many people have asked the question, but few have been patient enough to collect the data. how many licks does it take to get to the center of a tootsie pop? researcher corey heid decided to find out. he instructed a sample of 92 students to lick a tootsie pop along the non-banded side until they could taste the chocolate center. the mean number of licks was 356.1 with a standard deviation of 185.7 licks.calculate a 95% confidence interval for the true mean number of licks to get to the center of a tootsie pop. assume the conditions are met.

Answer:

0.6 gallons of pure saline

Step-by-step explanation:

15-12=3

3=×0.03

20 gallons ×0.03=0.6 gallons

The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

Answer:

a: (9,-9)

Step-by-step explanation:

We have `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

Given a function `f(x)` is defined by `f(x) = (x+7)/x`.

We need to find `f(a)`, `f(a+h)`, and the difference quotient `(f(a+h)-f(a))/h` where `h≠0`.

Solution:

`f(x) = (x+7)/x`

At `x=a`, we have

`f(a) = (a+7)/a`.

At `x = a + h`,

we have `

f(a+h) = [(a+h)+7]/(a+h)`.

So,

`f(a+h) = (a+h+7)/(a+h)`.

Now,

`f(a+h)−f(a)` is `[(a+h)+7]/(a+h) − (a+7)/a`.

LCM of `(a+h)` and `a` is `a(a+h)`.

So, we get `f(a+h)−f(a)` as `(a+h)(a+7)−a(a+h+7)/a(a+h)`.

On simplification, we have `f(a+h)−f(a)` as `(ah+7h)/(a(a+h))`.

Now, `(f(a+h)−f(a))/h` is `(ah+7h)/(ah+h^2)`.

On simplification, we have `(f(a+h)−f(a))/h` as `(h(a+7))/(ah+h^2)`.

Hence, `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

Given a function `f(x)` is defined by `f(x) = (x+7)/x`. We have found `f(a)`, `f(a+h)`, and the difference quotient `(f(a+h)-f(a))/h` where `h≠0`. Thus, we have `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

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:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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Answer:

hello,

Step-by-step explanation:

n+2*(2n-5)=20

5n-10=20

5n=30

n=6

Answer:

1/2 base * height = 16 in^2

1/2 * 8 in * H = 16 in^2

H = 32 in^2 / 8 in = 4 in         Equation # 4

The volume of a pyramid is 60 inches.

Given that,

A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.

V1 = 35 cubic inches

A1 = 15 square inches

h1 = 7 inches

A2 = 36 inches

h2 = 5 inches

To find  : What is V2

The following formula is used to determine a pyramid's volume:

V = (Base Area × Height)/3

V2 = (36 square inches multiplied by 5)/3

V2 = 60 cubic inches

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Answer:

824 punds of candy

Step-by-step explanation:

512 + 312

Total means together and adding. You would add the 2 numbers and get our answer.

To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:∫CF.v dlWhere v = (x²+2yz)i + y²j and dl = dx i + dy j + dz kTherefore,∫CF.(x²+2yz) dx + y² dy … (1)Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴

The above line integral is the required value. So, we need to evaluate this integral. To calculate the line integral of the given vector field, we will use the formula of line integral. For the given function, the formula will be:

∫CF.v dl

Where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

Therefore,

∫CF.(x²+2yz) dx + y² dy … (1)

Here, C is the curve from point (0,0,0) to (1,1,1) along the given route, that is, (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1).∴ The above line integral is the required value. So, we need to evaluate this integral.The integral is a line integral of a vector field, with the curve path of integration is given by C as follows: C: (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1)In other words, we need to evaluate the integral of the dot product of the vector field v with the differential of the curve:

∫CF.v dl...

where

v = (x²+2yz)i + y²j

and

dl = dx i + dy j + dz k

We must split the curve C into three distinct segments before we can start evaluating the integral. The segments will be from (0,0,0) to (1,0,0), from (1,0,0) to (1,1,0), and from (1,1,0) to (1,1,1).Let's start with the first segment, from (0,0,0) to (1,0,0). We can set x = t, y = 0, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = dt, dy = 0, dz = 0. We have:∫(0,0,0)to(1,0,0)

vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(t²+0)dt + 0 + 0= [t³/3]0to1= 1/3

Now, let's evaluate the second segment, from (1,0,0) to (1,1,0). We can set x = 1, y = t, z = 0, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = dt, dz = 0. We have:

∫(1,0,0)to(1,1,0)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+0)dx + t²dy + 0dz= 1∫0to1(t²)dt= [t³/3]0to1= 1/3

Finally, let's evaluate the third segment, from (1,1,0) to (1,1,1). We can set x = 1, y = 1, z = t, with t varying from 0 to 1, to parametrize this segment. Then dx = 0, dy = 0, dz = dt. We have:

∫(1,1,0)to(1,1,1)vdl = ∫0to1(x²+2yz)dx + y²dy + 0dz= ∫0to1(1²+2(1)(t))dx + 1²dy + 0dz= ∫0to1(1+2t)dt + 1(0to1)+ 0= [t²+t]0to1+ 1= 3/2

Therefore, the line integral is the sum of the integrals along the three segments:

∫CF.v dl= 1/3+ 1/3+ 3/2= 2

Thus, the value of the line integral of the given function v = x²+2yzi + y²j from (0,0,0) the point (1,1,1) by the route (0,0,0) + (1,0,0) + (1,1,0) + (1,1,1) is equal to 2.

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The required sample size can be calculated using a formula that takes into account the desired confidence level, margin of error, and estimated population proportion.

The formula to calculate the required sample size for estimating a population proportion is given by:

n = (\(Z^2\) * p * (1 - p)) / \(E^2\)

where:

- n is the required sample size

- Z is the z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)

- p is the estimated population proportion (66% in this case)

- E is the margin of error (4.5% expressed as a decimal, which is 0.045)

Substituting the values into the formula:

n = (\(1.645^2\) * 0.66 * (1 - 0.66)) / \(0.045^2\)

Simplifying the calculation:

n = 715.4

Since sample sizes must be whole numbers, rounding up to the nearest whole number, the required sample size is approximately 716. Therefore, in order to estimate the population proportion with 90% confidence and a margin of error of 4.5%, a sample size of at least 716 individuals would be needed.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

point 1 (0 , 0 ) x1 = 0 y1 = 0

point 2 (2 , -3) x2 = 2 y2 = -3

equation of the line = ?

Step 02:

Slope formula

Slope-intercept form of the line

y = mx + b

b = y-intercept = 0

m = - 3/2

y = -3/2 x + 0

y = -3/2 x

The answer is:

y = -3/2 x

The coordinates of the other two vertices are (2a, 0) and (2a, 2b).

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

                  A (0, 0)

              /       \  

           /            \

(a, 0) /                 \   (a, b)

      /                      \

  B      (2a, b)      C

(P, Q)                      (R, S)

Now,

The midpoint of AB.

a = P/2

P = 2a

0 = Q/2

Q = 0

So,

B = (2a, 0)

Now,

The midpoint of AC.

a = R/2

R = 2a

b = S/2

S = 2b

So,

C = (2a, 2b)

Thus,

The coordinates of B are (2a, 0)

The coordinates of C are (2a, 2b)

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Answer:

About 23.3

Step-by-step explanation:

We are going to use the Pythagorean Theorem to find the length of the other side.

The formula for it is \(a^{2} +b^{2} =c^{2}\)

Therefore, c squared is always the Hypotenuse which is made up a and b squared added together. The Hypotenuse is the longest side and the is the side that we are looking for.

So, \(20^{2} +12^{2} =c^{2}\)

\(400 + 144 = c^{2}\)

\(544 = c^{2}\)

c = Estimate 23.3

The hourly growth rate parameter for the bacterial population is approximately 0.0415, indicating an exponential growth model.

In a continuous exponential growth model, the population size can be represented by the equation P(t) = P0 * e^(rt), where P(t) is the population size at time t, P0 is the initial population size, e is the base of the natural logarithm, and r is the growth rate parameter. We can use this equation to solve for the growth rate parameter.

Given that the initial population size (P0) is 3000 bacteria and the population size after 6 hours (P(6)) is 3622 bacteria, we can plug these values into the equation:

3622 = 3000 * e^(6r)

Dividing both sides of the equation by 3000, we get:

1.2073 = e^(6r)

Taking the natural logarithm of both sides, we have:

ln(1.2073) = 6r

Solving for r, we divide both sides by 6:

r = ln(1.2073) / 6 ≈ 0.0415

Therefore, the hourly growth rate parameter for the bacterial population is approximately 0.0415.

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Answer:

12

Step-by-step explanation:

Answer:

x = 2.4

Step-by-step explanation:

4 ( 2x - 3 ) = 0.2 ( x + 5 ) + 5.72

8x - 12 = 0.2x + 1 + 5.72

7.8x = 12 + 1 + 5.72

7.8x = 18.72

x = 2.4

The line that passes through the point (-2,-1) and has a slope of 5. The equation of the line is y + 1 = 5(x + 2).

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

Using the slope and 1 point format:   (y- y₁) = m(x - x₁)  

where m = slope = 5, and point is (x₁, y₁). In this case point (x₁, y₁) = (-2, -1)

x₁ = -2,  y₁ = -1

Using: (y- y₁) = m(x - x₁)

y - -1 = 5(x - -2)

y + 1 = 5(x + 2).

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Answer:

The properties of trapezoid apply by definition (parallel bases).

The legs are congruent by definition.

The lower base angles are congruent.

The upper base angles are congruent.

Any lower base angle is supplementary to any upper base angle.

The diagonals are congruent.The bases are parallel by definition.

Each lower base angle is supplementary to the upper base angle on the same side.

Answer:

Step-by-step explanation:

3. parallel

4. neither

5. parallel

These are right. You can find the answer by plugging them into desmos. Good luck! Let me know if there is anything else I can help with :)

The volume of figure down below is 470.996 cubic in.

The volume of the cone is the product of one-third of the height, pie, and square of the radius that is;

The volume of the cone = 1/3(πr²)(height)

Since we can see that there are two cones combined together to form one figure.

So, Volume of first cone = 1/3(πr²)(height)

= 1/3(π 5²)(7)

= 1/3(π 25)(7)

= 183.166

Volume of second cone = 1/3(πr²)(height)

= 1/3(π 5²)(11)

= 1/3(π 25)(11)

= 287.83

Therefore, the volume of the figure is;

287.83 + 183.166

470.996

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Answer:

x = {1/3, 0}

Step-by-step explanation:

Answer: D)  y + 9 = -4(x -4)  

Step-by-step explanation:

The point-slope formula says that   y - b = m( x - a)  Where b is the y coordinate of a point, m is the slope and a is the x coordinate of the same point. Given the point (4,-9)  the x coordinate is 4 and the y coordinate is -9.

y - (-9) = -4(x - 4)   Reduce it.

y + 9 = -4(x -4)

Answer:

plnaa

Step-by-step explanation:

Answer:

redonda

Step-by-step explanation:

Answer:

MYSTREET AND MY INNER DEMONS YES

Step-by-step explanation:

watch them

Step-by-step explanation:

Scale factor of DEF : ABC = 5 : 15 = 1 : 3.

Hence perimeter of ABC = 12ft * 3 = 36ft.

Answer:

Rent for B = 1896
Rent for C = 3062

Step-by-step explanation:

the B and C apartment's monthly rent combined  is $4958
rent of B is 1166 less than rent C
so the equation is
X+ (X+1166) = 4958
X= rent B
X+1166 = rent C

simplifying the equation
2X + 1166 = 4958
subtracte 1166
2X = 3792  

X= 1896, so the rent for B is 1896
after adding the 1166
the rent for C is 3062