$2700 is compounded annually at a rate of 12% for 1 year.

Find the total amount in the compound interest account.

$___(rounded to the nearest cent.)

The amount he would pay is $46.40.

Percentage can be described as the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.

The amount paid = list price of the first shirt + [list price of the second shirt x ( 1 - percentage discount)]

$29 + [$29 x (1 - 0.4)]

$29 + ($29 x 0.6) = $46.40

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Based on the information, EFH and GHF does not have to be congruent.

Congruents angles are presented in the figure below. Congruent angles are angles that have the same measure or size. When two angles are congruent, they look exactly the same, even if they are in different orientations.

The symbol used to represent congruence is an equals sign with a tilde above it, like this: ≅. For example, if angle A and angle B have the same measure, we can write it as:

angle A ≅ angle B

Congruent angles play an important role in geometry because they allow us to compare and analyze different shapes and figures. In particular, when two angles are congruent, we can use this fact to make conclusions about other angles and sides of a shape.

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In circle O shown, points E, F, G, and H lie on the circle asshown and chords FH and GE intersect at J. Based on thisinformation alone, which two angles below do not have tobe congruent?m(1) angle FJE and angle HJG(2) angle EFH and angle HGE(3) angle EFH and angle GHF(4) angle FEG and angle FHG

Answer:

B, 248

Step-by-step explanation:

Out of 45 students in calc and 21 in stats, 14 are repeatedly counted. We can subtract 14 from one group so that this number does not overlap. For example, let us take the calc group:

45-14= 31

31+21 =52 students taking either calc or stats, NOT OVERLAPPED

Everyone else is not taking calc or stats, so 300-52= 248, or B

I hope this helps! :)

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Rates of change are the change of a quantity over another.

The rate of change in height of the water level is 36.51 cm per second.

Let the length of the top square be s, and the height be h.

The volume of the pyramid is:

\(\mathbf{V = \frac{1}{3}s^2h}\)

At time t, we have:

\(\mathbf{V = \frac{1}{3}s(t)^2h(t)}\)

The relationship between the side length and height is:

\(\mathbf{s : h=6 : 13}\)

Express as fractions

\(\mathbf{\frac{s }{ h}=\frac{6 }{ 13}}\)

Make s the subject

\(\mathbf{s=\frac{6 }{ 13}h}\)

So, we have:

\(\mathbf{V = \frac{1}{3}s^2(t)h(t)}\)

\(\mathbf{V = \frac{1}{3} \times (\frac{6 }{ 13}h(t))^2 \times h(t)}\)

\(\mathbf{V = \frac{1}{3} \times \frac{36}{ 169}h^2(t) \times h(t)}\)

\(\mathbf{V = \frac{1}{3} \times \frac{36}{ 169}h^3(t)}\)

Differentiate

\(\mathbf{V'(t) =3 \times \frac{1}{3} \times \frac{36}{ 169}h^2(t) \times h'(t)}\)

\(\mathbf{V'(t) =\frac{36}{ 169}h^2(t) \times h'(t)}\)

Make h'(t) the subject

\(\mathbf{h'(t) = \frac{169 \times V'(t)}{36 \times h^2(t)}}\)

The water level rises constantly at 70 cm^3/s, and the water level is 3 cm.

So, we have:

\(\mathbf{V'(t) = 70}\)

\(\mathbf{h(t) = 3}\)

\(\mathbf{h'(t) = \frac{169 \times V'(t)}{36 \times h^2(t)}}\) becomes

\(\mathbf{h'(t) = \frac{169 \times 70}{36 \times 3^2}}\)

\(\mathbf{h'(t) = \frac{169 \times 70}{36 \times 9}}\)

\(\mathbf{h'(t) = 36.51}\)

Hence, the rate of change in height of the water level is 36.51 cm per second.

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Answer:

The terms of the polynomial are relatively prime because the highest integer that divides them both is 1.

Step-by-step explanation:

Two numbers are said to be relatively prime if their greatest common factor ( GCF ) is 1 .

Now, the expression we are given in the question is a polynomial;

y² + 7.

The terms of the polynomial y² + 7 are y² and 7 and have no common factor and in fact cannot be factorized further. Thus, these terms are said to be relatively prime because the highest integer that divides them both is 1.

\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\stackrel{\textit{we'll be using this one}}{\downarrow }~\hfill }{log_a a^x = x\qquad \qquad a^{log_a x}=x} \end{array}\)

\(\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(2^{0.5x}=10\implies \log_2\left( 2^{0.5x} \right)=\log_2(10)\implies 0.5x=\log_2(10) \\\\\\ \cfrac{x}{2}=\log_2(10)\implies x = 2\log_2(10)\implies x = \log_2(10^2)\implies x = \log_2(100) \\\\\\ \stackrel{\textit{using the change of base rule}}{x = \cfrac{\log(100)}{\log(2)}\implies x = \cfrac{2}{\log(2)}}\implies x\approx 6.644\)

as far as the domain, or namely what values "x" can take on safely, I don't see any constraints, so it must be (-∞ , +∞).

The amount after 5 years on $100 using the compound interest is $122.

According to the question,

We have the following information:

Principal = $100

Interest Rate = 4%

Time= 5 years

We know that the following formula is used to find the total amount if there is compound interest:

Compound amount = \(P(1+\frac{r}{100})^{t}\) where P is the principal, r is interest rate and t is the time in years

(Note that there are different formulas for compound interest depending on how it is calculated.)

A = \(100(1+\frac{4}{100})^{5}\)

A = \(100(\frac{104}{100})^{5}\\100(1.04})^{5}\)

A = 100*1.22

A = $122

Hence, the amount after 5 years on $100 using the compound interest is $122.

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The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.

To find the percent change or growth rate of a quantity between two different values, you can use the formula:

Percent change = ( new value - old value ) / old value x 100%

The new value would be the population of the village after 10 years which is 450 people.

The old value is the initial population of the village which is 400

The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %

= 12. 5 %

The growth rate for the village is therefore 12. 5 % every ten years.

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If cost price is Rs. 120, profit is Rs. 25 then the selling price is Rs.145.

We have to find the selling price

The formula for find the selling price is given below:

Selling Price = Cost Price + Profit

Given that the Cost Price (C.P.) is Rs 120 and the profit is Rs 25.

we can substitute these values into the formula:

Selling Price = 120 + 25

When one hundred twenty is added with twenty five we get One hundred twenty five.

Selling Price = 145

Therefore, the selling price is Rs 145.

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C.P. = Rs 120, profit = Rs 25​ then find the selling price?

Answer:

625

Step-by-step explanation:

so we do 500/ 0.6 = 625

Graph 1 represents the inverse of the function \(f(x)=\sqrt{x+1} -2\)

What is the inverse of a function?

The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.

The inverse of \(\sqrt{x+1} -2\) is \(x^{2} +4x+3\).

Plotting the inverse, we get the graph to be option 1.

Therefore, graph 1 represents the inverse of the function \(f(x)=\sqrt{x+1} -2\)

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The inverse function of the function given as f(x) = \(\sqrt{x+1}\) - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.

The steps for finding the inverse function, the steps to be followed are:

The given function is f(x) = \(\sqrt{x+1}\) - 2  

Consider the given function as f(x) = y ⇒ y =  \(\sqrt{x+1}\) - 2

Then, on rewriting the function for x, we get

y + 2 =  \(\sqrt{x+1}\)

⇒ (y + 2)² = (x + 1)

⇒ x = y² + 4y + 4 - 1

⇒ x = y² + 4y + 3

Interchanging the variables y to x and x to y we get

y = x² + 4x + 3

Thus, the inverse of the given function is obtained. I.e,

f⁻¹(x) = x² + 4x +3

To identify the graph, the point that satisfies the given function is

f(x) = \(\sqrt{x+1}\) - 2; for x = -1,

f(-1) = -2

So, the point is (-1, -2).

Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).

From the given graphs, graph 1 shows this point on it. So, that is the required option.

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Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

To simplify the expression 3 x (3/4) whole to a unit fraction, we can start by multiplying the whole number 3 by the denominator of the fraction, which is 4:

3 x (3/4) = (3 x 4)/4 x (3/4) = 12/4 x 3/4

We can simplify the fraction 12/4 by dividing both the numerator and denominator by 4:

12/4 = 3

Substituting this back into the expression, we have:

3 x (3/4) = 3/1 x (3/4) = 9/4

Therefore, 3 x (3/4) whole is equal to the unit fraction 9/4.

The most biased type of sample among the three options is the b. convenience sample. therefore, option b. convenience sample.

A convenience sample is a non-random sample in which participants are selected based on their easy availability or accessibility.

This type of sampling technique often leads to a biased sample because it may not represent the entire population and may only include individuals who are easily accessible or willing to participate.

On the other hand, a random sample is a type of sampling technique in which every member of the population has an equal chance of being selected, which reduces the risk of bias.

A systematic sample is also a type of probability sampling in which members of the population are selected at regular intervals, which can help to reduce some types of biases.

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Answer:

0.4

Step-by-step explanation:

To complete the probability distribution table, we need to determine the probability of selecting each possible value of the random variable x.

Since there are 10 correctly calibrated speedometers and 2 that are not, there are a total of 12 speedometers, and the probability of selecting a speedometer that is not correctly calibrated on the first draw is 2/12 = 1/6. After the first draw, there are 11 speedometers remaining, including one that is not calibrated, so the probability of selecting a second speedometer that is not calibrated is 1/11. Finally, on the third draw, there are 10 speedometers remaining, including the one that is not calibrated, so the probability of selecting a third speedometer that is not calibrated is 1/10.

Using these probabilities, we can complete the probability distribution table as follows:

x P(x)

0 (10/12) * (9/11) * (8/10) = 0.60

1 3 * (1/6) * (5/11) * (8/10) = 0.36

2 3 * (1/6) * (1/11) * (8/10) = 0.02

3 (1/6) * (1/11) * (2/10) = 0.00

To find the mean of this probability distribution, we can use the formula:

mean = Σ(x * P(x))

where Σ denotes a sum over all possible values of x.

Using the values from the probability distribution table, we have:

mean = (0 * 0.60) + (1 * 0.36) + (2 * 0.02) + (3 * 0.00) = 0.40

Therefore, the mean of this probability distribution is 0.40.

Step-by-step explanation:

to find f(5)   in f(x) , just put in '5' where 'x' is in the equation

f(5) = 3 (5) + 2 = 17

Answer:

f(5) = 17

Step-by-step explanation:

Let's evaluate the function for f(5)

Insert 5 everywhere x appears:

Therefore f(5) = 17

The quantity of each colour beads that are in the necklace include the following:

Purple beads = 56

Purple beads = 56silver beads = 24

A ratio is defined as the mathematical expression that shows the number of times one value is contained in another value.

The number of purple beads = 14

The number of silver beads ,= 6

The total quantity of beads = 80

Therefore the total combination = 14+6 = 20

For purple beads = 14/20 × 80/1

= 1120/20 = 56

For silver beads = 6/20×80/1

= 480/20= 24

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The groundskeeper can only buy whole bags, they must buy 4 bags to have enough grass seed to cover the entire field.

To find the smallest number of bags needed, first calculate the area of the circular field using the formula for the area of a circle, A = π\(r^2\).

Where r is the radius of the circle. Since the diameter is 290 feet, the radius is 145 feet (290/2).

A = π(\(145^2\)) ≈ 66,026 square feet

Next, calculate the coverage of one pound of grass seed: 400 square feet.

Then, find out how many pounds of grass seed are needed to cover the entire field:

66,026 sq ft / 400 sq ft/lb

≈ 165.065 lbs

Since each bag weighs 50 pounds, divide the required pounds by the weight of one bag:

165.065 lbs / 50 lbs/bag

≈ 3.3013 bags

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Answer:

Total number of ways in which first, second and third prizes will be awarded = 560

Step-by-step explanation:

As given,

There are 16 players participated in a tennis tournament.

and 3 players will be awarded for first, second, and third prize.

As we know,

ⁿCₓ = \(\frac{n!}{x! (n-x)!}\)

n = the number of items.

x = how many items are taken at a time.

As given, n = 16 , x = 3

⇒¹⁶C₃ = \(\frac{16!}{3! (16-3)!} = \frac{16!}{3! (13)!} = \frac{16.15.14.13!}{3! (13)!} = \frac{16.15.14}{3!} = \frac{16.15.14}{3.2.1} = \frac{3360}{6} = 560\)

∴ we get

Total number of ways in which first, second and third prizes will be awarded = 560

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

The compound statement is a conjunction (AND) of two expressions, (p^q) and r. The truth value of the conjunction is true only if both expressions are true. In this case, since p is true, q is true, and r is false, the expression (p^q) is true (since both p and q are true), but the conjunction of (p^q) and r is false, because one of the expressions in the conjunction is false. Therefore, the truth value of the compound statement is False.

Answer:

9

Step-by-step explanation:

Answer:

1.a. 3

1.b. 4

1.c. 9

1.d. 1/2

1.e. 2.4

Step-by-step explanation:

Divide any second number by the corresponding first number.

1.a. 3/1 = 3

1.b. 20/5 = 4

1.c. 27/3 = 9

1.d. 2/4 = 1/2

1.e. 2.4/1 = 2.4

\(\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'\)

\(\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y\)

Sum up ;

\(\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80\)

\(\qquad\displaystyle \tt \dashrightarrow \: 4y = 80\)

\(\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4\)

\(\qquad\displaystyle \tt \dashrightarrow \: y = 20\)

So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years

Answer:

Sydney= 20, Devaughn= 60

Step-by-step explanation:

Let Sydney's age be 'x'

Devaughn's age = 3 times x = 3x

We Know That

The sum of their ages is 80.

So,

3x + x = 80

4x = 80

If we shift the 4 to the 80 side

x = 80/4

x = 20

So, Sydney's age is 20

Therefore, Devaughn's age =

3x = 3 times x

= 3 times 20

= 60

The solution is: the numeric value of (A, B, C, D, E) from the following three formulas are: A = 4, B = 10, C = 2, D = 5, E = 6.

Here, we have,

given that,

Formula:

AC x 1E = 4CD (1)

ADE x 1EC = AB (2)

AB + E9 = 11A (3)

now, we have to find the numeric value of (A, B, C, D, E) from the following three formulas.

However, A, B, C, D, E represent numbers between 0 and 9.

given example: If F = 1, G = 2, then 3FG would be 312.

now, we have,

Let, A = 4 and E = 6

as we have,

A+C = E

B-D = D

A + E = B

so, we get, C = 6 - 4 = 2

B = 6 + 4 = 10

2D = 10 => D = 5

Hence, The solution is: the numeric value of (A, B, C, D, E) from the following three formulas are: A = 4, B = 10, C = 2, D = 5, E = 6.

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Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

1. We are given the following premises:

  - p ⟹ ¬q (Premise 1)

  - q V r (Premise 2)

  - p V u (Premise 3)

  - ¬r (Premise 4)

2. To prove the conclusion, u, we need to use the premises and apply inference rules.

3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.

4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.

5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.

6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.

7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.

8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.

9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.

10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.

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The transformation to f(x) = √5x is a horizontal stretch by 1/5

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

f(x)=\root(5)(x)

Express properly

So, we have

f(x) = √5x

The above is a square root function

The parent function is f(x) =√x

The transformation of the function f(x) = √x to F(x) = √5(x) is a horizontal scaling by a factor of √5 i.e. horizontal stretch

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