² − 2x + 1

A + B

= 3x²( x − 1 ) + (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² - 3x³ + 4x² − 2x + 1

= x² − 2x + 1

This is a polynomial

A - B

= 3x²( x − 1 ) - (-3x³ + 4x² − 2x + 1)

= 3x³ - 3x² + 3x³ - 4x² + 2x - 1

= 6x³ - 7x² + 2x - 1

This is a polynomial

A * B

= 3x²( x − 1 ) * (-3x³ + 4x² − 2x + 1)

= (3x³ - 3x²) * (-3x³ + 4x² − 2x + 1)

= -9x^6 + 12x^5 - 6x⁴ + 3x³ + 9x^5 - 12x⁴ + 6x³- 3x²

= -9x^6 + 21x^5 - 18x⁴ + 9x³- 3x²

This is a polynomial

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The probability P(DD) of the letters D and D is 4/9

The letters of the alphabets used to generate the word ADD are given as

Sample space (letters) = {A, D, D}

It is assumed that when a card (i.e. letter) is selected, the card is returned to the set

This means that the selection is with replacement

These letters mean that

P(Letter D) = Count of letter D/Number of letters

So, we have the following representation

P(Letter D) = 2/3

Now, the sample space is

Sample space (letters) = {A, D, D}

These letters mean that

P(Letter D2) = 2/3

So, we have the probability equation

P(DD) = P(D) * P(D2)

This gives

P(DD) = 2/3 * 2/3

Evaluate

P(DD) = 4/9

So, the probability is 4/9

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Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.

A Gram-positive bacterium called S. epidermidis is a component of the flora of humans. Anaerobic bacteria are what it is. It promotes the growth of pathogens that are present in medical equipment. These may enter the bloodstream. Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling s. epidermidis.

Molds produce a class of antibiotics known as penicillium. Actinomycetes produce the antibody known as novobiocin, which has antibacterial characteristics. Gentamicin is one of the antibodies that can treat infections and aid in halting bacterial development.

Hence the answer is Based on the results from your experiment, rank the antibiotics from the most effective to the least in controlling epidermidis. These aid by halting bacterial growth and infection spread.

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