assume a player has come up to bat and gotten two hits in a game. what is the probability that both of those hits will be homers (home runs)?

Answer:

$7 Child Tickets $11 Adult Tickets

Step-by-step explanation:

x=adult tickets

y=child tickets

4x+3y=65

9x+6y=141

multiply the entire top equation by 2 making it

8x+6y=130 and the bottom stays the same so it would be

9x+6y=141 then you multiply one of the equations (mine will be the top one) by -1

so itll turn out to be

-8x-6y=-130

9x+6y=141

y cancels out and 9-8 is 1 so you are left with x

x=11 (adult tickets)

you plug the 11 into any x (mine will be in the top equation) and you substitute

4(11)+3y=65

44+3y=65

65-44=21

3y=21

3y/3=21/3

y=7(child tickets)

Answer:

price of adult ticket = $11

price of child ticket = $7

Step-by-step explanation:

Let x = price of adult ticket

y = price of child ticket

4x+3y=65. eq. 1

9x+6y=141. eq.2

solving for eqs. 1&2

x=11

y=7

Answer:

neither one of those are a dot plot

Step-by-step explanation:

Answer:

height of kids in class is the dot plot

Step-by-step explanation:

The perimeter of television is = 100 inches

The study of measuring geometric shapes and their qualities such as length, volume, shape, surface area, lateral surface area, and so on is known as mensuration. Mensuration will be covered in fundamental mathematics.

let the length be 16x and width be 9x

area given = 576 sq. inches

16x * 9 x = 576

144 \(x^{2}\) = 576

x = 24/12

x = 2

length = 32

width = 18

perimeter = (32 + 18)*2  =100 inches

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Lynne can buy 5 apples and 6 oranges with her $8.00.

The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,

we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25

Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.

Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.

Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.

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The average mean of all 40% of all adults in increase p-hats will be approximately 0.4.

If 40% of all adults in Ohio support the increase, this means that the population proportion is p = 0.4. We can use this value to calculate the mean of the sampling distribution of p-hat, which is given by the formula:

mean of p-hat = p

That is, the mean of the sampling distribution of p-hat is equal to the population proportion. In this case, the mean of the sampling distribution of p-hat is:

mean of p-hat = p = 0.4

So, if we take all possible samples of the same size from the population and calculate the proportion of adults who support the increase in each sample, the average mean of all those proportions (p-hats) will be approximately 0.4.

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Answer: x^2-22x+121

I believe this is correct.

The equation that represents the situation, in point-slope form, is:  \(\mathbf{y - 65 = 8(x - 5)}\)

Recall:

Thus, we are given the table as shown below (see attachment).

The slope, using (3, 49) and (5, 65) is calculated below:

\(slope = \frac{65 - 49}{5 - 3} = \frac{16}{2} \\\\\mathbf{slope (m) = 8}\)

To write the equation in point-slope form, substitute \((x_1, y_1)\) = (5, 65) and m = 8 into \(y - y_1 = m(x - x_1)\).

\(\mathbf{y - 65 = 8(x - 5)}\)

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Answer:

$50 each day

Step-by-step explanation:

240 - 90 = 150

150 / 3 = 50

The set builder form of the sets are

1) { | = ², where is a positive integer between 1 and 9}

2) { | = 5ⁿ, where n is a non-negative integer less than or equal to 5}

3) { | = 3, where is a positive integer between 1 and 6}

In set-builder notation, we use the curly brackets {} to enclose the elements of a set, and a rule or condition to define the elements that belong to the set.

Let's look at each of the sets given and express them in set-builder form:

{1, 4, 9,……..81}

This set contains the perfect squares of the numbers 1 to 9. To express it in set-builder notation, we can use the following rule:

{ | = ², where is a positive integer between 1 and 9}

{1, 5, 25, 125, 625, 3125}

This set contains the powers of 5, starting from 5⁰=1 up to 5⁵=3125. To express it in set-builder notation, we can use the following rule:

{ | = 5ⁿ, where n is a non-negative integer less than or equal to 5}

{3, 6, 9, 12, 15, 18}

This set contains the multiples of 3, from 3 to 18. To express it in set-builder notation, we can use the following rule:

{ | = 3, where is a positive integer between 1 and 6}

In this rule, we multiply 3 by the positive integers 1 to 6 to obtain the elements of the set.

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Complete Question:

Express the following sets in set-builder form.

1. {1, 4, 9,……..81}

2. {1, 5, 25, 125, 625, 3125}

3. {3, 6, 9, 12, 15, 18}

Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]

We're asked to use the definition of the derivative, which includes the terms:

limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.

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For any polygon with n sides, we can use the formula to calculate the sum of its interior angles. The formula is (n-2) x 180 degrees or (n - 2) x 180° / n.

There is a formula for the sum of the measurements of the interior angles of a polygon with n sides. The triangle, which has three sides, will be our first example. Its internal angles add up to 180 degrees. We can partition a polygon with n sides into triangles.

Let's take a polygon with n sides into consideration and draw all of its diagonals from one vertex. It is clear that n-2 triangles were produced. The total of the inner angles in each triangle is 180 degrees. The polygon's internal angles' total as a result is:

sum of the interior angles = (n-2) * 180 degrees

Alternatively, we can also use the formula:

sum of the interior angles are = (n - 2) x 180° / n

This formula is obtained by dividing the polygon into n-2 triangles, and the total sum of the interior angles will be (n-2) times the sum of the interior angles of a triangle, which is 180 degrees.

Therefore, for any polygon with n sides, we can use the formula to calculate the sum of its interior angles. The formula is (n-2) x 180 degrees or (n - 2) x 180° / n.

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Answer:Step-by-step explanation:

A,b,c

Therefore, there are 2,365,917,537,910 ways to select 10 pieces of gum from a bag of 250 pieces.

There are different ways to solve a combination problem like this one, but one common method is to use the formula for combinations. This formula is given by:

C(n,r)=\frac{n!}{r!(n-r)!}$$

Where n is the total number of objects in the set, r is the number of objects selected, and ! means factorial, which is the product of all positive integers up to a given number.

For example, 4!=4×3×2×1=24.

Using this formula, we can find the number of ways to select 10 pieces of gum from a bag of 250 pieces. We just need to plug in n=250 and

r=10 into the formula and simplify. The calculation is shown below:

C(250,10)=\frac{250!}{10!(250-10)!}$$

=\frac{250×249×248×...×242×241}{10×9×8×...×2×1}$$

=\frac{250×249×248×...×242×241}{10!}$$

=\frac{250}{10}×\frac{249}{9}×\frac{248}{8}×...\times\frac{242}{2}×\frac{241}{1}$$

=2,365,917,537,910

Therefore, there are 2,365,917,537,910 ways to select 10 pieces of gum from a bag of 250 pieces.

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The number of ways to select 10 pieces of gum from a bag of 250 pieces can be determined using the combination formula.

The combination formula is given by nCk,

where n is the total number of objects and k is the number of objects being selected.

In this case, n = 250 and k = 10.

Therefore, the number of ways to select 10 pieces of gum from a bag of 250 pieces is:

250C10 = 52,698,440,874 ways

So, the answer is 52,698,440,874 ways.

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Answer:Area = 4700 feet squared

Perimeter= 288 feet

Step-by-step explanation:

Length = 94 feet

Width = 50 feet

Area = Length × Width

= 94 feet × 50 feet

= 4700 feet squared

Perimeter = 2(Length + Width)

= 2(94 feet + 50 feet)

= 2(144 feet)

= 288 feet

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Answer:

a)  0.356

b)  1.1397

Step-by-step explanation:

a) log₇2

b) log₇ (¹⁴⁷/₁₆)

          log (7)

Answer:

most likely asking for something like this

Step-by-step explanation:

Answer:

Read the step-by-step for the entire answer!!!

Step-by-step explanation:

Whenever you have situations like these you have to look at it from the perspective given.

If you are throwing a ball it's going to start at ground 0 where the child is, therefore the height of the child is how high off the ground the ball is at 0 seconds.

If it is thrown, and it is stuck in the tree for a few seconds, then that means on the graph you will see an incline of the graph, and then a stale line for a few seconds as the ball is stuck in the same height for a few seconds.

After the ball falls down, then so will the height of the ball.

t - a function of time, is always on the x-axis because time variables are usually on the x-axis of a graph.

I choose seconds as a measurement of time because in a realistic situation a ball will be in the air for seconds.

h - the height of the ball, will be on the y-axis of the graph because it is a dependent variable (i.e. the height of the ball is dependent on how long the ball is in the air for).      

The image below is the graph.  

The fraction illustrated shows that the way to distribute the paper it will be 1 + 1/3 + 1/3.

From the information given, the teacher distributes a stack of paper to 3 groups and the paper to be distributed is 1 2/3 inches.

Therefore, from the complete question, the way that it can be distributed will be 1 + 1/3 + 1/3. It can be seen that the addition will be equal to 1 2/3.

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Answer:

I would just rewrite it as -6r^2 + 6r

A grouped frequency distribution table for the data is [5, 10), [10, 15), [15, 20), [20, 25), [25, 30), [30, 35), and [35, 40).

We are given that;

The weight (in kg) of 50 sacks of sugar

Now,

To find the frequency of each class, we can use a tally mark system or a calculator. For example, the frequency of the first class [5, 10) is 3, because there are 3 data values that are greater than or equal to 5 but less than 10: 8.70, 9.27, and 9.66. The frequency of the second class [10, 15) is 16, because there are 16 data values that are greater than or equal to 10 but less than 15: 10.37, 10.65, 10.67, 10.33, 10.05, 10.06, 10.98, 10.61, 10.62, 11.05, 11.24, 11.36, 11.69, 11.40, 12.82, and 12.86.

We can repeat this process for the remaining classes and fill in the table as follows:

Class Frequency

[5, 10) 3

[10, 15) 16

[15, 20) 7

[20, 25) 4

[25, 30) 9

[30,35) 6

[35,40) 5

Therefore, by the given frequency the answer will be [5, 10), [10, 15), [15, 20), [20, 25), [25, 30), [30, 35), and [35, 40).

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Step-by-step explanation:

Sum of angles in a triangle = 180°

Hence Angle 1 = 180° - 24° - 37° = 119°.

Answer:

Use Calculator

Step-by-step explanation:

E

The vector that has the same direction as (2, 6, -3) but has a length of 2 is (4/7, 12/7, -6/7).

To find the vector that has the same direction as (2, 6, -3) but has a length of 2, we will first normalize the given vector and then scale it by the desired length.

Calculate the magnitude (length) of the given vector (2, 6, -3).
Magnitude = √(x^2 + y^2 + z^2) = √(2^2 + 6^2 + (-3)^2) = √(4 + 36 + 9) = √49 = 7

Normalize the given vector by dividing each component by its magnitude.
Normalized vector = (x/magnitude, y/magnitude, z/magnitude) = (2/7, 6/7, -3/7)

Step 3: Scale the normalized vector by the desired length (2).
Scaled vector = (desired length * x, desired length * y, desired length * z) = (2 * 2/7, 2 * 6/7, 2 * -3/7) = (4/7, 12/7, -6/7)

So, the vector that has the same direction as (2, 6, -3) but has a length of 2 is (4/7, 12/7, -6/7).

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Answer:

10^2

Step-by-step explanation:

When we divide exponents we subtract the exponenets in the top (in this case 6-4). This will give us 10^2. You can also check this.

The equivalent expression for 10⁶ ÷ 10⁴ will be 10². Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The numbers are given below.

10⁶ and 10⁴

The division of the numbers 10⁶ and 10⁴ will be given below.

⇒ 10⁶ ÷ 10⁴

⇒ 10⁶ / 10⁴

⇒ 10⁶⁻⁴

⇒ 10²

The equivalent expression for 10⁶ ÷ 10⁴ will be 10². Then the correct option is A.

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1. The sum of four and nine times three

2. eighteen divided by the sum of two and seven  

                            \(\bold{\dfrac{18}{2+7}}\)

or:  18÷(2+7),   or:  18/(2+7)

3. Ten divided by the product of four and five  

                            \(\bold{\dfrac{10}{4\times5}}\)

or:  10÷(4×5), or:  10/(4×5)

4. The Difference of eleven and four times five  

5. The sum of one and two divided by twenty

                              \(\bold{\dfrac{1+2}{20}}\)

or:   (1+2)÷20,  or:   (1+2)/20

6. The sum of two and four and six times eight  

7. The sum of twelve and sixteen divided by the sum of three and four

                               \(\bold{\dfrac{12+16}{3+4}}\)  

or:   (12+16)÷(3+4),   or:   (12+16)/(3+4)

8. The difference of twenty-two and six divided by the sum of five and three

                              \(\bold{\dfrac{22-6}{5+3}}\)

or:  (22 - 6)÷(5+3),  or:  (22 - 6)/(5+3)    

Answer:In the following activity, write an equation to represent each verbal statement, and use it to find the value of each unknown number. Then, put the solution values in order from smallest to largest. [Note: The smallest solution is "first", and the largest solution is "fifth".]

1. fourth

The sum of a number and two is equal to the quotient of six and negative four.

2. first

The sum of a number and three is divided by five. The result is negative two.

3. third

The difference between a number and five is multiplied by negative two. The resulting product equals fourteen.

4. second

Half of a number is added to four. This sum is equivalent to negative one.

5. fifth

The difference between four times a number and five has a result of negative eight.

Step-by-step explanation:

You should originally invest $148.

To solve this problem, we need to use the formula for present value of a bond:

\(PV = C/(1+r)^t\)

where PV is the present value, C is the annual coupon payment, r is the annual interest rate, and t is the time to maturity in years.

We know that the General Electric bonds had a time to maturity of 87 years and an annual rate of 5.25%. We also know that they paid a total of $6,630 at maturity. Let's call the original investment amount X.

Using the formula, we can set up the following equation:

\(6,630 = X/(1+0.0525)^{87\)

Simplifying this equation, we get:

\(X = 6,630 * (1+0.0525)^{-87\)

Using a calculator, we get:

X = $147.91

Rounding this to the nearest dollar, the answer is:

$148

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Option B is the only choice because it solves both equations: y = x² − 3x + 2 and x − y = 2.

A formula that expresses the connection between two phrases along either side of a symbol. It typically contains an equal symbol and one variable. Similarly, 2x - 4 Equals 2.

To solve this problem, we can use the fact that the point of intersection between the quadratic function and the linear function is (2,0). This means that when we plug in x=2 into both equations, we get y=0.

Let's test each of the given options by plugging in x=2 and y=0 and see which one satisfies both equations:

Option A: y = x² + 3x + 2

x + y = 2

If we plug in x=2, we get:

y = 2² + 3(2) + 2 = 12

And if we plug in x=2 and y=0 into the second equation, we get:

2 + 0 = 2

This does not satisfy the second equation, since 2 ≠ 0. Therefore, option A is not the correct answer.

Option B: y = x² − 3x + 2

x − y = 2

If we plug in x=2, we get:

y = 2² − 3(2) + 2 = 0

And if we plug in x=2 and y=0 into the second equation, we get:

2 − 0 = 2

This satisfies both equations, so option B is a possible answer.

Option C: y = x² − 3x + 2

x − y = 3

If we plug in x=2, we get:

y = 2² − 3(2) + 2 = 0

And if we plug in x=2 and y=0 into the second equation, we get:

2 − 0 = 3

This does not satisfy the second equation, since 2 ≠ 3. Therefore, option C is not the correct answer.

Option D: y = x² − 3x + 2

x + y = 3

If we plug in x=2, we get:

y = 2² − 3(2) + 2 = 0

And if we plug in x=2 and y=0 into the second equation, we get:

2 + 0 = 3

This does not satisfy the second equation, since 2 + 0 ≠ 3. Therefore, option D is not the correct answer.

Therefore, the only option that satisfies both equations is option B: y = x² − 3x + 2 and x − y = 2.

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