You deposit $200 in an account earning 3.5% simple interest. How long will it take for the balance of the account to be $249? Write down the formulas you are going to use.

The equation is x/2=6

A statement that the values of two mathematical expressions are equal (indicated by the sign =).

Given here: Paul was thinking of a number. Paul halves the number and gets an answer of 6. Let the number be x and this number is halved and it becomes equal to 6

thus we can construct an equation as  follows:

x/2=6

Hence, The equation is x/2=6

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Final answer:

The equation formed based on the information that Paul halves the number to get 6 is x/2 = 6. Multiplying both sides by 2 gives us x = 12, which is the original number that Paul was thinking of.

Explanation:

The student question regarding forming an equation from a given word problem can be translated into: Paul halves the number and gets 6. To form an equation with x, we represent the unknown number as x, and then create an equation based on the information given. Since halving the number results in 6, the equation we form is x/2 = 6.

To find the value of x, we can multiply both sides of the equation by 2, which will give us x = 6 × 2. This simplifies to x = 12, which is the original number Paul was thinking of.

Answer:

(0, -6/5)

(-3, 0)

Step-by-step explanation:

y-intercept is when x is 0.

x-intercept is when y is 0.

Answer:

y-intercept: (-3,0)

x-intercept (0,-1.2)

Step-by-step explanation:

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:

Solution

V=πr2h=π·32·8≈226.19467

Step-by-step explanation:

Answer:

They are compatible

Step-by-step explanation:

The first thing is to say that an "ace" and that it is a "coarse"

"ace" is card number 1. Group A

"coarse" is a type of the deck, found from number 1 to card 13. Group B

Thus:

 Calculate A U B:

1 to 13 + 1 of the other types of cards in the deck.

At intersection B:

1 of "coarse"

Therefore, if group A is compatible with group B

Answer:

x=-2

Step-by-step explanation:

−5x−2+2x=−2x+4+2x

−3x−2=4

Step 2: Add 2 to both sides.

−3x−2+2=4+2

−3x=6

Step 3: Divide both sides by -3.

−3x

−3

=

6

−3

x=−2

Answer:

x=-2

Step-by-step explanation:

Answer:

90 and 55

Step-by-step explanation:

Answer:

75 degrees and 70 degrees

25 degrees and 120 degrees

90 degrees and 55 degrees

Step-by-step explanation:

edmentum

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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We need to see the circle

The formula for slope is [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex].

Subtract y1 from y2. (y1= -1, y2 = 3)

3 - -1 = 4

Now subtract x1 from x2. (x1 = 4, x2 = -4)

-4 -4 = -8

Divide the difference between the y coordinates by the difference between the x coordinates.

[tex]\frac{4}{-8}[/tex] or 4 ÷ -8 = -0.5

The slope between the two points is -0.5.

Hope this helpsss

The slope between the points (4, –1) and (–4, 3) is calculated using the slope formula and is found to be –0.5.

The slope of the line passing through the points (4,–1) and (–4,3) is calculated using the slope formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. For the given points:

Plugging these into the formula gives:

m = (3 - (–1)) / (–4 - 4) = 4 / –8 = –0.5.

The slope between the points (4, –1) and (–4, 3) is –0.5.

Answer:2 seconds s(2) max ht = 264 ft two answer pick one at least

Step-by-step explanation:

..A person standing cloes to the edge on the top of a 200-foot building throws a baseball ... t = -b/2a t = -64/-32

The highest altitude the object reaches is 1024 feet.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

h(t) = -16t² + 64t + 960

Now,

h'(t) = -16 x 2t + 64 = -32t + 64

h''(t) = -32

This means,

h(t) has a maximum altitude at h'(t) = 0

Now,

h'(t) = 0

-32t + 64 = 0

-32t = -64

t = 2

Now,

h(2) = -16 x 2² + 64 x 2 + 960

h(2) = -16 x 4 + 128 + 960

h(2) = -64 + 128 + 960

h(2) = 1024 feet

Thus,

The highest altitude is 1024 feet.

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Answer:

it is b

Step-by-step explanation:

Answer:

More

Step-by-step explanation:

because 2 hours and 30 min is 2.5 10 percent of a day is 2.4 so more

Answer:

He bought 19 tickets

Step-by-step explanation:

first you subtract $4.35 from $18.59 and the answer would be $14.25

then u take $14.25 and divide it by $0.75 and the answer from that would be 19

then the 19 would be the tickets

your done

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:

got it right on edg

Answer:

28

3.5*8

Step-by-step explanation:

Base multiply height

Answer:

B) Victoria's method is linear because the number of minutes increased by an equal number every month.

Step-by-step explanation:

Zach reading time written in sequence form is given as:

Victoria reading time written in sequence form is given as

The statement that best describes the methods used by Zach and Victoria to increase the time they spent reading a book is therefore:

B) Victoria's method is linear because the number of minutes increased by an equal number every month.

Answer:

B

Step-by-step explanation:

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:

They have corresponding angles that are congruent.

Step-by-step explanation:

The options of the question in the attached figure

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

therefore

The statement that must be true is

They have corresponding angles that are congruent.

Given:

The radius of the given diagram = 9 inches

The value of given angle = 120°

To find the length of the arc.

Formula:

The relation between arc (S), radius (r) and the angle ([tex]\theta[/tex]) is:

[tex]S[/tex]= [tex]2\pi r(\frac{\theta}{360})[/tex]

Now,

Putting, [tex]r = 9, \theta = 120 ^\circ[/tex] we get,

[tex]S = 2(\pi)(9)(\frac{120}{360} )[/tex]

[tex]S = 6\pi[/tex]

Hence,

The length of the arc is [tex]6\pi[/tex] inches.

Answer:

  6.3 km

Step-by-step explanation:

You want to know the total distance represented by segments of 600 m, 3 km, and 2km plus 700 m.

Kilo- is a prefix meaning 1000. A kilometer is 1000 meters. That means we can write the distances as ...

The total of these distances is found by adding the decimal values in the usual way.

  0.600 +3.000 +2.700 = 6.300

Marcia biked 6.3 km over the three days.

Answer:

42

Step-by-step explanation: I subtracted 950 from 1500 and that left me with 550 that i divided by 31.95 which left me with 17... but we keep it at 17 because we can't have half of a guest. Then you would add 17 to the 25 other guests you are paying for the answer of 42

Answer:

42

Step-by-step explanation:

1500-950=550

550÷32=17

17+25=42 guests

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:

The equation to describe the situation is  [tex]p-3=17.[/tex]

And, the total weight of the basket of apples was 20 pounds.

Step-by-step explanation:

The question is incomplete so, the complete question is below:

Liang bought a basket of apples to make pies for her friends. The basket of apples weighed p pounds. Before she had time to make the pies, she ate 3 pounds of apples. There are 17 pounds of apples left to make pies. Write an equation to describe this situation. What was the total weight of the basket of apples?

Now, to write an equation to describe the situation. And to find the total weight of the basket of apples.

So, the basket of apples total weighed = [tex]p\ pounds.[/tex]

Liang ate apples weighed = 3 pounds.

And the apples left for the pies weighed = 17 pounds.

Now, to write an equation describing the situation:

[tex]p-3=17.[/tex]

Thus, the equation is [tex]p-3=17.[/tex]

Now, to get the total weight of the basket of apples:

[tex]p-3=17\\\\Adding\ both\ sides\ by\ 3\ we\ get:\\\\p=20[/tex]

Hence, the basket of apples total weighed = 20 pounds.

Therefore, the equation to describe the situation is [tex]p-3=17.[/tex]

And, the total weight of the basket of apples was 20 pounds.

Answer:

44

Step-by-step explanation:

33÷3 = 11

11×1 =11(David)

11×5=55(Mark)

55-11=44

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: 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.

Answer:

Your Wrong (Tangent)

Step-by-step explanation:

A tangent is a straight line that touches the curve, like the curve part of the circle. I posted an image so you could see an example.

Answer:

E) tangent

Step-by-step explanation:

JKL is a straight line which touches the circle at one point, so it's a tangent

Answer:

d) This is a completely randomized design with two explanatory variables (factors).

Step-by-step explanation:

Explanatory variables are independent variables.

In this case, I prepared two explanatory variables, which are : (i)30-second ad

(ii) 60-second ad,

Then, the explanatory variables were assigned to 4 treatment groups, and each variable is done once or thrice.

All subjects are assigned randomly to all treatment groups, with each treatment group seeing one. We can conclude that this is a completely randomized design with two explanatory variables.