assuming the rest of your diet remains constant, how many days will it take you to lose 10 pounds? you must burn an extra 3500 calories to lose 1 pound of body weight. express your answer using two significant figures.

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle and π is a mathematical constant approximately equal to 3.14159.

In this case, the diameter of the circle is 58, so we can substitute this value into the formula:

C = πd

C = π(58)

C ≈ 182.09

Therefore, the circumference of the circle with diameter 58 is approximately 182.09 units. Note that the units of measurement were not specified in the question, so the units of the answer will depend on the units used for the diameter.

Answer:

x=2.4

y=2.5

z=3.3

Step-by-step explanation:

6/5=1.2

1.2 = scale factor

x=2x1.2=2.4

y=3/1.2=2.5

z=4/1.2=3.3

there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information.  The given information provides us with the ratio of red to blue counters in a bag, which is 2:5. This means that for every 2 red counters in the bag, there are 5 blue counters.

Let the number of red counters in the bag be 2x, where x is a constant. Then, the number of blue counters in the bag is 5x. We are also given that there are 9 more blue counters than before, so the new number of blue counters is 5x + 9.

We know that there are 35 counters in total, so we can write an equation based on this information:

2x + 5x + 5x + 9 = 35

Simplifying this equation, we get:

12x + 9 = 35

Subtracting 9 from both sides, we get:

12x = 26

Dividing both sides by 12, we get:

x = 2.1667

Since we cannot have a fraction of a counter, we can round x up to 3.

Therefore, the number of red counters in the bag is 2x = 2(3) = 6, and the number of blue counters in the bag is 5x + 9 = 5(3) + 9 = 24.

Finally, we can find the number of green counters in the bag by subtracting the number of red and blue counters from the total number of counters:

35 - 6 - 24 = 5

So there are 5 green counters in the bag.

In summary, there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information.

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The given series diverges to negative infinity as the terms cancel out, leaving only two terms at the beginning and end of the series.

To determine the convergence of the given series, we can use the telescoping series method.

Let's write out a few terms of the series to see if we can spot a pattern:

n=1: 1/2 - 3/4 = -1/4

n=2: 2/3 - 4/5 = -2/15

n=3: 3/4 - 5/6 = -1/8

n=4: 4/5 - 6/7 = -2/35

...

We can see that the terms of the series cancel out, leaving only two terms at the beginning and end of the series. Therefore, we can write the series as:

∑ (n/n+1 - n+2/n+3) = 1/2 - (n+2)/(n+3)

As n approaches infinity, the second term approaches 1, so the series diverges to negative infinity.

Therefore, the given series diverges.

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_____The given question is incomplete, the complete question is given below:

Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers

(∑ ∞ to n = 1) = (n/n+1 - n+2/n+3)

Answer:

eqn of line : x-3y=15

slope1=m= -coefficient of x/coefficient of y=1/3

As lines are parallel slope must be equal.

slope3=m'=1/3

passing points of second line =(0,7)

eqn of line = (y-y')=m(x-x')

=(y-7)=1/3(x-0)

=y-7=1/3x

=1/3x-y+7=0

=x-3y+21=0

Step-by-step explanation:

the expectation of buying one ticket is $2

Expectation if a person buys one ticket A person is interested in buying a ticket for a lottery that offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. The expected return is calculated using the following formula:

Expectation = (Probability of winning Prize 1 × Value of Prize 1) + (Probability of winning Prize 2 × Value of Prize 2) + (Probability of winning Prize 3 × Value of Prize 3)To determine the expectation, we must first determine the probability of winning each of the three prizes.

Since one thousand tickets are sold and only one person can win the first prize, the probability of winning the $1000 prize is 1/1000 or 0.001. Similarly, the probability of winning the $500 prize is 1/1000 or 0.001. Since five $100 prizes are available and only one person can win each prize, the probability of winning any one of the five $100 prizes is 5/1000 or 0.005.

Therefore, the expectation is calculated as follows: Expectation = (0.001 × $1000) + (0.001 × $500) + (0.005 × $100)Expectation = $1 + $0.50 + $0.50Expectation = $2Thus, the expectation of buying one ticket is $2. This means that the average value of a ticket is $2, and a person can expect to win $2 on average by purchasing a ticket. Since the cost of a ticket is $3, the expected return is less than the cost of the ticket, and therefore, it is not a good investment from a financial standpoint.

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Answer:

1+2=90° .so complementary angle

Answer: 18.75%

Step-by-step explanation:

To find the percent increase, we need to calculate the difference between the new speed and the old speed, divide that by the old speed, and then multiply by 100 to get the percentage increase.

The difference between the new speed and the old speed is:

38 - 32 = 6

To find the percentage increase, we divide the difference by the old speed and multiply by 100:

(6 / 32) x 100 = 18.75%

Therefore, Matt's typing speed increased by 18.75%.

The probability that a librarian chooses a fiction book, then a nonfiction book, then a fiction book is approximately 0.305.

The solution to this problem is a probability calculation.

To calculate the probability of selecting a fiction book, then a nonfiction book, then a fiction book from a selection of 10 nonfiction books and eight fiction books, we need to use the multiplication rule of probability.

The multiplication rule states that the probability of two or more independent events happening together is equal to the product of their individual probabilities.

To apply this rule, we'll break down the question into three events:

Probability of choosing a fiction book = 8/18 = 4/9

Probability of choosing a nonfiction book (after selecting a fiction book) = 10/17

Probability of choosing a fiction book (after selecting a nonfiction book) = 8/16 = 1/2

Now we can use the multiplication rule:4/9 * 10/17 * 1/2 = 0.305 (rounded to three decimal places)

Therefore, the approximate probability that the librarian will choose a fiction book, then a nonfiction book, then a fiction book is 0.305.

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The equation has a solution of -1

Algebraic expressions are defined as those expressions that are made up of variables, constants, factors, coefficients and terms.

They are also composed of mathematical operations, such as;

Also, note that linear equation are equations having the greatest degree of  x as 1.

An equation having a solution would have the x value.

From the equation given, we have that;

2x+2=x+1

collect the like terms

2x - x =1 - 2

subtract the values

x = - 1

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The information indicates that the correct answer is 9.76% annually.

The area of mathematics that deals with the characteristics of surrounding space, spatial interactions between distinct objects, and the shape of particular items.

It would take 19 years between 1996 and 2015 in all.

We are aware that the equation: gives a geometric mean of a collection of n positive numbers.

GM =  [tex]((x1)(x2)(x3).............)^{1/n}[/tex]

This would provide us with the product of these values' nth roots.

Thus, the following would be the formula indicating rate of rise over time: -

GM =  [tex](value at the end of the period / value at the start of the period)^{1/n} -1[/tex]

[value at the end of the period / value at the start of the period

Value at the conclusion of the time is equal to 241,364,256, hence the statement stands.

The initial value was 40,257,000.

n = 19

Using values, we obtain:

=[tex](241,364,256/40,257,000)^{1/19} -1[/tex]

= (5.995)1/19 - 1

= 0.0976

= 9.76% per year

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Answer:

20.65

Step-by-step explanation:

Ashley's tower is 30 centimeters taller than Mason's tower. Ashley's tower is 10 x (1/10) = 1 meter tall. Mason's tower, on the other hand, is 7 x (1/10) = 0.7 meters tall.

Ashley's tower is 10 blocks high and each block has a height of 0.1 meters since 1 meter is divided into 10 equal parts. Therefore, the total height of Ashley's tower is 10 x 0.1 = 1 meter. Mason's tower, on the other hand, is 7 blocks high and has a total height of 7 x 0.1 = 0.7 meters. The difference between Ashley's tower and Mason's tower is the height of Ashley's tower minus the height of Mason's tower, which is 1 meter - 0.7 meters = 0.3 meters. To convert meters to centimeters, we need to multiply by 100, so Ashley's tower is 0.3 x 100 = 30 centimeters taller than Mason's tower.

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The truth regarding the conditions for constructing a confidence interval for a population mean for the real estate market is that E. All conditions have been met.

For a confidence interval to be construction, sample should be randomly selected, sample size should be no more than 10% of the population size, and the sampling distribution should be approximately normal. This can be achieved if the sample size is large (typically n ≥ 30) and the data doesn't have strong skewness or outliers.

The question states that the realtor is working in a large city, and it is reasonable to assume that 100 home sales are less than 10% of all homes sold in the previous 6 months in this large city. So, this condition is met.

The realtor has randomly selected 100 home sales, so the random condition is met. All conditions have therefore been met to construct a confidence interval.

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Options for this question include:

Answer: True.

Step-by-step explanation:

Important differences are always statistically significant if small sample size is used

The maximum number of hours Connor can work in landscaping is 5 hours.

In mathematics, inequalities are statements that compare two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), and "!=" (not equal to).

Let's denote the number of hours Connor works in landscaping as x. Then we have the following system of inequalities:

x ≤ 15 - 12 (since Connor can work a maximum of 15 hours in total, and he already worked 12 hours walking dogs)

8(12) + 12x ≥ 160 (since Connor must earn no less than $160)

Simplifying the second inequality, we get:

96 + 12x ≥ 160

12x ≥ 64

x ≥ 64/12

x ≥ 5.33

Since we need to have a whole number of hours, the maximum number of hours Connor can work in landscaping is 5 hours. We can check that this satisfies both inequalities:

5 ≤ 15 - 12

5.33 (rounded up to the nearest whole number) × 12 + 8(12) = 68. 16 ≥ 160

Therefore,Let's denote the number of hours Connor works in landscaping as x. Then we have the following system of inequalities:

x ≤ 15 - 12 (since Connor can work a maximum of 15 hours in total, and he already worked 12 hours walking dogs)

8(12) + 12x ≥ 160 (since Connor must earn no less than $160)

Simplifying the second inequality, we get:

96 + 12x ≥ 160

12x ≥ 64

x ≥ 64/12

x ≥ 5.33

Since we need to have a whole number of hours, the maximum number of hours Connor can work in landscaping is 5 hours.

We can check that this satisfies both inequalities:

5 ≤ 15 - 12

5.33 (rounded up to the nearest whole number) × 12 + 8(12) = 68. 16 ≥ 160

Therefore, the answer is 5.

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A human organism developing in the uterus from the ninth week until birth is called a(n) fetus.

A fetus is the term used to describe a human organism that is developing in the uterus from the ninth week of gestation until birth. During this time, the fetus undergoes significant growth and development, as all of the major organs and body systems are formed and begin to function.

The ninth week of gestation is considered a significant milestone in fetal development, as most of the critical stages of organogenesis have been completed by this time. From this point onward, the fetus primarily grows and matures in preparation for life outside of the womb.

During the remaining weeks of gestation, the fetus undergoes a number of important developmental processes, including continued brain development, growth of the nervous system, and development of the lungs and other vital organs. At the same time, the fetus also gains weight and size, and begins to develop a layer of fat that will help to regulate body temperature after birth.

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The range of scores is 0 to 10. Since everyone in the class scored 6 out of 10, the lowest possible score is 0 and the highest possible score is 10.

The range is the difference between the highest and the lowest of the  given scores. In this case, it's 4 (10-6).

Therefore, the range of scores is 0 to 10. It is important to note that the range is a measure of the spread of scores in a dataset, and in this case, the spread is from the lowest possible score of 0 to the highest possible score of 10.

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Answer:

Step-by-step explanation:

The radical form for each expression is given as follows:

How to obtain the radical form of each expression?

The general format of the exponential expression is given as follows:

To obtain the radical form, we have that:

a is the radicand.

n is the exponent.

m is the root.

Hence the radical form of the exponential expression is given as follows:

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Cards are dealt from a standard shuffled deck of cards until the first ace is drawn. So the chance that the next card is a king is 0.05 percent.

            When drawing a card from a standard deck of 52 cards, the chance of drawing an ace is 4/52 or 1/13. After an ace has been drawn, there are 51 cards left in the deck, and 4 of them are kings.

           So, the probability of drawing an ace and then a king is

                     (1/13) × (4/51) = 4/663.

There are 4 different aces that could be drawn, each with the same probability of

                      (1/13) × (4/51) = 4/663,

So we multiply by 4 to account for all the possible aces that could be drawn.

Therefore, the total probability of drawing an ace and then a king is

                     (4/663) × 4 = 16/663.

         Once an ace has been drawn, there are 51 cards remaining in the deck, and only one of them is a king. Therefore, the probability of drawing a king after an ace has been drawn is 1/51.

         The probability that the next card is a king after the first ace is drawn is thus:

                    (16/663) × (1/51) = 16/33663

                                              = 1/2104.

      This simplifies to 0.0475 percent or approximately 0.05 percent.

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The correct statement regarding the best measure of the variability is given as follows: The IQR is the best measure of variability, and it = 6. The Interquartile Range (IQR of a data-set. As it not affected by outliers, it is the best measure of variability of a data-set. The quartiles for this problem are given as follows: First quartile: Q1 = 15. Third quartile Q3 = 21. Hence the IQR is obtained as follows: IQR = 21 - 15 IQR = 6

Answer: The IQR is the best measure of variability, and it equals 6.

IQR is the best way to measure the variability in this question and its also equal to six. I took the test just now and got it right i cant really explain anything else.

The height of the trapezoid is 7 ft.

The formula for the area of a trapezoid is:

A = 1/2 * (a + b)h

where A is the area, a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

Given A = 24.5 ft², a = 3 ft and b = 4 ft. We can solve for h. That is:

A = 1/2 * (a + b)h

24.5 = 1/2 * (3 + 4)h

24.5 = 1/2 * (7)h

24.5 = 3.5h

h = 24.5/3.5

h = 7 ft

Therefore, the height of the trapezoid is 7 ft.

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Answer:

area=188

Step-by-step explanation:

12×14=168 for the area of the rectangle

2×10=20

20÷2=10 for the area of triangle

168+10+10=188

area=188

Thus, the obtained formula for the arithmetic sequence is found as:

f(n) = -42 + 10(n - 1).

A list of integers called an arithmetic sequence has a constant difference between terms. Any number may be the first in an arithmetic sequence, but the distance between succeeding terms must remain constant.

Unreal numbers can be used in a series. I believe that the next step in an equation should be an actual real number.

The nth term formula for the arithmetic sequence is:

f(n) = a1 + (n - 1)d

arithmetic sequence -

−42, −32, −22, −12, −2 …

a1 = -42

d = -32 - (-42) = -32 + 42 = 10

So, formula for the sequence:

f(n) = -42 + (n - 1)10

f(n) = -42 + 10(n - 1)

Thus, the obtained formula for the arithmetic sequence is found as:

f(n) = -42 + 10(n - 1).

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Answer:21

Step-by-step explanation:

5x=180-75

5x=105

x=105/5

x=21

Answer:

Range = Highest number -Lowest number

= 13-2=11

Answer:

11

Step-by-step explanation:

Highest number = 13

Lowest number = 2

Range = highest number - lowest number

Range = 13 - 2 = 11

Answer:

Apparently it's 4800 according to desmos.

Step-by-step explanation:

Step-by-step explanation:

x y

-3 150

-2 300

-1 600

0 4800

As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.

The smallest positive integer y such that the product xy is a perfect cube is 3.

To find the value of y, we need to factorize x, which is 7 * 24 * 48.

We can then find the prime factorization of xy, which will help us determine the smallest integer y that will make the product a perfect cube.

Since 7, 24, and 48 are already factored, we can express x as:

x = 2⁴ * 3 * 7²

To make xy a perfect cube, we need to ensure that the exponents of all the prime factors are multiples of 3.

Therefore, we need to add a factor of 3 to the exponent of 2 in x to make it a multiple of 3. This gives us:

xy = 2⁷ * 3² * 7²

The smallest integer y that can make this product a perfect cube is 3, because we need to add a factor of 1 to the exponent of 2 in xy to make it a multiple of 3, and the smallest integer that can achieve this is 3.

Thus, the smallest positive integer y such that the product xy is a perfect cube is 3.


The question is: A number x is equal to [tex]$7\cdot24\cdot48$[/tex]. What is the smallest positive integer y such that the product xy is a perfect cube

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