Suppose you invest $2000 at an annual interest of 5.5% compounded continuously.
a. How much will you have in the account in 10 years?
b. How long will it take for the account to reach $5000?

31.25 g on the 5th day

no it will never by empty because even when it gets down to one singular piece of sugar you would technically just cut it in half, then that in half, yes it would get impossible, that's why you wouldn't actually do it, but if you typed it into a calculator it would just keep getting a smaller and smaller decimal.

The given  logarithmic expression statement is false. Because log₄7- log ₄3 = log₄(7/3).

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

Learn more about logarithm here

brainly.com/question/25710806

#SPJ4

Answer:

71

Step-by-step explanation:

ndndnrbrjen3n3nn3b2n2b2b

Answer:

3

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

(750÷100)2=15

750÷100=1%

The sine function with a phase shift of π/2 units to the right is given as follows:

B. y = 2sin(x + π/2).

The standard definition of a sine function is given as follows:

y = Asin(Bx + C) + D.

The parameters are given as follows:

For a phase shift of π/2 units to the right, the parameter C is given as follows:

C = π/2.

Hence option B is the correct option.

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

Read more on Functions here: https://brainly.com/question/29890699

#SPJ11

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

Read more on quadrilaterals:

https://brainly.com/question/23935806

#SPJ1

A large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, the probability of selecting 3 red marbles is 1/54.

The probability of selecting 3 red marbles is 1/54.What is a probability?

Probability refers to the likelihood or chance of an occurrence. The probability of an event occurring is the ratio of the number of favourable outcomes to the total number of possible outcomes.

A fraction or a decimal is used to express it.The total number of marbles in the bag is 10 + 5 + 7 = 22 marbles.

There are ten red marbles in the large bag, so the number of ways to select 3 red marbles from ten red marbles is:

\(10C_3 = (10 \times 9 \times 8) / (3 \times 2 \times 1) = 120\)

There are 22 marbles in the bag, therefore, the total number of ways to pick 3 marbles from 22 is:

\(22C_3 = (22 \times 21 \times 20) / (3 \times 2 \times 1) = 1540\)

Hence, the probability of choosing 3 red marbles out of the 22 marbles in the bag without replacement is:120/1540 = 1/54

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

The probability that a student who smokes is a graduate student is 0.071 or 7.1%.

Given that, the fraction of undergraduate students who smoke is 15% and the fraction of graduate students who smoke is 23%.

Let X be the event of being a graduate student and Y be the event of being a smoker, we need to find P(X|Y).

We will use Bayes theorem to find this probability.

P(X|Y) = P(Y|X)P(X)/P(Y)

We are given the following:

P(Y|X) = 0.23 (fraction of graduate students who smoke)

P(Y|X') = 0.15 (fraction of undergraduate students who smoke)

P(X) = 1/5 (one-fifth of the college students are graduate students)

P(X') = 4/5 (rest of the college students are undergraduates)

Now, let us find P(Y):P(Y) = P(Y|X)P(X) + P(Y|X')P(X') = (0.23)(1/5) + (0.15)(4/5) = 0.162

So,

P(X|Y) = (0.23)(1/5)/0.162 = 0.071

Thus, the probability that a student who smokes is a graduate student is 0.071 or 7.1%.

Therefore, the correct option is: 0.071.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Step-by-step explanation:

According to rules of Proportionality :

\(a = k \frac{b}{ {c}^{2} } \)

(A) When (a = 10, b = 8, c = 2)

K = 5

(B) When (b = 20, c = 5)

\(a = 5 \times \frac{20}{25} = 4\)

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x - (-2x) = 7x + 2x

              = 9x

Answer:

9.35

Step-by-step explanation:

because you take 3.5 away from 12.85

Answer:

9.35

Step-by-step explanation:

SAME EXPLANATION PO

Answer:

D

Step-by-step explanation:

Divide 16 by 4 to get the denominator of 4. Then divide 12 by 4 to get three. Therefore your answer is D. 3/4

Answer:

3/4

Step-by-step explanation:

All I did was divide the top and bottom number by 4. 12/4= 3 and 16/4=4

Answer:

the coefficient of x is 2/3 which is the constant.

The quotient between the two fractions will give:

(4/6)÷(3/12) = 8/3

Here we want to find the quotient between the fractions 4/6 and 3/12.

The quotient between any two fractions a/b and c/d can be solved as:

(a/b)÷(c/d) = (a*d)/(b*c)

Then our quotient can be solved in the following way as:

(4/6)÷(3/12) = (4*12)/(3*6)

(4*12)/(3*6) = (48/18)

Now we can simplify that fraction, if we divide both numerator and denominator by 2, we will get:

24/9

Now we can divide both by 3, then we will get the simplified fraction:

8/3.

That is the correct answer.

Learn more about fractions by reading:

https://brainly.com/question/11562149

#SPJ1

Answer: The answer is 2 2/3

Step-by-step explanation:  I got it right on edge

The factorized expressions is 3(x-4)(x-5).

We are given that;

The expression 3x² - 27x+60​

Now,

1.1.1 After simplification

-3(2x - 4y)² = -12(x-y)²

1.1.2 x+2/3*5x+1

= (3x+5)/(3x+3)

1.2.1 ny + 4z + 4y + nz

= (n+4)(y+z)

1.2.2 3x² - 27x+60

= 3(x-4)(x-5)

Therefore, by the expression the answer will be 3(x-4)(x-5).

To know more about an expression follow;

brainly.com/question/19876186

#SPJ1

Answer:

609638400

Step-by-step explanation:

Answer:

609638400

Step-by-step explanation:

Each row must alternate boys and girls, so every row is either BGBGB or GBGBG, where B denotes a boy and G denotes a girl. Since there are 8 girls and 7 boys, the teacher must have two rows of GBGBG and one row of BGBGB. There are three ways to choose this row, and once this is done, every seat is reserved for either a girl or a boy. There are 8! ways to arrange the girls in their seats, and 7! ways to arrange the boys, so the total number of seating arrangements is 3 * 7! * 8!

The triangles formed by the diagonals of the parallelogram are congruent by ASA, segments are therefore congruent and we get;

The segments \(\overline{AE}\) = \(\overline{CE}\), and \(\overline{BE}\) = \(\overline{DE}\) by definition

A parallelogram is a quadrilateral that have facing parallel sides.

The completed two column table to prove that the diagonals of a parallelogram bisect each other can be presented as follows;

Statements \({}\)                           Reasons

1. ABCD is a parallelogram \({}\)                      1. Given

2. ∠ABE and ∠CDE are alt. int angles\({}\)     2. Definition

3. ∠BAE and ∠DCE are alt. int angles\({}\)     3. Definition

4. ∠BCE and ∠DAE are alt. int angles\({}\)     4. Definition

5. ∠CBE and ∠ADE are alt. int angles\({}\)     5. Definition

6. \(\overline{AD}\) ≅ \(\overline{BC}\), \(\overline{AB}\) ≅ \(\overline{CD}\)                          \({}\)  6. Properties of a parallelogram

7. ΔBAE ≅ ΔDCE\({}\)                                       7. SAS congruence postulate

8. \(\overline{BE}\) ≅ \(\overline{DE}\), \(\overline{AE}\) ≅ \(\overline{CE}\)               \({}\)              8. CPCTC

9. \(\overline{AE}\) = \(\overline{CE}\) and \(\overline{BE}\) ≅ \(\overline{DE}\)                      \({}\) 9. Definition of congruence

Learn more on parallelograms here: https://brainly.com/question/27296302

#SPJ1

Answer:

7

Step-by-step explanation:

-x+2+5x=10(x-4)

4x+2=10x-40

2+40=10x-4x

42=6x

42/6=6x/6

7=x

Answer:

x = 7

Step-by-step explanation:

-x + 2 + 5x = 10 (x - 4)

=> 4x + 2 = 10x - 40

=> 4x - 10x = -40 - 2

=> -6x = -42

=> 6x = 42

=> x = 42/6

=> x = 7

The plane left Bristol airport at 16:55.

This is a problem from time and distance. We can solve this problem by following a few steps.

We have to know the relation between time, speed, and distance. The relation is denoted as,

t = s/v; t is denoted as time interval, v is denoted as velocity or speed in this case and s is denoted as displacement or distance.

We have to find the time. Here velocity is 162 mph and the total distance between  Bristol airport to Leeds Bradford airport is 216 miles.

t = 216 miles/ 162 mph = 1.33 hour = 80 minutes.

Therefore the plane left Bristol airport is, ( 18 hours 15 minutes - 80 minutes) = 16 hour 55 minutes = 16:55

To learn more about time and distance visit,

https://brainly.com/question/13269893?referrer=searchResults

#SPJ9

Given: Two similar triangles QRS and TRU

To Determine: The reflexive property to prove the similar triangles

Solution

We have been all that could lead to proving the similar triangles QRS and TRU

The space given has a the reason reflexive property

The reflexive property of equality states that a number is always equal to itself

From the image

Hence, the correct option is ∠QRS ≅ ∠ TRU, OPTION D

Answer:14=x

Step-by-step explanation:

The double integral of M = x over the domain D = {(x,y) ∈ ℝ²: y > 0 and x² + y² < 1} in polar coordinates is 0.

To calculate the double integral of M = x over the domain D = {(x,y) ∈ ℝ²: y > 0 and x² + y² < 1} using polar coordinates, we need to convert the integral into polar coordinates and then evaluate it.

In polar coordinates, the conversion formulas are:

x = r cos(θ)

y = r sin(θ)

The given domain D can be described in polar coordinates as follows:

0 < r < 1

0 < θ < π

Now, let's express the integral in terms of polar coordinates:

∬D M dA = ∫∫D x dA

Substituting x = r cos(θ) and y = r sin(θ):

∫∫D x dA = ∫∫D (r cos(θ)) r dr dθ

We need to determine the limits of integration for r and θ. Since 0 < r < 1 and 0 < θ < π, the integral becomes:

∫[0 to π]∫[0 to 1] (r² cos(θ)) dr dθ

Now we can evaluate this integral:

∫[0 to π]∫[0 to 1] (r² cos(θ)) dr dθ

= ∫[0 to π] [(1/3) r³ cos(θ)] from 0 to 1 dθ

= ∫[0 to π] (1/3) cos(θ) dθ

= (1/3) ∫[0 to π] cos(θ) dθ

Using the integral of cosine, we have:

= (1/3) [sin(θ)] from 0 to π

= (1/3) [sin(π) - sin(0)]

= (1/3) [0 - 0]

= 0

Therefore, the double integral of M = x over the domain D is equal to 0.

Learn more about Polar Coordinates

brainly.com/question/31904915

#SPJ11

Step-by-step explanation:

a. 1

_

8

b. 1

_

7

c. 10

_

21

espero que isso te ajude

Vamos a resolver las operaciones utilizando la regla de multiplicación de fracciones y luego simplificaremos los resultados.

a) \(\sf\:\frac{1}{6} \times \frac{3}{4}\\\)

Para multiplicar estas fracciones, multiplicamos los numeradores entre sí y los denominadores entre sí:

Numerador: \(\sf\:1 \times 3 = 3\\\)

Denominador: \(\sf\:6 \times 4 = 24\\\)

Entonces, \(\sf\:\frac{1}{6}\:\times\:\frac{3}{4} = \frac{3}{24}\\\)

Podemos simplificar esta fracción dividiendo tanto el numerador como el denominador por el máximo común divisor, que en este caso es 3:

\(\sf\:\frac{3}{24} = \frac{3 \div 3}{24 \div 3} = \frac{1}{8}\\\)

Por lo tanto, el resultado simplificado es \(\sf\:\frac{1}{8}\\\).

b) \(\sf\:\frac{1}{2} \times \frac{2}{7}\\\)

Aplicando la regla de multiplicación de fracciones:

Numerador: \(\sf\:1 \times 2 = 2\\\)

Denominador: \(\sf\:2 \times 7 = 14\\\)

Entonces, \(\sf\:\frac{1}{2} \times \frac{2}{7} = \frac{2}{14}\\\)

Podemos simplificar esta fracción dividiendo tanto el numerador como el denominador por el máximo común divisor, que en este caso es 2:

\(\sf\:\frac{2}{14} = \frac{2 \div 2}{14 \div 2} = \frac{1}{7}\\\)

Por lo tanto, el resultado simplificado es \(\sf\:\frac{1}{7}\\\).

c) \(\sf\:\frac{4}{7} \times \frac{5}{6}\\\)

Siguiendo la regla de multiplicación de fracciones:

Numerador: \(\sf\:4 \times 5 = 20\\\)

Denominador: \(\sf\:7 \times 6 = 42\\\)

Entonces, \(\sf\:\frac{4}{7} \times \frac{5}{6} = \frac{20}{42}\\\)

Podemos simplificar esta fracción dividiendo tanto el numerador como el denominador por el máximo común divisor, que en este caso es 2:

\(\sf\:\frac{20}{42} = \frac{20 \div 2}{42 \div 2} = \frac{10}{21}\\\)

No podemos simplificar aún más esta fracción, por lo que el resultado simplificado es \(\sf\:\frac{10}{21}\\\).

Resumiendo las respuestas:

a) \(\sf\:\frac{1}{6} \times \frac{3}{4} = \frac{1}{8}\\\)

b) \(\sf\:\frac{1}{2} \times \frac{2}{7} = \frac{1}{7}\\\)

c) \(\sf\:\frac{4}{7} \times \frac{5}{6} = \frac{10}{21}\\\)

Answer:

12

Step-by-step explanation:

Because you would divide the total number of points which is 48 by the number of games he's played which is 4 and you would get 12, since 48 divided by 4 is 12

Answer:12

Step-by-step explanation:hope this help

The critical t-values for a two-tailed, independent samples t-test (with 14 total participants) are not +2.145 and -2.145. So it is false.

The correct critical value for a two-tailed test with 14 degrees of freedom at the alpha level of 0.05 is ±2.145.

This means that any calculated t-value greater than 2.145 or less than -2.145 is statistically significant with a 95% confidence level.

The critical t-value for a two-tailed, independent sample t-test (with 14 total participants) is +2.145 or -2.145 is False.

In conclusion, the statement "The critical t-values for a two-tailed, independent samples t-test (with 14 total participants) is +2.145 and -2.145. Assuming we are using p = 0.05 as a cutoff" is False.

Learn more about t-test:

https://brainly.com/question/6501190

#SPJ11

Answer:

b

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180° , that is

∠ 1 + 92° + 30° = 180°

∠ 1 + 122° = 180° ( subtract 122° from both sides )

∠ 1 = 58°

Answer:

\(\huge\boxed{\sf < 1 = 58\°}\)

Step-by-step explanation:

So,

30 + 92 + ∠1 = 180

122 + ∠1 = 180

Subtract 122 to both sides

∠1 = 180 - 122

\(\rule[225]{225}{2}\)

Answer: $26.094 an hour

Step-by-step explanation:

First, add up the total hours:

10 + 3 + 15 + 4 = 32

Now, add up the total amount charged:

340 + 495 = 835

Now, divide the amount charged by the number of hours:

835 / 32 = *26.094

* or 26.09375 if it needs to be exact.

Answer:

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.

Step-by-step explanation:

In order to find the maxima or minima of a function, we have to take the first derivative and then put it equal to zero to find the critical values.

Given function is:

\(f(x) = x^2-10x+31\)

Taking first derivative

\(f'(x) = 2x-10\)

Now the first derivative has to be put equal to zero to find the critical value

\(2x-10 = 0\\2x = 10\\x = \frac{10}{2} = 5\)

The function has only one critical value which is 5.

Taking 2nd derivative

\(f''(x) =2\)

\(f''(5) = 2\)

As the value of 2nd derivative is positive for the critical value 5, this means that the function has a minimum value at x = 5

The value can be found out by putting x=5 in the function

\(f(5) = (5)^2-10(5)+31\\=25-50+31\\=6\)

Hence,

The function y = x 2 - 10x + 31 has a minimum  value of 6

Hence,

Option B. minimum is correct for the first blank

Option C. 6 is correct for second blank.