The distance between consecutive bases on a baseball field is 90 feet. A second baseman stands halfway between first base and second base, a shortstop stands halfway between second base and third base, and a pitcher stands halfway between first base and third base. Find the distance between the shortstop and the pitcher.

Answer:  Choice D.  \(\frac{5}{2}\)

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Work Shown:

\(\frac{7}{3}\cdot \frac{15}{14}\\\\\frac{7*15}{3*14}\\\\\frac{7*5*3}{3*7*2}\\\\\frac{7*5}{7*2} \ \text{ .... pair of 3s cancel}\\\\\frac{5}{2} \ \text{ .... pair of 7s cancel}\\\\\)

As you can see, the goal is to factor the numbers so that we find stuff that cancels out. By the time we reach 5/2, there isn't anything left to cancel. Therefore, the fraction is fully reduced at this point.

Answer:

4(7a + 3b) = 28a + 12b

Step-by-step explanation:

The sum of 7a and 3b: 7a + 3b

4 times the sum of 7a and 3b: 4(7a + 3b)

Expanding this out:

4(7a + 3b) = 28a + 12b

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

-15x + 44 = 8x - 12

-8x -8x

-7x + 44 = -12

- 44 - 44

-7x = -56

x = 8

Answer:

a. a = -12

b. a = 27

Step-by-step explanation:

a. Two lines that are parallel have the same slope, making the slopes equal ot each other:

\(-\frac{3}{2} =\frac{18}{a}\)

We can cross multiply and solve for a:

\(-3a = 36\\a = -12\)

b. Two lines that are perpendicular have the negative reciprocal of each other. This means that you would flip the fraction and multiply by a negative as shown below:

\(-\frac{3}{2} --> \frac{2}{3}\)

This would be the slope of the other line, so we can write:

\(\frac{2}{3} = \frac{18}{a}\)

as both expressions express the slope of the same line. We can cross multiply and solve to get:

\(2a = 54\\a = 27\)

Answer:

90% is the answer

Step-by-step explanation:

hope this helps.

Answer: p+13=173

Step-by-step explanation:

P and 13 more just means p + 13

the same as just means =

so put those together and you get p+13=173

The given function belongs to the linear family.

According to the statement

we have to find that the type which is belongs to the function f.

So, for this purpose, we know that the

To identify the function family, we do the following

Identify the variable --- the variable of the function is x

Check if the variable has any negative exponent -- x has no negative power

Identify the highest power of x -- The highest power of x is 1.

Then

When there is no negative exponent and the highest power of the variable is 1, then the function belongs to the linear family.

Next, we compare the function to its parent function.

The parent function of a linear function is:

y = x

And it is translated by the 8.

So, The given function belongs to the linear family.

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The side of the square of each block = 2 feet

Given,

Shelly sews a square blanket that has an area of 144 square feet.

and,  it has 36 square blocks, each the same size.

To find the approximate length of each side of a block

Now, According to the question:

36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks

= 144/ 36

= 4

The area of each square = 4 square feet

We know that

Area of square = side ^2

Side ^2 = 4

side = \(\sqrt{4}\)

Side = 2

Hence, The side of the square of each block = 2 feet

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Answer:373248

Step-by-step explanation:

72^3 = 373248

Two point charges, q1 = 3.99 nC located at x = 0.205 m and q2 = 5.01 nC at x = -0.302 m, are placed on the x-axis. The electric field and direction at a given point can be calculated using the principle of superposition.

The electric field at a point due to a point charge is given by Coulomb's law, E = kq/r^2, where E is the electric field, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the point where the electric field is being measured. To calculate the net electric field at a point due to multiple charges, we use the principle of superposition, which states that the total electric field at a point is the vector sum of the electric fields due to each individual charge.

In this case, we have two charges, q1 = 3.99 nC and q2 = 5.01 nC. The electric field at a point P on the x-axis, due to q1, can be calculated as E1 = kq1/r1^2, where r1 is the distance between q1 and point P. Similarly, the electric field at point P due to q2 can be calculated as E2 = kq2/r2^2, where r2 is the distance between q2 and point P. To find the net electric field at point P, we add the electric fields vectorially, E_net = E1 + E2.

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Answer: The  length of a rectangle is 5 more than two times the width. If the width of the rectangle  is represent by x  then what is the area of the rectangle?  

Step-by-step explanation:

Answer: 3 feet

Step-by-step explanation: The area of a rectangular garden can be represented by the function

f(x) = x(2x + 5)

Find the area if the length, x, is 3 feet.

Where the above is given, the required angle m∠BAC = 45°.

In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

According to conditions angle b = 90°

The sum of angles of a triangle= 180°

That is a + b + c = 180

Therefore, c = a

       a = (180 - b)/2

          = (180 - 90) / 2

          = 90 / 2

          = 45°

Hence, the required angle m∠BAC = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?

Answer:

\(1) \: {2}^{3} \\ 2) \: {3}^{6} \\ 3) \: {4}^{4} = 4 \times 4 \times 4 \times 4 = 256\)

Answer:

1) Area = 12cm²

2) x = 5cm

Surface area : 69cm²

Step-by-step explanation:

Opposites sides in a rectangle would equal the same.

so Top/bottom = 20+20=40

Front/back = 15+15=30

40+30=70cm²

94-70=24cm² for left and right side 24÷2=12cm²

2) Those lines represents what side it is equal too which also means the same.

3cm, you know that base x height = surface area so surface area ÷ height = base

15/3=5cm

x=5cm

Formula : Base x Height = One surface area

Front/Back= 15+15=30

Top/bottom = 5x3 = 15+15=30

side/side = 3x3=9

30+30+9=69cm²

14 left handed people would you expect in a group of 140 people .

According to the question, 3 people are left handed out of every 30 people.

We can solve this using unitary method ,

14 left handed people would you expect in a group of 140 people.

Another method:

Based on the given conditions, formulate : 140 * 3 / 30

Reduce the fraction : 14

get the result 14

Answer 14

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The partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned.

The given water wave function is graphed as z = 1 + sin(x - y) using Mathematica. The crests and troughs of the wave are aligned in the direction of zero change in the height function, which can be determined by analyzing the partial derivatives. The steepest descent from a crest to a trough corresponds to the direction perpendicular to the alignment of crests and troughs. These conclusions are consistent with the graph of the wave.

The water wave function z = 1 + sin(x - y) represents a snapshot of a frozen water wave. To graph this function using Mathematica, the x and y coordinates are assigned appropriate ranges, and the resulting z-values are plotted.

To determine the alignment of the crests and troughs, we examine the rate of change of the height function. Taking the partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned. Setting dz/dx = 0 gives cos(x - y) = 0, which implies x - y = (2n + 1)π/2, where n is an integer. This equation represents lines in the xy-plane along which the crests and troughs are aligned.  

For the steepest descent from a crest to a trough, we need to find the direction of maximum decrease in the height function. This direction corresponds to the negative gradient of the height function, which can be obtained by taking the partial derivatives dz/dx and dz/dy and forming the vector (-dz/dx, -dz/dy). Simplifying this vector, we get (-cos(x - y), cos(x - y)), which represents the direction perpendicular to the alignment of crests and troughs.    

Upon examining the graph of the wave, we can observe that the lines of alignment for the crests and troughs match the lines where the height function has zero change, confirming our conclusion from part (b). Similarly, the direction of steepest descent from a crest to a trough, indicated by the negative gradient, aligns with the steepest downward slopes on the graph.

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Answer:

Answer B

Step-by-step explanation:

B is:

\(3 (\sqrt{25} - 10) + 5 \\ 3(5 - 10) + 5 \\ 3 ( - 5) + 5 \\ - 15 + 5 = - 10\)

The simplified expression in exponential form would be 23^(a + b).

To simplify the numerical expression 23a x 23b, we can combine the like terms.

Step 1: Simplify 23a and 23b individually.

The expression 23a means multiplying 23 by a, and 23b means multiplying 23 by b. We cannot simplify them further because we do not have specific values for a and b.

Step 2: Combine the simplified terms.

When we multiply 23a by 23b, we multiply the coefficients (23 x 23) and the variables (a x b). Therefore, the simplified expression is:
(23 x 23) x (a x b)

Step 3: Calculate the coefficient and write the answer in exponential form.

The coefficient (23 x 23) is equal to 529. In exponential form, we can write it as 23^2. So the final simplified expression is:
23^2 x (a x b)

In summary, the simplified numerical expression 23a x 23b can be written as 23^2 x (a x b) in exponential form.

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Water vapor is an important component of the Earth's atmosphere, and it plays a crucial role in regulating the climate. water vapor makes up about 0-4% of the Earth's atmosphere by volume . So the correct option is A.

It is a greenhouse gas, which means that it can trap heat in the atmosphere and contribute to global warming. The amount of water vapor in the atmosphere can vary depending on location, temperature, and weather conditions. On average, water vapor makes up about 0-4% of the Earth's atmosphere by volume. This may seem like a small amount, but it has a significant impact on weather patterns and climate. As temperatures rise due to climate change, the amount of water vapor in the atmosphere is expected to increase, which could have further impacts on global climate.

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Applying the sine ratio and the Pythagorean theorem, the adjecent length to angle β is: A. 16.7 cm.

The sine ratio is given as, sin ∅ = opposite/hypotenuse.

Given the following in a right triangle:

Find the opposite side by applying the sine ratio:

0.292 = opp/17.5

Opposite = (0.292)(17.5)

Opposite = 5.11

Using the Pythagorean theorem, we have:

Adjacent length = √(17.5² - 5.11²)

Adjacent length = 16.7 cm.

Thus, applying the sine ratio and the Pythagorean theorem, the adjecent length to angle β is: A. 16.7 cm.

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Answer:

2.1 x 10^8

Step-by-step explanation:

The expression (7x10⁵)x(3x10²) in the standard form will be 2.1 x 10⁸.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is (7x10⁵)x(3x10²). The standard form of the expressions can be written as,

E = (7x10⁵)x(3x10²)

E = ( 7 x 3 ) x ( 10⁵⁺²)

E = 21 x 10⁷

E = 2.1 x 10⁸

Hence, the standard form is 2.1 x 10⁸.

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Answer:

\(\frac{5}{7}\) x + 2

Step-by-step explanation:

(\(\frac{2}{7}\) x - 6) + (\(\frac{3}{7}\) x + 8) ← remove parenthesis

= \(\frac{2}{7}\) x - 6 + \(\frac{3}{7}\) x + 8 ← collect like terms

= ( \(\frac{2}{7}\) x + \(\frac{3}{7}\) x ) + ( - 6 + 8 )

= \(\frac{2+3}{7}\) x + 2

= \(\frac{5}{7}\) x + 2

When the amplitude of the oscillator gradually decreases with time, we say it is a damped oscillator. The oscillator's behavior is said to be undamped if the amplitude remains the same over time.

Suppose that both the undamped and damped systems are set in motion with the initial conditions

y(0) = y0 and y′(0) = v0.

The amplitude of the damped response is half that of the amplitude of the undamped response at a time t equal to: t = (1/ωd)ln(A0/A0d), where A0 is the amplitude of the undamped response, A0d is the amplitude of the damped response, and ωd is the damped angular frequency.

What is a damped oscillator?

A damped oscillator is an oscillator that gradually loses energy over time as a result of the energy dissipation mechanism present in the oscillator.

A spring-mass system immersed in a viscous fluid, a pendulum and a guitar string are examples of oscillatory systems. When the amplitude of the oscillator gradually decreases with time, we say it is a damped oscillator. The oscillator's behavior is said to be undamped if the amplitude remains the same over time.

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Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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The main questions in the pre-lab assignment are:

1. What is/are the Question(s) of the Day?

2. Balance all five reactions listed in the procedure.

3. Write the chemical equation for the reaction of copper (II) hydroxide and hydrochloric acid to give copper (II) chloride and water.

4. Write the formula and name for the solid that copper (II) hydroxide becomes when heated.

5. Outline the key steps for properly using an analytical balance and indicate the number of decimal places that can be measured.

6. Calculate the percent recovery for a student who obtained 0.2331 grams of solid copper from a sample that initially weighed 0.3015 grams.

In the given pre-lab assignment, there are several questions and tasks related to the upcoming lab session on the chemical reactions of copper. The first question asks about the "Question(s) of the Day," which is not explicitly mentioned in the provided text. It might refer to the specific focus or objectives of the lab session.

The second task requires balancing all five reactions listed in the procedure, which is expected to be completed in the designated procedure section of the assignment, not in this particular section.

The third question asks to write the chemical equation for the reaction between copper (II) hydroxide and hydrochloric acid, producing copper (II) chloride and water. This reaction is an example of an acid-base reaction. In the equation, it is important to label the acid and base reactants.

The fourth task involves writing the formula and name for the solid that copper (II) hydroxide becomes when heated. The provided information does not mention the exact outcome, so it might be necessary to refer to additional resources or experimental data to determine the formula and name of the resulting solid.

The fifth task is to outline the key steps for properly using an analytical balance. The explanation should also include the number of decimal places that can be measured with this type of balance. It is important to follow the guidelines provided in the video posted on Brightspace, which will likely cover the necessary steps for accurate measurements using an analytical balance.

The final task involves calculating the percent recovery for a student who obtained 0.2331 grams of solid copper from a sample initially weighing 0.3015 grams. The formula for percent recovery is determined by dividing the actual yield (0.2331 g) by the theoretical yield (0.3015 g) and multiplying by 100%. The resulting percentage indicates how successful the student was in recovering the copper.

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Step-by-step explanation:

Decrease is   49500 - 44055 = 5445 dollars

What percent of 49500   is   5445 ?

5445 / 49500   x 100% = 11% decrease

The missing points are:

Because two points determine a line, you can draw altitude​ BD perpendicular to AC with height h.

By the definition of a sine ratio, sin(C) = h/a, which can be rearranged into​ a·sin(C) = h​.

The area of △ABC is A=1/2bh.

The substitution property of equality can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the commutative property of multiplication.

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