Solve the equation. ​

9(z + 3) = 45


​

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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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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The average velocity during [1,2] time period is 6cm/s.

This looks like an exercise that's building toward the idea of a derivative.

These calculations are done best with a calculator, but here's how the first interval is used:

Average velocity = (position at 2 - a position at 1) / (2 - 1)

It's really distance divided by time!

Position at t = 2: 4sin(2[tex]\pi[/tex])+3cos(2[tex]\pi[/tex])=4(0)+3(1)=3

Position at t = 1: 4sin([tex]\pi[/tex])+3cos([tex]\pi[/tex])=4(0)+3(-1)=-3

So over the interval [1, 2], the average velocity is [tex]\frac{3-(-3)}{2-1} =\frac{6}{1} =6[/tex]

∴ Average velocity=6cm/s

I used a spreadsheet to calculate the average velocity over the other intervals and a couple of shorter ones, too.  (See attached image.)

As these intervals get shorter (the right endpoint is approaching 1), the average velocity gets closer and closer to the instantaneous velocity. An estimate would be -12.6.

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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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Since the probability that a player gets a hit on any given at bat is independent of the other at bats, we can find the probability that Mark has fewer than 3 hits in his next 6 at bats by simply multiplying the probability of getting a hit on each at bat. Since Mark has a probability of 0.155 of getting a hit on any given at bat, he has a probability of (0.155)^3 of getting exactly 3 hits in his next 6 at bats. Therefore, the probability that he has fewer than 3 hits in his next 6 at bats is 1 - (0.155)^3  approx 0.76

Answer:

The probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.

Step-by-step explanation:

A batting average is the number of hits a player has divided by the number of times they have been at bat. In this case, Mark has a batting average of 0.155, which means that he has hit 0.155 of the times he has been at bat.

To find the probability that Mark will have fewer than 3 hits in his next 6 at bats, we can use the binomial probability formula. The formula for binomial probability is:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where "n" is the number of trials, "x" is the number of successes, "p" is the probability of success on a single trial, and "1-p" is the probability of failure on a single trial.

In this case, the number of trials is 6, the number of successes is 3, and the probability of success on a single trial is 0.155. Plugging these values into the formula, we get:

P(3) = (6 choose 3) * 0.155^3 * (1-0.155)^(6-3)

To calculate the probability that Mark will have fewer than 3 hits in his next 6 at bats, we need to sum the probabilities of 0, 1, and 2 hits. We can use the binomial probability formula to calculate the probability of each of these outcomes, and then add them together to find the total probability.

For 0 hits, the probability is:

P(0) = (6 choose 0) * 0.155^0 * (1-0.155)^(6-0) = 0.009

For 1 hit, the probability is:

P(1) = (6 choose 1) * 0.155^1 * (1-0.155)^(6-1) = 0.054

For 2 hits, the probability is:

P(2) = (6 choose 2) * 0.155^2 * (1-0.155)^(6-2) = 0.141

Adding these probabilities together, we get the total probability that Mark will have fewer than 3 hits in his next 6 at bats:

P(0 or 1 or 2) = 0.009 + 0.054 + 0.141 = 0.204

Therefore, the probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.

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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Answer:

Step-by-step explanation:

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

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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The point of intersection of the equations C = 100t + 5000 and C = 75t + 7000 represents the  the point in time where the cost of installing either will be the same.

Linear equations are equations where the right hand side and left hand side involves expressions with one or more variables for which the highest degree of the variable being 1.

We have two linear equations given,

C = 100t + 5000 and C = 75t + 7000.

The point of intersection of these linear equations will be when both the equations are equal.

100t + 5000 = 75t + 7000

100t - 75t = 7000 - 5000

25t = 2000

t = 2000/25

t = 80

This is the point in time where the cost of installing either will be the same, that is after 80 months.

Cost of installing = (100 × 80 ) + 5000 = 13,000

Or                         = (75 × 80) + 7000 = 13000

Hence the point of intersection of these equations represent the point in time where the cost of installing either will be the same.

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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 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

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

The statement contained within FST that agrees with the statement that the research participant is an active partner in the endeavor is: We can only know women's experiences by paying attention to women's own interpretations of these experiences.

FST stands for Food Science and Technology. It is scientific journal reviewed by peers. It acknowledges all the branches of science and technology that deal with packaging and engineering of foods and food products.

Research is the detailed and in-depth study of any subject that includes discovering facts about it as well as inventing new facts. It includes learning from the existing facts and generating new knowledge.

Therefore, the research is the only detailed way for FST.

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The order of the distances, from least to greatest, is given by the following option:

D. 40, 675/16, 586/13, square root of 2,111, 10 square root of 27.

To order the distances, we have to find them all in the same format.

For this problem, I will use the decimal format for all the distances, meaning that:

Then the decimal distances are given as follows:

Then option D orders the distances correctly.

The problem is given by the image shown at the end of the answer.

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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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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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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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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.

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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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:

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

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.

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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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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Answer: y=6x

Step-by-step explanation: You have to find the relationship between x and y. For this, 1 (x) times 6 = 6 (y). 2 (x) times 6 = 12 (y). This pattern will repeat in this table for eternity, so the relationship is y=6x.

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

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.)