A catcher throws a baseball from home plate to third base. If he throws the ball horizontally at a speed of 42 m/s and it falls 2 meters below his release point,
how far was he from home plate?

A) 84.0m
B) 39.8m
C) 21.0m
D) 26.8m

The position of the particle at time t = 1 would be -1.

To find the position of the particle at time t = 1, we need to integrate the velocity function v(t) from t = 0 to t = 1, and add it to the initial position x = -2:

x(1) = -2 + ∫[0,1] v(t) dt

Integrating v(t), we get:

x(1) = -2 + ∫[0,1] (6t² + 8t - 5) dt

x(1) = -2 + [2t³ + 4t² - 5t] from 0 to 1

x(1) = -2 + [2(1)³ + 4(1)² - 5(1)] - [2(0)³ + 4(0)² - 5(0)]

x(1) = -2 + [2 + 4 - 5]

x(1) = -2 + 1

x(1) = -1

Therefore, the position of the particle at time t = 1 is -1.

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Answer: 28/52

Step-by-step explanation: its easy

Answer:

28/52. You will get it right.

Answer:

33 - 24x

Step-by-step explanation:

a. He made mistake here

9+(4)(5x+-6)

b.

9 - 4(5x - 6)

= 9 + (- 4)(5x - 6)

= 9 + (- 4)(5x) - (- 4)(6)

= 9 + (- 20x) - (- 24)

= 9 - 20x + 24

= 9 + 24 - 24x

= 33 - 24x

Answer:

x-3

Step-by-step explanation:

Anand's business charges $25 for a 10-mile ride, which is less than Moussa's overall expenses.

In comparison to Moussa, Anand's business costs less per mile.

Let's examine why by contrasting the costs charged by the two businesses for a 10-mile trip:

With a $3 pick-up fee and $2.20 per mile,

Moussa's business costs a total of $3 + $2.20*10 = $25.

Less than Moussa's overall expense,

Anand's business charges $25 for a 10-mile ride.

For all other distances mentioned in the table, we can verify that Anand's business charges less per mile than Moussa's. Thus, it is accurate that

"Anand's company charges less per mile than Moussa's."

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Answer: (-3, 0)

Step-by-step explanation:

         First, we will graph these equations. See attached. One has a y-intercept of 3 and then moves right one unit for every up down (we get this from the slope of 1). The other has a y-intercept of 4, and then moves down two units for every unit right (we get this from the slope of 1).

         The point of intersection is the solution, this is the point at which both graphed lines cross each other. Our solution is:

                         (-3, 0)     x = -3, y = 0

Answer:

(-3, 0)

Step-by-step explanation:

When we graph the equations:

y = x + 3,

y = -2 - 6,

we can see that they intersect at (-3, 0).

Therefore, that is the solution to the system.

— Extra note —

When graphing a line from a slope-intercept form equation (y = mx + b), we know the following:

m is the line's slope (rise over run)

b is the y-coordinate of the line's y-intercept

Answer:1,208 square centimeters

Step-by-step explanation:

Answer:

I'm sorry, I cannot create a labeled diagram of the circular fountain in the public park or find its map location in coordinates without more specific information about the park and fountain. However, I can provide some general information about circular fountains.

To find the map location in coordinates of the center of a circular fountain, you would need to know the specific location of the park and fountain. Once you have the location, you can use a mapping tool or website to find the coordinates of the center of the fountain.

To find the distance from the center of the fountain to its circumference, you would need to know the radius of the fountain. Once you have the radius, you can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. The distance from the center of the fountain to its circumference is equal to the radius of the fountain.

I hope this information helps. If you have more specific information about the circular fountain in the public park, please let me know and I can try to provide more detailed information.

(A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

What is the rate of change?

The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.

A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.

Using the formula for an annual rate of change (r):

final value = initial value * [tex](1 - r)^t[/tex]

where t is the number of years and r is the annual rate of change expressed as a decimal.

Substituting the given values, we get:

$15,000 = $44,000 * (1 - r)¹⁴

Solving for r, we get:

r = 0.0804

So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.

B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:

r = 0.0804 * 100% = 8.04%

C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.

Substituting the known values, we get:

value in 2009 = $15,000 * (1 - 0.0804)³

value in 2009 = $11,628.40

Rounding to the nearest $50, we get:

value in 2009 = $11,650

Hence, (A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

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Answer:16.7

Step-by-step explanation: So the first step is to add all of the numbers in the second column. (15,18,14,16,19,18). At the end of your problem it says 100. So you have 6 different numbers, and 100. You will do 100 divided by 6. Finally you will get 16.66 and you will just round it.

The probability of selecting a divisor of 6 is 66.7%.

It is expressed as a number between 0 and 1, where 0 represents an impossible event (it will never occur) and 1 represents a certain event (it will always occur).

1, 2, 3, and 6 can be divided by 6.

To find the probability (p) of selecting a divisor of 6, we need to divide the number of divisors of 6 by the total number of possible outcomes, which is also 6 (since there are 6 positive integers from 1 to 6).

So, p(divisor of 6) = number of divisors of 6 / total number of outcomes

= 4 / 6

= 2 / 3

We can multiply this fraction by 100 to get the percentage:

p(divisor of 6) = 2 / 3 * 100

= 66.7%

Rounded to the nearest tenth, the answer is 66.7%. Therefore, the probability of selecting a divisor of 6 is 66.7%.

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The equatiοn οf the circle is (x + 6)(x+6) + (y + 2)(y+2) = 9.

A circle is a twο-dimensiοnal geοmetric figure that cοnsists οf all pοints that are equidistant frοm a single fixed pοint called the center. A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane in such a way that its distance frοm a fixed pοint is always cοnstant.

Tο find the equatiοn οf a circle, we need the cοοrdinates οf the center and the radius.

The center οf the circle is given as (-6, -2), sο the cοοrdinates οf the center are (h, k) = (-6, -2).

The pοint (-9, -2) is οn the circle, sο its distance frοm the centre is equal tο the radius. We can use the distance fοrmula tο find the radius:

[tex]\rm r = \sqrt{((x_2 - x_1)\times (x_2 - x1) + (y_2 - y_1)\times(y_2 - y_1))}[/tex]

[tex]= \sqrt{((-3)^2 + 0^2)[/tex]

= 3

Therefοre, the radius οf the circle is 3.

Nοw we can use the standard fοrm οf the equatiοn οf a circle, which is:

(x - h)(x-h)+ (y - k)(y-k)= r*r

Substituting the values we fοund, we get:

Simplifying:

(x + 6)(x+6) + (y + 2)(y+2) = 9

Therefοre, The equatiοn οf the circle is [tex](x + 6)(x+6) + (y + 2)(y+2) = 9[/tex].

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Answer:

Step-by-step explanation:

divide both by 100 to get

3072/1

answer: 3072

Therefore, the doubling time is approximately 10.83 years.

a) The exponential function that describes the amount in the account after time t, in years, is given by:

[tex]$A(t) = A_0 e^{rt}$[/tex]

where $A_0$ is the initial investment, $r$ is the annual interest rate as a decimal, and $t$ is the time in years. Since the interest is compounded continuously, we have $r = 0.064$.

Substituting the given values, we get:

[tex]$A(t) = 10,405 e^{0.064t}$[/tex]

b) To find the balance after 1 year, we plug in $t=1$ into the exponential function:

[tex]$A(1) = 10,405 e^{0.064(1)} \approx 11,069.79$[/tex]

Similarly, we can find the balance after 2, 5, and 10 years:

[tex]$A(2) = 10,405 e^{0.064(2)} \approx 11,778.79$[/tex]

[tex]$A(5) = 10,405 e^{0.064(5)} \approx 14,426.77$[/tex]

[tex]$A(10) = 10,405 e^{0.064(10)} \approx 19,682.08$[/tex]

c) The doubling time can be found using the formula:

[tex]$t_{double} = \frac{\ln 2}{r}$[/tex]

Substituting $r = 0.064$, we get:

[tex]$t_{double} = \frac{\ln 2}{0.064} \approx 10.83$ years[/tex]

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Answer:

-2x × 10^1 + 8 × 10^0

or

-2x × 10 + 8 × 1

Step-by-step explanation:

Multiply the following to put them in standard form

-4 (5x-2)=

-20x +8

standard form

-2x × 10^1 + 8 × 10^0

or

-2x × 10 + 8 × 1   (remember  PEMDAS)

Answer:

y > x² – 2x – 3

y > 3x + 4

Step-by-step explanation:

I took the test;. hoped this help.

Answer:

98+x=154

x=154-98

x=56

x-4=20

x=20+4

x=24

x+25=-10

x=-10-25

x=-35

P(X >= 15) ≈ 0.271 is an unusual event would be one that has a very low probability of occurring (e.g., less than 5%).

What is probability?

Probability is a numerical measurement that represents the likelihood or chance of an event happening. The value of probability always lies between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

a) To find the probability that at least 15 out of 18 U.S. college graduates expect to stay at their first employer for three or more years, we can also use the CDF of the binomial distribution:

P(X >= 15) = 1 - P(X < 15)

Using a calculator or statistical software, we find:

P(X >= 15) ≈ 0.271

An unusual event would be one that has a very low probability of occurring (e.g., less than 5%). Therefore, these outcomes could be considered unusual.

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For the given cone, the approximate volume of the toy top is 106.81 cubic centimeters. The three dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.

Volume is a three-dimensional quantity that measures the amount of space occupied by an object or a region in space.

The volume of the toy top can be calculated by finding the volumes of the cone and cylinder and then adding them together.

The volume of the cone is given by the formula V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius and h is the height of the cone. In this case, the slant height is given, so we need to use the Pythagorean theorem to find the height:

h = [tex]\sqrt{(l^2 - r^2)[/tex] = [tex]\sqrt{(10^2 - 6^2)[/tex] = √(64) = 8 cm

Therefore, the volume of the cone is:

V_cone = (1/3)π[tex]r^2[/tex]h = (1/3)π([tex]6^2[/tex])(8) ≈ 100.53 [tex]cm^3[/tex]

The volume of the cylinder is given by the formula V = π[tex]r^2[/tex]h, where r is the radius and h is the height of the cylinder. In this case, the diameter is given, so we need to divide by 2 to get the radius:

V_cone = (1/3)πh = (1/3)πr = d/2 = 1 cm = 2 cm

Therefore, the volume of the cylinder is:

V_cylinder = π[tex]r^{2}[/tex]h = π([tex]1^{2}[/tex])(2) ≈ 6.28

The total volume of the toy top is:

V = V_cone + V_cylinder ≈ 100.53 + 6.28  ≈  106.81 T

Therefore, the approximate volume of the toy top is 106.81 cubic centimeters.

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The answer is 0.351

To estimate the proportion p of American adults with monthly credit card debt, the sample proportion can be used as an estimate. The sample ratio is simply the number of people in the sample with monthly credit card debt divided by the total number of people in the sample.

p hat = 587/1669

p-hat = 0.3511 (rounded to four decimal places)

Therefore, based on this sample, the percentage of adult Americans with monthly credit card debt is estimated to be approximately 0.351. After rounding to three decimal places, its estimate is 0.351.

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When the x-values rise while the y-values fall, this is known as a declining pattern. So, as x increases from 3 to 6, the graph declines. When the point on the graph at the interval's left end is higher than the interval's right end, the average rate of change will be declining.

An indicator of how much the function changed on average per unit throughout that time is the graph's average rate. In the graph of the function, it is calculated from the slope of the straight line joining the interval's ends. So, by applying the average rate of change formula, the slope of a graphed function is calculated.

Hence divide the y-value change by the x-value change in order to determine the average rate of change. When analyzing changes in observable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

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The complete question is:

Choose the intervals where the graph has a decreasing average rate of change. The graph is attached below:

x = 0 to x = 13

x = 3 to x = 6

x = 4 to x = 8

x = 6 to x = 10

Answer:

Step-by-step explanation:

Given the figure with triangle ABC similar to triangle EDC and AB=8 mi, ED=2 mi, BD = 7.5 mi, you want the measures of CD and AE.

Similar triangles will have corresponding sides proportional. That means ...

  ED/CD = AB/CB

  2/CD = 8/(7.5 -CD)

Inverting the ratios and multiplying by 8 gives ...

  4·CD = 7.5 -CD

  5·CD = 7.5 . . . . . . . add CD

  CD = 1.5 . . . . . . . . . divide by 5

The distance AE is the hypotenuse of a right triangle with side lengths 7.5 and (8+2) = 10. The Pythagorean theorem can be used to find AE:

  AE² = 7.5² +10² = 56.25 +100 = 156.25

  AE = √156.25 = 12.5

AE = 12.5 miles, the distance to the mall.

__

Additional comment

You may recognize these triangles are 3-4-5 triangles. ABC has a scale factor of 2, so has side lengths 6-8-10. EDC has a scale factor of 1/2, so has side lengths 1.5, 2, 2.5. The triangle with AE as its hypotenuse is the sum of these, so has a scale factor of 2.5 (miles).

  AE = (2.5 miles) · 5 = 12.5 miles

To find the price of the chair in the furniture store, we need to calculate the retail price, which is the wholesale price plus the markup. The markup is calculated by multiplying the wholesale price by the markup rate as a decimal:

markup = 0.22 x $181 = $39.82

So the retail price is:

$181 + $39.82 = $220.82

Rounding to the nearest cent, we get the final answer:

The price of the chair in the furniture store is $220.82.

The sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.

To solve the triangle, we need to find the values of the remaining sides and angles. We can start by using the Law of Sines, which states that:

a / sin A = b / sin B = c / sin C

where a, b, and c are the sides of the triangle, and A, B, and C are the angles opposite to those sides.

Using the given values, we can write:

a / sin 51 = 7 / sin B

a / sin 51 = 10 / sin C

To solve for a, we can use either of the two equations above. Let's use the first one and solve for sin B:

sin B = (7 / sin 51) * sin B

sin B = 7 / (sin 51 / sin B)

sin B = 7 / sin(180 - 51 - B)

sin B = 7 / sin(129 - B)

Using the sine rule, we can determine the angle B:

sin B / 7 = sin(129 - B) / 10

sin B = (7/10) * sin(129 - B)

sin B = (7/10) * (sin 129 * cos B - cos 129 * sin B)

sin B = (7/10) * sin 129 * cos B - (7/10) * cos 129 * sin B

(7/10 + (7/10) * cos 129) * sin B = (7/10) * sin 129 * cos B

sin B = (7/10) * sin 129 * cos B / (7/10 + (7/10) * cos 129)

sin B = sin 51.5

B = sin(sin B)

B = sin(sin 51.5)

B ≈ 51.5°

We can now find the remaining angle, C:

C = 180 - A - B

C = 180 - 51 - 51.5

C ≈ 77.5°

Finally, we can use the Law of Sines again to find the remaining side, a:

a / sin A = c / sin C

a / sin 51 = 10 / sin 77.5

a = (10 * sin 51) / sin 77.5

a ≈ 8.3

Therefore, the sides of the triangle are a ≈ 8.3, b = 7, and c = 10, and the angles are A = 51°, B ≈ 51.5°, and C ≈ 77.5°.

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Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693

If 58% = 58÷100 of the people have been vaccinated, then;

1 - (58/100) = 42% = 42÷100 of the people who have not been vaccinated.

Now:

Probability, P( > 1 ), that at least one of the selected four has been vaccinated is given by;

P( > 1 ) = 1 - P(0)                 -----------(1)

Where;

P(0) = probability that all of the four have not been vaccinated.

P(0) = P(1) x P(2) x P(3) x P(4)×p(5)

Where;

P(1) = Probability that the first out of the four has not been vaccinated

P(2) = Probability that the second out of the four has not been vaccinated

P(3) = Probability that the third out of the four has not been vaccinated

P(4) = Probability that the fourth out of the four has not been vaccinated

P(5)=Probability that the fifth out of the five has not been vaccinated

Remember that 42÷100 of the population has not been vaccinated. Therefore,

P(1) = 42÷100    

P(2) = 42÷100

P(3) = 42÷100

P(4) = 42÷100

P(5)=42÷100

P(0) = (42÷100) x (42÷100) x (42÷100) x (42÷100)×(42÷100)

P(0) = (42÷100)⁵

P(0) = (0.42)⁵

P(0) = 0.013067

Therefore, from equation (1);

P( > 1 ) = 1 -0.013067

P( > 1 ) = 0.98693

Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.98693

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Answer: No, you cannot always divide by e^x. When e^x equals zero, dividing by it would result in an undefined value or division by zero error.

For example, consider the function f(x) = e^x. We know that e^x is never equal to zero for any value of x. Therefore, we can always divide by e^x for any value of x, and the resulting quotient will be well-defined.

However, if we consider the function g(x) = 1 / e^x, we cannot always divide by e^x. When e^x equals zero, g(x) will be undefined. In fact, there is no value of x for which e^x is equal to zero, so the function g(x) is well-defined for all values of x.

In summary, dividing by e^x is allowed for most cases, except when e^x equals zero.

Step-by-step explanation:

Answer:

[tex]\frac{13}{21}[/tex]

Hope this helps!

Step-by-step explanation:

[tex]\frac{39}{63}[/tex]  ( Simplify both numerator and denominator by 3 )

39 ÷ 3 / 63 ÷ 3

[tex]\frac{13}{21}[/tex]

1) Not a triangle as According to the triangle inequality theorem  ,2)Triangle. as According to the triangle inequality theorem    ,  3)Not a triangle. ,  4)Not a triangle., 5)Triangle. ,  6)Not a triangle.,  7) Not a triangle., 8)Equilateral triangle. 9)Not a triangle   10)  Triangle.

what is  triangle ?

A triangle is a two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry, and it is formed by connecting three non-collinear points. The sum of the angles in a triangle is always 180 degrees.

In the given question,

Not a triangle. (6 + 5 = 11 > 3)

Explanation: According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. However, in this case, 6 + 5 is equal to 11, which is not greater than the third side of length 3.

Triangle. (5 + 12 > 13)

Explanation: The sum of the two smaller sides (5 and 12) is greater than the largest side (13), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.

Not a triangle. (2 + 2 = 4 > 3)

Explanation: Similar to the first case, the sum of the two smaller sides (2 and 2) is equal to 4, which is not greater than the third side of length 3.

Not a triangle. (1 + 2 = 3 > 4)

Explanation: Again, the sum of the two smaller sides (1 and 2) is equal to 3, which is not greater than the third side of length 4.

Triangle. (6 + 8 > 10)

Explanation: The sum of the two smaller sides (6 and 8) is greater than the largest side (10), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.

Not a triangle. (1 + 1 = 2 > 2)

Explanation: Similar to cases 1 and 3, the sum of the two smaller sides (1 and 1) is equal to 2, which is not greater than the third side of length 2.

Not a triangle. (4 + 5 = 9 > 7)

Explanation: In this case, the sum of the two smaller sides (4 and 5) is greater than 7, but the difference between the two larger sides (7 - 5) is smaller than the smallest side (4), violating the triangle inequality theorem.

Equilateral triangle. (All sides are equal)

Explanation: All sides are equal, satisfying the criteria for an equilateral triangle.

Not a triangle. (1 + 3 = 4 > 5)

Explanation: The sum of the two smaller sides (1 and 3) is greater than the largest side (5), but the difference between the two larger sides (5 - 3) is smaller than the smallest side (1), violating the triangle inequality theorem.

Triangle. (3 + 4 > 5)

Explanation: The sum of the two smaller sides (3 and 4) is greater than the largest side (5), satisfying the triangle inequality theorem. Therefore, a triangle can be formed with these side lengths.

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The area of the shaded region is 1.916 ft²

Area is a measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, circle, or any other shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, or square meters.

To calculate the area of the shaded region, we need to find the area of the entire circle and subtract the area of the unshaded portion.

The central angle corresponding to the shaded region is 110 degrees. The entire circle has a central angle of 360 degrees.

The unshaded portion of the circle is the sector that corresponds to the central angle of 360 - 110 = 250 degrees. The area of a sector of a circle with radius r and central angle θ is given by the formula:

A = (θ/360)πr²

Substituting θ = 110 degrees and r = 2 ft, we get:

A = (110/360)π(2)

A =  (0.305)π(2)

A =  (0.305)π(2)

A = 0.61π

A = 1.916 ft²

Therefore, the area of the shaded region is 1.916 ft².

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Complete question:

Calculate the area of the shaded region. the apothem is 2 ft, and the shaded area is 110 degrees. the figure is a circle