There are 60 feet between the bases on a softball diamond. How far does a catcher throw drone home plate to second base

Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.0889.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the sample size are given as follows:

[tex]\pi = 0.71, n = 100[/tex]

Hence, the margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.71(0.29)}{100}}[/tex]

M = 0.0889.

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x 's measure is already given

x=20°

Answer:

∡x = 20°

∡y = 160°

∠z = 160°

Step-by-step explanation:

Angles on a straight line sum to 180°

⇒ ∠z + 20° = 180°

⇒ ∠z = 180° - 20°

⇒ ∠z = 160°

The central angle measure equals the corresponding arc measure.

⇒ ∡x = 20°

⇒ ∡y = ∠z = 160°

Answer:

31.73 grams

Step-by-step explanation:

70.83 g - 39.1 g = 31.73 g

The amount of plywood that he needs to buy will be 21 square feet.

Let the prism with a length of L of the rectangular surface.

And the dimension of the triangle is A, B, and C. Then we have

SA = 2(area of triangle) + 3(area of rectangle surface)

A triangular prism.

The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.

The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.

Then the area of the triangle will be

⇒ 1/2 x 2 x 1.5

⇒ 1.5 square feet

The area of the rectangles will be

⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5

⇒ 18 square feet

Then the surface area of the triangular prism will be

Surface area = 2 x 1.5 + 18

Surface arae = 3 + 18

Surface area = 21 square feet

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[tex]\sqrt{-1} + 2 = i+2 = 2+i[/tex]

if its diameter is 9, that means its radius is half that, or 4.5.

[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4.5 \end{cases}\implies \begin{array}{llll} SA=4\pi (4.5)^2\implies SA=81\pi \\\\\\ SA\approx 254.47~in^2 \end{array}[/tex]

The surface area of the basketball with diameter of 9 in will be 254.34 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given that, a basketball has a diameter of 9 inches we need to find its surface area,

Since, the basketball is in the shape of the sphere and the surface area of the sphere = 4π×radius²

Therefore, the surface area of the basketball =

= 4×3.14×(9/2)²

= 4×3.14×4.5×4.5

= 254.34 in²

Hence the surface area of the basketball with diameter of 9 in will be 254.34 in².

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Answer:

1/20

Step-by-step explanation:

number of favourable outcomes/number of outcomes

Answer: y=-1/5x+4

Step-by-step explanation: use the equation y=mx+b (x,y)->(5,3) 5 is an x value and 3 is a y value so you want to plug in these values into the equation. 3=-1/5(5)+b. We already know our slope so just plug it into m. Now multiply -1/5 and 5 which is -1. 3=-1+b you want to isolate b so you can find the intercept. Add one to both sides so it cancels out. 4=b we found our y-intercept so we can write the equation now. y=-1/5x+4

Answer:

Slope= - 7/9

Step-by-step explanation:

m=rise/run

m=8-1= 7

    -3-6=-9

m=7/-9

- 7/9

Hi student, let me help you out! :)

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We are asked to find the slope of

[tex]\star\mathrm{(6,1)}\star[/tex]

[tex]\star\mathrm{(-3,8)}\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the formula:

[tex]\star\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}\star[/tex]

Where:

[tex]\star[/tex] y2 and y1 are y-coordinates

[tex]\star[/tex] x2 and x1 are x-coordinates

So substitute the values accordingly:

[tex]\star\mathrm{\cfrac{8-1}{-3-6}}[/tex]

Simplify!

[tex]\star\mathrm{\cfrac{7}{-9}}[/tex]

Which is the same thing as...

[tex]\star\mathrm{-\cfrac{7}{9}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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Answer:

for the x values: -2,-1,0,1,2

y-values: 13, 6, 5, 4, -3

Step-by-step explanation:

Answer:

C angle H = 75.4

Step-by-step explanation:

In order to find the measure of angle H we must first find the value of x

Firstly it's good to know that the sum of the angles in a quadrilateral always add up to 360 degrees

Knowing this we can create an equation.

Since the angle measures must add up to 360 degrees we know that angle F + angle E + angle H + angle G = 360

Plugging in the given expressions for each angle we acquire

14x - 11 + 5x + 21 + 6x + 16 + 8x - 7

We can now solve for x

==> combine like terms

33x + 19 = 360

==> subtract 19 from both sides

33x = 341

==> divide both sides by 33

x = 10 1/3

Now that we have identified the value of x and we can plug in x = 10 1/3 into the given expression of angle H and evaluate to get the measure

Angle H = 8x - 7

==> plug in x = 10 1/3

Angle H = 8(10 1/3) - 7

==> multiply 8 and 10 1/3

Angle H = 82.7 - 7

==> subtract 7 from 82.7

Angle H = 75.6

C is the closest answer

Answer:

C. m∠H = 75.4°

Step-by-step explanation:

all sides of a quadrilateral add up to 360°

So, (5x + 21) + (14 - 11) + (6x + 16) + (8x - 7) = 360

Add like terms:

33x + 19 = 360

33x = 360 - 19

33x = 341

x = 341/33

x = 10.33...

Substitute:

∠H = 8x - 7

∠H = 8(10.3) - 7

∠H = 75.4°

The volume of the rectangular prism is 17 cubic units

The given parameters are:

The volume is calculated as:

Volume = Length * Width * Height

Substitute known values

Volume = 5 * 2 * 1.7

Evaluate

Volume = 17

Hence, the volume of the prism is 17 cubic units

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Step-by-step explanation:

Since , internal sum of angle of triangle is 180°

So,

66 + x +49 + x+83 = 180

or, 198 + 2x = 180

or, 2x = 180 -198

or, 2x = -18

hence, x = - 9

Now angle A = x + 49

= (-9) + 49

= 40

Hence measure of angle A is 40°.

Answer:

40

Step-by-step explanation:

From triangle law ,

66 + x +49 + x+83 = 180

or, 198 + 2x = 180

or, 2x = 180 -198

or, 2x = -18

hence, x = - 9

Now angle A = x + 49

= (-9) + 49

= 40

Hence, answer is 40.

The minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The minimum and maximum mass measurement is determined from the uncertainty in the measurement.

For a given uncertainty of 2.2%, the minimum and maximum mass measurement is calculated as follows;

2.2% of 1.5 kg = 0.022 x 1.5 kg = 0.033 kg

minimum mass = 1.5 kg - 0.033 kg = 1.467 kg

maximum mass = 1.5 kg + 0.033 kg = 1.533 kg

Thus, the minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The complete question is below:

what is the minimum and maximum mass of 1.5 kg if the uncertainty in measurement is 2.2%?

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Using the normal distribution, it is found that there is a 62.4% probability that a data value is between 37 and 41.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 38, \sigma = 2[/tex]

As a proportion, the probability that a data value is between 37 and 41 is the p-value of Z when X = 41 subtracted by the p-value of Z when X = 37, hence:

X = 41:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{41 - 38}{2}[/tex]

Z = 1.5

Z = 1.5 has a p-value of 0.933.

X = 37:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{37 - 38}{2}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.309.

0.933 - 0.309 = 0.624,

0.624 = 62.4% probability that a data value is between 37 and 41.

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Since the square root of

x=√x

and the cube root of

x=3√x

and their product

=√x × 3√x

= x1/2 × x1/3 [Since, n√a =a 1/n]

=x1/2+1/3 [Since, a^m ×a^n =a^m+n]

=x^3+2 /6

= x 5/6

Therefore, required product is

=√6x5

Answer:

[tex]x^2y^3[/tex]

Step-by-step explanation:

[tex]\text{Square of}~ x =x^2\\\\\text{Cube of}~ y = y^3\\\\\text{Product} = x^2y^3[/tex]

The closest among the choices is Choice C. $105.  Differences in amount may vary in the rounding off of the decimal numbers.

The complete question is given below as:-

Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses.

Card A

Card B

Amount

$1,879.58

$861.00

APR

14%

10%

Monthly Payment

$43.73

$18.29

After 5 years, how much will Marcia have saved in interest by consolidating the two balances?

a.

$1,526.40

b.

$2,422.80

c.

$105.00

d.

$227.40

The amount received by an employee by giving the service or work to any frim will be termed as the income.

Given:

Card A - 1,879.58 ; APR 14%; monthly -43.73

Card B -    861.00 ; APR 10% ; monthly -18.29

5 years x 12 months/yr = 60 months.

Card A = 43.73 x 60 = 2,623.80

Card B = 18.29 x 60 = 1,097.40

Total : 2,623.80 + 1,097.40 = 3,721.20

Lowest APR is 10%. monthly rate: 0.83%

Total Card balance: 1,879.58 + 861 = 2,740.58

A = P * (r(1+r)^n) / [(1+r)^n -1]

A = 2,740.58 * [0.0083 (1.0083)^60] / [(1.0083)^60 - 1]

A = 2,740.58 * 0.014/0.64

A = 2,740.58 * 0.022

A = 60.29 monthly payment.

60.29 x 60 = 3,617.40

Separate cards: 3,721.20

Consolidated:     3,617.40

Difference: 103.80

Therefore closest among the choices is Choice C. $105.  Differences in amount may vary in the rounding off of the decimal numbers.

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Answer:

A

Step-by-step explanation:

Pick any two sides....their sum must be greater than the third side....

  a+b > c

  a+c > b

  c + b > a

The two true statements are the second statement (both lines contain the point (0,0)) and the fourth statement (If the Wilson family buys 3 pizzas, they will get more slices than the Hernandez family).

First, we know that the Hernandez family orders 3 large pizzas, such that they cut each pizza in the same number of slices, getting a total of 24 slices.

Then the number of slices that they get for each pizza is:

24/3 = 8

So from each large pizza, they get 8 slices.

So the relation between the number of pizzas bought (x) and the number of slices (y) is:

y = 8*x

In the other hand for the Wilson family we have the relation:

y = 10*x

Where y and x are the same ones as the defined above.

Then the true statements are:

"If the Wilson family ordered 3 large pizzas from the same restaurant as the Hernandez family, they would have more slices than the Hernandez family after each family cut their pizzas into slices."

This is true because Wilson family cuts each pizza in 10 slices, while the Hernandez family cuts each pizza in 8 slices.

"For each family, a graph of the relationship between number of pizzas, x, and number of slices, y, goes through the point (0, 0) and is a straight line."

The point (0, 0) means that if they buy 0 pizzas, they get 0 slices, which is true, so both relations contain this point.

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Answer:

this is the answer I got hope it helps

The number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be 3.5 hours.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

David's phone battery level drops 6 percentage points each hour when he is not playing a game on it.

When David does play a game on his phone, the phone battery level drops 18 percentage points each hour.

On a particular day, the phone battery level was at 100 percentage points at 12:00 noon and at 22 percentage points at 6:00 P.M.

If David did not charge his phone during this time.

Then the number of hours he spent playing the game between 12:00 noon and 6:00 P.M. on that day will be

Let x be the number of no gaming hours and y be the number of gaming hours.

Then the equation will be

6x + 18y = 100 - 22

6x + 18y = 78

  x + 3y = 13 ...1

    x + y = 6 ...2

By solving the equations 1 and 2, we have

x = 2.5 hours and y = 3.5 hours

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Answer:

hope you can understand

The measure of center that will be used to emphasize the average height of the students is frequency of the numbers.

The average height of the students is calculated as follows;

Average = total height/number of students

total height = 135  + 130 + 170 + 170 + 160 + 90 = 855

Average = (855)/(6)

Average = 142.5 cm

From the given heights of the students, 170 cm has the highest frequency and will influence the average height more.

Thus, the measure of center that will be used to emphasize the average height of the students is frequency of the numbers.

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Based on the entries into the TVM solver, the expression that will return the same value for PV is [tex]\frac{(620) (( 1 + 0.066)^{108} - 1) }{(0.066) (1 + (0.066))^{108}}[/tex].

The formula for present value for this series of cashflows is:

= [tex]\frac{(Payment) (( 1 + Interest rate)^{Number of years} - 1) }{(Periodic interest) (1 + (Periodic interest))^{Number of years}}[/tex]

Based on the P/Y and the C/Y being 12, the number of periods given in the graphing calculator will be the same in the formula, which is 108 periods.

The interest rate of 6.6% will also be the same in the formula.

The best option is therefore option B which has all these figures and so will give the same present value.

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Answer: 0.0055 and 108

aka ($620) ((1+0.0055)^108 -1 / (0.0055) (1+0.0055)^108

Step-by-step explanation: Just did it, Good luck! :)

#1

Scale ratio

#2

Unknown is actual length

So the ratio is

#3

The proportion is

#4

Must be multiplied with 0.75

#5

Actual length is 7.5ft

Answer:

Question 1

Given scale:  1 in = 10 ft

[tex]\textsf{Therefore, the scale as a ratio}=\sf \dfrac{\boxed{10}\:ft}{\boxed{1}\:in}[/tex]

Question 2

The ratio of the garden's actual length to its length in the drawing:

[tex]\sf \dfrac{x\:ft}{0.75\:in}[/tex]

Question 3

Therefore, the proportion is:

[tex]\sf \dfrac{10\:ft}{1\:in}=\dfrac{x\:ft}{0.75\:in}[/tex]

Question 4

Multiply both sides of the proportion by 0.75 to find x

Question 5

[tex]\begin{aligned}\textsf{Proportion}: \quad \quad \;\sf \dfrac{10\:ft}{1\:in} & = \sf \dfrac{x\:ft}{0.75\:in}\\\\\textsf{Mulitply both sides by 0.75}: \quad \sf 0.75\cdot \dfrac{10}{1} & = \sf 0.75 \cdot \dfrac{x}{0.75}\\\\\textsf{Simplify}: \quad \quad \quad \sf 7.5 & = \sf x\end{aligned}[/tex]

Therefore, the actual length of the garden is 7.5 ft

By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.

In this question we know the quantity of coins in a box and such coins are part of the coin collection. By definition of percentage we have the total quantity of coins in the collection:

x = 10*(100/20)

x = 50

By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.

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Answer:

4 I promise

jhjhhhhjjj bug check txt TC gym c rectify txt

g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)

h(x) = f(x - ¹/₂) ------->  x-intercept at (1.5, 0)

j(x) = f(x) - ¹/₂ ------->  vertical asymptote at x = 0

m(x) = function decreases as x increases

We are given the function;

f(x) = In (x)

Now, from the given tiles and when we punch the respective values for the given functions, we can say that;

g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)

h(x) = f(x - ¹/₂) ------->  x-intercept at (1.5, 0)

j(x) = f(x) - ¹/₂ ------->  vertical asymptote at x = 0

m(x) = function decreases as x increases

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Answer: Hope this explains everything for you!

y= -2x+3

Step-by-step explanation:

y= 2x-1 is wrong

First, we will start by identifying the y-int, the y-int is when x is zero. The y-int is 3 since when x is 0, y is 3, (0,3).

y= 2x+3 (So that means -1 is actually 3)

Plus even if your slope is 2, since from the 2 points you go up 2 and run by 1, if you're not going to calculate it with 2 points, you need to see if its uphill, downhill, etc. (More info in the image below) The slope is actually negative meaning it is -2.

So the equation of the line is actually y= -2x+3