If n -2 = 1/16, then n could be which of the following?


-1/4
4
-4
-8
1/4

Answer:

No, I do not agree with the conjecture because 1 is not a prime number.

Step-by-step explanation:

A prime number is one that can be divided by 1 and itself only. Thus it can be expressed in 2 factors only, 1 and the number itself.

Examples are; 2, 3, 5, 13, 19 , 23 etc.

So, 2 = 1 x 2

      3 = 1 x 3

     23 = 1 x 23

Prime numbers must be expressed as the product of 1 and the number.

The conjecture that every prime number can be expressed as the product of two prime numbers is false. Because 1 is not a prime number, since it has no 2 factors.

Using the concept of probability, the probability that the first experiment is successful is 70.97%

To calculate the probability that the first experiment is successful, we use the relation thus :

Inserting the values into the formula :

Therefore, the probability value is 70.97%

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To find the average service revenue per hour in each month and the overall average for the six-month period, the monthly service revenue per hour must be calculated and then the overall average can be calculated. Here's how to find the average service revenue per hour in each month and the overall average for the six-month period.

The table shows the service revenue per hour for each of the 6 months. Month Revenue Hours Revenue per hour January $ 4,000 200 $ 20 February $ 3, 500175 $ 20 March $ 5, 000250 $ 20 April $ 5, 500275 $ 20 May $ 4, 000200 $ 20June$3,500175$20Step 1: Monthly Service Revenue per Hour January: $4,000 ÷ 200 hours = $20 per hour February: $3,500 ÷ 175 hours = $20 per hour

March: $5,000 ÷ 250 hours = $20 per hour April: $5,500 ÷ 275 hours = $20 per hour May: $4,000 ÷ 200 hours = $20 per hour June: $3,500 ÷ 175 hours = $20 per hour  Therefore, the service revenue per hour is $20 per hour every month. Step 2: Overall Average Service Revenue per Hour The overall average service revenue per hour is obtained by adding all the service revenue per hour figures together and dividing by the number of months.$20 + $20 + $20 + $20 + $20 + $20 = $120Then $120 ÷ 6 = $20The overall average service revenue per hour is $20.

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Answer:

204

Step-by-step explanation:

separate into 2 squares/rectangles

13×12(because 20-8 since you cut it in half)

8×6

156+48=204

According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.

The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.

To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.

Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)

So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.

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Answer:

A) 1/9

B) 2/3

C) 6 (I think)

D) 6 (isn't it the same as question C?)

Step-by-step explanation:

Remember this formula:

Probability = number of favorable outcomes divided by the number of possible outcomes

a) 4 / 36 = 1/9

b) 6 * 4 = 24 / 36 = 2/3

c) 24 - 18 = 6

d) 6

I can't do all of them but I tried my best.

Hope this helped...

Answer:

same answer

Step-by-step explanation:

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Answer:

5x + 2y = –14

Step-by-step explanation:

Graph the points and find the equation from there.

Answer:

the answer is 5x + 2y = –14 their right

Step-by-step explanation:

Answer:

F<12-8

F<4 thefore the answer is F<4

The given statements are proved using set theory.

A⊆B, then X\B⊆X\A.

A⊆X iff A=X\(X\A).

X\B⊆X\A, then A⊆B.

a. Proving that if A⊆B, then X\B⊆X\A:

Assuming that A⊆B, then we can say that if x∈X\B, then x∉B.

Because A is a subset of B, x∉A implies x∉B. If x∉B, then x∈X\A.

As a result, X\B⊆X\A.

b. Proving that A⊆X if and only if A=X\(X\A):

Suppose A⊆X.

Then X\(X\A) = X ∩ A (the intersection of X and A) since the elements in X\A are precisely those that are not in A but in X.

Hence A = X ∩ A, which implies A ⊆ X\(X\A).

Conversely, suppose A = X\(X\A).

Let a be any element of A. This implies that a∈X but a∉X\A, so a∈A.

Therefore, A⊆X.

c. Proving that if A⊆X and X\B⊆X\A, then A⊆B:

If X\B⊆X\A, then B⊇A.

So, it remains to show that A⊆B. If a∈A, then either a∈B (because A⊆B) or a∈X\B (since a∉B).

If a∈X\B, then a∈X\A by X\B⊆X\A.

Therefore, a∉X\A, implying that a∉A.

This shows that A⊆B, and hence, the claim is true.

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Based on the given information, the probability of event B is approximately 0.33.

To calculate the probability of event B, we need to determine the number of favorable outcomes for event B and the total number of possible outcomes. From the provided table, we see that event B has 12 occurrences.

Now, to find the total number of possible outcomes, we need to consider the given values for events A, B, and the number 6. The table shows that event A has 18 occurrences, event B has 12 occurrences, and there is an additional value of 6. To calculate the total number of possible outcomes, we sum up these values:

Total number of possible outcomes = 18 + 12 + 6 = 36

Next, we can use the formula for probability:

P(B) = (Number of outcomes favorable to B) / (Total number of possible outcomes)

Plugging in the values, we have:

P(B) = 12 / 36

Dividing 12 by 36 gives us 0.33 as the decimal representation of the probability. Rounding to the nearest hundredth, we find that the probability of event B is approximately 0.33.

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The value of x that makes m║n is 40°

In geometry, the line that intersects two straight lines at distinct points is known as a transversal.

The angles that are formed when two parallel lines are intersected by a third line i.e a transversal are corresponding angles.

Note:

Two corresponding angles are formed by a transversal with two parallel lines that are equal

Here we have

The angle made by the intersecting line with line m is 120°

And the angle made by the same line with line n is 3x°

Let us assume that m║n  

From above observations

The given angle are corresponding angles

=> 3x° = 120°

=> x° = 40°  

Therefore,

The value of x that makes m║n is 40°

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Answer:

The number is 37

Step-by-step explanation:

The given parameters are;

The unit digit of a two-digit number = 4 + The tens digit

2 × The two-digit number  = 1  + The reversed number

Let x represent the unit digit and y represent the tens digit, we have;

x = 4 + y

2 × yx = xy + 1

Which gives;

2 × yy+4 = 2y2y+8

xy + 1 = 4 + yy + 1

y + 1 = 2y + 8 - 10 (we assume that the product of 2 and the unit digit is more than 10 so we subtract 10 from the product to equate the unit digits of the two numbers

10 + 1 - 8 = 2y - y

10 - 7 = y

y = 3

x = y + 4 = 3 + 4 = 7

x = 7

Therefore, the number = 37.

Answer:

37

Step-by-step explanation:

Answer:

1) 1 3/10

2) 5/6

Step-by-step explanation:

4/5+1/2=x     8/10+5/10=13/10= 1 3/10

1/3÷ 2/5=x    1/3x5/2=5/6

Answer:

1.3 and 0.03333333333

Step-by-step explanation:

The statement claims that if there are two branches of the complex logarithm function defined on open balls G1 and G2, and they coincide at a point z0 in the intersection of G1 and G2, then they must be equal at every point in the intersection.

Suppose we have g1 and g2 as two branches of the complex logarithm function defined on G1 and G2 respectively. Let z be any point in the intersection of G1 and G2. Since z is in the intersection, it belongs to both G1 and G2, and therefore both g1(z) and g2(z) are well-defined.

Now, since g1 and g2 coincide at z0, we have g1(z0) = g2(z0). We want to show that g1(z) = g2(z) for every z in the intersection.

Consider the curve C that connects z0 and z in the intersection. Since both g1 and g2 are continuous on their respective domains, g1(z) and g2(z) are continuous along C. By the identity theorem for analytic functions, if two functions are equal on a connected curve, then they are equal everywhere within their common domain.

Therefore, since g1(z) = g2(z) at z0 and they are continuous along the curve C, we can conclude that g1(z) = g2(z) for every z in the intersection of G1 and G2.

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the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

To find the set difference C - A, we need to remove all elements from A that are also present in C. Let's examine the sets:

C = {0, 6, 12, 18}

A = {2, 4, 6, 8, 10, 12}

We compare each element of A with the elements of C. If an element from A is found in C, we exclude it from the result. After the comparison, we find that the elements 2, 4, 8, 10 are not present in C.

Thus, the set difference C - A is {0, 18}, as these are the elements that remain in C after removing the common elements with A.

Therefore, the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.

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The approximate measure of the largest angle in the triangle is of:

θ = 63.4º.

The vertices of the triangle are given as follows:

N(2,2) and P(0,-2).

The triangle is symmetric over the y-axis, hence the remaining vertex is given as follows:

M(-2,2).

The side lenghts of the triangle are given as follows:

The height of the triangle is of:

4 units.

Hence the base angle is:

The tangent is:

tan(θ) = opposite side/adjacent side

Hence:

tan(θ) = 4/2

tan(θ) = 2

θ = arctan(2)

θ = 63.4º.

The diagram given by the image at the end of the answer represents the situation.

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Answer:

-6

Step-by-step explanation:

Hope this helps!!!

To prove the statement "If 7x > 56, then x > 8" indirectly, we assume the opposite of the desired conclusion and show that it leads to a contradiction.

Assume that 7x > 56 but x ≤ 8. We will show that this assumption leads to a contradiction.

Since x ≤ 8, multiplying both sides of the inequality by 7 (which is a positive number) gives us:

7x ≤ 7 * 8

7x ≤ 56

However, this contradicts the initial assumption that 7x > 56. If 7x ≤ 56, then it cannot be simultaneously true that 7x > 56.

Since our assumption led to a contradiction, we conclude that the opposite of our assumption must be true. Therefore, if 7x > 56, then x > 8. This completes the indirect proof.

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Answer:

D

Step-by-step explanation:

Since the formula of circumference is 2πr

Answer:

Jennifer would save $0.25 per ounce.

Step-by-step explanation:

With the 32-ounce jar, the price per ounce is $0.25 per ounce. With the 8-ounce jar, the price is $0.50 per ounce. Jennifer would do better to buy the 32-ounce jar, as she would save $0.25 per ounce with that choice.

The  correct relation symbol

1. LN < RN

2.  LR > LN

3. RN > LN

4. m∠L < m∠N

5. m∠N = m∠R

To determine the correct relation symbols in the given situations, we need to compare the given values in the triangle ∆LRN.

A. In ∆LRN, m∠L = 61° and m∠R = 48°.

LN < RN: The measure of ∠L is greater than the measure of ∠R. By the angle-side relationship, this indicates that the side opposite ∠L (LN) is shorter than the side opposite ∠R (RN). Therefore, LN < RN.

LR > LN: The sum of the measures of ∠L and ∠R is greater than 180° (61° + 48° = 109°), indicating that ∆LRN is an obtuse triangle. In an obtuse triangle, the longest side is the one opposite the obtuse angle, which is LR. Therefore, LR > LN.

RN > LN: In a triangle, the length of any side is greater than the length of the side opposite the smaller angle. Since ∠L is greater than ∠R, the side opposite ∠L (LN) is shorter than the side opposite ∠R (RN). Therefore, RN > LN.

B. In ∆LRN, LN = 8cm, RN = 12cm, and LR = 15cm.

m∠L < m∠N: In a triangle, the measure of any angle is larger than the measure of the angle opposite the shorter side. Since LN is the shortest side, the angle opposite LN (∠L) will have a smaller measure than the angle opposite the longer side, which is ∠N. Therefore, m∠L < m∠N.

m∠N = m∠R: In an isosceles triangle, the angles opposite the equal sides are congruent. Since LR = LN, it indicates that ∆LRN is an isosceles triangle, and therefore, m∠N = m∠R.

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The empirical probability of drawing the cards will be 6 / 55.

The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.

Given that a card is drawn one at a time from a well-shuffled deck of 52 cards. In 13 repetitions of this experiment, 1 king is drawn.

The number of kings in a well-shuffled deck consists of 52 cards which is 4.

The number of ways of drawing consists of 4 kings in 13 repetitions which is ¹³C₄.

In 13 repetitions, 2 kings are drawn by ¹³C₂ ways,

The empirical probability will be calculated as,

P(E) = ¹³C₂ / ¹³C₄

P(E) = [ (13!) / (13-2)! ] ÷ [ (13!) / ( 13-4)!(4!) ]

P(E) = ( 4 x 3 ) / ( 11 x 10)

P(E) = 6 / 55

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Answer:

2 point something times

Answer:

2 times

I hope this helps!

Therefore, the volume of liquid needed to fill a sphere of radius r to height h = r/3 is (92/81)πr^3.

To find the volume of liquid needed to fill a sphere of radius r to a height h = r/3, we first need to find the volume of the spherical cap that makes up the top portion of the sphere.

The volume of a spherical cap is given by the formula:

V = (1/3)πh^2(3r - h)

where h is the height of the spherical cap and r is the radius of the sphere.

Substituting h = r/3, we get:

V = (1/3)π(r/3)^2(3r - r/3)

= (1/3)π(r^2/9)(8r/3)

= (8/27)πr^3

This is the volume of the spherical cap that makes up the top portion of the sphere. To find the volume of liquid needed to fill the sphere to the given height h, we need to subtract this volume from the total volume of the sphere.

The total volume of the sphere is given by the formula:

V = (4/3)πr^3

Substituting the value of V for the spherical cap, we get:

V = (4/3)πr^3 - (8/27)πr^3

= (92/81)πr^3

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The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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Answer:

l + w = 25 and lw = 136

w(25 - w) = 136

25w - w² = 36

w² - 25w - 136 = 0

(w - 17)(w - 8) = 0

w = 8, so l = 17

The dimensions of the bookmark are 8 cm by 17 cm.

Answer:

No, they are not equivalent.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can increase the sample size.

The margin of error refers to the statistic measurement that expresses the level of random sampling error in the outcomes of a survey. If the margin of error of the result is high, the confidence level would be low that a result reflects the census of the entire population. It indicated the difference between the actual and estimated results in a random survey sample. The margin of error is generally used in non-survey contexts to show observational error in reporting measured quantities. In order to minimize the margin of error associated with a confidence interval estimate for a population mean, the researchers can increase the sample size to capture the actual trend of the population more accurately.

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Main Answer:The correct answer is "equality of three or more population means."

Supporting Question and Answer:

What is the purpose of the one-way analysis of variance (ANOVA) test?

ANOVA helps to assess whether these differences are statistically significant by comparing the variation between the groups to the variation within the groups.

Body of the Solution:The one-way analysis of variance (ANOVA) is used to test for" the equality of three or more population means". ANOVA compares the variation between the groups (due to differences in means) to the variation within the groups (due to individual differences within each group) to assess whether the observed differences in means are statistically significant. Therefore, the correct answer is:

"equality of three or more population means."

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