If a coin is tossed three times, find probability of getting
1) Exactly 3 tails
2) Atmost 2 heads
3) Atleast 2 tails
4) Exactly 2 heads
5) Exactly 3 heads​

Answer:

∠3 and ∠10 are;

B. Alternate exterior angles

Step-by-step explanation:

From the given diagram, we have;

∠3 and ∠10 are angles on the same transversal

The location of ∠3 and ∠10 are on the outer (exterior) part of the two lines crossed by the transversal that forms ∠3 and ∠10 such that the two lines comes between the angles

∠3 and ∠10 are on the alternate sides of the transversal such that ∠3 is below the transversal and ∠10 is above the transversal

Therefore, ∠3 and ∠10 are alternate exterior angles.

Answer:

36

Step-by-step explanation:

Find the rule for the sequence.

The change from 1 to 3 is +2.

The change from 3 to 6 is +3.

The change from 6 to 10 is + 4.

The change from 10 to 15 is + 5

Essentially, you are adding 1 and then adding it to the current number. The next 3 numbers are:

Change of +6: 15 + 6 = 21

Change of +7: 21 + 7 = 28

Change of +8: 28 + 8 = 36

36 is your 8th term.

~

Answer:

c

Step-by-step explanation:

Whats the question

Answer:

i cant see the question could u repost it plz thx :)

Step-by-step explanation:

Answer:

\(a^{4}-2a^{2} -24\)

Step-by-step explanation:

We do FOIL to solve this

Answer:

The solution of this system of linear equations is \((x,y) = (-3,-2)\).

Step-by-step explanation:

Let be the following system of linear equations:

\(2\cdot x - 7\cdot y = 8\) (1)

\(-3\cdot x + 2\cdot y = 5\) (2)

From (1) we clear \(y\):

\(2\cdot x -8 = 7\cdot y\)

\(y = \frac{2\cdot x - 8}{7}\)

And we apply this variable in (2):

\(-3\cdot x+2\cdot \left(\frac{2\cdot x -8}{7} \right)= 5\)

\(-3\cdot x +\frac{4}{7} \cdot x -\frac{16}{7} = 5\)

\(-\frac{17}{7}\cdot x = \frac{51}{7}\)

\(x = -\frac{51}{17}\)

\(x = -3\)

And the value of \(y\) is:

\(y = \frac{2\cdot (-3)-8}{7}\)

\(y = -\frac{14}{7}\)

\(y = -2\)

The solution of this system of linear equations is \((x,y) = (-3,-2)\).

Answer: It is a function

Step-by-step explanation: Every input has one output, so it’s a function. If this was asking whether the tables shows a linear relationship, the answer will be no, but this is asking whether it is a function.

The polar curve r = -2 sin θ can be graphed by first plotting the graph of r as a function of θ in Cartesian coordinates. To do this, we can set r = y and θ = x, and then plot the resulting equation y = -2 sin x.

This graph will have the shape of a sinusoidal wave with peaks at y = 2 and troughs at y = -2.
To sketch the same polar curve in Cartesian form, we can use the conversion equations x = r cos θ and y = r sin θ. Substituting in the given polar equation, we get x = -2 sin θ cos θ and y = -2 sin² θ. Simplifying these equations, we get x = -sin 2θ and y = -2/3 (1-cos² θ). This graph will have the shape of a four-petal rose.
The graphs from Part (a) and Part (b) are different because they represent different equations. Part (a) is the graph of y = -2 sin x, which is a sinusoidal wave. Part (b) is the graph of a four-petal rose. However, both graphs share some similarities in terms of their shape and symmetry. They are both symmetrical about the origin and have a repeating pattern.
In conclusion, we can sketch a polar curve by first graphing r as a function of θ in Cartesian coordinates and then converting it to Cartesian form. The resulting graphs may look different, but they often share similar patterns and symmetries.

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Answer:

15

Step-by-step explanation:

16 - 2x3 +5

16 - 6 +5

16 - 1

15

The production level for maximum profit is 37 units. We have to find the production level for maximum profit and the profit. The profit equation is: P(x) = -0.05x^2 + 3.7x - 4 .

Substituting x = 37 in the total profit function,

P(37) = -0.05(37)^2 + 3.7(37) - 4P(37)

= $68.05

The profit at 37 units is $68.05.

Therefore, the profit at maximum profit is $68.05.

R(x) = 4x and C(x) = 0.05x^2 + 0.3x + 4 The total profit equation is given by: P(x) = R(x) - C(x) .

We have to find the production level for maximum profit and the profit. Find the derivative of the total profit function. P(x) = R(x) - C(x)P(x)

= 4x - (0.05x^2 + 0.3x + 4)P(x)

= -0.05x^2 + 3.7x - 4P'(x)

= -0.1x + 3.7

The above expression is the derivative of the total profit function. P'(x) = 0, for the maximum profit .At maximum profit, the first derivative of the profit function is equal to zero.-0.1x + 3.7 = 0-0.1x

= -3.7x

= 37 units

The production level for maximum profit is 37 units. The profit equation is: P(x) = -0.05x^2 + 3.7x - 4

Substituting x = 37 in the total profit function,

P(37) = -0.05(37)^2 + 3.7(37) - 4P(37)  

= $68.05

The above expression is the derivative of the total profit function. P'(x) = 0, for the maximum profit .The profit at 37 units is $68.05. Therefore, the profit at maximum profit is $68.05.

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Answer:

For you it might just be a jacket, but for Andy it was originally a symbol of strength. In the story Andy talked about how proud he was to have been accepted into the gang called, “The Royals”. When he was accepted into the gang, he was given a purple silk jacket, that said “Royals” on it.

Answer:

TQM ARI :3

Step-by-step explanation:

The number of bottles collected by the high school is 1922 bottles since the total collected bottles is 3627.

The total number of bottles collected by both elementary and high schools is 3627 bottles, which means that the number of bottles collected by the high school can be determined as the total bottles minus the ones collected by the elementary school:

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All 3 angles of a triangle always add up to 180 degrees.

This is because a triangle is a three-sided polygon and the sum of the angles in any polygon is always 180 degrees multiplied by the number of sides minus 2. Therefore, in a triangle, which has three sides, the sum of the angles is 180 x (3-2) = 180 degrees. This rule is known as the "triangle angle sum theorem" and is a fundamental property of triangles. It is important to note that this rule applies to all types of triangles, whether they are right triangles, acute triangles, or obtuse triangles. Understanding this theorem is crucial in solving geometric problems related to triangles.

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To reverse the order of integration, we need to rewrite the limits of integration in terms of the other variable.
The value of the given integral by reversing the order of integration is (5/12)(\(e^{24}\) - 1).

The given integral is ∫∫ \(5e^{(2x)}\) dx dy, where the limits of x are from 0 to 4 and the limits of y are from 0 to 3y.
To integrate with respect to y first, we need to express the limits of y in terms of x.
From the limits of y given, we have 0 ≤ y ≤ 3y, which simplifies to 0 ≤ y.
Now we need to find the upper limit of y. To do this, we set the expression for the upper limit equal to the constant 12, which is the upper limit of x.
So we have 3y = 12, which gives y = 4.
Thus, the limits of integration become ∫∫ \(5e^{(2x)}\) dy dx, where the limits of y are from 0 to 4 and the limits of x are from 0 to 3y.
Now we can integrate with respect to y:

∫∫ \(5e^{(2x)}\) dy dx = ∫ 0^4 ∫ 0^(3y) \(\int\limits^4_0 \int\limits^{(3y)}_0 5e^{(2x)} dx dy\)
= \(\int\limits^4_0  [5/2 e^{(2x)}]_0^{(3y)} dy\)
= \(\int\limits^4_0  [5/2 (e^{(6y)} - 1)] dy\)
= \([5/12 (e^{(6y)} - 1)]_0^4\)
= \((5/12)(e^{24} - 1)\)
Note that the order of integration can be reversed if the integrand is continuous on a rectangular region that contains the original region of integration.

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The expression 4 10/5 is the same as 4 + 10/5. It has a whole part (4) and a fraction part (10/5).

To find out if this expression is equivalent to 6, we need to simplify the fraction part:

We can simplify the fraction part in a whole number (2), so we have that:

So the answer is Yes, 4 10/5 is equivalent to 6.

Answer: 15) 97

16) 16

17) 24

Step-by-step explanation:

15) (x-75) + (x-52)+ 293=360

x - 75 + x - 52 + 293 = 360

2x - 127 + 293 = 360

2x + 166 = 360

        2x  = 194           [Subtract 166 from both side]

          x  = 97             [Divide by 2 from both side]

16) (4x+15)+(5+6x)=180         The angle of a straight line is 180.

4x + 15 + 5 + 6x = 180

10x + 20 = 180

        10x = 160            [Subtract 20 from both side]

            x = 16               [Divide by 10 from both side]

17) (x+17)+(2x+1)= 90               These two angle combined equal to 90.

x + 17 + 2x + 1 = 90

3x + 18 = 90          

3x = 72                         [Subtract 18 from both side]

x = 24                           [Divide by 3 from both side]

Answer:

1/2

Step-by-step explanation:

If Best Shirts Design Company can make of order in of an hour. The order can the company complete in an hour will be 1/2.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that Best Shirts Design Company can make of order in of an hour.

We have to find the order can the company complete in an hour

We'll apply division by Splitting into equal halves or groups, the division may be used for the given case.

The order can the company complete in an hour is obtained by taking the ratio of orders completed to the time.

=1/2

Thus, if Best Shirts Design Company can make of order in an hour. The order can the company complete in an hour will be 1/2.

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Answer:

x=−1 or x=1 or x=−7

Step-by-step explanation:

x3+7x2−x−7=0

Step 1: Factor left side of equation.

(x+1)(x−1)(x+7)=0

Step 2: Set factors equal to 0.

x+1=0 or x−1=0 or x+7=0

x=−1 or x=1 or x=−7

Answer:

x=-7,-1,1

Step-by-step explanation:

The correct simplification of the expression is  4x¹⁴y¹⁷

Given,

The expression is (2x⁷ y)² (y⁵)³

To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ

Implement the product rule to (2x⁷y)².

Here, we have a = 2x⁷ , b = y and n = 2

=(2x⁷)² y²(y⁵)³

= 2²(x⁷)² y²(y⁵)³

= 4(x⁷)² y²(y⁵)³

Now exponents should be multiplied while using the product rule.

The product rule is (aˣ)ⁿ = aˣⁿ

We apply this to (x⁷)² and (y⁵)³

So the expression becomes,

=4x⁷·² y² (y⁵·³)

= 4x¹⁴ y² y¹⁵

∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ

∴ 4x¹⁴ y¹⁵ ⁺ ²

= 4x¹⁴ y¹⁷

Hence we get the answer as 4x¹⁴ y¹⁷

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Answer:

33 seconds i believe, im pretty sure its all about multiplication

Answer: The value of x is 38.4

Answer:D

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

You can basically just drop the plus sign and remove the parenthesis because the plus sign doesn't alter negatives.

-6+(-12)

-6-12= -18

Answer:-18

Step-by-step explanation:

Answer: 45%

From my common sense

If the graph line goes up, she wins.

If the graph line goes down, she loses.

1. Count the amounts of times which the graph line goes up.

(btw the first game she won because the graph line started at 1)

= 9

2. Calculate the winrate of her 20 games

= 9/20 * 100

= 45%

The function f : Z x Z → Z x Z defined by \(f(m,n) = (5m+4n, 4m+3n)\) is bijective, with its inverse given by \(f^{-1}(m,n) = (-3m + 4n, 4m - 5n)\). This means that for every pair of integers (m,n), the function f maps them uniquely to another pair of integers, and the inverse function \(f^{-1}\) maps the resulting pair back to the original pair.

The inverse of the function f(m,n) = (5m+4n, 4m+3n) is \(f^{-1}(m,n) = (-3m + 4n, 4m - 5n)\).

To show that the function f is bijective, we need to prove both injectivity (one-to-one) and surjectivity (onto).

Injectivity:

Assume f(m1, n1) = f(m2, n2), where (m1, n1) and (m2, n2) are distinct elements of Z x Z.

Then, (5m1 + 4n1, 4m1 + 3n1) = (5m2 + 4n2, 4m2 + 3n2).

This implies 5m1 + 4n1 = 5m2 + 4n2 and 4m1 + 3n1 = 4m2 + 3n2.

By solving these equations, we find m1 = m2 and n1 = n2, proving injectivity.

Surjectivity:

Let (a, b) be any element of Z x Z. We need to find (m, n) such that f(m, n) = (a, b).

By solving the equations 5m + 4n = a and 4m + 3n = b, we find m = -3a + 4b and n = 4a - 5b.

Thus, f(-3a + 4b, 4a - 5b) = (5(-3a + 4b) + 4(4a - 5b), 4(-3a + 4b) + 3(4a - 5b)) = (a, b), proving surjectivity.

Since the function f is both injective and surjective, it is bijective. The inverse function \(f^{-1}(m, n) = (-3m + 4n, 4m - 5n)\) is obtained by interchanging the roles of m and n in the original function f.

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The middle 99.7% of Aaron's finishing times in the 400 meter race would fall within the interval of 72.5 to 87.5 seconds.

According to the empirical rule, for a normal distribution, approximately 99.7% of the data falls within three standard deviations of the mean. In this case, the mean finishing time for Aaron is 80 seconds, with a standard deviation of 2.5 seconds.

To determine the interval of times that represents the middle 99.7% of his finishing times, we multiply the standard deviation by three and add/subtract the result from the mean. Therefore, the interval would be:

Mean ± (3 * Standard Deviation)

80 ± (3 * 2.5) seconds

80 ± 7.5 seconds

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The median number of hurricanes per year reaching the East Coast from 1944 through 2000 is two.

Median number is the middle value of a set of numbers. It is the number found at the midpoint of a sorted data set, when all the numbers are arranged in numerical order from lowest to highest. The median number is used to determine the average of a set of numbers, and is often used to represent the central tendency of the data. To calculate the median, first arrange the numbers from lowest to highest, then locate the middle value. If there is an even number of values, the median is the average of the two middle numbers.

This is calculated by taking the middle value of the data set. In this case, there were 18 years with one hurricane, 16 years with two hurricanes, 13 years with three hurricanes, and six years with four hurricanes. Thus, the median number of hurricanes in this data set is two.

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Alexandria can expect to spend about $128.25 on school lunches for the year if she forgets to bring her lunch about once a week.

If Alexandria forgets to bring her lunch 15% of the time, then she will need to buy a school lunch on 15% of the 180 school days:

15% of 180 = 0.15 × 180 = 27 school days

So, Alexandria will buy a school lunch 27 times during the school year.

The average cost of a school lunch is $4.75.

So the total cost of buying school lunches for the year will be:

27 × $4.75 = $128.25

Therefore, Alexandria can expect to spend about $128.25

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