Lochlon transfers his investment into a money market account. The account now earns compound interest of 1. 95% annually with a maturity date of 5 years

Step-by-step explanation:

.5 / 1.5    is  1/3       (1/3)^2  = 1/9

Answer: 0.09

Step-by-step explanation:

0.5 ÷ 1.5 = 0.3 0.3squared = 0.09

The determinant of the given matrix a is: det(a) = b2c2 + a2c2 + a2b2 - 2a2b2 - 2a2c2 + 2abc.

The determinant of a 3x3 matrix can be found using the formula:

det(A) = a11(a22a33 - a32a23) - a12(a21a33 - a31a23) + a13(a21a32 - a31a22)

Substituting the given matrix values, we get:

det(a) = 1(b2c2 - c(b2) + a2(c2) - c(a2) + a(b2) - a(b2)) - a(1c2 - c1 + a2c - c(a2) + a - a(a2)) + a(1b2 - b1 + a(b2) - b(a2) + a - a(b2))

Simplifying this expression, we get:

det(a) = b2c2 + a2c2 + a2b2 - a2b2 - b2c - a2c - a2b + a2c + abc - abc - a2c + ac2 + ab2 - ab2 - abc

Simplifying further, we get:

det(a) = b2c2 + a2c2 + a2b2 - 2a2b2 - 2a2c2 + 2abc

Thus, the determinant of the given matrix a is:

det(a) = b2c2 + a2c2 + a2b2 - 2a2b2 - 2a2c2 + 2abc.

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The degrees of freedom that should be used in the pooled-variance t-test is 193.

The formula for calculating degrees of freedom (df) for a pooled-variance t-test is:

df = \((s_1^2/n_1 + s_2^2/n_2)^2 / ( (s_1^2/n_1)^2/(n_1-1) + (s_2^2/n_2)^2/(n_2-1) )\)

where \(s_1^2\) and \(s_2^2\) are the sample variances, \(n_1\) and \(n_2\) are the sample sizes.

Substituting the given values, we get:

df = \([(4^2/16) + (6^2/25)]^2 / [ (4^2/16)^2/(16-1) + (6^2/25)^2/(25-1) ]\)

df = \((1 + 1.44)^2\) / ( 0.25/15 + 0.36/24 )

df = \(2.44^2\) / ( 0.0167 + 0.015 )

df = 6.113 / 0.0317

df = 193.05

Rounding down to the nearest integer, we get:

df = 193

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To calculate the degrees of freedom for the pooled-variance t test, we need to use the formula:  df = (n1 - 1) + (n2 - 1) where n1 and n2 are the sample sizes of the two groups being compared. The degrees of freedom for this pooled-variance t-test is 39 (option B).

However, before we can use this formula, we need to calculate the pooled variance (s*).

s* = sqrt(((n1-1)s1^2 + (n2-1)s2^2) / (n1 + n2 - 2))

Substituting the given values, we get:

s* = sqrt(((16-1)4^2 + (25-1)6^2) / (16 + 25 - 2))

s* = sqrt((2254) / 39)

s* = 4.02

Now we can calculate the degrees of freedom:

df = (n1 - 1) + (n2 - 1)

df = (16 - 1) + (25 - 1)

df = 39

Therefore, the correct answer is B. df = 39.

To calculate the degrees of freedom for a pooled-variance t-test, use the formula: df = n1 + n2 - 2. Given the information provided, n1 = 16 and n2 = 25. Plug these values into the formula:

df = 16 + 25 - 2
df = 41 - 2
df = 39

So, the degrees of freedom for this pooled-variance t-test is 39 (option B).

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Finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. Here are a few methods to find the square root:

Prime Factorization: This method involves breaking down the number into its prime factors. Pair the factors in groups of two, and take one factor from each pair. Multiply these selected factors to find the square root. For example, to find the square root of 36, the prime factors are 2 * 2 * 3 * 3. Taking one factor from each pair (2 * 3), we get 6, which is the square root of 36.

Estimation: Approximate the square root using estimation techniques. Find the perfect square closest to the number you want to find the square root of and estimate the value in between. Refine the estimate using successive approximations if needed. For example, to find the square root of 23, we know that the square root of 25 is 5. Therefore, the square root of 23 will be slightly less than 5.

Using a Calculator: Most calculators have a square root function. Simply input the number and use the square root function to obtain the result.

It's important to note that finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

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Answer:

21+3x=-15

-21 -21

3x=-36

÷3 ÷3

x=-12

x=-12

The department store purchased men's baseball caps for ₱132 and sells them for ₱229. The rate of markup based on the selling price needs to be determined.

To find the rate of markup based on the selling price, we need to calculate the difference between the selling price and the cost price (purchase price), and then express it as a percentage of the selling price.

The cost price is ₱132, and the selling price is ₱229. The difference between the selling price and the cost price is ₱229 - ₱132 = ₱97.

To find the rate of markup, we divide the markup by the selling price and multiply by 100 to express it as a percentage:

Rate of Markup = (Markup / Selling Price) * 100

In this case, the markup is ₱97 and the selling price is ₱229.

Rate of Markup = (₱97 / ₱229) * 100 ≈ 42.39%

Therefore, the rate of markup based on the selling price is approximately 42.39%.

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The driver's percent value-added time is approximately 18.57%.

The percent value-added time, we need to consider the total time spent in non-value-added activities (waiting in line, eyes tested, and photograph taken) compared to the total time spent, including value-added activities.

Total time spent = Time in line + Time for eyes test + Time for photograph = 57 minutes + 9 minutes + 4 minutes = 70 minutes

Value-added time = Time for eyes test + Time for photograph = 9 minutes + 4 minutes = 13 minutes

Percent value-added time = (Value-added time / Total time spent) * 100

= (13 minutes / 70 minutes) * 100

≈ 18.57%

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Answer:

2^32

Step-by-step explanation:

The solution to the equation 8^x/2=2^3/8×4^3/4 is x = 15/14

To simplify an expression: to remove brackets, unnecessary terms and numbers

\(8^{x/2} = 2^{3/8} * 4^{3/4}\)

\(2^{3x/2} = 2^{3/8} * 2^{2 (3/4)}\)

using law of Indices

\(2^{3x/2} = 2^{3/8 + 6/4}\)

\(\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}\)

\(\frac{3x}{2} = \frac{3+12}{8}\)

\(\frac{3x}{2} = \frac{15}{8}\)

cross multiply

24x =30

Divide both sides by 24

\(\frac{24x}{24} = \frac{30}{28}\)

x = 15/14

Therefore, the solution to the equation is x = 15/14

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The mean of the sampling distribution of the sample proportions is 0.67.

The standard deviation of the sampling distribution of the sample proportions is 0.052.

Population = Large

Household with cable TV = 67%

Sample size (n) = 81

The mean of sampling distribution (μx) = p = 67% = 67/100 = 0.67

The standard deviation of the sampling distribution,

Standard deviation (σ) :

                        σ = \(\sqrt{( p*(1 - p)) /n }\)

                      ⇒σ  = \(\sqrt{( 0.67*(1 - 0.67)) /81 }\)

                     ⇒ σ= \(\sqrt{( 0.67 * 0.33) /81 }\)

                     ⇒σ= \(\sqrt{( 0.2211 /81 }\)

                     ⇒ σ= \(\sqrt{0.002729}\)

                     ⇒σ = 0.052

Therefore,

The mean of the sampling distribution of the sample proportions is 0.67.

The standard deviation of the sampling distribution of the sample proportions is 0.052.

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Answer:

B and c I think lolll

Answer:

isoceles right triangle

Step-by-step explanation:

1. it has a right angle

2. it has to equivalent sides

Answer:.

Step-by-step explanation: It wont show on my device sir/ma´am/person. Maybe its because of my device ..if not it could possibly be perhaps you somehow put a wrong file? Not to sure on this problem. But i truly hope its just my device and not yours. But other than that; enjoy your day!

(Btw, please dont give me anything. I didnt even answer what you need help on. But wish you luck on it.)

Answer:

D. x^3 - 11

Step-by-step explanation:

y = ∛ x + 11

x = ∛ y + 11

x^3 = y + 11

x^3 - 11 = y

Hopefully this helped!

Brainliest please?

Answer:

$28

Step-by-step explanation:

Multiply 40 by 30% (.30) which gives you an answer of 12

Subtract 12 from 40 and that gives you 28

$28

Answer:

48

Step-by-step explanation:

AB+CB=AC which is 18+30 which is 48

Answer:

C. 48

Step-by-step explanation:

This distance of AC is the same as the distance between BC plus the distance between AB. In other words: AB + BC = AC

AB = 18

BC = 30

30 + 18 = AC

AC = 48

Answer:

-20c-160

Step-by-step explanation:

-10(9c-7c+8)-80

-10(2c+8)-80

-20c-80-80

-20c-160

The probability she makes at least 65 is 0.0139.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

\(\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}\)

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Answer:

C

Step-by-step explanation:

Substitute the given values into the expression

\(\frac{v}{2}\) + (\(\frac{3}{4}\) - w )

= \(\frac{1}{2}\) + (\(\frac{3}{4}\) - \(\frac{5}{8}\) ) ← evaluate parenthesis

= \(\frac{1}{2}\) + (\(\frac{6}{8}\) - \(\frac{5}{8}\) )

= \(\frac{1}{2}\) + \(\frac{1}{8}\)

= \(\frac{4}{8}\) + \(\frac{1}{8}\)

= \(\frac{5}{8}\)

Answer:

1,000 sq ft

Step-by-step explanation:

Part A:

To find the total area of both rooms (length x width):

(x+4)(2x+6+x-4)

(x+4)(2x+2+x)

2x²+2x+x²+8x+8+4x

= 3x²+14x+8

Part B:

If the length of the game room = 12 ft, we can solve for x:

Game room = (x-4)=12; therefore x=16

Plug 16 in for x in the equation from Part A:

3x²+14x+8 becomes 3(16)²+14(16)+8

= 1,000 sq ft

Answer:

1) NO

2)YES

3)YES

4)NO

5)NO

Answer:

Area : 27.5

Perimeter : 20

Step-by-step explanation:

All sides of a regular pentagon have the same length

1 side = 4

4x5 = 20 = Perimeter

Pentagon area formula :

1/4(sqrt(5(5+2sqrt(5)))x)

Plug x in (side length)

27.53

round to nearest tenth

27.5

The simplified expression of \(x^{-2/3} . x^{6/7}\) is \(x^{4/21}\)

The expression \(x^{-2/3} . x^{6/7}\) can be simplified as follows:

using law of indices,

xⁿ . xᵇ = xⁿ⁺ᵇ

Therefore,

\(x^{-2/3} . x^{6/7}\) = \(x^{-2/3 + 6/7}\)

\(x^{-2/3 + 6/7} = x^{ -14+18/ 21}\)

\(x^{-2/3 + 6/7} = x^{ -14+18/ 21} = x^{4/21}\)

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Answer:

Draw the figure that illustrates what is to be proved. ...

List the given statements, and then list the conclusion to be proved. ...

Mark the figure according to what you can deduce about it from the information given. ...

Write the steps down carefully, without skipping even the simplest one.

Step-by-step explanation:

Answer:

For the first question the answer is 50(0.2 + 1)^2 = 72

For the second question it is y = 32

Step-by-step explanation:

In case you need to see how i got it...it's below

For number 1, y is proportional to (x + 1)^2

The equation would be y(x +1)^2 = k(the constant). Then I substituted numbers you gave me in the equation which was : 50(0.2 + 1)^2 = k(72)

For number 2 I used this equation: y (x + 1)^2 = 72. I substituted x for 0.5. The equation will be: y(0.5 + 1)^2 = 72. Then I got 32 for y.

Hope this helps:)

Answer:

For the first question the answer is 50(0.2 + 1)^2 = 72

For the second question it is y = 32

Step-by-step explanation:

In case you need to see how i got it...it's below

For number 1, y is proportional to (x + 1)^2

The equation would be y(x +1)^2 = k(the constant). Then I substituted numbers you gave me in the equation which was : 50(0.2 + 1)^2 = k(72)

For number 2 I used this equation: y (x + 1)^2 = 72. I substituted x for 0.5. The equation will be: y(0.5 + 1)^2 = 72. Then I got 32 for y.

Hope this helps:)

Step-by-step explanation:

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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To prove that if every subspace of V having dimension n−1 is invariant under T, then T must be a scalar multiple of the identity operator, we can proceed with the following steps:Assume that every subspace of V having dimension n−1 is invariant under T.

Let's consider an arbitrary vector v in V and construct the subspace U = Span(v). Since U is a subspace of V and has dimension n−1 (since the dimension of U is 1), it must be invariant under T.Since U is invariant under T, for any u ∈ U, T(u) must also be in U.

Let's express the vector v as v = c * u, where c is a scalar and u is a non-zero vector in U. Applying T to v, we have T(v) = T(c * u) = c * T(u).

Since T(u) ∈ U, it can be written as T(u) = d * u, where d is a scalar.

Substituting T(u) = d * u into the expression for T(v), we have T(v) = c * (d * u) = (c * d) * u.

Comparing T(v) = (c * d) * u with the expression v = c * u, we can see that T(v) is a scalar multiple of v.

Since this holds true for any vector v in V, we can conclude that T is a scalar multiple of the identity operator.

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A

Explanation

Step 1

remember some properties of the logarithms:

then

I hope this helps you

We can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.

To find the equation of clean pulsations for a left-mounted beam with a simple support on the right, we can use the differential equation that describes the deflection of the beam. Assuming the beam is subject to a distributed load and has certain boundary conditions, the equation governing the deflection can be written as:

d^2y/dx^2 + (chx)^2 * y = 0

Where:

y(x) is the deflection of the beam at position x,

d^2y/dx^2 is the second derivative of y with respect to x,

ch(x) is the hyperbolic cosine function.

To solve this differential equation, we can assume a solution in the form of y(x) = A * cosh(kx) + B * sinh(kx), where A and B are constants, and k is a constant to be determined.

Substituting this assumed solution into the differential equation, we get:

k^2 * (A * cosh(kx) + B * sinh(kx)) + (chx)^2 * (A * cosh(kx) + B * sinh(kx)) = 0

Simplifying the equation and applying the given identity (chx)^2 - (shx)^2 = 1, we have:

(A + A * chx^2) * cosh(kx) + (B + B * chx^2) * sinh(kx) = 0

For this equation to hold for all values of x, the coefficients of cosh(kx) and sinh(kx) must be zero. Therefore, we get the following equations:

A + A * chx^2 = 0

B + B * chx^2 = 0

Simplifying these equations, we have:

A * (1 + chx^2) = 0

B * (1 + chx^2) = 0

Since we are looking for nontrivial solutions (A and B not equal to zero), the expressions in parentheses must be zero:

1 + chx^2 = 0

Using the identity (sinx)^2 + (cosx)^2 = 1, we can rewrite this equation as:

1 + (1 - (sinx)^2) = 0

Simplifying further, we get:

2 - (sinx)^2 = 0

Solving for (sinx)^2, we find:

(sin x)^2 = 2

Since the square of the sine function cannot be negative, there are no real solutions to this equation. Therefore, we can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.

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Answer:

The first choice

Step-by-step explanation:

I know this because I have one, but also, it says in the options to avoid monthly fee section.