an urn contains four balls numbered 2, 2, 5, and 6. if a person selects a set of two balls at random, what is the expected value of the sum of the numbers on the balls?

Answer:

Step-by-step explanation:

4(2n+3)=12

8n + 12=12

8n        = 0

 n        = 0

9514 1404 393

Answer:

Step-by-step explanation:

Maybe you want to find possible values of n.

  4(2n +3) > 1 . . . . . an expression of the problem statement

  8n +12 > 1 . . . . . . eliminate parentheses

  8n > -11 . . . . . . . . subtract 12

  n > -11/8 . . . . . . . . divide by 8

The solution to the system of equation graphed is (-1, -3)

Given the system of equations graphed on the plane expressed as:

f(x) = 3x

g(x) = 4x + 1

Equate

f(x) = g(x)

3x = 4x + 1

3x - 4x = 1

-x = 1

x = -1

Determine the value of y

y = 3x

y = 3(-1)

y = -3

Hence the solution to the system of equation graphed is (-1, -3)

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Answer:nothing

Step-by-step explanation:

Answer:

11 nickels, 15 dimes, 22 quarters

Step-by-step explanation:

number of nickels = x

number of dimes = x+4

number of quarters = 2x

- - - - - -

total of nickels = 5x cents

total of dimes = 10x + 40 cents

total of quarters = 50x cents

- - - - - -

755 = 5x + 10x + 40 + 50x

755 = 65x + 40

715 = 65x

x = 11

x+4 = 15

2x = 22

Answer:

  1 = 1; 2 = 3 -1; 3 = 3; 4 = 3 +1; 5 = 9 -3 -1;

  6 = 9 -3; 7 = 9 -3 +1; 8 = 9 -1; 9 = 9; 10 = 9 +1

  11 = 9 +3 -1; 12 = 9 +3; 13 = 9 +3 +1

Step-by-step explanation:

You want the numbers 1 – 13 expressed in terms of the digits 1, 3, 9 using operations +, -, and ×.

The digits 1, 3, 9 represent the place values of numbers in base 3. This means we can use the base-3 representation of a number to give a clue as to how to represent it using these digits.

The digits of a base 3 number are 0, 1, 2. We don't have a 2 to work with, but we know that 2 = 3 -1, so we can use that fact. Here is an example:

  5 = 12₃ = 1×3 + (3 -1)×1 = 3 +3 -1

  = 20₃ -1 = (3 -1)×3 -1 = 9 -3 -1

After writing a few numbers, we notice the signs go in the progression +, -, 0 where 0 means the digit is not included. The attachment shows the sums that make the numbers 1–13.

__

Additional comment

We could, of course, use the allowed "other digits" to include 2. For example, ...

  5 = 3 + 2×1

  6 = 2×3

<95141404393>

The equation of the line in slope intercept form is y = 2x - 2.

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the slope of the line can be found as follows:

using (0, - 2)(2, 2)

m = 2 + 2 / 2 - 0

m = 4 / 2

m = 2

Therefore, the y-intercept can be solved as follows:

using (0, -2)

y = 2x + b

-2 = 2(0) + b

b = -2

Therefore, the equation is y = 2x - 2

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Answer:

27

Step-by-step explanation:

The first angle you get with 180-61 = 119

The second angle you get by the rules of the circle which is 68/2 = 32

And finally X= 180 - 119 - 32 = 27

Answer:

x = 8

Step-by-step explanation:

These angles are supplementary (they add up to 180):

4x + 148 = 180

4x = 180 - 148

4x = 32

x = 8

Answer:

B) A=135, B=77

Step-by-step explanation:

A + 45 = 180

135(A) + 45 = 180

103 + B = 180

104 + 77(B) = 180

Answer:

As the value of x increases, the value of y decreases

Answer: 4x10^2

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

the correct answer is B. ŷ = -157 + 40.2x; yes, because the r-value is high. The regression line would be a good predictor of other data points because of the strong linear relationship between x and y, as indicated by the high r-value.

To determine the line of regression, we can use linear regression analysis. The regression line is a straight line that best represents the relationship between the two variables. It is determined by minimizing the sum of squared deviations between the observed values and the predicted values of the response variable.

Using a calculator or statistical software, we can find that the regression line for this data set is:

ŷ = -22.2933 + 32.0472x

The r-value (correlation coefficient) for this data set is 0.969, which is relatively high. This indicates a strong positive linear relationship between x and y.

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Answer:

cos A = 12/13 = 0.9231

(angle A = 22.62°)

Step-by-step explanation:

cos A = 12/13 = 0.9231

ANSWER=

cos A = 12/13 = 0.9231

(angle A = 22.62°)

EXPLANTION=

cos A = 12/13 = 0.9231

Answer:

There are 0 solutions

Answer:

Zero

Step-by-step explanation:

Let's solve the equation first.

For now, I will focus on the LHS and simplify that:

3(x + 2) = 3x + 1

3x + 6 = 3x + 1

Rearrange

3x - 3x = 1 - 6

Simplify

0x = -5

0 = -5 which isn't true

So 3(x + 2) = 3x + 1 has 0 solutions.

a) we can be 95% confident that the true percentage of inaccurate orders falls within this range based on the data collected. b) The confidence interval for Restaurant A (14.4% to 22.4%) does not overlap with the reported percentage for Restaurant B (0.159).

In a study comparing the accuracy of fast food drive-through orders, Restaurant A had 305 accurate orders out of a total of 369 orders, with 64 orders that were not accurate. To estimate the percentage of orders that are not accurate, a 95% confidence interval can be calculated.

a. The 95% confidence interval estimate of the percentage of orders that are not accurate at Restaurant A is approximately 14.4% to 22.4%. This means that we can be 95% confident that the true percentage of inaccurate orders falls within this range based on the data collected.

b. Comparing the results from part (a) to the 95% confidence interval for the percentage of orders that are not accurate at Restaurant B, which is reported as 0.159, we can conclude that Restaurant A has a higher percentage of inaccurate orders. The confidence interval for Restaurant A (14.4% to 22.4%) does not overlap with the reported percentage for Restaurant B (0.159), indicating a statistically significant difference between the two restaurants in terms of order accuracy.

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Answer:

$5.25

Step-by-step explanation:

Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

Answer:

1) -2

2) 8/3

3) 1/2

4) -1/2

5) 5/9

6) -4

Step-by-step explanation:

The slope formula is:

rise/run

The difference in the Y  value is the rise and the difference in the x is the run.

for number 1, you would do

8-4/1-3

4/-2

slope = -2

and so on

The scale factor of 10cm to 5m is 50.

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;

scale factor = new dimension / old dimension

Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm

therefore 5m = 5× 100 = 500cm

therefore scale factor = 500/10 = 50

This means the scale factor of 10cm = 5m is 50

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Answer:

Step-by-step explanation:

Actually Welcome to the Concept of the linear equations..

Here given value of x= 5 and y =1 , so we get as,

5a + b = 38 and 5b - a = 8

so, now we multiply equation no. 2 by 5 all over.

==> 25b - 5a = 40....(1)

hence adding new equation and equation no. 1

26b = 78

b = 78/26

hence b = 3 , and a = 7

Answer:

Step-by-step explanation:

8 - 3x + 5 + 4x

-3x + 4x + 8 + 5

x + 13

Answer:

Coordinates of M and N are

(-3, -2.5) and (3, -1)

The order is not important since we are not told where M and N points actually are. The attached graph will make this clear

Step-by-step explanation:

The two equations are

\(4y=x-7 \textrm{\space ( Eq 1)}\)

and

\(x^2 + xy = 4 + 2y^2 \textrm{ (Eq 2)}\)

Adding 7 to both sides of Eq 1 gives us

\(x = 4y + 7\)

Eq2 can be re-written as

    \(x^2 + xy - 4 - 2y^2 = 0 \textrm{ (Eq 3)}\)

The above is done by subtracting \(4 + 2y^2\) on both sides of Eq 2

Substituting for \(x = 4y + 7\) in Eq 3 gives us  

\(\left(4y+7\right)^2+\left(4y+7\right)y-4-2y^2 = 0\)    

Let's examine the first two terms and simplify

\((4y+7)^2 = \left(4y\right)^2+2\cdot \:4y\cdot \:7+7^2\) = \(16y^2+56y+49\)   (A)

\(\left(4y+7\right)y = 4y^2 + 7y\)      (B)

So Eq 3 can be reduced to a quadratic equation with one variable, \(y\)

(A) + (B) - \(4 -2y^2\) = \(6y^2+56y+49+4y^2+7y-4-2y^2\)

Grouping like terms we get

\(16y^2+4y^2-2y^2+56y+7y+49-4\)

Adding similar terms we get

\(18y^2+63y+45 = 0\)

We can divide both sides of the equation by 9 to make it easier to solve using the equation for the solutions of a quadratic equation

Dividing both sides by 9 we get

\(2y^2+7y+5 = 0\)

Use the quadratic formula

\(y_1, y_2 = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

where a is the coefficient of \(y^2\), \(b\) the coefficient of \(y\) and \(c\) the constant

Here \(a = 2, b = 7\) and \(c = 5\)

So we get

\(y_1, y_2 = \frac{-7\pm \sqrt{7^2-4\cdot \:2\cdot \:5}}{2\cdot \:2}\) = \(\frac{-7\pm \:3}{2\cdot \:2}\)    

The above is obtained by noting that

\(\sqrt{7^2-4\cdot \:2\cdot \:5}} = \sqrt{49-40} =\sqrt{9} = 3\)

\(y_1=\frac{-7+3}{2\cdot \:2},\:y_2=\frac{-7-3}{2\cdot \:2}\)

\(y_1 = \frac{-7+3}{2\cdot \:2} = \frac{-4}{4} = -1\)   (using the + component)

\(y_2 = \frac{-7-3}{2\cdot \:2} = \frac{-10}{4} = -2.5\)

Find \(x_1\) and \(x_2\) by substituting each of these values in the equation for \(x\)

\(x_1 = 4(-1) + 7 = -4 + 7 = 3\)

Therefore the coordinates of M and N are

 \((-3, -2.5)\) and \((3, -1)\)

The order is not important since we are not told which are M and N points. See the attached graph for a visual depiction

Hope that helps :)

Answer:

\(\sf M =\left(-3, -\dfrac{5}{2}\right), \quad N= \left(3, -1 \right)\)

Step-by-step explanation:

Given:

\(\begin{cases}4y = x - 7\\x^2+xy=4+2y^2\end{cases}\)

To find the points at which the line and the curve intersect, rewrite the first equation to make y the subject by dividing both sides by 4:

\(\implies y=\dfrac{1}{4}x-\dfrac{7}{4}\)

Substitute the expression for y into the second equation and solve for x:

\(\implies x^2+x\left(\dfrac{1}{4}x-\dfrac{7}{4}\right)=4+2\left(\dfrac{1}{4}x-\dfrac{7}{4}\right)^2\)

\(\implies x^2+\dfrac{1}{4}x^2-\dfrac{7}{4}x=4+2\left(\dfrac{1}{16}x^2-\dfrac{7}{8}x+\dfrac{49}{16}\right)\)

\(\implies \dfrac{5}{4}x^2-\dfrac{7}{4}x=4+\dfrac{1}{8}x^2-\dfrac{7}{4}x+\dfrac{49}{8}\)

\(\implies \dfrac{5}{4}x^2-\dfrac{7}{4}x=\dfrac{1}{8}x^2-\dfrac{7}{4}x+\dfrac{81}{8}\)

\(\implies \dfrac{5}{4}x^2=\dfrac{1}{8}x^2+\dfrac{81}{8}\)

Multiply both sides by 8:

\(\implies 10x^2=x^2+81\)

\(\implies 9x^2=81\)

\(\implies x^2=9\)

\(\implies x=\sqrt{9}\)

\(\implies x=\pm3\)

To find the y-values of the coordinates of the points of intersection (M and N), substitute the found values of x into the expression for y:

\(x=3 \implies y=\dfrac{1}{4}(3)-\dfrac{7}{4}=-1\)

\(x=-3 \implies y=\dfrac{1}{4}(-3)-\dfrac{7}{4}=-\dfrac{5}{2}\)

Therefore:

\(\sf M =\left(-3, -\dfrac{5}{2}\right), \quad N= \left(3, -1 \right)\)

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

The pattern of error seems to be adding 4 and subtracting 10 in each calculation.

In the first example, the student adds 4 to the correct sum of 10 and 6, resulting in 14 instead of the correct answer of 16. In the second example, the student subtracts 10 from the correct difference of 11 - 5, resulting in 1 instead of the correct answer of 6.

From these examples, we can observe a consistent pattern in the errors made by the student. Specifically, the student is adding 4 to the correct sum and subtracting 10 from the correct difference. This suggests that the student may have misunderstood or misapplied the rules of addition and subtraction.

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Answer:

They all have equal bases.

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

x=5

hope this helps !!:)

Step-by-step explanation: