the function below satisfies the mean value theorem on the specified interval.find the value of c in the interval (1,2) where 1.2/x 1.6 (1,21)

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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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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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 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:

Step-by-step explanation:

1)

She takes medicine at the moment 0

24(1/2)^0

24 · 1

24 mg

2)

24 (1/2)^1

24 (1/2)

12 mg

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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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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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.

One example of a problem involving multiplication of fractions that can be made easier using the associative property is as follows:

Given the expression (2/3) * (4/5) * (6/7), we can use the associative property to rearrange the terms and simplify the expression. Specifically, the associative property states that the order in which we perform operations does not change the result. In this case, we can rearrange the terms as follows:

(2/3) * (4/5) * (6/7) = (4/5) * (2/3) * (6/7)

Then, we can simplify the expression using the commutative property of multiplication (which states that the order of the terms does not affect the result of the multiplication):

(4/5) * (2/3) * (6/7) = (2/3) * (4/5) * (6/7)

Finally, we can simplify the expression by multiplying the fractions:(2/3) * (4/5) * (6/7) = (12/21).

Using the associative property allows us to rearrange the terms and simplify the expression, making the problem easier to solve.

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: Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.

Step-by-step explanation: Let Q be the present age of Queens University College and G be the present age of GAGE University College.

Since the present age of Queens University College is three times that of GAGE University College, we can write the equation Q = 3G.

After 5 years, the difference of their ages will be 30 years, so we can write the equation Q + 5 = G + 30.

Substituting the first equation into the second equation, we get 3G + 5 = G + 30.

Solving for G, we find that G = 15.

Substituting this value into the equation Q = 3G, we find that Q = 3 * 15 = 45.

Thus, the present age of Queens University College is 45 years, and the present age of GAGE University College is 15 years.

Answer:

16 possible outcomes

Step-by-step explanation:

The sample space of Brittney's experiment is the set of all possible outcomes of flipping four coins. Since each coin can either land on heads or tails, there are two possible outcomes for each coin. Therefore, there are a total of 2^4 = 16 possible outcomes for the experiment. These outcomes can be represented as a list, with each outcome represented by a string of four "H"s and "T"s, where "H" represents a heads and "T" represents a tails. For example, one possible outcome of the experiment could be "HHHT" (two heads, one tails, one heads), and another could be "TTTT" (four tails). The complete sample space of Brittney's experiment would include all 16 possible outcomes.

Answer:

Step-by-step explanation:

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

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

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: B. 21.77%

Step-by-step explanation: See picture. I'm currently taking the test right now

Answer:

  (b)  21.77%

Step-by-step explanation:

Using the given tax rate table, you want to know the effective tax rate on a taxable income of $192,700.

The tax will be the sum of the taxes due in each of the brackets. This sum can be simplified to make the tax computation a little less work.

  tax = 0.10(10275) +0.12(41175 -10275) +0.22(89075 -41175) +0.24(17050 -89075) +0.32(192700 -170050)

  = 10275(0.10 -0.12) +41175(0.12 -0.22) +89075(0.22 -0.24) +170050(0.24 -0.32) +192700(0.32)

  = 192700(0.32) -(10275(0.02) +41175(0.10) +89075(0.02) +170050(0.08))

  = 192,700(0.32) -19708.50

  tax = 41955.50

The tax as a percentage of the taxable income is ...

  tax/income × 100% = 41955.50/192700 × 100% ≈ 21.77%

The effective tax rate is about 21.77%.

__

Additional comment

We can use this same idea to simplify the tax table all around. The various tax computations are shown in the second attachment. Interestingly, the tax due is the maximum of the computations for the different brackets. The graph shows the effective tax rate (%) as a function of income. The effective rate for $192,700 is marked.

Because the tax tables are written with discontinuities, there can be some confusion about the amount that fits in each bracket. For example, the tax on 10276 is not 10% of 10275 plus 12% of zero. Rather it is 10% of 10275 plus 12% of (10276 -10275), for a total of $1027.62.

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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

As per the concept of probability, the probability of getting head is 99.5%.

The term probability in statistics is known as the possible way of getting the particular event.

Here we have given that

And we need to find the probability of getting  head.

Here we know that the number of coins is 10.

So, the sample space for the 10 coins is calculated as,

Here we already know that for each of the 10 coin tosses, we have either a head (H) or a tail (T).

so, the total number of probability of 10 coins is 210 strings in the sample space.

Here we know that the only option of all tails doesn't have head in it.

So, the number tosses that have head in it is calculated as,

=> 210 - 1

=> 209

Therefore, the probability is calculated as,

=> P = 209/210

=> P = 0.995

Therefore, the probability in percentage is 99.5%

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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

The City A and Abilene are nearest to each other

The Austin and Abilene are farthest apart from each other

Here the two angles of the triangle = 59 degrees and 64 degrees

The sum of the angles in a triangle is 180 degrees

Then the third angle will be

59 + 64 + x = 180

123 + x = 180

x = 180 - 123

x = 57 degrees

The third city name is not visible so consider it as city A

Part a

Here the smallest angle is 57 degrees

Opposite side of the angle will be the smallest distance

That is the distance between city A and Abilene

Part b

Here the largest angle is 64 degrees

The opposite side of the angle will be largest distance

That is the distance between Austin and Abilene

Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other

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Answer:12

Step-by-step explanation:

24/2 = 12 bc 12*2=24

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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By using the mean formula, the mean grade across all four classes was 83.25%.

The mean is a measure of central tendency that represents the average value of a set of data

The formula for calculating the mean:

Mean = (x1 + x2 + x3 + ... + xn) / n

Where:

x1, x2, x3, ..., xn are the individual values in the set

n is the total number of values in the set

Mean = (74 + 82 + 86 + 91) / 4

Mean = 333 / 4

Mean = 83.25

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the probability that the card selected is a spade or a queen is given by P= 0.25

In a deck, there are:

total card = 52

spade = 13

Required

Determine the probability that a selected card is a spade

This is represented as: P(Spade) and it is calculated using:

P= card / spade

Substitute 13 for Spade and 52 for Cards

P = 13/52

 = 0.25

Hence, the required probability is 0.25

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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

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

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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Answer:

3 or 3.16227766017

Step-by-step explanation: