The length between the bases on a baseball field is 90 feet. A scale drawing shows the distance between the bases are 2 1/5 inches. one inch on this drawing equals how many feet?

Answer:

ok

Step-by-step explanation:

Answer:

  n = 7

Step-by-step explanation:

You have a geometric sequence with first term 625 and common ratio 1/5, and you want to know the number of the term whose value is 1/25.

The general term of a geometric sequence is ...

  tn = t1·r^(n-1)

Using the given values, we can solve for n:

  1/25 = 625·(1/5)^(n-1)

  1/(5^2·5^4) = 1/5^(n-1) . . . . . . divide by 625; write as powers of 5

Comparing exponents of 5, we have ...

  6 = n -1

  7 = n

The value of n for which tn = 1/25 is 7.

__

Additional comment

The attachment shows the first 7 terms of the sequence.

<96141404393>

The volume we're looking for is the volume of both cones in the figure.

The volume of a cone is  \(V=\pi r^2\frac{h}{3}\) .

So, \(V_{tot} = V_{1} + V_2\) .

Cone 1's variables:

r = 2.6

h = 5

Cone 2's variables:

r = 2.6

h = 3

Now we can just plug and chug!

\(V_{tot} = [(3.14)(2.6^2)(\frac{5}{3} )] + [(3.14)(2.6^2)\frac{3}{3} )]\\V_{tot} = [(3.14)(6.76)(1.67)] + [(3.14)(6.76)(1)]\\V_{tot} = (35.45) + (21.23)\\V_{tot} = 56.68\)

V = c. 56.6 cubic units

The value of the given expression 3 x 2,746 is 8,238.

We are given the expression:-

3 x 2,746

We have to find the value of the given expression using place value.

According to the data given in the question, we can write,

In 2746,

The place value of 6 is 6

The place value of 4 is 4*10 = 40

The place value of 7 is 7*100 = 700

The place value of 2 is 2*1000 = 2000

Hence, we can write,

3*2746 = 3*2000 + 3*700 + 3*40 + 3*6 = 6000 + 2100 + 120 + 18 = 8,238.

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Answer:208

Step-by-step explanation:

The probability that an adult sampled at random will weigh between 136 pounds and 164 pounds can be calculated using the properties of the normal distribution.

To find the probability, we need to calculate the area under the normal curve between the two weight values. We can convert the given weights into z-scores (standardized scores) using the formula:

z = (x - μ) / σ

where x is the given weight, μ is the mean weight, and σ is the standard deviation.

For the lower weight value of 136 pounds:

z1 = (136 - 146) / 12.7 = -0.79

For the upper weight value of 164 pounds:

z2 = (164 - 146) / 12.7 = 1.42

Now, we can look up the corresponding z-scores in the standard normal distribution table or use a calculator to find the area under the curve between these z-scores. The probability is equal to the difference between these two areas.

Using a standard normal distribution table or calculator, we find the area to the left of z1 (0.2139) and the area to the left of z2 (0.9236). Therefore, the probability of an adult weighing between 136 and 164 pounds is:

P(136 < x < 164) = P(-0.79 < z < 1.42) = P(z < 1.42) - P(z < -0.79) = 0.9236 - 0.2139 = 0.7097

The probability that an adult sampled at random will weigh between 136 and 164 pounds is approximately 0.7097 or 70.97%. This means that there is a 70.97% chance of randomly selecting an adult whose weight falls within this range in the town of Metaluna, assuming the weights follow a normal distribution with a mean of 146 pounds and a standard deviation of 12.7 pounds.

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The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

they would have to pay $80.22

Answer:

470 cm³

Step-by-step explanation:

Volume of rectangular prism = width × length × height

⇒ Volume of whole rectangular prism = 9 cm × 10 cm × 8 cm

                                                                = 720 cm³

Side lengths of the missing piece:

⇒ Volume of the missing piece = 5 cm × 10 cm × 5 cm

                                                    = 250 cm³

⇒ Volume of irregular figure = 720 cm³ - 250 cm³

                                                = 470 cm³

The measure of angle QRS is 46 degrees.

First, let us understand the like terms;

Like terms in algebra are terms that have the same variables and powers. The coefficients do not have to be the same.

We are given;

Angle PRS = 98 degrees

Angle PRQ = (3x - 8) degrees

Angle QRS = (2x + 6) degrees

Also, the sum of angle PRQ and angle QRS is 98 degrees.

So,

(2x + 6) + (3x - 8) = 98 degrees

Combine like terms.

5x - 2 = 98 degrees

5x = 100 degrees

x = 20 degrees

Put the value of the x into the expressions for the given angle measures.

Angle QRS = 2x + 6 = 2(20) + 6 = 46 degrees

Angle PRQ = 3x - 8 = 3(20) - 8 = 52 degrees

Thus, the measure of angle QRS is 46 degrees.

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a) The mean income to 2 DP is £23714.28. b. If Deva's income is excluded, then the mean income will be £16,500.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

a.

Andy = £9500

Bevan = £25000

Cheryl = £11250

Elliott = £12750

Frankie = £29500

Grace = £11000

Deva = £72000

Total Income = £166,000

To get the mean Income, we will divide the total income by 6 which is the number of people.

= £166,000/7

= £23714.28

b. If Deva's income is excluded, there'll be 6 people left.

Total income = £99000

Mean income = £99,000/6

= £16,500

a) The mean income to 2 DP is £23714.28. b. If Deva's income is excluded, then the mean income will be £16,500.

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The area of the rhombus is approximately 112.5 square centimeters.

In a rhombus, all internal angles are equal, so we know that the opposite angles are congruent.

Additionally, the diagonals of a rhombus bisect each other at right angles, forming four congruent right triangles.

Let's denote the length of one diagonal as 15 cm, and the lengths of the sides of the rhombus as a.

Using the Pythagorean theorem, we can find the length of the other diagonal.

Let's label it as d.

In each right triangle, the hypotenuse is the length of a side, which is a, and one leg is half the length of the diagonal, which is 15/2 = 7.5 cm.

Applying the Pythagorean theorem, we have:

a² = (7.5)² + (7.5)²

a² = 56.25 + 56.25

a² = 112.5

a = √112.5

a ≈ 10.61 cm

Thus, the length of each side of the rhombus is approximately 10.61 cm.

Since the diagonals of a rhombus are perpendicular bisectors of each other, the other diagonal (d) is equal to the square root of the sum of the squares of the two sides.

Hence:

d² = a² + a²

d² = 2a²

d = √(2a²)

d = √(2 \(\times\) 10.61²)

d ≈ √(2 \(\times\) 112.5)

d ≈ √225

d ≈ 15 cm

So, the length of the other diagonal is approximately 15 cm.

To find the area of the rhombus, we can use the formula:

Area = (diagonal₁ \(\times\) diagonal₂) / 2

Substituting the values, we get:

Area = (15 \(\times\) 15) / 2

Area = 225 / 2

Area = 112.5 cm²

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The number of significant figures for each given value is as follows: 0.098200 has 5 significant figures, 1.68×10^4 has 3 significant figures, 78,000,120 has 9 significant figures, and 1.008 has 4 significant figures.

Significant figures represent the precision and accuracy of a number. They include all the digits that carry meaning in a measurement or calculation. In the case of 0.098200, all the digits are non-zero and are considered significant. Therefore, it has 5 significant figures.

For 1.68×10^4, the number is written in scientific notation. The digits before the multiplication sign represent the significand, which in this case is 1.68. The exponent of 10 indicates the number of places the decimal point is moved to obtain the actual value. In this case, it is 4, which means the decimal point is moved four places to the right. The significand, 1.68, has three significant figures, and the exponent of 10 does not affect the significant figures. Therefore, the value has 3 significant figures.

In 78,000,120, the zeros are considered significant because they are between nonzero digits. Hence, all the digits contribute to the significant figures, resulting in 9 significant figures.

Lastly, for 1.008, the trailing zero after the decimal point is significant, as it indicates precision. Therefore, it has 4 significant figures.

In summary, the number of significant figures for each given value is 0.098200 with 5 significant figures, 1.68×10^4 with 3 significant figures, 78,000,120 with 9 significant figures, and 1.008 with 4 significant figures.

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Answer:

40

Step-by-step explanation:

x is being multiplied by 8 to get y

so 5 x 8 = 40

The original price of the ski jacket is $184.

What is price?

The sum of money paid or the amount of compensation offered by one party to another in exchange for goods or services is known as a price. The cost of production can take on different names depending on the circumstance. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price".

Given:

Paula bought a ski jacket on sale for $8 less than half its original price.

She paid $84 for the jacket.

We have to find the original price of the ski jacket.

Let

The original price = x

The amount she bought it = x/2 - 8

She paid $84 for the jacket

Therefore,

84 = x/2 - 8

Add 8 on both sides,

84 + 8 = x/2 - 8 + 8

92 = x/2

x = 184

Hence, the original price of the ski jacket is $184.

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========================================================

Explanation:

We're given f(1) = 3.2 which says the first term of the sequence is 3.2

To find the second term, we use the other equation, which is the recursive equation. Plug in x = 1 to get...

f(x+1) = 2.5*f(x)

f(1+1) = 2.5*f(1)

f(2) = 2.5*f(1)

f(2) = 2.5*3.2

f(2) = 8

The second term is 8. We multiplied the previous term (3.2) by the factor 2.5 to get this second term.

The third term is handled pretty much in a similar fashion

third term = 2.5*(second term)

third term = 2.5*8

third term = 20

Lastly, the fourth term f(4) is...

f(x+1) = 2.5*f(x)

f(3+1) = 2.5*f(3)

f(4) = 2.5*f(3)

f(4) = 2.5*20

f(4) = 50

The fourth term is 50.

The first four terms are: 3.2, 8, 20, 50

The diameter of the circular plate is 16.3 inches (rounded to the nearest tenth of an inch).

The given figure can be visualized as a circle with two perpendicular chords of length 7 inches each.

The chords are bisected perpendicularly by two segments passing through the center, each of length 6 inches.

Now, we have to find the diameter of the circular plate.

To find the diameter, we have to draw a perpendicular line to the center from one of the endpoints of a chord.

This will give us a right triangle with one side as 3 inches (half of the length of the chord) and the hypotenuse as the radius of the circle.

Using Pythagoras theorem, we get:

r² = 3² + 6² = 45r = √45 = 3√5 inches

Since the radius is 3√5 inches, the diameter is 6√5 inches.

To get the value of the diameter to the nearest tenth of an inch, we substitute 3.16 for √5.

Therefore, the diameter of the circular plate is:

Diameter = 6(3.16) = 18.96 inches ≈ 16.3 inches (rounded to the nearest tenth of an inch).

Thus, the diameter of the circular plate is 16.3 inches (rounded to the nearest tenth of an inch).

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Answer:

B

Step-by-step explanation:

For every 7 boxes the market also sells 6 cans; therefore 13 cans and boxes are being sold.
If 26 cans and boxes were sold in total today, then 26/13 = 2
this means 2 of the 6 cans and 7 boxes;
2x6=12 cans
2x7=14 boxes
Therefore, the market sold 12 cans and 14 boxes today

Answer:

B.  12 cans and 14 boxes

Step-by-step explanation:

To calculate how many cans and boxes of food the market sold, set up and solve a system of equations.

Let "x" be the number of cans of food the market sold.

Let "y" be the number of boxes of food the market sold.

According to the given information, we know that the ratio of cans to boxes is 6 : 7. Therefore:

\(x :y=6:7\)

   \(\dfrac{x}{y}=\dfrac{6}{7}\)

  \(7x=6y\)

As the total number of cans and boxes sold is 26, this can be expressed as x + y = 26.

Therefore, the system of equations that models the given scenario is:

\(\begin{cases}7x=6y\\x + y = 26\end{cases}\)

To solve the system of equations, use the method of substitution.

Rearrange the second equation to isolate y:

\(y=26-x\)

Substitute this into the first equation to eliminate the term in y, and solve for x:

\(7x=6(26-x)\)

\(7x=156-6x\)

\(7x+6x=156-6x+6x\)

\(13x=156\)

\(13x \div 13=156 \div 13\)

\(x=12\)

Substitute the found value of x into the rearranged equation and solve for y:

\(y=26-12\)

\(y=14\)

Therefore, the market sold 12 cans and 14 boxes of food.

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The exact value of the expression \(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16\ is\ (2 + \sqrt2)/4\).

We can use the following trigonometric  identity:

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

We have:

\(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16 \\= cos(3\pi /16 - \pi /16) \\= cos \pi /8\)

Now, using the half-angle identity \(cos(\theta/2) = ^+_-\sqrt{[(1 + cos \theta)/2]\), we can simplify cos π/8:

\(cos \pi /8 \\= cos(\pi /4 - \pi /8) \\= cos \pi /4\ cos \pi /8 + sin \pi /4\ sin \pi /8 \\= 1/\sqrt{2} \times \sqrt{[(1 + cos \pi /4)/2]} + 1/\sqrt{2} \times \sqrt{[(1 - cos \pi /4)/2]} \\= 1/\sqrt{2} \times \sqrt{[(1 + 1/\sqrt{2})/2]} + 1/\sqrt{2} \times \sqrt{[(1 - 1/\sqrt{2})/2] }\)

\(= 1/\sqrt{2} \times \sqrt{[(2 + \sqrt{2})/4] }+ 1/\sqrt{2} \times \sqrt{[(2 - \sqrt{2})/4]} \\= 1/2 \times \sqrt{(2 + \sqrt{2})} + 1/2 \times \sqrt{(2 - \sqrt{2})} \\= \sqrt{2}/2 + \sqrt{2}/2\sqrt{2} + \sqrt{2}/2 - \sqrt{2}/2\sqrt{2} \\= \sqrt{2}/2 + \sqrt{2}/4 \\= (2 + \sqrt{2})/4\)

Therefore, the exact value of the expression \(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16\ is\ (2 + \sqrt2)/4\).

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Answer:

OK

Step-by-step explanation:

To solve for C let us do these steps

1. Put the term of C on one side and the other terms on the other side

Subtract 32 from both sides to move the term 32 to the other side

2. Make the coefficient of C = 1

Divide both sides by 9/5

You can Multiply the bracket (F- 32) by 5/9

Answer:

Parallelogram and rectangle

Step-by-step explanation:

Answer:

parallelogram and rectangle

Answer:

5s^2 - 4s - 12

Step-by-step explanation:

Answer:

5s^2+4-12

Step-by-step explanation:

Answer:

Your answer is 9x^6*y^2π

Step-by-step explanation:

The formula for a circle is πr^2, with r as the radius.

Since 3x^3*y is the radius, you put that value in to get the equation:

(3x^3*y)^2*π

Once simplified, you get 9x^6*y^2π.

You can simplify further using the value of π, but it depends if the questions wants you to or not, mostly it doesn't.

I hope this was helpful.

Answer:          1/2

If 2 students are drinking punch

and 2 are drinking lemonade that would mean it would be 2/4

but if you were to simplify by dividing both by 2

it would be 1/2.

Answer:

the 4th one

Step-by-step explanation:

it shows that k is greater than 11

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

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

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)