Coronary bypass surgery: A healthcare research agency reported that
41% of people who had coronary bypass surgery in 2008
were over the age of 65. Twelve coronary bypass patients are sampled.
Part 1 of 2
(a) What is the mean number of people over the age of 65 in a sample of 12
coronary bypass patients? Round the answer to two decimal places.
The mean number of people over the age of 65 is ?
Part 2 of 2
(b) What is the standard deviation of the number of people over the age of 65
in a sample of 12 coronary bypass patients? Round the answer to four decimal places.
The standard deviation of the number of people over the age of 65 is ?

This exponential function represents decay, as the base (0.93) is less than 1.

The percentage rate of decrease is 7%, as this is the difference between 1 and 0.93. Exponential decay occurs when the rate of change of a quantity is proportional to the quantity itself.

In this case, the quantity is Y, and the rate of change is 0.93. As the value of x increases, the value of Y decreases at a rate of 7%. This is because the base (0.93) is multiplied by Y each time x increases, resulting in a decrease in Y.

For example, if x = 1, then Y = 190(0.93) = 176.7. If x = 2, then Y = 190(0.93)^2 = 164.9. As x increases, Y decreases at a rate of 7%.

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Answer:

I think it is D.

Step-by-step explanation:

152-43=109

Answer:

C

Step-by-step explanation:

angle DEC=180-152=28

AB//DEF --> angle A=angle DEC = 28 (alternate angle)

angle B=angle D=43

angle DCE=180-43-28=109

angle ACB= angle DCE = 109 (vertical angle)

angle ACD=180-109 = 71

angle BCE-angle ACD = 71 (vertical angle)

Answer:

5:30 pm

Step-by-step explanation:

105/70 = 1.5

The required time consumed to burn the calories gained from the slice of pizza is 1.36 hr.

Given that,
A slice of pizza supplies 217 kcal (217 cal). if a person weighing 140 lb expends 80 kcal per mile when walking at 2.0 miles per hour.

here,
1 mile = 80 kcal used,
1 kcal used = 1/80 mile
217 kcal used = 217/80 mile = 2.71 miles
Now,
2 miles = 1 hour,
2.71 miles = 2.71/2 hours
2.71 miles = 1.36 hours

Thus, the required time consumed to burn the calories gained from the slice of pizza is 1.36 hr.

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We are told that Sarina's piano teacher gave her a large candy bar

The candy bar has 2 and 1/2 servings and one serving has a mass of 39 grams.

We wsnt to determine the mass of the whole candy bar.

The mass of the candy bar can be found to be equal to;

Therefore, we get the mass of the candy bar as;

Therefore, the mass of the candy bar is 97.5 grams

Answer:

  3

Step-by-step explanation:

The Roman numerals at left indicate generations I through III are shown on the chart. 3 generations are shown.

To differentiate the function f(x) = -x^(2/3) using first principles, we can use the difference of cubes formula.  To calculate the second derivative of f(x), we need to differentiate the function twice using the power rule.

(a) To differentiate f(x) = -x^(2/3) using first principles, we need to apply the difference of cubes formula:  

f'(x) = lim(h->0) [(-x^(2/3) - (-x)^(2/3)) / h]

By using the difference of cubes formula, we can simplify the expression:

f'(x) = lim(h->0) [(-x^(2/3) + x^(4/3) - x^(2/3)) / h]

= lim(h->0) [(x^(4/3) - 2x^(2/3)) / h]

Simplifying further and taking the limit as h approaches 0, we find the derivative of f(x) as:

f'(x) = 4/3 * x^(1/3)

(b) To calculate the second derivative of f(x), we differentiate f'(x) with respect to x using the power rule:

f''(x) = d/dx (4/3 * x^(1/3))

= 4/3 * (1/3) * x^(-2/3)

= 4/9 * x^(-2/3)

Therefore, the second derivative of f(x) is 4/9 * x^(-2/3).

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$56  is the least amount of additional money Sofia can spend to get the sushi they need

Two or more expressions with an Equal sign is called as Equation.

Sofia had ordered and paid for 24 pieces of sushi already and Sushi comes in rolls

Each roll=12 pieces at $8

Let r is additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces,

Unit rate of roll is 76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12×7=84 pieces

We know that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8×7

=$56

Hence, $56  is the least amount of additional money Sofia can spend to get the sushi they need

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Answer:

slope is 1

y = x + 2

Step-by-step explanation:

The probability of getting exactly 3 heads when a penny is flipped 9 times is approximately 0.1641.

The expression that represents the probability of getting exactly 3 heads when a penny is flipped 9 times is:

p(3 successes) = (9 C 3) * (0.5)^3 * (0.5)^(9-3)

Where:

"p(3 successes)" represents the probability of getting 3 heads.

"9 C 3" represents the number of ways to choose 3 flips out of 9 flips (also known as the binomial coefficient). This is calculated as 9! / (3! * (9-3)!), which simplifies to 84.

"0.5" represents the probability of getting heads on a single flip of a fair penny.

"(0.5)^(9-3)" represents the probability of getting tails on the remaining 6 flips, since the probability of getting either heads or tails on a single flip is 0.5.

Simplifying the expression, we get:

p(3 successes) = (9 C 3) * (0.5)^9

p(3 successes) = (84) * (0.5)^9

p(3 successes) ≈ 0.1641

Therefore, the probability of getting exactly 3 heads when a penny is flipped 9 times is approximately 0.1641.

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\(\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y) \\\\\\ \sin(x+y)=\sin(x)\left( \cfrac{\sqrt{2}}{2} \right)\cos(x)\left( \cfrac{\sqrt{2}}{2} \right) \\\\[-0.35em] ~\dotfill\\\\ \cos(y)=\sin(y)=\cfrac{\sqrt{2}}{2}\hspace{5em}\cos\left( \frac{\pi }{4} \right)=\sin\left( \frac{\pi }{4} \right)=\cfrac{\sqrt{2}}{2}\hspace{5em}y=\cfrac{\pi }{4}\)

Answer:

r= -1.2

Step-by-step explanation:

first use distributive property

- 3(4r - 8) = 36 - 2r

-12r +24 = 36-2r

+2r.           +2r

-10r +24= 36

-24.           -24

-10r = 12

/-10.     /-10

r= -1.2

Answer:

Step-by-step explanation:

Equation: -3(4r - 8) = 36 - 2r

Step 1:

-12r + 24 = 36 - 2r       Multiply (4r - 8) by -3 using the Distributive Property.

Step 2:

-10r + 24 = 36        Add -12r and -2r by 2r.

Step 3:

-10r = 12        Subtract 24 and 36 by 24.

Step 4:

r = -12/10          Divide both sides by -10

Step 5:

r = -6/5           Simplify the fraction.

The recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

We can use the method of finite differences to find a possible recursive formula for this sequence.

First, let's compute the first few differences:

f(4) - f(1) = 6

f(7) - f(4) = 6

Since the second differences are zero, we can assume that the sequence is a quadratic sequence. Let's write it in the form f(n) = an^2 + bn + c. We can solve for the coefficients using the given values:

f(1) = a(1)^2 + b(1) + c = 6

f(4) = a(4)^2 + b(4) + c = 12

f(7) = a(7)^2 + b(7) + c = 18

Solving for a, b, and c, we get:

a = 1

b = 5

c = 0

Therefore, the recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.

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Answer:

B

Step-by-step explanation:

y = \(\frac{1}{4}\) is the equation of a horizontal line parallel to the x- axis.

A line perpendicular to it will be a vertical line parallel to the y- axis with equation

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (- 6, - 9 ) with equation

x = - 6 → B

Answer:

B

Step-by-step explanation:

i just looked at the question and knew, its pretty easy

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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The density of glycerin at 60°C is approximately 19.9592 g/cm³.

To find the density of glycerin at 60°C, we can use the volume expansion coefficient and the given density at 20°C.

The formula for volume expansion is:

ΔV = β * V₀ * ΔT

where:

ΔV is the change in volume,

β is the volume expansion coefficient,

V₀ is the initial volume, and

ΔT is the change in temperature.

In this case, we want to find the change in density, so we can rewrite the formula as:

Δρ = -β * ρ₀ * ΔT

where:

Δρ is the change in density,

β is the volume expansion coefficient,

ρ₀ is the initial density, and

ΔT is the change in temperature.

Given:

ρ₀ = 20 g/cm³ (density at 20°C)

β = 5.1 x 10⁻⁴ °C⁻¹ (volume expansion coefficient)

ΔT = 60°C - 20°C = 40°C (change in temperature)

Substituting the values into the formula, we have:

Δρ = - (5.1 x 10⁻⁴ °C⁻¹) * (20 g/cm³) * (40°C)

Calculating the expression:

Δρ = - (5.1 x 10⁻⁴) * (20) * (40) g/cm³

≈ - 0.0408 g/cm³

To find the density at 60°C, we add the change in density to the initial density:

ρ = ρ₀ + Δρ

= 20 g/cm³ + (-0.0408 g/cm³)

≈ 19.9592 g/cm³

Therefore, the density of glycerin at 60°C is approximately 19.9592 g/cm³.

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Answer:

there was a total of 954 people at the pool

Step-by-step explanation:

Answer: 246

Step-by-step explanation:

One way to solve 2(a - 1.1) = 5.8 is divide both sides by 2 and then add 1.1 on both sides to find a = 4.

To solve 5/2 b - 2 3/4= 7 1/4, add 2 3/4 on both sides, and then multiply both sides by 2/5 to find b = 4.4

In the equation a and b divide the same value.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given equation is

2(a - 1.1) = 5.8

divide both sides by 2

a - 1.1 = 5.8/2

a - 1.1 = 2.9

Add 1.1 on both sides:

a - 1.1 + 1.1 = 2.9 + 1.1

a = 4.

Another equation is

5/2 b - 2 3/4= 7 1/4

add 2 3/4 on both sides:

5/2 b= 7 1/4 + 2 3/4

Convert the mixed fraction to improper fraction:

5/2 b  = 29/4 + 15/4

5/2 b  = 44/4

Multiply both sides by 2/5:

b = (44/4) × (2/5)

b = 11× (2/5)

b = 22/5

b = 4.4

Both number 4 a and 4.4 is divisible by 4.

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The design that resulted in the shortest line is the one that minimized the distance between the start and end points.

This can be achieved by using a straight line design, as it is the shortest distance between two points. In other words, the shortest line design is the one that does not have any curves or detours, and instead goes directly from the start point to the end point. This is because the shortest distance between two points is always a straight line, and any other design would result in a longer line. Therefore, the design that resulted in the shortest line is the one that used a straight line.

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Answer:

lost 120

Step-by-step explanation:

10% of 1200 is 120 so you subtract 120 from 1200

Answer:

120

Step-by-step explanation:

Loss = (Loss%)(C.P)

Loss = (10%)(1200)

Loss = (10/100)(1200)

Loss = 120

the base of the triangular window is 24 feet and the height is 10 feet.

Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.

The formula to calculate the area of a triangle is:

Area = (1/2) × base × height

In this case, we can write the equation as:

120 = (1/2) × base × h

Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:

base = 2h + 4

Substituting this expression for the base into the area equation, we have:

120 = (1/2) × (2h + 4) × h

Now we can solve this equation for the height.

Multiplying both sides of the equation by 2 to remove the fraction:

240 = (2h + 4) × h

Expanding the right-hand side:

240 = 2h² + 4h

Rearranging the equation and setting it equal to zero:

2h² + 4h - 240 = 0

Now we can solve this quadratic equation. Factoring out a 2:

2(h² + 2h - 120) = 0

Factoring the quadratic expression inside the parentheses:

2(h + 12)(h - 10) = 0

Setting each factor equal to zero:

h + 12 = 0   or   h - 10 = 0

Solving these equations, we get:

h = -12   or   h = 10

Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.

Substituting the height value back into the expression for the base:

base = 2h + 4

    = 2(10) + 4

    = 20 + 4

    = 24

Therefore, the base of the triangular window is 24 feet and the height is 10 feet.

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Answer:

29 times

Step-by-step explanation:

Given :

Society X ;

Population = 100

Number of facts known = 10

Average fact known per person = known fact / population = 10 / 100 = 0.1

Society X:

Population = 19

Common fact known by 9 = 5

Specialized fact, known by 10 = 5 * 10 = 50

Total facts = common + specialized = 55

Average fact known per person = 55 / 19 = 2.8947368 fact per person

Number of times society Z is better :

2.8947368 / 0.1 = 28.947 times

Approximately 29 times

Answer:

V≈3310.94ft³

Step-by-step explanation:

explanation is in screenshot.

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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After the hurricane and the disease, 48% of the original population of rats is left.

We have,

After the hurricane, 40% of the rats were wiped out, which means

100% - 40% = 60% of the rats survived.

Then, after the disease spread through stagnant water, 20% of the remaining rats were killed.

This means 100% - 20% = 80% of the rats that survived the hurricane are still left.

To find the percentage of the original population of rats that is left after both events, we multiply the percentages:

Percentage left = 60% * 80% = 0.6 * 0.8 = 0.48

Finally, we convert the decimal value back to a percentage:

Percentage left = 0.48 * 100% = 48%

Therefore,

After the hurricane and the disease, 48% of the original population of rats is left.

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Answer:

the answer is 45

Step-by-step explanation:

12/20 is 3/5. this is the probability.

then, we multiple with 75

3/5 × 75 =45

no solution xd

x=5

x/3=5 => x=15

x=5 x=15 contradicts

Answer:

A square pyramid is composed of an eight-sided square base, four triangular sides, five vertices, and five vertices. This pyramid has a square base with a peak at the top. The fact that a square pyramid is a polyhedron was noted.

Step-by-step explanation:

The three-dimensional geometric shape of a square pyramid has a square base and four triangular sides that are joined at the vertex. Five facets make up its polyhedron shape (pentahedron). Four triangles joined at the vertex and a square base make up a square pyramid. Three sides, a square base, and a central vertex characterize the triangle side faces. The tallest point of the pyramid is known as its "apex." The base is represented by the bottom square. Faces are the three triangular vertices of the triangle. When viewed from the bottom up, a pentahedron is a five-sided, three-dimensional shape that resembles a square pyramid.