the composition of the senate of the 107th congress is 53 republicans, 42 democrats, and 5 independents. a new committee is being formed to study ways to benefit the arts in education. if 3 senators are selected at random to head the committee, find the probability

Answer: sides across from each other are parallel

- Diagonals bisect each other

- opposite sides are congruent

- opposite angles are congruent

Answer:

Answer: A = (x + 20)(x + 10) − 12 is the correct answer

Step-by-step explanation:

We would take the length and width of the patio and subtract it by the area that does not need to be painted.

I got this right on the test!

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Step-by-step explanation:

Answer:

It is 0.578

Step-by-step explanation:

0.00578

to 2 significant figures

0.00578

0.578

Final answer:

0.00578 rounded to two significant figures is 0.0058, as you only count the first two non-zero digits and apply the standard rules of rounding off.

Explanation:

To correct the number 0.00578 to two significant figures, we need to identify the first two non-zero digits as those are the ones considered significant. Here, the non-zero digits are 5 and 7. Therefore, to maintain two significant figures, we need to round the third digit (8), keeping in mind the rules of rounding: if the third digit is 5 or more, we round up the second digit by 1.

In this case, since the third digit is 8, which is more than 5, we round up the second digit by 1. Hence, the number becomes 0.0058. Since we must retain only two significant figures, we do not count the zeros before the '5' as they are merely placeholders. Finally, to two significant figures, 0.00578 is correctly rounded to 0.0058.

Answer:

Step-by-step explanation:

8000x0.04=

$320

Answer:

$320.

Step-by-step explanation:

.04 x 8000 = 320

Feel free to let me know if you need more help! :)

Answer:

add middle numbers and divide by two.

Step-by-step explanation:

When you need to find the median with an odd set of numbers, you arrange the numbers in order from least to greatest and find the number in the middle of the set:

1 2 3

median is 2.

But, when you have an even set of numbers, you take the two middle numbers, add them together, then divide them by two (it's like finding the mean of those two middle numbers):

1 2 3 4

2 3

2+3=5

5÷2=2.5

median is 2.5

Answer: take the middle two numbers and divide them

Step-by-step explanation: when you line them up orderly from lowest to highest you need to cross out the numbers until you reach the final 2 or 1. If you have one number left that number is the answer. If you are left with 2 numbers you add them together and divide them by 2 and you will get your answer.

Final answer:

To find the extrema of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4, one must apply the method of Lagrange multipliers and solve for the critical points that satisfy both the original function and the constraint.

Explanation:

To find the maximum and minimum values of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4 using Lagrange multipliers, we need to set up the Lagrange function, also known as the Lagrangian, which incorporates the original function and the constraint. The Lagrangian for this problem is L(x, y, z, λ) = x²y²z² + λ(4 - x² - y² - z²), where λ is the Lagrange multiplier.

We then take the partial derivatives of L with respect to x, y, z, and λ and set them equal to zero:

∂L/∂x = 2xyz² - 2xλ = 0

∂L/∂y = 2xy²z - 2yλ = 0

∂L/∂z = 2xyz² - 2zλ = 0

∂L/∂λ = 4 - x² - y² - z² = 0

By solving this system of equations, we can find the values of x, y, z, and λ that maximize or minimize the function f under the given constraint.

Answer:

1 + 2y + y²

Step-by-step explanation:

Suppose,we want to expand a given binomial of the form;

( 1 + y)ⁿ we will have

1 + ny + n(n - 1)y²/2! + n(n - 1)(n - 2)y³/3! + ....

hence:

( 1+y)² = 1 + 2y + 2(2-1)y²/2!

= 1 + 2y + y²

Answer: Please see answer in explanatory column

Step-by-step explanation:

STEP 1 - Since the survey is not an experimental one which occurs in a laboratory with a control and interference with sample.

Then the professor will use an observational study is in which he will observe the  behavior of the students  in a systematic manner without interfering with the students behavior so as to know how satisfied the students are with the course.   After getting to know how satisfied the students are for his course he would record the behavior that he or she observes and rate accordingly

STEP 2:The sampling strategy the Professor can use in carrying out the research is a Stratified sampling which occurs when the population to be observed is divided into groups known as strata which contains similar cases grouped together, then a second sampling, mostly a random sampling where the professor will randomly sample few students from the different strata to get his observations. for example, the students divided in 4 groups of 40 students represents each strata placed in common according to the different teaching assistant, then the professor can then randomly sample few students from each strata from a class of the 120 students.

This study is an observational study. A possible sampling strategy for this study could be stratified sampling.

(a) This study is an observational study since the researcher is not manipulating any variables or assigning participants to groups. The researcher is simply observing and collecting data on the students' satisfaction with the course.

(b) A possible sampling strategy for this study could be stratified sampling. The researcher could divide the 160 students into four strata based on their lab sections and then randomly select a certain number of students from each stratum to participate in the survey. This ensures that each lab section is represented in the sample.

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Answer:

1500%

Step-by-step explanation:

From March 2004 - March 2006, this is 2 years. The number of "6-month" period there are in 2 years is:

2* 12 = 24 months

24/6 = 4  "6 month periods"

So, it doubles "4" times in that time frame.

Let Initial population be 100 (In March 2004).

1 times double = 100 * 2 = 200

2 times double = 200 * 2 = 400

3 times double = 400 * 2 = 800

4 times double = 800 * 2 = 1600

So, population goes from 100 to 1600. How much percentage increase is that?

To get percentage increase, we find the increase and divide by original (initial amount). Then multiply by 100 to get percentage. So,

1600 - 100 = 1500 increase

1500/100 = 15

15 * 100 = 1500%

        Percentage increase in the number of blogs from March'04 to March'06 will be 1500%.

          [tex]P(t)=P_0(1+r)^t[/tex]

          Here, [tex]P(t)=[/tex] Final value

          [tex]P_0=[/tex] Initial value

          [tex]r=[/tex] Growth rate

          [tex]t=[/tex] Period of 6 months

Given in the question,

"Number of blogs are doubled in every six months"

[tex]P(t)=2P_0[/tex]

[tex]2P_0=P_0(1+r)^1[/tex]

2 = (1 + r)

r = 1 Or 100%

Therefore exponential function will be,

[tex]P(t)=P_0(2)^t[/tex]

To find the increase in blogs from March 2004 to March 2006,

Number of six monthly periods in 2 years = 4

[tex]P(4)=P_0(2)^4[/tex]

P(4) = 16(P₀)

Percentage increase in blogs = [tex]\frac{P(4)-P_0}{P_0}\times 100[/tex]

                                                  [tex]=\frac{16P_0-P_0}{P_0}\times 100[/tex]

                                                  = 1500%

     Therefore, percentage increase in the number of blogs will be 1500%.

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Answer: 9 and -4

Step-by-step explanation:

9 and 4 are both factors of 36, however we want to multiply to -36 so one of them must be a negative.

The two must also add up to 5, so that means -9 and 4 would not work as those would add to -5, leaving 9 and -4 left as the answer.

The value of two numbers multiply by -36 and added to 5 would be - 36 and 5.

Used the concept of the equation that states,

Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that,

The multiplication of two numbers = - 36

The addition of two numbers = 5

Let us assume that the two numbers are x and y.

Hence the equations become,

x + y = 5   .. (i)

And, xy = - 36  .. (ii)

From (i);

x = 5 - y

Substitute the above value in (ii);

(5 - y)y = - 36

5y - y² = - 36

y² - 5y - 36 = 0

y² - (9 - 4)y - 36 = 0

y² - 9y + 4y - 36 = 0

y (y - 9) + 4 (y - 9) = 0

(y + 4) (y - 9) = 0

This gives,

y = - 4

y = 9

Substitute both the values in (i);

Put x = - 4

x - 4 = 5

x = 9

Put x = 9;

x + 9 = 5

x = - 4

Therefore, the two numbers are 9 and - 4.

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Answer:

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

The mean is given by:

[tex] \bar X = 13.6[/tex]

And the deviation is given by:

[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]

Step-by-step explanation:

For this case we define the random variable X as "number of years of education of self-employed individuals in the U.S." and we know the following properties:

[tex] E(X) = 13.6 , Sd(X) = 3[/tex]

And we select a sample of n = 100

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

Solution to the problem

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

The mean is given by:

[tex] \bar X = 13.6[/tex]

And the deviation is given by:

[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]

Answer:

a) Mean of the sampling distribution = 13.6 years

b) Standard deviation of the sampling distribution = 0.3

[tex]\bar {x} = N(13.6, 0.3)[/tex]

Step-by-step explanation:

Population mean, [tex]\mu = 13.6 years[/tex]

Population standard deviation, [tex]\sigma = 3.0 years[/tex]

Sample size, n = 100

a) Mean of the sampling distribution = mean of the normal distribution

[tex]\mu_{s} = \mu\\\mu_{s} = 13.6 years[/tex]

b) Standard deviation of the sampling distribution, [tex]\sigma_{s} = \frac{\sigma}{\sqrt{n} }[/tex]

[tex]\sigma_{s} = \frac{3}{\sqrt{100} } \\\sigma_{s} = \frac{3}{10} \\\sigma_{s} = 0.3[/tex]

Answer:

D

Step-by-step explanation:

65% × 78 =

(65 ÷ 100) × 78 =

(65 × 78) ÷ 100 =

5,070 ÷ 100 =

50.7;

Answer:

A 120

Step-by-step explanation:

you divide 120 by 0.65 to find 78

The probability that a person will take longer than 21 days to pass it is 0.12

Explanation:

Given:

Mean time, μ = 14 days

Standard deviation, ρ = 6 days

Let x be the time to pass the kidney stones.

Probability that a person will take longer than 21 days to pass it.

We need to find z score first

Z score = [tex]\frac{x - u}{p}[/tex]

Z score = [tex]\frac{21-14}{6}[/tex]

            = 1.166

Probability that a person will take longer than 21 days to pass it = P(x > Z)

                                                                                                          = P(x > 1.16)

                                                                                                          = 0.12

Therefore, the probability that a person will take longer than 21 days to pass it is 0.12

Answer:

[tex]\bar{x}= 200[/tex]

Step-by-step explanation:

We are given the following in the question:

Population mean = 200

Population standard deviation = 50

Sample size, n = 100

We have to estimate the expected value of the sample mean.

The best point estimate for the sample mean is the population mean.

Thus, we can write:

[tex]\bar{x}= \mu = 200[/tex]

Thus, the expected value of the sample mean is 200.

Answer:

-1/2

Step-by-step explanation:

Use Rise over run

Rise 8 - 10 = -2

Run 2 - (-2) = 4

The slope is - 1/2

Answer:

applying one way ANOVA:

R² = SSR / SST

    = 0.133/1.807

     =0.0734

Source of Variation SS     df       MS       F   P-value    F0.05(2.27)

treatments               0.133      2      0.066      1.069   0.3574      3.354

error                       1.675     27     0.062    

Total                        1.807     29    

as p value is not significantly low:

Do the ANOVA results indicate that the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (HA)? -No

Step-by-step explanation:

Answer:

C 32

Step-by-step explanation:

[tex]f(x) = 8 \sqrt{143 - x} \\ f(127) = 8 \sqrt{143 - 127} \\ f(127) = 8 \sqrt{16} \\ f(127) = 8 \times 4 \\ \huge \red{ \boxed{ f(127) = 32}}[/tex]

Answer:

The final approximation integral answer is 1.8975

Answer:

Required average rate of change over the interval [1.9, 2] is 5.9, [1.99, 2] is 5.99, [2, 2.1] is 6.1, [2, 2.01] is 6.01 and the instantaneous change at x=2 is 6.

Step-by-step explanation:

Given function is,

[tex]f(x)=x^2+2x+9[/tex]

To find the avarage rate of change over given intervals. We know from Lagranges Mean value theorem, the average rate of change of a function F(x) over a interval [tex]a\leq x\leq b[/tex] is, [tex]\frac{f(b)-f(a)}{b-a}[/tex].

(a) On the interval,

[tex]\frac{f(2)-f(1.9)}{2-1.9}= \frac{17-16.41}{0.1}=5.9[/tex]

[tex]\frac{f(2)-f(1.99)}{2-1.99}= \frac{17-16.9401}{0.1}=5.99[/tex]

(b) On the interval,

[tex]\frac{f(2.1)-f(2)}{2.1-2}= \frac{17.61-17}{0.1}=6.1[/tex]

[tex]\frac{f(2.01)-f(2)}{2.01-2}= \frac{17.0601-17}{0.01}=6.01[/tex]

(c) Instantaneous rate of change at x=2 is,

[tex]\lim_{x\to 2}\frac{\Delta y}{\Delta x}=\lim_{x\to 2}\frac{f(2)-f(x)}{2-x}[/tex]

[tex]=\lim_{x\to 2}\frac{17-x^2-2x-9}{2-x}[/tex]

[tex]=\lim_{x\to 2}\frac{-(x+4)(x-2)}{-(x-2)}[/tex]

[tex]=\lim_{x\to 2}(x-4)[/tex]

[tex]=6[/tex]

Hence the results.

Answer:

a) Expected value = 6.406

Variance = 4.905

Standard deviation = 2.45

b) The probability is 0.08547

Step-by-step explanation:

a) Let's suppose that:

X₁ = number of 6´s

X₂ = number of Jack, Queen, King or Aces

The mean of X₁ is:

MeanX₁ = n * p = 20 * (1/6) = 3.33

The variance of X₁ is:

[tex]Var-X_{1} =np(1-p)=3.33(1-(1/6))=2.775[/tex]

The mean of X₂ is:

MeanX₂ = 10 * (16/52) = 3.076

The variance of X₂ is:

[tex]Var-X_{2} =3.076(1-(16/52))=2.13[/tex]

The expect value of X is:

Xexp = MeanX₁ + MeanX₂ = 3.33 + 3.076 = 6.406

The variance of X is:

VarX = VarX₁ + VarX₂ = 2.775 + 2.13 = 4.905

The standard deviation is:

Xdevi = 4.905/2 = 2.45

b) The probability of drawing at least five six out of 20 rolls is equal to:

∑(1/6)ˣ(5/6)²⁰⁻ˣ = 0.231 with x = 5

The probability of at least 4 Jack, Queen, Kings or Aces is:

∑(16/52)ˣ(1-(16/52))¹⁰⁻ˣ = 0.37 with x = 4

The probability of given event is equal to:

P = 0.231 * 0.37 = 0.08547

Answer:

Step-by-step explanation:

Hello!

The variable of the study is

X: taxi fare from Logan Airport to downtown Boston.

This variable has a normal distribution

Suppose a sample of 7 taxi fares was taken and a 95%CI for the population mean was calculated obtaining:

$[20.51; 24.21]

The confidence level is a way of estimating the value of a population parameter of interest just like the point estimation. The difference is that instead of obtaining one value that may or may not be close to the true value of the parameter you obtain the range of values the parameter may take with a certain level of confidence.

The confidence level of an interval is the probability under which it is built. This probability indicates that if they build 100 confidence intervals, we expect 95 to contain the value of the parameter of interest we are trying to estimate.

As mentioned before in this case the parameter of interest is:

μ: population mean of taxi fares from Logan Airport to downtown Boston

And the 95% CI can be interpreted as:

We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.

I hope this helps!

Answer: A ( the data in shelter A show more spread than the data in shelter B )

Step-by-step explanation:

Answer: A

Step-by-step explanation: shelter A

Answer: the interest owed is $21

Step-by-step explanation:

The question is incomplete. The complete question is:

Sari Tagore obtains a $1000 loan to purchase a laser printer. Her interest rate is 7% ordinary interest for 108 days. What is the interest owed?

Solution:

When calculating ordinary interest, we assume that a year has 360 days. We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the loan

P represents principal or amount borrowed.

R represents interest rate

T represents duration in years

From the information given,

P = 1000

R = 7%

T = 108 days. Converting to years, it becomes 108/360

Therefore

I = (1000 × 7 × 108/360)/100

I = $21

Answer:

The dimensions of the page are

3.46 ft by 5.20 ft

Step-by-step explanation:

Let

x---> the length of the sheet of paper in feet

y ---> the width of the sheet of paper in feet

[tex]A=xy[/tex]

[tex]A=18\ ft^2[/tex]

so

[tex]18=xy[/tex]

[tex]y=\frac{18}{x}[/tex] -----> equation A

Remember that

[tex]1\ ft=12\ in[/tex]

Convert the margins into feet

[tex]9\ in=9\12=0.75\ ft[/tex]

[tex]6\ in=6\12=0.50\ ft[/tex]

so

we know that

The area of the largest printed area is given by

[tex]A=(y-0.75-0.75)(x-0.50-0.50)[/tex]

[tex]A=(y-1.50)(x-1)[/tex]

[tex]A=xy-y-1.50x+1.50[/tex]

substitute equation A in the above expression

[tex]A=x(\frac{18}{x})-\frac{18}{x}-1.50x+1.50\\[/tex]

[tex]A=18-\frac{18}{x}-1.50x+1.50[/tex]

[tex]A=19.50-\frac{18}{x}-1.50x[/tex]

Now we have an output (A) in terms of only one variable (x),

so

we differentiate:

[tex]\frac{dA}{dx}=\frac{18}{x^2}-1.50[/tex]

equate to zero

[tex]\frac{18}{x^2}=1.50[/tex]

[tex]x^2=12\\x=3.46\ ft[/tex]

Find the value of y

[tex]18=(3.46)y\\y=5.20\ ft[/tex]

therefore

The dimensions of the page are

3.46 ft by 5.20 ft

The required dimensions are,

[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]

The formula of the area of the rectangle is [tex]A=l \times b[/tex]

Let [tex]A[/tex] be the area of the paper then,

[tex]A=(x+18)(y+12)...(1)[/tex]

And the printed area is [tex]xy=18...(2)[/tex]

Now, from the equation (1) and (2) we get,

[tex]A=(x+18)(\frac{18}{x}+12)\\ A=234+12x+\frac{324}{x} ..(3)[/tex]

Now, differentiating equation (3)

[tex]\frac{dA}{dx}=12-\frac{324}{x^2} \\\frac{dA}{dx}=0\\12-\frac{324}{x^2} =0\\x=3\sqrt{3}[/tex]

Substituting the obtained value of [tex]x[/tex] into the equation (2)

[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]

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Answer:

it's 20

Step-by-step explanation:

I just had the same question and I got it right it's 20.

There are 20 flowers in the garden and there are 4 flowers that have a height that is 7 1/4 inches or greater

From the complete question, there are 20 points in the line plot.

Each point represents a flower

Hence, there are 20 flowers in the garden

Using the same line plot in (a), there are 4 points in the line plot where the flower height is either 7 1/4 or more

Hence, there are 4 flowers that have a height that is 7 1/4 inches or greater

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Answer:

(See explanation)

Step-by-step explanation:

The expression is simplified as follows:

[tex]63 + 81[/tex]

[tex]9 \times (7+9)[/tex]

[tex]9\times 16[/tex]

[tex]144[/tex]

This answer can be checked by summing the previous formula:

[tex]63 + 81[/tex]

[tex]144[/tex]

Answer: A.13

Step-by-step explanation:

Look at the attached picture ⤴

Hope it will help u...

Answer:

0.5

Step-by-step explanation:

you have to combine like terms

Answer:

[tex](C)\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]

Step-by-step explanation:

To rationalize the expression:

[tex]\dfrac{5-\sqrt{7} }{9-\sqrt{14} }[/tex]

In order to rationalize any Surdic expression, what is needed is to multiply both the numerator and the denominator of the rational function by the conjugate of the denominator.

In the example above:

The denominator is: [tex]9-\sqrt{14}[/tex]

Its conjugate therefore is: [tex]9+\sqrt{14}[/tex]

Therefore, we multiply the fraction by the expression:

[tex]\dfrac{9+\sqrt{14} }{9+\sqrt{14} }[/tex]

Answer:

c

Step-by-step explanation: