Solve for 2 sin A sin B =

To prove that a^3+b^3 is bigger or equal to ¼, we can use mathematical induction. This involves two steps:

To begin, let's consider the base case where a and b are equal to 0. In this case, a^3+b^3 is equal to 0^3+0^3, which is 0. Since 0 is greater than or equal to ¼, the statement is true for the base case.

Next, we can assume that the statement is true for some arbitrary values of a and b (i.e., the inductive hypothesis). That is, we can assume that a^3+b^3 is bigger or equal to ¼.

To complete the proof, we need to show that a^3+(b+1)^3 is also bigger or equal to ¼. To do this, we can use the fact that (a+1)^3 = a^3+3a^2+3a+1. Since the inductive hypothesis states that a^3+b^3 is bigger or equal to ¼, we can say that a^3+(b+1)^3 = a^3+b^3+3a^2+3a+1 is also bigger or equal to ¼.

Therefore, by mathematical induction, we have shown that a^3+b^3 is bigger or equal to ¼ for all values of a and b.

Answer:

A) 60,480 cubic inches

B) 87 Fish

C) $155.73

Step-by-step explanation:

This will be long.

1) 5ft x 4ft x 3ft can be rewritten as 60in x 28in x 36 in.

      This will get you 60,480in^3 or 60,480 cubic inches.

2) We take that 60,480 in^3 and divide it by the 690 needed per fish.

       60,480 / 690 = 87.65. Since we need to make sure we can't go over, that gives us 87 fish.

3) We take that 87, and multiply it by 1.79

        87 x 1.79 = $155.73

On solving the provided question we can say that NILE is not unique for this case

Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.

Note: the probability is equal to the mass function for Y :2

since,  ML criteria, we choose p which maximizes the probability.

If Y 0, L (p) is maximized at p 0.25.

If Y 2, L (p) is maximized at p 0.75.

[tex]But if Y 1, L (p) has the same value at both as shown above; that is,[/tex]

L (0.25) L (0.75) for y — 1.

NILE is not unique for this case

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The total number of hours [h] that it will take to try the possible combinations are → h = {(x/40) - 2} + 1.

Given is that a thief tried 80 combinations to open the safe lock the

first hour, then 40 every hour after that.

Assume that their are total of [x] possible combinations for the lock. Then we can write the expression for the total number of hours [h] that it will take to try the possible combinations as -

x = 80 + 40(h - 1)

(x - 80) = 40(h - 1)

(h - 1) = (x - 80)/40

(h - 1) = {(x/40) - 2}

h = {(x/40) - 2} + 1

Therefore, the total number of hours [h] that it will take to try the possible combinations are → h = {(x/40) - 2} + 1.

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Total service charges is 23.45 when Alan Booker's service fees included a basic charge is 6.95.

Given that,

Alan Booker's service fees included a basic charge, the payment of eight bills, the replacement of a lost card, and four atm transactions—two in-network and two out-of-network.

We have to find the total service charges.

We know that,

Alan borker

Basic charge is 6.95

Bill payments is 3×0.5= 1.5

Card replacement is 5

ATM Transactions

National is 2×2 =4

Out of network is 2×3 =6

Total service charges is 23.45

Therefore, Total service charges is 23.45 when Alan Booker's service fees included a basic charge is 6.95.

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The inverse of the function f(x) = -1/2√x + 3, x ≥ -3 is y = (6 - 2x)²

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

f(x)=-1/2sqrtx+3, x>_-3

Express properly

So, we have

f(x) = -1/2√x + 3, x ≥ -3

Write out the function

f(x) = -1/2√x + 3

Express as an equation

y = -1/2√x + 3

Swap x and y

This gives

x = -1/2√y + 3

Subtract 3 from both sides

-1/2√y = x - 3

So, we have

√y = 6 - 2x

Take the square of both sides

y = (6 - 2x)²

Hence, the inverse is  y = (6 - 2x)²

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Transversion is known as point mutation in DNA.

Transversion is a term used in molecular biology. It refers to a point mutation in DNA in which a single (two ring) purine (A or G) is changed for a (one ring) pyrimidine (T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ionizing radiation or alkylating agents. It can only be reversed by a spontaneous reversion.

So, here 5'AGCCTAC3' we can replace (A or G) with (T or C)

So, the answer should be :

5'ATCCTAC3'

Here we have replaced G with T and other things are same

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The full question will be like this

Assume that a wild-type sequence is 5'AGCCTAC3'. Indicate the sequence that might be produced by a transversion. Which of the following sequences might be produced by a transversion?

A) 5'AGTCTAC3'

B) 5'AGCCGCCGCCGCCTAC3'

C) 5'AGCCCAC3'

D) 5'ATCCTAC3'

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Answer:12

Step-by-step explanation:

24/2 = 12 bc 12*2=24

As per the desire to test to see if the average is still 95 degrees or whether it has changed. The results will be as follows:

a) The null hypothesis and the alternative hypothesis must be identified before we can set up the statistical test at a 0.01 significance level. The average melting point, which is still 95 degrees, has not altered, according to the null hypothesis. The other theory is that the average melting point, which was 95 degrees, has changed.

Next, we must establish the test's critical value. The critical value will be the amount that corresponds to a p-value of 0.01 because we are choosing a significance level of 0.01. We may use the usual normal distribution to determine the critical value because we are presuming that the melting point distribution is normally distributed with a standard deviation of 1.20.

Using the sample data, we discover that a sample of 16 melting points has an average temperature of 94.32 degrees. A one-sample z-test can be used to examine whether this sample average differs noticeably from the 95 degree long-term average.

where x is the sample average (94.32), is the long-term average (95), σ is the standard deviation of the melting points (1.20), and n is the sample size (16).

Plugging these values into the formula, we get:

z = (94.32 - 95) / (1.20 / √16) = -0.83

We are unable to rule out the null hypothesis because the z-score is smaller than the critical value. As a result, we draw the conclusion that 95 degrees still serve as the average melting point.

b) The range of values that would be deemed statistically significant at the 0.01 significance level constitutes the critical region for this test. The range of values that would be regarded as significantly different from the long-term average of 95 degrees is the critical zone in terms of the sample average. The range of values that would be associated with a p-value of less than 0.01 is known as the critical zone in terms of the z-score.

The required z-score value for a one-sided test with a significance level of 0.01 is 2.326. Therefore, any number more than 2.326 is the critical zone in terms of the z-score. This relates to a range of values that are significantly higher than 95 degrees based on the sample average.

The essential z-score values for a two-sided test with a 0.01 significance level are -2.326 and 2.326. Therefore, any value between -2.326 and 2.326 constitutes the key zone in terms of the z-score. This relates to a range of values that are significantly higher or lower than 95 degrees, based on the sample average.

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Answer:

2x - (5x - 6) + (-3x + 2)

Step-by-step explanation:

L'expression -6x + 8 est la forme réduite de:

-3x + 3x + 2 *4

= 0x + 8

= 8

pas vrai

__________________________

2x - 8x *5 + 3

= 2x - 40x + 3

= -38x + 3

pas vrai

__________________________

2x - (5x - 6) + (-3x + 2)

=2x - 5x + 6 - 3x + 2

= -6x + 8

Corriger

__________________________

- (3x + 5) + (-2x + 3) - x

= - 3x - 5 - 2x + 3 - x

= - 6x + 2

pas vrai

(veuillez pardonner mon français.)

Answer:

x=7

Step-by-step explanation:

y = log(x + 3) and y = 1.

Substitute y =1 into the equation

1 = log(x + 3)

Raise each side to base 10 since log (x+3) has a base 10 implied

10^1 = 10^ log(x+3)

10 = x+3

Subtract 3 from each side

10-3 = x+3-3

7 =x

Answer:

3 or 3.16227766017

Step-by-step explanation:

Using system of linear equation, the number of quarter is 7 and nickel is 4

System of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

To solve this problem, we need to write a system of linear equation.

let;

1 nickel = 5 cent

1 quarter = 25 cent

25x + 5y = 195 ... eq(i)

x = 3 + y ...eq(ii)

Put eq(ii) into eq(i)

25(3 + y) + 5y = 195

75 + 25y + 5y = 195

75 + 30y = 195

30y = 195 - 75

30y = 120

y = 4

put y = 4 in equation (ii)

x = 3 + 4

x = 7

The number of quarter is 7 and nickel is 4

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The answer is B & D

Answer:

Step-by-step explanation:

i'd say the 2nd one and the last one

Because the 2nd one is a straight line that is pointing up showing that it's increasing.

And the last one because the line is going up meaning it's increasing

In case whereby Afia bought shoes that were on sale for 30% off the regular price and Afia saved  $12` the regular price of the shoe is  $40.

It should be noted that the Regular price  can be described as the price at which the goods or services are openly and actively sold  with the producer or  supplier to the public  with repect to the continuing basis for a substantial period of time.

The amount of savings can be divided by the percentage off to find the

Since the sale for 30% off the regular price, then regular price.

(12/0.30) = 40

hence the regular price was $40

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The population of a country increases by 31 years approximately.

differentiation:

To differentiate is to identify the differences between things, and to discriminate among them. There are a number of simple rules which can be used to allow us to differentiate many functions easily.

If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x".

Let population =x, at time t years.

Given  [tex]\frac{dx}{dt} \alpha X[/tex]

⇒  [tex]\frac{dx}{dt}=Kx[/tex]

where k is a constant of proportionality

 or  [tex]\frac{dx}{x} =Kdt[/tex].  Integrating, we get lnx=kt+lnc

⇒  [tex]\frac{x}{c}=e^{Kt}[/tex] or [tex]X=ce^{kt}[/tex]

If initially, i.e., when time t=0,x=x0 then xo=ce^0=c

[tex]X-Xoe^{kt}[/tex]

Given X=2Xo t=20 then,

[tex]2Xo=Xoe^{20k} \\\\= > 2=e^{20k} \\[/tex]

ln2=20k---(1)

To find t, when t triples X=3Xo

[tex]3Xo=Xoe^{kt} \\\\3=e^{kt}[/tex]

ln3=kt(2)---(2)

Dividing equation (2) by (1) then

[tex]\frac{t}{20} =\frac{ln3}{ln2}[/tex]

 or

[tex]t=20*\frac{ln3}{ln2}[/tex]

t=20*1.5849

t=31 years (approx)

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Answer:

The answer is A:22

We can start by finding out 5^2 which is just 5 times 5 because it is 5 times itself 2 times (as the little two tells us how many times to multiply 5 by itself). The answer is 25. 25-3=22

5×5-3

=25-3

=22 is the answer

The graph of y = f(x) is graphed. The end behavior of f(x) is as x → ∅ f(x) → -∅ and x → -∅ , f(x) → - ∅

The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +∅) and the left end of the x-axis (as x approaches ∅), the end behavior of a function represents the trend of the graph. Look at the polynomial function's leading term to identify its end behavior. The leading term will dominate the graph since it has the largest power and will thus increase much more quickly than the other terms as x gets very large or very small.

Given,

Graph of y = f(x)

End behavior of f(x) is:

as x → ∅ f(x) → -∅ and x → -∅ , f(x) → - ∅

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Answer:

Step-by-step explanation:

nCr = n! / r!(n-r)!

n=46

r=6

=46!/6!(46-6)!

=46!/[6!(40)!]

=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)

Cancel out 40!

=46*45*44*43*42*41/(6*5*4*3*2*1)

=6744109680/720

=9366819

Possible different selection 9366819

Multiply by 6, 7, 8, and 9 fill in the puzzle so that the product in each column and row is the same is 3024.

What  is Multiply?

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

[tex]\begin{aligned}& 6 \times 8=48 \\& 6 \times 9=54 \quad \text { find the common } \\& \text { multiple } \\& 9 \times 7=63 \quad 6 \times 7 \times 8 \times 9=3024 \\&\end{aligned}[/tex]

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Refer to the images uploaded. Please let me know if this answer works out for you. I also would appreciate a rate :)

Answer:

Step-by-step explanation:

71/5 70/5 = 14 with 1/5 = .2 this together = 14.2

Yes, knowing the value of b, the slope of the regression line, allows us to predict the correlation coefficient value with accuracy.

Regression and correlation techniques can be used to establish links between variables.

Every day, we refer to any form of association as a "correlation," using that word.

To determine whether or if there is a relationship between the variables under investigation, correlation analysis is used.

Although regression illustrates how the variables are related,

Correlation and regression analysis can be shown graphically using scatter plots.

According to the question,

If we know the value of the slopes of the regression line say byx and bxy

We can Calculate the value of Correlation coefficient by using the relation

=> r = √(byx × bxy)

Hence , Yes We can accurately guess the value of correlation when slope of regression line is given

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The chance that the average of the draws will be in the range 73 to 77 is 0.6826 when the average ticket value per box is 75, while the standard deviation is 10.

Given that,

The average ticket value per box is 75, while the standard deviation is 10. With replacement from this box, 25 random draws are conducted in total.

We have to find the chance that the average of the draws will be in the range 73 to 77.

We know that,

Take

μ=75,σ=10

X₁=73, X₂=77

We need to compute P(73≤X≤77)

The corresponding p-values are calculated by using control limit theorem

Z=X-μ/σ

Z₁=73-75/10=-2/10=-1/5

Z₂=77-75/10=2/10=1/5

We get,

P(73≤X≤77)

P(-1/5≤z≤1/5)

P(z≤1/5)-P(z≤-1/5)

0.6826

Therefore, the chance that the average of the draws will be in the range 73 to 77 is 0.6826 when the average ticket value per box is 75, while the standard deviation is 10.

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By algebra properties, the power expression 3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ is divisible by 10 as it is equivalent to (3ⁿ - 2ⁿ⁻¹) · 10.

According to number theory, a natural number is divisible by another natural number if the result is a natural number. In this case we must determine if a power expression is divisible by 10 according to algebra properties.

First, write the whole expression:

3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ

Second, use algebra properties until the multiple is found:

(3ⁿ⁺² + 3ⁿ) + (- 2ⁿ⁺² - 2ⁿ)

3ⁿ · (3² + 1) + 2ⁿ · (- 2² - 1)

3ⁿ · 10 - 2ⁿ · 5

3ⁿ · 10 - 2ⁿ⁺¹⁻¹ · 5

3ⁿ · 10 - 2ⁿ⁻¹ · 10

(3ⁿ - 2ⁿ⁻¹) · 10

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The quantity of 30% acid content and 10% acid content used is 0.15 liters and 1.35 liters respectively

Let

x + y = 1.5

0.3x + 0.1y = 1.5 × 0.12

0.3x + 0.1y = 0.18

x + y = 1.5

0.3x + 0.1y = 0.18

From (1)

x = 1.5 - y

Substitute into (2)

0.3x + 0.1y = 0.18

0.3(1.5 - y) + 0.1y = 0.18

0.45 - 0.3y + 0.1y = 0.18

- 0.3y + 0.1y = 0.18 - 0.45

-0.2y = -0.27

divide both sides by -0.2

y = -0.27 / -0.2

y = 1.35

Substitute into (1)

x + y = 1.5

x + 1.35 = 1.5

x = 1.5 - 1.35

x = 0.15

Therefore, 0.15 30% acid content and 1.35 10% acid content is needed.

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The equation that correctly represents the given problem is;

¹/₂p - 2 = 18

We are told that p is the time it takes Tomás to bike to the park.

Now, we are given that;

Time taken by Tomás to bike to the community center = 2 minutes less than half the time it takes him to bike to the city park.

Time taken by Tomás to bike to the community center = 18 minutes

Thus, correct equation can be expressed as;

¹/₂p - 2 = 18

And if we need to solve p, we can just make p the subject of the equation and solve accordingly.

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The complete question is;

Which equation represents this problem?

The time it takes Tomás to bike to the community center is 2 minutes less than half the time it takes him to bike to the city park. It takes Tomás 18 minutes to bike to the community center.

Let p = the time it takes Tomás to bike to the park.

Answer:

True

Step-by-step explanation:

Use the distance formula: x^2 + y^2 = d^2; where d=distance

x = x2 - x1

y = y2 - y1

(10, -2), (4, 6)  ==> (x1=10, y1=-2), (x2=4, y2=6)

x = 4 - 10  ==> plug in 4 for x2 and 10 for x1

x = -6

y = 6 - (-2)  ==> plug in 6 for y2 and -2 for y1

y = 6 + 2

y = 8

(-6)^2 + (8)^2 = d^2  ==> plug in x and y back into the distance formula

36 + 64 = d^2

100 = d^2  ==> simplify

d = [tex]\sqrt{100}[/tex]

distance = 10  ==> True