A baker has 6 pounds of sugar. He divides into 3 containers. He then uses 1 container to bake pies. Which expression shows how many pounds of sugar the baker used?

Answer:

351.5625

1,440,000

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{General form of an Exponential Function}\\\\$y=Ae^{kt}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $k$ is a constant.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]

Given:

(Let t = time in minutes).

If the doubling period is 15 minutes, then at t = 135 minutes, y = 180,000:

[tex]\implies 90000=Ae^{120k}[/tex]

[tex]\implies 180000=Ae^{135k}[/tex]

Divide the second equation by the first to eliminate A, and solve for k:

[tex]\implies \dfrac{180000}{90000}=\dfrac{Ae^{135k}}{Ae^{120k}}[/tex]

[tex]\implies 2=\dfrac{e^{135k}}{e^{120k}}[/tex]

[tex]\implies 2=e^{135k} \cdot e^{-120k}[/tex]

[tex]\implies 2=e^{15k}[/tex]

[tex]\implies \ln 2 = \ln e^{15k}[/tex]

[tex]\implies \ln 2 =15k \ln e[/tex]

[tex]\implies \ln 2 =15k[/tex]

[tex]\implies k=\dfrac{1}{15}\ln 2[/tex]

Substitute t = 120, y = 90000 and the found value of k into the formula and solve for A:

[tex]\implies 90000=Ae^{\left(120 \cdot \frac{1}{15}\ln 2\right)}[/tex]

[tex]\implies 90000=Ae^{\left(8\ln 2\right)}[/tex]

[tex]\implies 90000=Ae^{\ln256}[/tex]

[tex]\implies 90000=256A[/tex]

[tex]\implies A=\dfrac{90000}{256}[/tex]

[tex]\implies A=351.5625[/tex]

Therefore, the function that models the scenario is:

[tex]\large\boxed{y=351.5625e^{\left(\frac{1}{15}t \ln 2\right)}}[/tex]

So the initial population at time t = 0 was:

To find the size of the bacteria population after 3 hours, substitute t = 180 into the found formula:

[tex]\implies y=351.5625e^{\left(\frac{1}{15}(180) \ln 2\right)}[/tex]

[tex]\implies y=351.5625e^{\left(12 \ln 2\right)}[/tex]

[tex]\implies y=351.5625e^{\left(\ln 4096\right)}[/tex]

[tex]\implies y=351.5625 \cdot 4096[/tex]

[tex]\implies y=1440000[/tex]

Therefore, the size of the bacterial population after 3 hours was:

The initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

If n₀ is the initial size of a population experiencing exponential growth, then the population n(t) at time t is modeled by the function:

n(t) = n₀(e[tex])^{rt}[/tex]

Where r is the relative rate of growth expressed as a fraction of the population.

Given:

Doubling period = 15 minutes

At t = 120 minutes, n(t) = 90,000

If the doubling period is 15 minutes, then at t = 120+15 = 135 minutes,

90000 = n₀(e[tex])^{120r}[/tex]

18000 =  n₀(e[tex])^{135r}[/tex]]

To find the r:

Take ratio of both of the equations,

90000 / 18000 = n₀(e[tex])^{120r}[/tex]  /   n₀(e[tex])^{135r}[/tex]

2 = (e[tex])^{135r}[/tex] . (e[tex])^{-120r}[/tex]

r = 1/15 ln2

Substitute the value of r, t and y.

90000 = n₀(e[tex])^{120r}[/tex]

90000 = 256n₀

n₀ = 351.5652

Now, the function

n(t) = n₀(e[tex])^{rt}[/tex]

n(t) = (351.5652)(e[tex])^{(1/15)(180)(ln2)}[/tex]

n(t) = 1440000

Therefore, the initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.

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The colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

Given is that a colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm.

The logistic model is given as -

y(t) = {c/(1 + a[tex]e^{-bt}[/tex])}

For y(t) = 2000

2000 = {c/(1 + a[tex]e^{-bt}[/tex])}

(2000/c) = 1/(1 + a[tex]e^{-bt}[/tex])

(1 + a[tex]e^{-bt}[/tex]) = (2000/c)

a[tex]e^{-bt}[/tex] = (2000/c) - 1

a[tex]e^{-bt}[/tex] = (2000 - c)/c

[tex]e^{-bt}[/tex] = (2000 - c)/(ac)

(-bt)log{e} = log {(2000 - c)/(ac)}

- bt = log(2000 - c) - log(ac)

- bt = log(2000 - c) - log(a) + log(c)

t = - {log(2000 - c) - log(a) + log(c)}/b

Therefore, the colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

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By using properties of triangle, it can be calculated that-

The pilot is 2740 miles from her starting position.

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.

Here,

The diagram has been attached

Time = 130 minutes = 2 hrs 10 minutes = [tex]2 + \frac{10}{60}[/tex] hours = [tex]\frac{13}{6}[/tex] hours

Speed = 600 miles per hour

Distance = [tex]\frac{13}{6} \times 600[/tex] = 1300 miles

Now,

Time = 145 minutes = 2 hrs 25 minutes = [tex]2 + \frac{25}{60}[/tex] hours = [tex]\frac{29}{12}[/tex] hours

Distance = [tex]\frac{29}{12}\times 600[/tex] = 1450 miles

Angle = [tex]10^{\circ}[/tex]

[tex]c^2 = 1300^2 + 1450^2 - 2\times 1300\times 1450\times cos(180-10)\\c^2 = 1690000 + 2102500 - (-3712725.2)\\c^2= 7505225.2\\c= \sqrt{7505225.2}\\c = 2740[/tex]

The pilot is 2740 miles from her starting position.

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Answer:

5

Step-by-step explanation:

The slope or gradient of the line

using this formula as our guide line

y = mx +b

where m = slope

x = x– intercept

b = y– intercept

so

y = 5x + 12

the slope will be 5

i hope i helped pls rate as brainliest

Answer:

y = 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we need to add and subtract the fractions given. To do this, we need to find a common denominator for all of the fractions.

The least common multiple of 4, 16, and 12 is 48, so we can rewrite each fraction with a denominator of 48:

1/4 = 3/12

29/16 = 87/48

9735/12 = 4047/48

Then, we can add and subtract the fractions as follows:

3/12 + 87/48 - 4047/48 = (3 - 4047)/48 = -4044/48 = -84/16

Therefore, the final answer is -84/16, or -5 and 1/16 in simplified form.

Answer:

x=6

Step-by-step explanation:

9-3=6 or 6+3=9

The graph of the linear equation, y + 1 = 1/3(x - 3), is given in the attachment below.

A linear equation is an equation of the form "y = mx + b," where x and y are variables, and m is the slope and b is the y-intercept.

To graph a linear equation, of y + 1 = 1/3(x - 3), you can use the following steps:

Rewrite the equation in slope-intercept form to determine its slope (m) and the y-intercept (b).

y + 1 = 1/3(x - 3)

y + 1 = 1/3x - 1

y = 1/3x - 1 - 1

y = 1/3x - 2

The slope (m) of the line would be 1/3, which is the rise over the run of the line.

The y-intercept (b) of the line would be -2, which means the line will intercept the y-axis at -2.

The graph of y + 1 = 1/3(x - 3) is shown in the image below.

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Thus ,  it  is False. As there is confidence level is not given, then cant calculate the sample size.

The standard deviation in statistics is a measure of how widely spread a set of values can be or how much they can vary. A low standard deviation denotes that values are typically close to the mean of the collection, whereas a high standard deviation indicates that values are dispersed across a greater range.

Here,

The standard error of the sample mean is equal to 2 for samples of size n if all conceivable samples of that size are taken from a population with an infinite mean and standard deviation.

In the above statement confidence level is not given.

Thus ,  it  is False. As there is confidence level is not given, then cant calculate the sample size.

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Answer:

415 miles

Step-by-step explanation:

Start with the speed equation:

speed = distance/time

Now solve the speed equation for distance:

distance = speed × time

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

Answer:

415 miles

Step-by-step explanation:

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

d=rt

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

Add the miles together

220+195 = 415 miles

The data Customers on file who visited the store during coupon promo is 32% .

a) We use Z-test for testing hypothesis in this case because it is single proportion.

b) The P-value is 0.0017.

c) As P value < α = 0.05 , So we reject the null hypothesis.

d) Yes, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.

The Null and Alternative hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.

Sample size ,n = 4,500

Significance level, 0.05

a) We use z-test, because this is single proportion hypothesis test.

Below are the null and alternative Hypothesis,

Null Hypothesis, H₀ : p = 0.3

Alternative Hypothesis, Hₐ : p > 0.3

b) Test statistic,

z = (p-cap - p)/sqrt(p×(1-p)/n)

z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)

z = 2.93

Using the Z-table, the P value at significance level 0.05 and z = 2.93 is 0.0017

As we see P-value < α = 0.05, so, reject the null hypothesis.

Yes, Lotions and Potions should continue to offer this promotion in order to increase visits.

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The cotangent of the angle is -√570/30

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

(√30/7,-√19/7)

This means that

(x, y) = (√30/7,-√19/7)

The cot(θ) is calculated as

cot(θ) = y/x

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

cot(θ) = (-√19/7)/(√30/7)

Evaluate

cot(θ) = -√19/√30

Rationalize

cot(θ) = -√570/30

Hence, the value of cot(θ) is -√570/30

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Answer:

$44,334.34

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=6000e^{0.05 \times40}[/tex]

[tex]\implies A=6000e^2[/tex]

[tex]\implies A=6000(7.3890560...)[/tex]

[tex]\implies A=44334.33659...[/tex]

Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).

[tex] \Large{\boxed{\sf Slope = 3}} [/tex]

[tex] \\ [/tex]

The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.

[tex] \\ [/tex]

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]

Where m is the slope of the line.

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]

[tex] \\ [/tex]

Now, substitute these values into the formula:

[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer:

slope = 3

How to Solve:

The question is asking us to find the slope, given two points.

These points are (0,0) and (4,12).

We will use the slope formula:

[tex]\boldsymbol{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

Plug in the data:

[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]

[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]

Simplify the fraction to its lowest terms:

[tex]\boldsymbol{m=3}[/tex]

Therefore, the slope is 3.

Option (b) is correct as mean of top five scorers on soccer team is 8 from given bar graph.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

Mean = (Sum of values)/(Total observations)

Using above formula, we get

Calculating mean for given bar graph,

[tex]=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8[/tex]

So, mean score of five players comes out to be 8.

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The common ratio is 1/5. By dividing each word by the term before it, we may find the geometric progression's common difference.

The common ratio in geometric progression is the ratio of any term in the sequence to divided by the first term.

The Formula to calculate the common ratio in geometric progression, a, ar, ar2, ar3, ar4, ar5… is,

Common ratio = ar/ a = ar2/ ar = ……. = an/ an-1

As stated in the definition, we can compute the common difference of a geometric progression by dividing any term by its preceding term.

Given, the geometric sequence is 625, 125, 25, 5, 1,....

We have to find the common ratio of the given geometric sequence.

In geometric sequence, a, b, c, d, … the common ratio r is given by

r = b/a = c/b = d/c.

So, r = 125/625 = 25/125 = 5/25 = 1/5;

r = 1/5

Therefore, the common ratio is r = 1/5.

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Answer:

B. 25/125

Step-by-step explanation:

Thus after 12 minutes concentration of drug is 0.045.

The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula [tex]c(t) = 0.05(1-e^{-0.2t} )[/tex]

Drug concentration is amongst the most important determinants of clinical response to a drug.

Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.

Thus after 12 minutes concentration of the drug is = C(5).

Now

C(5) = [tex]0.05(1-e^{-0.2t} )[/tex]

= [tex]0.05(1-e^{-2.4} )[/tex]

= 0.05(1-0.0907)

= 0.05×0.9093

= 0.045

The drug concentration is 0.045.

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Part (A)

Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.

P/Q = R/S

where,

In this case,

Therefore, we go from this

P/Q = R/S

to this

(1.8)/6 = h/60

Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.

--------------

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

Part (B)

Let's cross multiply and solve for h.

(1.8)/6 = h/60

1.8*60 = 6h

108 = 6h

6h = 108

h = 108/6

h = 18

--------------

Answer:

A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

B). 18 meters tall

Step-by-step explanation:

We see TWO right triangles in this problem:

These triangles are proportional so we can make a ratio out of them

the height of the man over the side of the triangle (6m)

and the height of the tower over the length of its triangle (60m)

Set these equal to each other to complete part A

[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

And by using cross multiplication (which is what you do for ratios), solve for h!

For a quick example of cross multiplication, I've attached a picture.

Now let's do it!

1.8 × 60 = 6 × h

108 = 6h

108/6 = h

h = 18

The height of the cell phone tower is 18 meters.

Answer:

She Does NOT

Step-by-step explanation:

3/4 is .75 1 1/3 is 1.33 3/4*2= 1.5 which is more than 1.33

The height of the cliff in terms of A, B and h are 40 meters.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

A man standing on the deck of a ship.

Let C be the position of man.

And the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively 60° and 30°.

That means, ∠DCH = 60° and  ∠BCD = 30°.

The diagram is given in the attached image.

HD = x And BD = 10 meters.

In right-triangle ΔCDH,

we have,

tan60° = HD / CD

√3 = x / CD

CD = x/√3

In right-triangle  ΔCDB,

we have,

tan30° = BD/CD

CD = 10√3

So, the distance of the ship from the cliff is 10√3 meters.

Comparing, the both values of CD,

 10√3 =  x/√3

x  =  10√3 × √3

x = 10 × 3

x = 30 meters.

Now, the total height of cliff  = BD + DH

= 10 + 30

= 40 meters.

Therefore, the height of the cliff is 40 meters.

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Answer:

$4.50

Step-by-step explanation:

Use a proportion:

$6.75 is to 3 bags as x is to 2 bags.

6.75/3 = x/2

3x = 2 × 6.75

x = 4.50

Answer: $4.50

Answer:

  $4.50

Step-by-step explanation:

Given 3 bags of cat food cost $6.75, you want the cost of 2 bags.

Unless there is a volume discount (or surcharge), the price is proportional to the quantity. That means 2 bags will cost 2/3 the amount that 3 bags cost.

  cost of 2 bags = 2/3 · $6.75 = $4.50

Amelia would spend $4.50 on 2 bags of cat food.

Answer:

6/1.5

Step-by-step explanation:

You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!

Answer:

  20^2 = 400, the 2nd power of 20

Step-by-step explanation:

Given that k=20^20 and 20^k/k^20 = 20^n, you want the largest power of 20 that divides n.

Taking the base-20 logarithm of both equations, we have ...

  [tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]

Substituting for k and log(k), we get ...

  [tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]

This shows us the largest power of 20 that is a factor of n is 20².

The motion of the object on the graph, can best be represented as an object that d. was at rest and is accelerating uniformly.

The object on the graph is accelerating such that the acceleration is stable and uniform. This is why the speed - time line is a straight and diagonal line to show that the speed is proportional to time.

We know that the object started from rest because at the point where time was 0, the object was not accelerating and so was not moving. As time moves on, the object increases speed, thereby accelerating.

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Answer:

5x+48=130

Step-by-step explanation:

5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.

The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:

p(s) = 4s

Integral = ∫2s5s ds

= ∫2s5s dx

= [s2/2]2s5s

= (25/2) - (4/2)

= 20/2

= 10

Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.

To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.

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The domain and range of the given function are  {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.

The given function is

f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)

The domain of the function can be given as;

Domain : {-2, 0, 1, 2, 3}

Range : {-3, 0, 2, 3, 4}

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