Find the value of 11 1/4 . Write fractions in the form a/b.

Answer:

The answer is below

Step-by-step explanation:

The box contains 5 red and 4 white balls.

A) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was (Upper A )Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81

P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81

The probability that at least 1 ball was​ red = 25/81 + 20/81 + 20/81 = 65/81

B) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was not Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)

P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72

The probability that at least 1 ball was​ red = 20/72 + 20/72 + 20/72 = 60/72

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

Answer:

  c

Step-by-step explanation:

A piecewise-defined function is properly graphed when the pieces of the definition match the pieces of the graph. To identify the function, match the pieces of the function with the pieces of the graph.

__

The domain is the horizontal extent of the graph. The discontinuity in the graph at x=2 tells you the domain of the function will be divided into 2 parts.

The solid dot on the part of the graph that extends to the left tells you that x=2 and points to its left are one part of the domain: x ≤ 2.

The open dot on the part of the graph that extends to the right tells you that x=2 is not part of the domain for that section. It will be x > 2.

Recognizing that these are the domain definitions already eliminates choices B and D.

The answer choices (or your examination of the graph) tell you that the two lines are described by ...

The y-intercept for the line to the left of x=2 is clearly at y=2, so we now know the match-up between domains and function definitions is ...

  \(y=\begin{cases}x+2&x\le2\\x+1&x > 2\end{cases}\)

This eliminates choice A.

The correct answer choice is C:

  \(\boxed{\textsf{c.}\quad y=\begin{cases}x+1&x > 2\\x+2&x\le2\end{cases}}\)

This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:

5x + y = 10

x + y = 6

x + 4y = 12

The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.

To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.

For example, using the first and second equations, you can solve for x in terms of y as follows:

x = 6 - y (from the second equation)

y = 10 - 5x (from the first equation)

Substituting y = 10 - 5x into the third equation, you get:

x + 4(10 - 5x) = 12

Simplifying this equation, you get:

-19x + 40 = 0

Solving for x, you get:

x = 40/19

Using x = 40/19 and the equation x + y = 6, you can solve for y as:

y = 6 - x = 6 - 40/19 = 94/19

Therefore, the minimum value of 3x + 2y subject to the given constraints is:

3(40/19) + 2(94/19) = 222/19

And the values of x and y that minimize this expression are:

x = 40/19 and y = 94/19.

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This is a linear programming problem with three constraints and two variables, where the objective is to minimize the expression 3x + 2y subject to the following constraints:

5x + y = 10

x + y = 6

x + 4y = 12

The first constraint represents a straight line in the x-y plane, the second constraint represents another straight line, and the third constraint represents yet another straight line. The feasible region is the region where all three constraints are satisfied simultaneously, which is the intersection of the three lines.

To solve this problem, you can use the method of substitution or elimination to solve for one variable in terms of the other in two of the equations, and then substitute this expression into the third equation to obtain a single equation in one variable. You can then solve for that variable, and use back-substitution to find the values of the other variable.

For example, using the first and second equations, you can solve for x in terms of y as follows:

x = 6 - y (from the second equation)

y = 10 - 5x (from the first equation)

Substituting y = 10 - 5x into the third equation, you get:

x + 4(10 - 5x) = 12

Simplifying this equation, you get:

-19x + 40 = 0

Solving for x, you get:

x = 40/19

Using x = 40/19 and the equation x + y = 6, you can solve for y as:

y = 6 - x = 6 - 40/19 = 94/19

Therefore, the minimum value of 3x + 2y subject to the given constraints is:

3(40/19) + 2(94/19) = 222/19

And the values of x and y that minimize this expression are:

x = 40/19 and y = 94/19.

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The calculated scale factor from ABC to A'B'C is 1/3

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

The triangles

From the triangles, we have the following parameters

A = (0, 3)

A' = (0, 1)

Using the above as a guide, we have the following:

Scale factor of the dilation = A'/A

So, we have

Scale factor of the dilation = (0, 1)/(0, 3)

Evaluate

Scale factor of the dilation = 1/3

Hence, the scale factor of the dilation is 1/3

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The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Step-by-step explanation:

trapezium means especially

AD || BC

AC = BC tells us that ABC is an isoceles triangle (both legs are identically long, which makes also their angles with their baseline AB equal).

therefore, A1 = B = 80°.

and because the sum of all angles in a triangle is always 180°, we get

180 = 80 + 80 + C1

C1 = 20°

(e)(1)

because of the law of a line intersecting parallel lines with the same angles, and AC is intersecting the parallel lines AD and BC, we know that

C1 = A2 = 20°

(e)(2)

because also the sum of all angles around a single point on one side of a line is 180°, we know D1 + D2 = 180°.

we also know that D2 is an angle in an equilateral triangle (that means all 3 sides are equally long, and therefore all 3 angles are equal too = 180/3 = 60°) and therefore

D2 = 60°.

therefore, D1 = 180 - 60 = 120°.

so, for the triangle ACD we have

180 = A2 + D1 + C2 = 20 + 120 + C2

C2 = 40° = 2×20 = 2×C1

(f)(1)

a kite is a quadrilateral, and as such the sum of all angles is 360°.

again remember the symmetry of a kite, so the angles at H and at F must be equal.

H = F = x

so, we have

360 = 110 + 50 + H + F = 110 + 50 + 2x

200 = 2x

x = 100°

(f)(2)

after drawing EG we see that this line splits the kite into 2 equal (ahem, congruent) triangles due to the symmetry of a kite exactly along that line.

and that splits both angles E and G in half for each of the triangles.

again, the sum of all angles in a triangle is 180°, so

180 = 110/2 + 50/2 + x = 55 + 25 + x = 80 + x

x = 100°

Answer: 21

Step-by-step explanation:  im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah

Answer:

21

Step-by-step explanation:

I did the test

Hope this helps :)

a. Greg can eat 8 breakfasts from 1 box.

b. The cost of 1 breakfast from a regular-sized box is $34.32.

c. Greg will enjoy 4 breakfast more.

a. A regular-sized box contains 12 servings. If Greg eats 1 1/2 servings for breakfast every day, the number of breakfasts that Greg can eat from 1 box will be:

= 12 ÷ 1 1/2

= 12 ÷ 1.5

= 8

b. Since the regular-sized box of cereal costs $4.29. The cost of 1 breakfast from a regular-sized box of cereal cost Greg will be:

= 8 × $4.29

= $34.32

c. If Greg purchased the family-sized box of cereal that contains 18 servings, the number of breakfasts will be:

= 18 ÷ 1.5

= 12 breakfast

The difference will be:

= 12 - 8

= 4 breakfast more.

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\(\textit{surface area of a sphere}\\\\ SA = 4\pi r^2~~ \begin{cases} r= radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies SA=4\pi (9)^2\implies SA=324\pi\)

Answer:

Total = 42+58 = 100

Now,

percentage of mint gum = 42/100 × 100%

= 42%

42% of packs contained mint gum.

Answer:

MacKenzie earns 155.20 more than Anielle

Step-by-step explanation:

The expansion will be 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

We can expand (2d+3)^6 using the binomial theorem, which states that:

(a + b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn-1 * a^1 * b^(n-1) + nCn * a^0 * b^n

where nCk is the binomial coefficient, given by:

nCk = n! / (k! * (n-k)!)

Expanding (2d+3)^6 using this formula, we get:

(2d+3)^6 = 6C0 * (2d)^6 * 3^0 + 6C1 * (2d)^5 * 3^1 + 6C2 * (2d)^4 * 3^2 + 6C3 * (2d)^3 * 3^3 + 6C4 * (2d)^2 * 3^4 + 6C5 * (2d)^1 * 3^5 + 6C6 * (2d)^0 * 3^6

Simplifying each term using the binomial coefficient formula, we get:

(2d+3)^6 = 1 * 64d^6 * 1 + 6 * 32d^5 * 3 + 15 * 16d^4 * 9 + 20 * 8d^3 * 27 + 15 * 4d^2 * 81 + 6 * 2d * 243 + 1 * 1 * 729

Simplifying each term further, we get:

(2d+3)^6 = 64d^6 + 1152d^5 + 9720d^4 + 43740d^3 + 98415d^2 + 145458d + 729

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Answer:

3x2^y

Step-by-step explanation:

brainleist plss

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

Answer:

\(m=- \frac{7}{2}\)

Step-by-step explanation:

The slope of a line passing through the two points \(\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}\) and\(\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}\) is given by \(\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}\).

We have that \(x_1=3\), \(y_1=10\), \(x_2=1\), \(y_2=17\).

Plug the given values into the formula for slope: \(m=\frac{\left(17\right)-\left(10\right)}{\left(1\right)-\left(3\right)}=\frac{7}{-2}=- \frac{7}{2}\)

Answer: the slope of the line is \(m=- \frac{7}{2}\).

Answer:

slope = - \(\frac{7}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{x_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )

m = \(\frac{17-10}{1-3}\) = \(\frac{7}{-2}\) = - \(\frac{7}{2}\)

Answer:

1. a. A

2. c. C

3. a. A > C

Step-by-step explanation:

Absolute value is the translation of the number inside | ? | into a positive number.

Examples:

| -245 | = 245

| -47 | = 47

| 69 | = 69

| 21 | = 21

| -4 | = 4

The number of trials and the probability of obtaining success will be given as P(X ≤ 2) = 0.9728.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X \sim B(n,p)

The probability that out of n trials, there'd be x successes is given by

\(\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

Assume the random variable X has a binomial distribution with the given probability of obtaining success.

Then the number of trials and the probability of obtaining success will be

P(X ≤ 2), n = 4, p = 0.2

Then we get

\(\rm P(X =2) = \: ^4C_2(0.2)^2(1-0.2)^{4-2}\\\\P (X=2) = 6 \times 0.0256 \\\\P (X=2) = 0.1536\)

Then the cumulative probability will be

\(\rm P(X\leq 2) = 0.9728\)

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1) A(1,2),A'(-1,2) : a reflection across the y-axis

2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin

3) A(1,2),  A'(-1,4):  a translation of 2 units left and 2 unit up

4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin

5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The given point is A(1,2).

The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).

Therefore, A(1,2)→A'(-1,-2).

A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)

Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).

The rule of a reflection across the y-axis is (x,y)→(−x,y).

Therefore, A(1,2)→A'(-1,2)

A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)

Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).

The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)

Therefore, A(1,2)→A'(-2,1)

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Answer:

Step-by-step explanation:

Answer:1.5

Step-by-step explanation:

Y=1/2 of x

The given statement that if the null hypothesis is actually true, then there is a 5% chance that the researcher will end up rejecting the null hypothesis in error is; TRUE

Null hypothesis is defined as a type of statistical hypothesis that proposes that no statistical significance exists in a given set of observations.

Alternative hypothesis is defined as a statement used in statistical inference experiment that is contradictory to the null hypothesis .

Now, when the p-value is less than or equal to the significance level, we reject the null hypothesis and accept the alternative hypothesis but if  the p-value is greater than the significance level, we fail to reject the null hypothesis.

In conclusion, if the null hypothesis is true, then it means that the p-value is greater than the significance level and as such there is only a 5% chance that the researcher will end up rejecting the null hypothesis in error.

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Answer:

150 people

Step-by-step explanation:

Lets call the total amount of people at the talent show x. Since 3/6=1/2, we know that half the people are girls, 1/3 are boys. If we added 1/2 and 1/3 we get 5/6, 1-5/6=1/6, so now we know that 1/6 of the people are adults. Because it says "If there were 50 more girls than adults" so from that we can see that 1/2x =1/6x+50. If we were to simplify the equation, we 1/3x=50, so x=150

Answer:

about 71.62 square inches

Step-by-step explanation:

The circumference of the circle is 30 inches.

\(2\pi \times r = 30\)

\(r = \frac{15}{\pi} \)

\( a = \pi { (\frac{15}{\pi} )}^{2} = 71.62\)

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

Step-by-step explanation:

if L = 6W, then

P = 2L+2W = 12W+2W = 14W

a) 6W/14W = 3/7

b) L:W = 6W:W = 6:1

see a) for L:P

c) 14W = 342.44

W = 24.46

L = 146.76

The number of solutions in the equation is (b) two real solutions

The quadratic equation is given as

-5x2 + 4x + 1 = 0.

Rewrite properly as

−5x² + 4x + 1 = 0

The discriminant of a quadratic equation is calculated using

d = b² - 4ac

In the equation −5x² + 4x + 1 = 0, we have

a = -5, b = 4 and c = 1

Substitute a = -5, b = 4 and c = 1 in d = b² - 4ac

So, we have

d = (4)² - 4 * (-5) * (1)

Evaluate

d = 36

Because the discriminant is greater than 0, the equation has two solutions and the type of solution is real solution

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Rays: BD, AC, CA, AB. Lines:  AC

A line is a straight path of points that has no beginning or end

A ray is a portion of a line which has one endpoint and extends forever in one direction

Let's put the definitions:

Note: the arrow is an indication no endpoint

So we have ray BD (it starts from the dot at B and the arrow shows it extends forever  in the direction of D)

We have ray AC (it starts from the dot at A and the arrow shows it extends forever  in the direction of C)

We also have ray CA (it starts from the dot at C and the arrow shows it extends forever  in the direction of A)

Then ray AB (it starts from the dot at A and the arrow shows it extends forever  in the direction of B)

Then  line AC (it's bounded by 2 arrows, so it has no endpoint)

Therefore, the rays are BD, AC, CA and AB, and the line is AC. So the 1st option is the answer

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'x^2+bx-ax-ab' is the area of a rectangle with a length of x-a and a width of x + b.

What is area of rectangle?

A rectangle basically is a four-sided shape with four right angles. It is one of the most basic shapes in geometry and can be defined by its length and width. The area of a rectangle is the product of its length and width. This measure is typically expressed in square units, such as square feet or square meters. The area of a rectangle can also be found by multiplying the length and width of a given rectangle.

L=x-a

B=x+b

Area of rectangle=?

Area of rectangle=l*b

                           =(x-a)(x+b)

                            =x² + bx - ax - ab​

Hence, the correct option is Option (E) x² + bx - ax - ab​.

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Answer: = 240 mph.

Step-by-step explanation:

Let x = speed of the plane.

t= time taken

As per given, we have

\(t=\dfrac{450}{x+30}\ \ \ ...(i)\\\\ t=\dfrac{350}{x-30}\ \ \ ...(ii)\)    [Time = distance / speed]

From (i) and (ii), we get

\(\dfrac{450}{x+30}=\dfrac{350}{x-30}\\\\\Rightarrow\ 450(x-30)=350(x+30)\\\\\Rightarrow\ 450x-13500=350x+10500\\\\\Rightarrow\ 450x-350x=10500+13500\\\\\Rightarrow\ 100x=24000\\\\\Rightarrow\ x=240\)

Hence, the speed of the plane = 240 mph.