Use the Law of Sines to complete an expression that represents the angle measure x.

Answer:

The value of the quantity after 21 days is 2,347.59.

Step-by-step explanation:

The exponential growth function is

[tex]A=A_0(1+r)^t[/tex]

A= The number of quantity after t days

[tex]A_0[/tex]= initial number of quantity

r= rate of growth

t= time in days.

A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 2 weeks = 14 days.

Now A= (2×830)= 1660

[tex]A_0[/tex] = 830

t = 14 days

r=?

Now plug all value in exponential growth function

[tex]1660=830(1+r)^{14}[/tex]

[tex]\Rightarrow \frac{1660}{830}= (1+r)^{14}[/tex]

[tex]\Rightarrow 2= (1+r)^{14}[/tex]

[tex]\Rightarrow (1+r) ^{14}=2[/tex]

[tex]\Rightarrow (1+r)=\sqrt[14]{2}[/tex]

[tex]\Rightarrow r=\sqrt[14]{2}-1[/tex]

Now, to find the quantity after 21 days, we plug [tex]A_0[/tex] = 830, t= 21 days in exponential function

[tex]A=830( 1+\sqrt[14]{2}-1)^{21}[/tex]

[tex]\Rightarrow A=830(\sqrt[14]2)^{21}[/tex]

[tex]\Rightarrow A=830(2)^\frac{21}{14}[/tex]

[tex]\Rightarrow A=830(2)^\frac{3}{2}[/tex]

[tex]\Rightarrow A=2,347.59[/tex]

The value of the quantity after 21 days is 2,347.59.

Final answer:

To calculate the value of a quantity after 21 days when it doubles every 2 weeks with an initial value of 830, use the exponential growth formula [tex]N(t) = N_0 \times 2^{t/T}[/tex]. Plugging in the values, the quantity after 21 days is 2347.14, to the nearest hundredth.

Explanation:

Calculating Exponential Growth

To find the value of a quantity after 21 days when it has an initial value of 830 and doubles every 2 weeks, we can use the formula for exponential growth:

N(t) = N_0 × 2^(t/T)

Where:
N(t) is the future value after time t,
N_0 is the initial value (830),
t is the time period in days (21 days),
T is the doubling period in days (2 weeks = 14 days).

First, we convert 21 days into weeks: 21 days / 7 days per week = 3 weeks.

Next, let's find the value after 3 weeks. We plug our values into the exponential growth formula:

[tex]N(3) = 830 \times 2^{3/2}[/tex]

To calculate 3/2 weeks in terms of doubling periods:

3 weeks / 2 weeks per doubling period = 1.5 doubling periods.

Now we can calculate the quantity:

N(21) = [tex]830 \times 2^{1.5}[/tex] = 830 × 2.828 = 2347.14

To the nearest hundredth, the value of the quantity after 21 days is 2347.14.

Answer:

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.

Step-by-step explanation:

Answer:

40 in

Step-by-step explanation:

A= l x w

2 x 9 = 18

2 x 11 = 22

Then add together because the shape is together:

18 + 22 =

40

Answer:

15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4 minutes

Standard Deviation, σ = 0.25 minutes

We standardize the given data.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(more than 4.25 minutes to solve a problem)

[tex]P( x > 4.25) = P( z > \displaystyle\frac{4.25 - 4}{0.25}) = P(z > 1)[/tex]

[tex]= 1 - P(z \leq 1)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x > 4.25) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]

Thus,15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.

The correct answer is approximately 15.87%.

To solve this problem, we can use the properties of the normal distribution. Given that the average time Scott takes to solve a problem is 4 minutes with a standard deviation of 0.25 minutes, we can calculate the z-score for the time of 4.25 minutes to determine how many standard deviations away from the mean this time is.

The z-score formula is:

[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]

where[tex]\( X \)[/tex]is the value in question[tex](4.25 minutes), \( \mu \)[/tex] is the mean (4 minutes), and [tex]\( \sigma \)[/tex] is the standard deviation (0.25 minutes).

 Plugging in the values, we get:

[tex]\[ z = \frac{4.25 - 4}{0.25} = \frac{0.25}{0.25} = 1 \][/tex]

 Now, we look up the z-score of 1 in the standard normal distribution table or use a calculator to find the corresponding area to the left of this z-score. This area represents the probability that Scott will take 4.25 minutes or less to solve a problem.

The area to the left of a z-score of 1 is approximately 0.8413, or 84.13%. This is the cumulative probability up to 4.25 minutes.

 To find the probability that it will take Scott more than 4.25 minutes, we subtract this value from 100% (since the total area under the normal distribution curve is 1, or 100%):

[tex]\[ P(X > 4.25) = 1 - 0.8413 = 0.1587 \][/tex]

Converting this to a percentage, we get:

[tex]\[ 0.1587 \times 100\% \approx 15.87\% \][/tex]

Therefore, it will take Scott more than 4.25 minutes to solve a problem approximately 15.87% of the time.

Answer:

  x = 2 or -3

Step-by-step explanation:

The product will be zero when one of the factors is zero.

First factor:

  x - 2 = 0

  x = 2 . . . . . add 2 to both sides of the equation

Second factor:

  x + 3 = 0

  x = -3 . . . . .subtract 3 from both sides of the equation

The values of x that solve this equation are x = 2 and x = -3.

Answer:

B x m

Step-by-step explanation:

Example: 75 x minutes

So no matter how much bottles you have, you just have to multiply the minutes.

Answer:I think it would be 75 divided by b = m

Step-by-step explanation:

Answer:

We choose C

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo

Basically, interquartile range represents the width or "dispersion" of the set. [1] The interquartile range is determined by the difference between the top quartile (25% highest) and lower quartile (25% lowest) point of the data set.

From the picture, we can find that:

So the interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.

We choose C

Answer:

Step-by-step explanation:

Answer:

(-\infty,-1/2) U (1/2,+\infty)

Step-by-step explanation:

You have the following series:

[tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex]

You calculate the radius of convergence by using the formula:

[tex]R= \lim_{n \to \infty} |\frac{a(x)_n}{a(x)_{n+1}}|= \lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^{n+1}}{n+1}}|\\\\=\lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^n(2x)}{n+1}}|=\lim_{n \to \infty}|\frac{n+1}{2xn}|=|\frac{1}{2x}|\lim_{n \to \infty}|1+\frac{1}{n}|=|\frac{1}{2x}|[/tex]

The radius of convergence is R=1/2x.

Hence, the interval of convergence is

|2x| < 1

|x| < 1/2

By evaluating in the extrems of the interval:

[tex]\sum_{n=1}^{\infty} \frac{(2 (\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(1)^n}{n}=0\\\\\sum_{n=1}^{\infty} \frac{(2 (-\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]

for x=-1/2 we obtain an Alternating Harmonic Series, for x=1/2 we obtain the divergent harmonic series. Thus the interval is:

(-\infty,-1/2) U [1/2,+\infty)

Answer:

Step-by-step explanation:

Recall the ratio test. Given a series [tex]\sum_{n=1}^{\infty}a_n[/tex] if

[tex] \lim_{n\to \infty} \left|\frac{a_{n+1}}{a_n}\right|<1[/tex]

Then, the series is absolutely convergent.

We will use this to the given series [tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex], where [tex] a_n = \frac{(2 x)^n}{n}[/tex]. Then, we want to find the values for which the series converges.

So

[tex] \lim_{n\to \infty} \left|\frac{(2x)^{n+1}}{n+1}\cdot \frac{n}{(2x)^n}\right|<1[/tex], which gives us that

[tex] |2x|\cdot\lim_{n\to \infty} \frac{n}{n+1}<1[/tex]

We have that [tex]\lim_{n\to \infty} \frac{n}{n+1}=1[/tex]. Then, we have that

[tex]|2x|<1[/tex],

which implies that |x|<1/2. So for [tex]x \in (-1/2,1/2)[/tex] the series converges absolutely.

We will replace x by the endpoints to check convergence.

Case 1, x=1/2:

In this case we have the following series:

[tex]\sum_{n=1}^{\infty} \frac{1}{n}[/tex] which is the harmonic series, which is know to diverge.

Case 2, x=-1/2:

In this case we have the following series:

[tex]\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]

This is an alternating series with [tex]b_n = \frac{1}{n}[/tex]. Recall the alternating series test. If we have the following

[tex]\sum_{n=1}^\infty (-1)^nb_n [/tex] and[tex] b_n[/tex] meets the following criteria : bn is positive, bn is a decreasing sequence and it tends to zero as n tends to infinity, then the series converge.

Note that in this case, [tex]b_n = \frac{1}{n}[/tex] si always positive, its' limit is zero as n tends to infinity and it is decreasing, hence the series converge.

So, the final interval of convergence is

[tex] [\frac{-1}{2}, \frac{1}{2})[/tex]

Answer:

Option b

Step-by-step explanation:

Complete question is

Carl bought 7 packs of pencils. He now has 42  pencils. He writes that 42 is 6 times as many as 7.  Which comparison sentence below can he use to

show the comparison?

A. 7 more than 6 is 42.

B. 7 is 6 times as many as 42.

C. 42 is 7 times as many as 6.

D. 6 is 7 times as many as 42

Solution -

It is given that Carl has 42 pencils.

It is not sure in which pack - the one with 6 pencils or the one with 7 pencils.

But when Carl wrote that  "42 is 6 times as many as 7". By this he means that the present number of pencils i.e 42 is equal to 6 times the number of pencils in the pack of 7

Then, it becomes clear that Carl has 6 times the number of pencils in the pack of 7 pencils

Option B is correct

Answer: 780

Step-by-step explanation: 30 numbers times 26 letters.

30 x 26=780

Final answer:

To find the total number of outcomes for selecting a number between 1 and 30 and a letter from the alphabet, you multiply the outcomes of each event together, resulting in 30 numbers multiplied by 26 letters, which equals 780 total outcomes.

Explanation:

The question asks for the total number of outcomes when picking a number from 1 to 30 and a letter from the alphabet. In mathematics, to calculate the total number of outcomes for two independent events, you multiply the number of outcomes for each event. There are 30 different outcomes for picking a number from 1 to 30, and, assuming a standard English alphabet, there are 26 outcomes for picking a letter from A to Z.

To find the total number of outcomes when one event is selecting a number and another event is selecting a letter, you multiply the two: 30 (numbers) × 26 (letters) = 780 total outcomes.

The function shown in the given table is a linear function.

Given that, to determine whether the table shows a function is linear or non-linear.

The connection between sets of values is what makes up a function. For instance, in the formula y=f(x), a set of y exists for each value of x. The independent variable is called x, while the dependent variable is called Y.

Here,

Table,
x  = 17   18   19  
y  = 8    10   12
From the observation of the table, it is been observed that the value of x changes by 1 unit, and correspondingly the value of y changes by 2 units. So, the relationship arises is a linear function.

Thus, the function shown in the given table is a linear function.

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Answer:

Step-by-step explanation:

The ratio between the gold and silver in the first piece = 2:3

The ratio between the gold and silver in the second piece =3:7

The ratio in the mixture = 5:11

We want to have 8 gram of the new mixture.

Let the gram of alloy taken from the first piece=x

Therefore: gram of alloy would be taken from the second piece=(8-x)

This gives:

[tex]\dfrac{2}{5}x+ \dfrac{3}{10}(8-x)=\dfrac{5}{16}*8[/tex]

We simplify the equation above for the value of x.

[tex]\dfrac{2x}{5}+ \dfrac{3(8-x)}{10}=\dfrac{5}{2} \\\dfrac{4x+24-3x}{10}=\dfrac{5}{2}\\\dfrac{x+24}{10}=\dfrac{5}{2}\\2x+48=50\\2x=50-48\\2x=2\\x=1[/tex]

Therefore to create 8 gram of gold and silver alloy with gold-silver ratio 5:11, we take 1 grams of one of the alloy and 7 grams of the other alloy.

Answer: $1.5 millions

Step-by-step explanation:

Since the population is in millions and a million is like a fraction many millions.

Therefore, the minimum amount of money you could reasonably expect to spend in order to qualify for this amendment for the ballot is $1.5 millions

Answer:

230° is equal to  [tex]\displaystyle \frac{23 \pi}{18}[/tex]  radians.

General Formulas and Concepts:

Trigonometry

Degrees to Radians Conversion: [tex]\displaystyle \frac{n\pi}{180}[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables.

n = 230°

Step 2: Find Radians

∴ 230° is equal to  [tex]\displaystyle \frac{23 \pi}{18}[/tex]  radians.

---

Topic: Pre-Calculus

Unit: Trigonometry

Answer:

Equations:

y + 10x = 23

y + 15x = 33

cost of basket with 25 apples = $53

Step-by-step explanation:

A basket with 10 apples cost $23 and a basket with 15 apples cost $33. Note that these costs also include the cost of the basket, which is same in both case. Let the cost of empty basket with "y" and cost of each apple be "x"

Cost of basket and 10 apples is $23. We can transform this statement into an equation as:

y + 10x = 23                                     Equation 1

Similarly,

Cost of basket and 15 apples is $33. This gives us another equation:

y + 15x = 33                                     Equation 2

Subtracting Equation 1 from Equation 2 , we get:

y + 15x - (y +10x) = 33 - 23

5x = 10

x = 2

Using the value of x in equation 1, we get:

y + 10(2)= 23

y = 23 - 20

y = 3

This means, cost of basket is $3 and cost of each apple is $2.

Now we can calculate the cost of basket with 25 apples, which will be:

Cost of basket + Cost of 25 apples = Total Cost

3 + 25(2) = 3 + 50 = $53

Answer:

10=23

15=23

25=53

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

Answer:

a = (cx - by)/x

Step-by-step explanation:

ax + by  = cz

ax = cz - by

a = (cx - by)/x

Can I get brainliest

Answer:

7 11/12

Step-by-step explanation:

amount of the flour

= 2 3/4 + 4 1/2 + 2/3

= 11/4 + 9/2 + 2/3

= 33/12 + 54/12 + 8/12

= 95/12

= 7 11/12

make as the brainliest

Answer:

Wofford College

Step-by-step explanation:

Answer:

* LOOK AT THE PICTURE's*

I hope this helps and is the right one

The converse of the parallelogram side theorem states, If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

To prove this statement, we will assume that the opposite sides of a quadrilateral are congruent and demonstrate that it must be a parallelogram.

If both the opposite sides are parallel then we can easily prove that a parallelogram

Given: Quadrilateral PQRS, where PQ is congruent to RS and PR is congruent to QS.

To prove: PQRS is a parallelogram.

Proof:

Since PQ is congruent to RS (given), the segment PQ is parallel to the segment RS by the converse of the corresponding sides of congruent triangles are congruent (CPCTC). Since PR is congruent to QS (given), the segment PR is parallel to the segment QS by CPCTC.

Now we have both pairs of opposite sides of PQRS parallel, which satisfies the definition of a parallelogram.

Therefore, by proving that both pairs of opposite sides are PQRS parallel, we have shown that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

This completes the proof of the converse of the parallelogram side theorem.

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Answer:

You cannot simplify this. One has ab, and one has only b. So that is the most simplified it can get.

Answer: There are no like terms.

Step-by-step explanation:

Answer:

The data that we have is:

total people: 2545

male survivors: 406

male who died: 1651

total males: 406 + 1651 = 2057

female survivors: 362

female who died: 126

total females: 362 + 126 = 488.

We want to know:

for the percentages, we must calculate the quotient between the total numbers of the set, and the number in the particular category we are looking for.

% male survivors = (number of male survivors/total number of males)*100%.

                             = (406/2057)*100% = 19.73%

% male who died = (1651/2057)*100% = 80.2%

% female survivors = (362/488)*100% = 74.18%

% female who died = (126/488)*100% = 25.82%

Answer:

insufficient information

Step-by-step explanation:

If the order of the points is unknown, the distances AB and CD imply no particular distance for BD.

Answer:???

Step-by-step explanation:

Answer:

As the stake is 3 m long we will take it as the radius of the circle and find the area as per:

22/7*3*3=22/7*9=198/7m^2

198/7 metre square.

Answer:

Solve the equation for  

x   by finding   a ,  b , and  c  of the quadratic then applying the quadratic formula.

Exact Form:

x= 7 + 2 √ 5

Decimal Form:

x = 11.47213595 …

Step-by-step explanation:

Hi there! Hopefully this helps!

Answer: 11.47(to 2 decimal places).

Isolate one of the square roots: √(2x−5) = 1 + √(x−1)

Square both sides: 2x−5 = (1 + √(x−1))^2

We have removed one square root.

Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)

Simplify: 2x−5 = 2√(x−1) + x

Subtract x from both sides:  x−5 = 2√(x−1)

Now do the "square root" thing again:

Isolate the square root:  √(x−1) = (x−5)/2

Square both sides:  x−1 = ((x−5)/2)^2

We have now successfully removed both square roots.

Let's continue with the solution.

Expand right hand side:  x−1 = (x^2 − 10x + 25)/4

Since it is a Quadratic Equation! let's put it in standard form.

Multiply by 4 to remove division:  4x−4 = x^2 − 10x + 25

Bring all to left:  4x − 4 − x^2 + 10x − 25 = 0

Combine like terms:  −x^2 + 14x − 29 = 0

Swap all signs:  x^2 − 14x + 29 = 0

Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:

2.53 and 11.47 (to 2 decimal places)

2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.

11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.

Answer:

Solution

V=πr2h=π·32·8≈226.19467

Step-by-step explanation:

Answer:

C. (x + 4) and (x - 1)

Step-by-step explanation:

The middle number is 3 and the last number is -4.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 3

Multiply together to get -4

Can you think of the two numbers?

Try -1 and 4:

-1+4 = 3

-1*4 = -4

Fill in the blanks in

(x+_)(x+_)

with -1 and 4 to get...

(x + 4) and (x - 1)

Answer:

Option D) 0.92

Step-by-step explanation:

We are given the following probability distribution in the question:

    x:       0         1         2         3      4      5

P(X):    0.78    0.14    0.03    0.01    0    0.04

We have to find the probability that a randomly selected student will be absent no more than one day.

Thus, we have to evaluate:

[tex]P(x\leq1)\\=P(X=0) + P(X = 1)\\=0.78 + 0.14\\=0.92[/tex]

0.92 is the probability that a randomly selected student will be absent no more than one day.

Thus, the correct answer is

Option D) 0.92

Answer:

Option D

Step-by-step explanation:

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