a baseball diamond is a square with sides of 90 feet. what is the shortest distance ,to the nearest tenth of a foot, between first base and third base?

ok, let's assume the rate is 0.075 per minute, if we convert that to percentage that'd be 0.075*100 or 7.5% per minute, so we can assume the bread is cooling off at 7.5% per minute after coming out of the oven at 340°F and we need it at 80°F so we can slice it and put some butter on it.

now, we can look at this from a Decay standpoint and say

we have a temperature of 340°F, decaying at 7.5% per minute, how long before it turns into 80°F?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 80\\ P=\textit{initial amount}\dotfill &340\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=minutes \end{cases}[/tex]

[tex]80 = 340(1 - 0.075)^{t}\implies \cfrac{80}{340}= 0.925^t\implies \cfrac{4}{17}=0.925^t \\\\\\ \log\left( \cfrac{4}{17} \right)=\log(0.925^t)\implies \log\left( \cfrac{4}{17} \right)=t\log(0.925) \\\\\\ \cfrac{ ~~ \log\left( \frac{4}{17} \right) ~~ }{\log(0.925)}=t\implies 18.56\approx t\qquad \textit{almost 19 minutes}[/tex]

The distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles. Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).

1. Find the distance from the satellite to the points of tangency Solution: Firstly, we need to draw a rough diagram of the scenario to easily understand it. Consider a satellite revolving around an alien planet in a synchronous orbit 18,000 miles above its surface.

We can see that B and D are the points of tangency of the satellite signal with the planet, and C is the center of the planet. Hence, the figure will look like the following: Image Source: Synchronous Orbit - Wikimedia Commons Now, we need to find the distance from the satellite to the points of tangency.

Hence, the distance from the satellite to the points of tangency, B and D, is 61861.9 miles (approximately 61862 miles).2. Find the percentage of the planet's equator within range of the satellite's signal Solution: We can see that the planet's equator can be represented by a circle with a radius of 3500 miles. Hence, the circumference of the circle would be 2π × 3500 miles ≈ 21991.5 miles.

We know that the satellite's signal can be received directly up to a distance of 61862 miles from it. Hence, the length of the portion of the equator within range of the satellite's signal would be twice the distance from the satellite to the point of tangency, which is 2 × 61862 ≈ 123724 miles. Now, we need to find the percentage of the planet's equator within range of the satellite's signal.

Hence, we need to find the time taken for the satellite signal to reach points B and E. We can see that the distance from the satellite to point B is 61862 miles and the distance from the satellite to point E is 3500 miles. Hence, the time taken for the satellite signal to reach point B would be: Time taken to reach point B = Distance / Speed = 61862 / 186000 ≈ 0.332 seconds Now, we need to find the time taken for the satellite signal to reach point E.

Hence, the time difference between the satellite signal reaching points B and E is approximately 0.07 seconds.4. Find the speed of the satellite Solution: We know that the satellite takes 36 hours to complete one revolution around the planet along with the point directly below it on the planet's surface. Hence, we need to find the distance travelled by the satellite in 36 hours to find its speed.

We can see that the distance travelled by the satellite in one revolution is equal to the circumference of the circle with a radius of 3500 miles, which is 2π × 3500 miles ≈ 21991.5 miles. Hence, the distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles.

Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).

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Answer:

The Answer to This question Is x + 5 So Basically 5

Answer:

96π

Step-by-step explanation:

the shape is made up of a cylinder and a cone.

Volume of cylinder = π r ² h

= π (3)² (9)

= 81π.

Volume of cone = (1/3) X vertical height X π r ²

= (1/3) (5) π (3)²

= 15π

volume of composite solid = 81π + 15π = 96π

There are 1440 minutes in a day (24 hours x 60 minutes = 1440 minutes).

To convert 4320 minutes to days, divide 4320 by 1440:

4320 ÷ 1440 = 3

Therefore, 4320 minutes is equivalent to 3 days.

Answer: 3 days

Step-by-step explanation:

Answer:

[tex]3.23*10^{16}[/tex]

Step-by-step explanation:

Just multiply. You have to do:

[tex](1.12*10^7)*(2.88*10^9)\\=3.23*10^{16}[/tex]

Answer:

D

Step-by-step explanation:

3.6 years will have passed when 115 grams of thorium 234 is left.

(a) To find the amount of thorium 234 left after 0.5 years, we can substitute t = 0.5 and A0 = 1000 into the given equation and solve for At:

[tex]A_t = A0e^{(-10.498t)}\\\\A_t = 1000e^{(-10.498(0.5))}\\\\A_t = 679.6\ grams[/tex]

Therefore, approximately 679.6 grams of thorium 234 will be left after 0.5 years.

(b) To find when 115 grams of thorium 234 will be left, we can set At = 115 in the given equation and solve for t:

[tex]A_t = A_0e^{-10.498t}\\\\115 = 1000e^{-10.498t}\\\\ln(115/1000) = -10.498t\\\\t = 3.6\ years[/tex]

Therefore, approximately 3.6 years will have passed when 115 grams of thorium 234 is left.

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Answer:

3/10

Step-by-step explanation:

7/10 – 2/5

=7/10 – 4/10

=(7–4)/10

=3/10

Answer:

0.3

Step-by-step explanation:

The monthly cost for 56 minutes of calls is given as follows:

$18.05.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

For 38 minutes of call, the price increases by $4.94, hence the slope of the linear function, representing the cost per minute, is given as follows:

m = 4.94/38

m = 0.13.

56 minutes is 30 minutes less than 86 minutes, hence the cost is given as follows:

C(56) = 21.95 - 30 x 0.13

C(56) = $18.05.

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The term (x - 1) is a factor of both of the given polynomials:

x² + x - 2

2x² - 5x + 3

If (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:

p(a) =0.

So, if x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.

a) x² + x - 2

Evaluate it in x = 1.

1² + 1 - 2 = 0

it is zero, so (x - 1) is a factor.

b) 2x² - 5x + 3

Evaluating this in x = 1.

2*1² - 5*1 + 3

2 - 5 + 3 = 0

(x - 1) is a factor.

Then the correct option is the last one, it is a factor of both polynomials.

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Step-by-step explanation:

Part A:

To find the composite function, we need to plug in the expression for s(w) into f(s):

f(s(w)) = 2s(w) + 30

= 2(40w) + 30

= 80w + 30

Therefore, the composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is f(s(w)) = 80w + 30.

Part B:

The units of measurement for the function f(s(w)) are the same as the units of measurement for f(s) and s(w). From the given information, we know that s(w) represents the number of seeds planted per week and f(s) represents the number of flowers bloomed based on the number of seeds planted. Thus, the units of measurement for f(s(w)) are "flowers" per week.

Part C:

To evaluate the composite function f(s(w)) for 35 weeks, we need to substitute w = 35 into the expression we found in Part A:

f(s(35)) = 80(35) + 30

= 2,830

Therefore, Lily can expect 2,830 flowers to bloom after planting 40 seeds per week for 35 weeks.

Answer: c

Step-by-step explanation:

i took the test

Your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.

Since the final exam counts for 15% of the course grade, the weighted average can be calculated as follows:

Weighted average = (0.85 × 80%) + (0.15 × final exam score)

If we assume that your friend wants to get the highest possible grade, then they would need to get a perfect score on the final exam, which would be 100%.

Plugging this into the equation above, we get:

Weighted average = (0.85 × 80%) + (0.15 × 100%) = 83%

Therefore, the best course grade your friend can earn is 83%.

We can set up an equation where x is the minimum score needed on the final exam:

Weighted average = (0.85 × 80%) + (0.15 × x) = 75%

Simplifying this equation, we get:

0.85 × 80% + 0.15x = 75%

68% + 0.15x = 75%

0.15x = 7%

x = 46.67%

Therefore, your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.

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The total cash due at signing is $3800.

Option A is the correct answer.

We have,

The total cash due at signing is the sum of the down payment, security deposit, acquisition fee, and the first month's lease payment.

So,

Down payment = $2500

Security deposit = $375

Acquisition fee = $500

First month's lease payment = $425

The total cash due at signing is:

= $2500 + $375 + $500 + $425

= $3800

Thus,

The total cash due at signing is $3800.

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Answer:

[tex]f(x) = (x - 4)(x + 3) [/tex]

[tex]f(x) = {x}^{2} - x - 12[/tex]

About 71 members of the group are expected to be between 51 years old and 59 years old.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:

68%.

Out of 104 people, the number of people with ages in the range is given as follows:

0.68 x 104 = 71 people. (rounded to the nearest integer).

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Answer:

LN and NK

Step-by-step explanation:

A perpendicular bisector of a line segment divides the line segment into 2 equal halves.

Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.

The two equal halves are segment LN and segment NK.

Therefore, segment LN is congruent to segment NK.

The surface area of the prism given is 362 m².

Given is a prism.

We have to find the total surface area of the prism.

The given prism has to be divided in to various other known figures to find the total area.

By drawing a line vertically through the top of the prism, we get two rectangular prism.

Surface area of a rectangular prism = 2 [lw + wh + lh], where l, w and h are length, width and height respectively.

Surface area of big rectangular prism = 2[(6 × 6) + (6 × 7) + (6 × 7)]

                                                               = 240 m²

Surface area of smaller rectangular prism = 2[(3 × 4) + (4 × 7) + (3 × 7)]

                                                                      = 122 m²

Total area of the prism = 240 m² +  122 m²

                                      = 362 m²

Hence the surface area is 362 m².

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Answer:

4π cm

Step-by-step explanation:

A minute hand travels a full revolution along a circular path in 60 minutes

The distance from the center to the tip of the minute hand = 8 cm

We can consider the movement of the minute hand as being on the circumference of  a circle with radius = 8 cm

Circumference = 2π · r

=  2π · 8

= 16π

I5 minutes = 15/60 = 1/4th

So in 15 minutes the minute hand will cover only 1/4th of the full circle

Therefore distance traveled by tip of minute hand

= 1/4 x 16π = 4π cm

The mixed fraction expression 2³/₄ can be rewritten as: ⁴/₄ + ⁴/₄ + ³/₄

There are different fractions such as mixed fraction, improper fraction, proper fraction e.t.c.

Now, we are given the fraction as an improper fraction in the form of 2³₄.

Rewriting as a whole number and a fraction gives:

2 + ³/₄

Breaking down the whole number into a fraction is done as:

1 + 1 + ³/₄

= ⁴/₄ + ⁴/₄ + ³/₄

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The reason for not applying method of addition and subtraction on first and third term shown below.

The reason why the method of addition and subtraction cannot always be applied to convert a trinomial with exact roots in the first and third terms into a perfect square trinomial is because the second term may not be a perfect square or a multiple of the square root of the first term multiplied by the square root of the third term.

In order to convert a trinomial into a perfect square trinomial using the method of addition and subtraction, the coefficient of the second term must be twice the product of the square root of the first term and the square root of the third term. If this condition is not met, the trinomial cannot be transformed into a perfect square trinomial using this method.

Therefore, it is important to consider the coefficients and terms of the trinomial to determine if the method of addition and subtraction can be applied successfully.

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Answer:

x-intercept = -7

y-intercept = 1

rate of change = 1.25

Step-by-step explanation:

X and Y intercept are pretty to find.

Rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

So for our case it will be [tex]\frac{-0.75-(-2)}{-8-(-9)}[/tex]

The answer will be 1.25

The probability of the point being in region A is 0.5294.

The area of the entire figure can be found by adding the areas of the four triangles:

Area of entire figure

= Area of triangle ABC + Area of triangle ACD + Area of triangle ABD + Area of triangle BCD

= (1/2)(5)(3) + (1/2)(3)(4) + (1/2)(4)(3) + (1/2)(3)(4)

= 7.5 + 6 + 6 + 6

= 25.5 square inches

Similarly, the area of region A can be found by adding the areas of triangles ABC and ABD:

Area of region A

= Area of triangle ABC + Area of triangle ABD

= (1/2)(5)(3) + (1/2)(4)(3)

= 7.5 + 6

= 13.5 square inches

Therefore, the probability of the point being in region A is:

P(A) = Area of region A / Area of entire figure

P(A) = 13.5 / 25.5

P(A) = 0.5294

So the probability of the point being in region A is 0.5294.

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The surface area of the cylinder is 603.19 square meters

From the question, we have the following parameters that can be used in our computation:

Radius, r = 8 meters

Height, h = 4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 8 * (8 + 4)

Evaluate

Surface area = 603.19

Hence, the surface area is 603.19 square meters

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The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Answer:

7c1 is an algebraic expression that evaluates to 47. The expression is made up of two terms, 7 and c1. The letter c is a variable and the number 1 represents the exponent of the variable. Therefore, 7 multiplied by the c to the power of 1 is equal to 7 times c, which is equal to 47.

6p4 is an algebraic expression that evaluates to 6,040. The expression is made up of two terms, 6 and p4. The letter p is a variable and the number 4 represents the exponent of the variable. Therefore, 6 multiplied by the p to the power of 4 is equal to 6 times p to the fourth power, which is equal to 6,040.

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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The total area that needs to be covered which is indicated by the shaded area would be =220ft²

To calculate the area that needs to be covered, the formula that should be used is the formula for the area of a rectangle which is given below as follows;

Area of rectangule =2( length×width)

where ;

length = 22ft

width = 5ft

area = 2× 22×5

= 220ft²

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