What is the distance between the points (3, 7) and (15, 16) on a coordinate plane?

Answer:

84 feet to the nearest foot.

Step-by-step explanation:

We have a right angled triangle with adjacent side (A) = 100 and you want to find the height of the tower, the opposite side (O).

A = 100 , O = ? so we need the tangent , (from SOH-CAH-TOA).

tan 40 = O/ 100

O = 100 tan 40

= 83.9 feet.

Final answer:

To determine the height of the tower, we can use the tangent of the angle of elevation, 40 degrees, multiplied by the distance, 100 feet, which results in approximately 84 feet.

Explanation:

To find the height of a tower with an angle of elevation of 40°, observed from 100 feet away, you can use trigonometric functions. Specifically, the tangent function, which is defined as the ratio of the opposite side (the height of the tower we're looking for) to the adjacent side (the distance from the tower).

We have:

The angle of elevation (θ) = 40°

The distance from the tower (adjacent side) = 100 feet

The height of the tower can be calculated as:

height = tan(θ) × adjacent side
= tan(40°) × 100 feet

Using a calculator, we find:

height = tan(40°) × 100
= 0.8391 × 100
≈ 84 feet (to the nearest foot)

Therefore, the tower is approximately 84 feet high.

Answer:

B

Step-by-step explanation:

Since the d value is changed, we're talking about a vertical transformation. Since d > 0, the graph is shifted up.

Answer:

j:19 days

s:23 days

23-19=4

4 days

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

Their average rate of speed is 53 miles per hour.

Step-by-step explanation:

Given : A family on a vacation drives 123 miles in 2 hours then gets stuck in traffic and goes 4 miles in the next 15 minutes. The remaining 191 miles of the trip take [tex]3\frac{3}{4}[/tex] hours.

To find : What was their average rate of speed to the nearest tenth of a mile per hour ?

Solution :

We know, [tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

Total distance traveled by family on vacation is

D= 123 miles + 4 miles + 191 miles = 318 miles

Total time taken by family on vacation is

T= 2 hours + 15 minutes + [tex]3\frac{3}{4}[/tex] hours

T= 2 hours + [tex]\frac{15}{60}[/tex] hours + [tex]3\frac{3}{4}[/tex] hours

T= [tex]2+ \frac{1}{4}+ \frac{15}{4}[/tex] hours

T= [tex]\frac{8+1+15}{4}[/tex] hours

T= [tex]\frac{24}{4}[/tex] hours

T= 6 hours

Substitute the value in the formula,

[tex]\text{Speed}=\frac{318}{6}[/tex]

[tex]\text{Speed}=53[/tex] miles per hour.

Therefore, Their average rate of speed is 53 miles per hour.

Tommy has 3 and 1/3 jars but 3 of them are full .

Okay so 5*2/3 =10/3 which is 3 1/3

Answer:

The number of banana splits sold was [tex]28[/tex]

Step-by-step explanation:

Let

x-----> the number of sundaes sold

y-----> the number of banana splits sold

we know that

[tex]2x+3y=156[/tex] -----> equation A

[tex]x=y+8[/tex] ----> equation B

substitute equation B in equation A and solve for y

[tex]2(y+8)+3y=156[/tex]

[tex]2y+16+3y=156[/tex]

[tex]5y=156-16[/tex]

[tex]5y=140[/tex]

[tex]y=28[/tex]

Answer:

True

Step-by-step explanation:

We have the serie:

[tex]\frac{1}{25}+ \frac{1}{36} + \frac{1}{49}+...[/tex]

To test whether the series converges or diverges first we must find the rule of the series

Note that:

[tex]5^2 = 25\\\\6^2 = 36\\\\7^2 = 49[/tex]

Then we can write the series as:

[tex]\frac{1}{5^2}+ \frac{1}{6^2} + \frac{1}{7^2}+...[/tex]

Then:

[tex]\frac{1}{5^2}+ \frac{1}{6^2} + \frac{1}{7^2}+... = \sum_{n=5}^{\infty}\frac{1}{n^2}\\\\\sum_{n=5}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+4)^2}[/tex]

The series that have the form:

[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]

are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].

In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges

Answer: Defualt

Step-by-step explanation: Dan

Answer:

Step-by-step explanation:

We must calculate the lateral area of a cylinder.

The formula is:

[tex]A=2\pi rH[/tex]

r - radius

H - height

We have H = 6 cm and r = 3.5.

Substitute:

[tex]A=2\pi(3.5)(6)=42\pi\ cm^2[/tex]

Use [tex]\pi\approx\dfrac{22}{7}[/tex]

[tex]A\approx42\left(\dfrac{22}{7}\right)=(6)(22)=132\ cm^2[/tex]

Answer:

Step-by-step explanation:

The question is incomplete. p(x 16) is actually [tex]P(X\geq 16)[/tex] ; p(x 15) is actually [tex]P(X\leq 15)[/tex] and e(x) is [tex]E(X)[/tex]

Wherever a random variable X can be modeled as a binomial random variable we write :

X ~ Bi (n,p)

Where ''n'' is the number of Bernoulli experiments taking place (whose variable is called binomial random variable).

And where ''p'' is the success probability.

In a Bernoulli experiment we define which event will be a ''success''

In order to calculate the probabilities for the variable X we can use the following equation :

[tex]P(X=x)=f(x)=(nCx).(p^{x}).(1-p)^{n-x}[/tex]

Where ''[tex]P(X=x)[/tex]'' is the probability of the variable X to assume the value x.

Where ''[tex]nCx[/tex]'' is the combinatorial number define as :

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

In our question

X ~ Bi (20,0.70)

Now let's calculate the probabilities :

[tex]f(12)=P(X=12)=(20C12).(0.70)^{12}.(1-0.70)^{20-12}=0.1144[/tex]

[tex]f(16)=P(X=16)=(20C16).(0.70)^{16}.(1-0.70)^{20-16}=0.1304[/tex] (I)

[tex]P(X\geq 16)[/tex] ⇒

[tex]P(X\geq 16)=P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)[/tex] (II)

[tex]P(X=17)=(20C17).(0.70)^{17}.(1-0.70)^{20-17}=0.0716[/tex] (III)

[tex]P(X=18)=(20C18).(0.70)^{18}.(1-0.70)^{20-18}=0.0278[/tex] (IV)

[tex]P(X=19)=(20C19).(0.70)^{19}.(1-0.70)^{20-19}=0.0068[/tex] (V)

[tex]P(X=20)=(20C20).(0.70)^{20}.(1-0.70)^{20-20}=0.0008[/tex] (VI)

Using (I), (III), (IV), (V) and (VI) in (II) :

[tex]P(X\geq 16)=0.1304+0.0716+0.0278+0.0068+0.0008=0.2374[/tex]

Now :  

[tex]P(X\leq 15)[/tex]

[tex]P(X\leq 15)=1-P(X\geq 16)[/tex]

[tex]P(X\leq 15)=1-0.2374=0.7626[/tex]

Finally,

[tex]E(X)=[/tex] μ (X)

[tex]E(X)[/tex] is the mean of the variable X

In this case, X is a binomial random variable and its mean can be calculated as

[tex]E(X)=(n).(p)[/tex]

In the question :

[tex]E(X)=(20).(0.70)=14[/tex]

The binomial experiment with n = 20 and p = 0.70 indicates that the probabilities are;

f(12) ≈ 0.1144

f(16) ≈ 0.1304

P(X ≥ 16) ≈ 0.2375

P(X ≤ 15) ≈ 0.7265

E(X) = 14

A binomial experiment is a statistical experiment that consists of a specified number of independent trials, in which each the trials has only two possible outcomes. The probability of success is the same for all trials and the trials are independent, such that the outcome of one trial does not affect the outcome of the other trials.

In a binomial experiment with n = 20 and p = 0.7, the probability of exactly k successes in n independent trials can be found from the following probability mass function.

f(k) = [tex]_nC_k[/tex] × [tex]p^k[/tex] × [tex](1 - p)^{(n-k)}[/tex]

Where [tex]_nC_k[/tex] is the binomial coefficient, which can be calculated an [tex]_nC_k[/tex] = n!/(k!·(n - k)!)

Using the formula the probabilities can be calculated as follows;

f(12) = ₂₀C₁₂ × 0.70¹² × 0.3⁸ = 125970 × 0.70¹² × 0.3⁸ ≈ 0.1144

f(16) = ₂₀C₁₆ × 0.70¹⁶ × 0.3⁴ = 4845 × 0.70¹⁶ × 0.3⁴ ≈ 0.1304

P(X ≥ 16) = f(16) + f(17) + f(18) + f(19) + f(20) ≈ 0.2375

P(X ≤ 15) = 1 - P(X ≥ 16) ≈ 1 - 0.2375 = 0.7625

The expected value of the binomial random variable X is; E(X) = n·p, where n is the number of trials and p is the probability of success on a single trial.

E(X) = n·p = 20 × 0.7 = 14

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Answer:

Step-by-step explanation:

Well 7 is the only number that can be divided by itself and 1

Answer:

Hello!

Great question.

The correct answer would be "Prime Number."

Step-by-step explanation:

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.

Answer:THE ANSWER IS

300% PLEASE BRAINEST ME!

Answer:

The answer is D hope this helps

Step-by-step explanation:

Answer:

See below  

Step-by-step explanation:

7)

AT² = 11² + 4² = 121 + 16 = 137

AT = √137

sinA = DT/AT = 11/√137 = (11√137)/137

cosA = AD/AT = 4/√137 = (4√137)/137

tanA = DT/AD                 = 11/4

sinT = AD/AT = 4/√137 = (4√137)/137

cosT = DT/AT = 11/√137 = (11√137)/137

tanT = AD/DT                 = 4/11

9)

AT² = 8² + 3² = 64 + 9 = 73

AT = √73

sinA = LT/AT = 8/√73 = (8√73)/73

cosA = AL/AT = 3/√73 = (3√73)/73

tanA = LT/AL                = 8/3

sinT = AL/AT = 3/√73 = (3√73)/73

cosT = LT/AT = 8/√73 = (8√73)/73

tanT = AL/LT                = 3/8

11)

    6² =  4² + RT²

  36 = 16  + RT²

RT² = 20

RT =√20 = √(4× 5) = 2√5

 sinA = RT/AT = (2√5)/6 = (√5)/3

cosA = AR/AT = 4/6        = 2/3

tanA = RT/AR = (2√5)/4 = (√5)/2

 sinT = AR/AT = 4/6        = 2/3

cosT = RT/AT = (2√5)/6 = (√5)/3

tanT = AR/RT = 4/(2√5)  = (2√5)/5

Answer:

150 miles

Step-by-step explanation:

Find the unit rate (MPH) by dividing miles travlled by hours.

    300/6 = 50 MPH

    250/5 = 50 MPH

Multiply the hours on day 3 (3) by 50 MPH

    3*50 = 150 miles

Answer:

150 miles

Step-by-step explanation:

The relationship between speed, time and distance is such that the product of speed and time is distance.

Given that they drove the same speed throughout the trip

Speed on day one given that distance covered is 300 miles in 6 hours,

Speed = 300 miles/ 6 hours

= 50 miles per hour

Speed on day two given that distance covered is 250 miles in 5 hours

= 250 miles/ 5 hours

= 50 miles per hour

If on the third day, the speed is maintained and they drove for 3 hours,

Distance covered = 50 miles per hour × 3 hours = 150 miles

Answer:

x=2

Step-by-step explanation:

The formula for inverse variation is

xy = k

We know x = 4 and y = 8

4*8= k

32 = k

xy = 32

We want to find x when y = 16

x*16 = 32

Divide each side by 16

16x/16 = 32/16

x =2

Answer:

xy=32

16x=32

x=2

Answer:

3975

Step-by-step explanation:

fog functions are basically f(g(o)).

So for this problem, it would be f(g(-7)).

Plug in -7 to the g(x) equation first, and you should get -63.

Then plug -63 into the f(x) equation, and you should finish with 3975.

Answer:

B.   y = e^(-2/x).

Step-by-step explanation:

dy/dx = 2y / x^2

Separate the variables:

x^2 dy = 2y dx

1/2 * dy/y =  dx/x^2

1/2  ln y = = -1/x  + C

ln y = -2/x +  C

y = Ae^(-2/x)  is the general solution ( where A is a constant).

Plug in the given conditions:

e = A e^(-2/-2)

e = A * e

A = 1

So the specific solution is y = e^(-2/x).

Final answer:

The separable differential equation [tex]dy/dx = 2y/x^2[/tex] can be solved by separating variables, integrating both sides, and then applying the given initial condition y(-2) = e to find the specific solution, which is [tex]y = e^{-2/x},[/tex] corresponding to answer option B.

Explanation:

To solve the given separable differential equation [tex]dy/dx = 2y/x^2[/tex], we first separate the variables:

[tex]\( \frac{dy}{y} = \frac{2}{x^2}dx \)[/tex]

Next, we integrate both sides:

[tex]\( \int \frac{1}{y}dy = \int 2x^{-2}dx \)[/tex]

Which gives:

[tex]ln|y| = -2/x + C[/tex]

Now, we apply the initial condition y(-2) = e to find C:

ln(e) = [tex]-2/(-2) + C \Rightarrow 1 = 1 + C \Rightarrow C = 0[/tex]

Thus, the specific solution is:

[tex]y = e^{-2/x}[/tex]

So, the correct answer is option B, y equals e raised to the negative 2 over x power.

Answer:

x ≈ 5 years

Step-by-step explanation:

Given amount = A = 500 mg

Decay rate = r = 10% per year

Remaining amount = L = 295.25 mg

The formula to calculate remaining amount after x years decay =

L = A((100-r)/100)^x

By putting values in this formula, we get

295.25 = 500 ((100-10)/10)^x

295.25 = 500 (0.90)^x    

295.25/500 = 0.90^x

0.5905 = 0.90^x

0.90^x =0.5905

taking log on both sides

ln(0.90^x) =ln(0.5905)

x*ln(0.90) =ln(0.5905)  using property of log

x = ln(0.5905)/ln(0.90)

x = 4.9984

x ≈ 5 years

➷ Find the multiplier:

28/100 = 0.28

1 - 0.28 = 0.72

Multiply the total amount by this multiplier:

40,000 x 0.72 = 28,800

She will make $28,800

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

She will make 28,800 dollars after tax.

Step-by-step explanation:

just subtract 28 percent of 40,000.

Or even simpler just follow peachy's instructions cause she/he did her crud right. a percentage is the same as a decimal. 1 percent is 0.01. since 28 percent is 0.28 we subtract 0.28 from one, because 1 is 100 percent. Also,all of this is the same as subtracting 28 percent of 40,000 from 40,000 1 - 0.28= 0.72, and multiply 40,000 by 0.72.

All credit on this part is peachy's thank her/his answer and give her/him brainliest. :)

btw why i say him/her, he/she, and her/his is because I dot want to assume gender

Answer:

6√3 cm

Step-by-step explanation:

The hypotenuse of a right triangle is 12 centimeters, and the shorter leg is 6 centimeters then the other leg is 6√3

Answer:

C. 20

Step-by-step explanation:

The given limit is

[tex]\lim_{x \to 2} (3x^3 +x^2-8)[/tex]

This a limit of a polynomial function.

We plug in the limit directly to obtain;

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(2)^3+(2)^2-8[/tex]

We simplify to get;

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(8)+4-8[/tex]

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=24+4-8[/tex]

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=20[/tex]

The correct choice is C

Answer:

Part 5) [tex]x=50\°[/tex]

Part 6) [tex]x=15\°[/tex]

Step-by-step explanation:

Part 5) we know that

[tex](2x-10)\°+90\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)

solve for x

[tex]2x=180\°-80\°[/tex]

[tex]2x=100\°[/tex]

[tex]x=50\°[/tex]

Find the value of the labeled angle

[tex](2x-10)\°=2(50\°)-10\°=90\°[/tex] ----> is a right angle

Verify the answer

we know that

In a quadrilateral the sum of the internal angles must be equal to 360 degrees

so

[tex](2x-10)\°+90\°+(180-x)\°+x\°=360\°[/tex]

[tex](2x+260)\°=360\°[/tex]

substitute the value of x

[tex]2(50\°)+260\°=360\°[/tex]

[tex]360\°=360\°[/tex] ------> is true, therefore the value of x is correct

Part 6) we know that

[tex](8x+10)\°+(4x-10)\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)

solve for x

[tex]12x=180\°[/tex]

[tex]x=15\°[/tex]

Find the value of each labeled angle

[tex](8x+10)\°=8(15\°)+10\°=130\°[/tex]

[tex](4x-10)\°=4(15\°)-10\°=50\°[/tex]

[tex]130\°[/tex] and [tex]50\°[/tex] are supplementary angles

In spherical coordinates, we set

[tex]x=\rho\cos\theta\sin\varphi[/tex]

[tex]y=\rho\sin\theta\sin\varphi[/tex]

[tex]z=\rho\cos\varphi[/tex]

so that the volume element under this transformation becomes

[tex]\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

The region [tex]E[/tex] is given by the set

[tex]\left\{(\rho,\theta,\varphi)\mid0\le\rho\le1,0\le\theta\le2\pi,0\le\varphi\le\dfrac\pi3\right\}[/tex]

so that the integral is

[tex]\displaystyle\iiint_Ey^2z^2\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^6\sin^2\theta\sin^3\varphi\cos^2\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]

[tex]\displaystyle=\left(\int_0^{\pi/3}\sin^3\varphi\cos^2\varphi\,\mathrm d\varphi\right)\left(\int_0^{2\pi}\sin^2\theta\,\mathrm d\theta\right)\left(\int_0^1\rho^6\,\mathrm d\rho\right)[/tex]

[tex]=\dfrac{47}{480}\cdot\pi\cdot\dfrac17=\dfrac{47\pi}{3360}[/tex]

The volume of the solid using the triple integral [tex]\mathbf{\iiint_E y^2z^2 dV \ \ is \ \ = \dfrac{47 \pi}{3360}}[/tex]

Given that;

Then the spherical coordinates can be expressed as:

where;

Now, the expression for the solid E in the spherical coordinates can be computed as:

[tex]\mathbf{E = \Big \{ ( \rho , \theta, \phi )\Big| 0 \leq \rho \leq 1, 0 \leq \phi \leq \dfrac{\pi}{3}, 0 \leq \theta \leq 2 \pi \Big \} }[/tex]

and the volume of the solid using the triple integral is calculated as:

[tex]\mathbf{\iiint_E y^2z^2 dV = \iiint _E \ y^2 z^2 \ dx dy dz }[/tex]

[tex]\mathbf{\implies \iiint _E \ y^2 z^2 \ dx dy dz = \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \int ^1_0 \ (\rho sin \phi sin \theta )^2 ( \rho cos \phi )^2 \rho^2 sin \phi d \rhod \phi d \theta }[/tex]

[tex]\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \ \int^1_0 \ \rho^6 d \rho d \phi d \theta }[/tex]

[tex]\mathbf{\implies \int ^{2 \pi}_{0} \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi sin^2 \theta \Big [ \dfrac{\rho^7}{7} \Big]^1_0 \ d \phi d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta \int ^{\dfrac{\pi}{3}}_{0} \ sin^3 \phi cos^2 \phi \ d \phi d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta \int ^{\dfrac{\pi}{3}}_{0} \ sin \phi( 1- cos^2 \phi)cos^2 \phi \ d \phi d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \phi}{5}- \dfrac{cos ^3 \phi}{3} \Bigg ] ^{\dfrac{\pi}{3}}_{0} d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{cos^5 \dfrac{\pi}{3}}{5}- \dfrac{cos ^3 \dfrac{\pi}{3}}{3}- \dfrac{cos^5 0}{5}+ \dfrac{cos^3 0}{3} \Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{2}{15}- \dfrac{17}{480} \Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{(480\times 2) -(15\times 17)}{15\times 480}\Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{1}{7} \int ^{2 \pi}_{0} sin ^2 \theta\Bigg [\dfrac{705}{15\times 480}\Bigg ] d \theta }[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \int ^{2 \pi}_{0} 2sin ^2 d \theta}[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \int ^{2 \pi}_{0} (1-cos 2\theta) \ d \theta}[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \Bigg [\theta - \dfrac{sin 2 \theta }{2}\Bigg] ^{2 \pi}_{0}}[/tex]

[tex]\mathbf{\implies \dfrac{47}{6720} \Bigg [2 \pi\Bigg] }[/tex]

[tex]\mathbf{\iiint_E y^2z^2 dV = \dfrac{47 \times 2 \pi}{6720}} }[/tex]

[tex]\mathbf{\iiint_E y^2z^2 dV = \dfrac{47 \pi}{3360} }[/tex]

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(2l+2w) is that right

Answer: 14 cars 4 left over

Step-by-step explanation:

74/5=14.8

14 x 5 = 70

4 wheels left over

Answer:log(x-3)

Step-by-step explanation:

log(A)-log(B) is log(A/B) then this would be log[(x^2-9)/(x+3)]

x^2-9 is (x-3)(x+3) then the answer is log(x-3)

Answer:

a) [tex]N_0=250\; k=0.15 [/tex]

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies [tex]t=0[/tex]. And [tex]N(0)=N_0[/tex]. The process is:

[tex]N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250[/tex]

b) After 2 days means [tex]t=48[/tex]. So, we just replace and operate:

[tex]N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}[/tex]

c) [tex]N(t_1)=4000; \;t_1=?[/tex]

[tex]N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h [/tex]

d) [tex]t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)[/tex]

[tex]N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h [/tex]

Answer:

[tex]1\frac{2}{3}\ kg[/tex]

Step-by-step explanation:

we know that

To find out how much the guests ate, multiply the total amount of kg of mashed potatoes by the 4/12 fraction

so

[tex]5(\frac{4}{12})=\frac{20}{12}\ kg[/tex]

convert to mixed number

[tex]\frac{20}{12}=\frac{12}{12}+\frac{8}{12}=1\frac{8}{12}\ kg[/tex]

simplify

[tex]1\frac{8}{12}=1\frac{2}{3}\ kg[/tex]

The guests consumed 1.67 kilograms of the 5 kilograms of mashed potatoes that the chef had made.

To solve this problem, we need to multiply the total amount of mashed potatoes made by the fraction that the guests consumed.

Given that the chef cooked 5 kilograms of mashed potatoes and the guests ate 4/12 (which simplifies down to 1/3) of this amount, we multiply these two together.

So, the calculation would be 5 × 1/3 = 1.67 kilograms.

Therefore, the guests ate 1.67 kilograms of mashed potatoes.

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The side length of the canvas is best found by using the quadratic formula

because the equation is prime. Solving the equation produces two

approximate measurements, and one must be discarded for being

unreasonable.

I took the test and this was correct.

An example of dependent events is drawing a red marble from the same jar without replacing the first marble, which changes the probabilities for the second draw. This is known as sampling without replacement, which contrasts with independent events where the item is replaced and the probabilities remain unchanged.

An example of dependent events is drawing a red marble out of the same jar, without replacing the first marble. This creates a dependency because removing the first marble affects the outcome chances for the subsequent draw. If the jar starts with four blue and three white marbles and you draw one blue marble and do not replace it, the jar then contains three blue and three white marbles. Therefore, the probability of drawing another blue marble has changed from the original draw.

Dependent events are associated with sampling without replacement, which means once an item is drawn, it is not put back into the population from which it was taken, altering the probabilities of subsequent draws. In contrast, independent events, such as drawing and replacing a marble, do not affect the subsequent probabilities, since the composition of the jar remains unchanged with each draw.