1. Solve.
Z - 4 = 10

Answers

Answer 1

Answer:

Where Z is the exhaustive multitude of the whole numbers

Answer 2

[tex]\text{Hello there!}\\\\\text{If you're solving for z:}\\\\z-4=10\\\\\text{Add 4 to both sides}\\\\z=14\\\\\text{Your answer would be:}\,\boxed{z=14}[/tex]


Related Questions

ransactions to a computer database are either new items or changes to previous items. The addition of an item can be completed less than 100 milliseconds 94% of the time, but only 20% of changes to a previous item can be completed in less than this time. If 30% of transactions are changes, what is the probability that a transaction can be completed in less than 100 milliseconds? Round your answer to two decimal places (e.g. 98.76).

Answers

Answer:

The probability that a transaction can be completed in less than 100 milliseconds if 30% of transactions are changes is 0.718

Step-by-step explanation:

Let A be the vent of new item

Let B be the event of transaction completed in less than 100 milliseconds

[tex]A^c = \text{change item}[/tex]

Since we are given that  30% of transactions are changes,

So, [tex]A^c =0.3[/tex]

We are given that The addition of an item can be completed less than 100 milliseconds 94% of the time

So, [tex]P(B|A)=0.94[/tex]

We are also given that only 20% of changes to a previous item can be completed in less than this time.

So,[tex]P(B|A^c)=0.2[/tex]

[tex]P(A)=1-P(A^c) = 1 - 0.3 = 0.7[/tex]

So, the probability that a transaction can be completed in less than 100 milliseconds :

= [tex]P(B|A)  \times P(A) +P(B|A^c) \times P(A^c)[/tex]

= [tex]0.94  \times 0.7 +0.2 \times 0.3[/tex]

= [tex]0.718[/tex]

Hence the probability that a transaction can be completed in less than 100 milliseconds if 30% of transactions are changes is 0.718

Final answer:

The overall probability that any transaction can be completed in less than 100 milliseconds is approximately 76%.

Explanation:

Given the probability that new additions are completed in less than 100 milliseconds is 94% and the changes in data are 20%. Also, we know that only 30% of transactions are changes. We are required to find the overall probability that a transaction can be completed in less than 100 milliseconds. This situation involves a mixed probability, where some transactions are additions (70% of them) and some are changes (30% of them). Therefore, we calculate as follows:

Probability (Transaction < 100 ms) = (0.7 * 0.94) + (0.3 * 0.2)

By calculating the expression above we find the overall probability of a transaction being completed in less than 100 milliseconds to be approximately 0.76 or 76%.

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find the sum of the whole numbers from 1 to 720

Answers

Answer:

The sum of the whole numbers from 1 to 720 is 259560.

Step-by-step explanation:

To find : The sum of the whole numbers from 1 to 720 ?

Solution :

The whole numbers from 1 to 720 form an arithmetic progression,

The first term is a=1

The last term is l=720

The number of terms n=720

The sum formula of A.P is

[tex]S_n=\frac{n}{2}[a+l][/tex]

Substitute the values in the formula,

[tex]S_{720}=\frac{720}{2}[1+720][/tex]

[tex]S_{720}=360\times 721[/tex]

[tex]S_{720}=259560[/tex]

Therefore, The sum of the whole numbers from 1 to 720 is 259560.

Write the following as a ratio: 304 calories burned in 56 minutes

Answers

Answer:

The required ratio is 38 : 7

Step-by-step explanation:

Given,

304 calories burned in 56 minutes,

That is, the number of calories burnt in 56 minutes = 304

So, the ratio of the calories burnt and time in minutes  = [tex]\frac{304}{56}[/tex]

∵ HCF(304, 56) = 8,

Thus, the ratio of price of photos and number of photos = [tex]\frac{304\div 8}{56\div 8}[/tex]

= [tex]\frac{38}{7}[/tex]

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Seven hundred and eighty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum​ area?

Answers

Answer:

Step-by-step explanation:

Suppose the dimensions of the playground are x and y.

The total amount of the fence used is given and it is 780 ft. In terms of x and y this would be 3x+2y=780 (we add 3x because we want it to be cut in the middle). Therefore,  y= 780/2-3/2x. Now, the total area (A )to be fenced is

A=x*y= x*(390-3/2x)=-3/2 x^2+390x

Calculating the derivative of A and setting it equals to 0 to find the maximum

A'= -3x+390=0

This yields x=130.

Therefore y=780/2-3/2*130=195

Thus, the maximum area is 130*195=25,350ft^2

Final answer:

The rectangle's dimensions that maximize the total enclosed area are 130 feet (length) and 260 feet (width), resulting in a maximum area of 33,800 square feet.

Explanation:

This problem is about optimization, specifically in the context of a rectangle’s dimensions and area. Here's how to solve it step-by-step:

Firstly, visualize the fenced area as a rectangle divided int two equal rectangles. The total fencing used makes up perimeter which consists of three lengths (L) and two widths (W), i.e. 3L + 2W = 780 feet.

To simplify, express one variable in terms of the other. From the equation above, we can express W as (780 - 3L)/2.

The area of a rectangle is given by L × W. Substituting W from the equation above, Area = L * (780 - 3L)/2.

To maximize this area, find its maximum point using differentiation: d(Area)/dL = 0. You will find that L = 130 feet.

Substitute L = 130 feet into the width equation to find W = 260 feet. So, the maximum enclosed area is L * W = 130 * 260 = 33,800 square feet.

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Which number is both a factor and a multiple of 14

Answers

Answer:

7 is both a factor and a multiple

7 is the factor of 14 and 7 has 14 as its multiple.

What is Factor?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Given:

We have the Number 14.

So, the factors of 14 = 1, 2, 7, 14.

and, 7 can act as factor of 14.

also, 7 has multiple 14.

Hence, 7 is the required number.

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For any neZ^+, prove that the integers 8n +3 and 5n+2 are relatively prime. Compute the multipliers to compute inverse of one number with respect to the other number.

Answers

Answer:

See step-by-step explanation below

Step-by-step explanation:

This problem is solved using the Euclidean algorithm; to prove that the integers 8n + 3 and 5n + 2 are relative prime we have to prove that:

gcd(8n + 3, 5n + 2) = 1

gcd (8n + 3, 5n + 2) = gcd (3n + 1, 5n + 2) = gcd (3n + 1, 2n + 1) = gcd(n, 2n + 1) = gcd(n,1) = 1

gcd(8n + 3, 5n + 2) = 1

Final answer:

The integers 8n + 3 and 5n + 2 are relatively prime because their GCD is 1, as shown through the Euclidean algorithm. To compute the multipliers for the inverse of one number with respect to the other, one can backtrack through the Euclidean algorithm stages.

Explanation:

To prove that the integers 8n + 3 and 5n + 2 are relatively prime for any positive integer n, we need to show that their greatest common divisor (GCD) is 1. We can use the Euclidean algorithm to find the GCD of two numbers:

Let's say a = 8n + 3 and b = 5n + 2.

We compute a - b, which is [tex](8n + 3) - (5n + 2) = 3n + 1.[/tex]

Now we find the GCD of b and (a - b), which is GCD(5n + 2, 3n + 1).

Repeating the process, we have [tex](5n + 2) - (3n + 1) \times int((5n + 2) / (3n + 1)) = (5n + 2) - (3n + 1) \times 1 = 2n + 1.[/tex]

The GCD of (3n + 1) and (2n + 1) must now be found.

Continuing similarly, we eventually arrive at a difference of 1, demonstrating that the original two numbers are indeed relatively prime.

To find the multipliers for the inverse of one number with respect to the other, we can backtrack through the Euclidean algorithm steps, expressing each remainder as a linear combination of the two original numbers. This process will yield the required multipliers showing the inverse relationship.

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Consider a survey involving the cookie preferences of a sample of 1,214 adults. If 9% answered "sugar/shortbread," find the decimal and reduced fraction of that percentage.


decimal :

reduced fraction :

Answers

Final answer:

To convert 9% to both a decimal and a reduced fraction: as a decimal, 9% is 0.09; as a reduced fraction, it is 9/100, which cannot be further reduced.

Explanation:

The question is about converting a percentage to a decimal and a reduced fraction. To find the decimal equivalent of 9%, you divide 9 by 100, which gives 0.09. For the reduced fraction, since 9% is equivalent to 9/100, you look for the greatest common divisor of 9 and 100, which is 1. Therefore, the fraction 9/100 is already in its reduced form since no number other than 1 divides both 9 and 100 evenly.

In summary:

Decimal: 0.09

Reduced fraction: 9/100

You may already use algebra in your daily life for several things. How do you imagine that you will use basic algebraic equations in your healthcare career? Explain...


Please gave me an idea guys

Answers

Answer:

Depending on the path that we decide to take, the algebra can help us in many forms.

As an example in the pharmaceutical/medical area, the nurses and doctors use basic algebra formulas to calculate dosages on different drugs depending on variables such as the weigh of each patient (commonly expressed as X or Y).

They used to have some paper sheets with formulas for different drug preparations (liquid ones particularly) within hospitals to avoid errors in medication.

Algebra is an area of mathematics that deals with the study of symbols and the rules for manipulating these symbols. Elementary algebra is used in virtually every field and occupation there is. Algebra is also employed in healthcare.

As a healthcare provider, it is important to be able to read vital signs. Many of these are expressed as algebraic equations. Such equations can also be important when it comes to administering the right doses of medicine or converting different units of measurement.

In a study of stress levels in U.S. army recruits stationed in Iraq, researchers obtained a complete list of the names of recruits in Iraq at the time of the study. They listed the recruits alphabetically and then numbered them consecutively. One hundred random numbers between one and the total number of recruits were then generated using a random-number generator on a computer. The 100 recruits whose numbers corresponded to those generated by the computer were interviewed for the study. What is the population of interest in this study?

Answers

Answer:

The population in a statistical study is determined by all the individuals that could be part of the study, that is, all the individuals that have common characteristics that make them individuals of interest to the researcher.

In the study of the previous statement, the population is made up of all recruits from the US Army. UU. in Iraq at the time of the study.

Step-by-step explanation:

Final answer:

The population of interest in the study of stress levels among U.S. army recruits stationed in Iraq is all U.S. army recruits stationed in Iraq at the time of the study.

Explanation:

The question asks about the population of interest in a study of stress levels among U.S. army recruits stationed in Iraq. In this context, the population of interest refers to the entire group of individuals that the researchers aim to understand or make inferences about based on their study. Given the details of the study, the population of interest in this case includes all U.S. army recruits stationed in Iraq at the time of the study.

Can Someone please explain how to solve this. The directions say, "Solve the system by graphing. Then check your solution."​

Answers

Try this suggested solution (see the attached picture, the answer is [-2;1]).

1 step to drow the graph required in the condition;

2 step to find intersection point (this is the A point);

3 step, check stage, to solve the system of two equations.

4 to compare the results in step 2 and step 3.

Nori placed an order for 10 chairs that cost d dollars each and 2 tables that cost D dollars each. Write an expression for the total cost of the chairs and tables. 20d 10d + 2D 200 10D + 2d

Answers

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Cost of each chair be d dollar

Cost of each table be D dollar

Number of chairs = 10

Number of tables = 2

cost of 10 chairs become [tex]10\times d=10d[/tex]

cost of 2 tables become [tex]2\times D=2D[/tex]

So, the total cost of chairs and tables would be

[tex]10d+2D=Total\ cost[/tex]

Hence, Second option is correct.

Are the rational numbers closed under multiplication?

Answers

Answer:

Yes, The rational numbers are closed under multiplication.

Step-by-step explanation:

A rational number is a number which can be expressed in the form of a fraction [tex]\frac{x}{y}[/tex], where x and y are integers and y ≠ 0.

Now, closure property of multiplication states that if two rational numbers are multiplied then the product is also a rational number. Thus, if r and t are rational numbers, then

r×t = s, where s is the product of r and t

s is also a rational number.

Hence, the rational numbers are closed under multiplication.

This can be better explained with the help of an example [tex]\frac{3}{4} \times \frac{2}{5} = \frac{6}{20}[/tex],

It is clear that [tex]\frac{6}{20}[/tex] is a rational number.

An urn contains ten marbles, of which give are green, two
areblue, and three are red. Three marbles are to be drawn from
theurn, one at a time without replacement. What is the
probabilitythat all three marbles drawn will be green?

Answers

Answer:

[tex] \frac{5\cdot 4\cdot 3}{10\cdot 9 \cdot 8}\approx 0.083[/tex]

Step-by-step explanation:

Getting all three marbles of green color only happens if every draw is a green marble. On the first marble draw, the urn has 10 marbles in it, out of which 5 are green. So the probability of drawing a green marble on this first draw is [tex]\frac{5}{10}[/tex]

Then, once this has happened, the second draw also needs to be a green marble. At this point in the urn there are only 9 marbles left, and only 4 of them are green. So the probability of drawing a green marble at this point is [tex] \frac{4}{9}[/tex]

Afterwards, on the last draw, a green marble also needs to be drawn. At this point there are only 8 marbles left on the urn, and only 3 of them are green. So the probability of drawing a green marble on this last draw is [tex] \frac{3}{8}[/tex]

Therefore the probability of drawing all three marbles of green color is

[tex] \frac{5}{10}\cdot\frac{4}{9}\cdot\frac{3}{8}\approx 0.083[/tex]

Prove that the curve a(t) = (cost, sin 2t, cos 2t) is regular on R and that it self-intersects at (1,0,1). Check the self-intersection part by using algebra and also by using Geofte

Answers

Answer:

The function a (t) is a vector function composed of the component functions [tex]a_ {1} (t) = cost, a_ {2} (t) = sin2t[/tex] and [tex]a_ {3} (t) = cos2t[/tex]. How [tex]a_ {1} (t), a_ {2} (t), a_ {3} (t)[/tex] are infinitely derivable functions in R, so they are regular functions in R.

Now, for[tex]t = 0[/tex], you have to [tex]a (0) = (cos (0), sin2 (0), cos2 (0)) = (1, 0, 1)[/tex]. How the functions [tex]a_ {1} (t), a_ {2} (t), a_ {3} (t)[/tex] are periodic functions with period [tex]2 \pi,[/tex] the vector function [tex]a (t)[/tex] will take the same point [tex](1, 0 , 1)[/tex] at [tex]t = 2n\pi, n = 0, 1, 2, 3, ...[/tex] then the vector function is auto-intercepted

Step-by-step explanation:

if demontra divided negative 100 by negative 2 and got negative 200 did why was the answer wrong and was anything done right?

Answers

Answer:

Step-by-step explanation:

Demontra has to divide negative 100 by negative 2, which means she has to do:

[tex]\Rightarrow \frac {-100}{-2}[/tex]

This can be written as:

[tex]\Rightarrow \frac {-1\times 100}{-1\times 2}[/tex]

-1 / -1 = 1

Also, 100 / 2 = 50

So,

[tex]\Rightarrow \frac {-1\times 100}{-1\times 2}=50\times 1=50[/tex]

She got -200 which is wrong as she muliplied the numbers which is also wrong as -100 × -2 = 200

She did not done anything right.

Calculate:
(Round two decimal places for final answer)

3gallons (gal) =_____liters (L)

Answers

Answer:

13.64 litres

Explanation

Since 1 gallon = 4.546 litres

Therefore...3 gal

; 3 × 4.546 = 13.64 litres

Jacob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45. Find out how many of each (quarters and dimes) Jacob has. What do the unknowns in this system represent and what are the two equations that that need to be solved? Finally, solve the system of equations.

Answers

Answer:  The required number of quarters is 23 and that of dimes is 37.

Step-by-step explanation:  Given that Jacob has 60 coins consisting of quarters and dimes and the combined value of the coins is $9.45.

We are to find the number of quarters and dimes.

Let x and y represents the number of quarters and dimes respectively.

Then, according to the given information, we have

[tex]x+y=60~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.25x+0.10y=9.45\\\\\Rightarrow 25x+10y=945\\\\\Rightarrow 5x+2y=189~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Multiplying equation (i) by 2, we have

[tex]2(x+y)=2\times60\\\\\Rightarrow 2x+2y=120~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

Subtracting equation (iii) from equation (ii), we get

[tex](5x+2y)-(2x+2y)=189-120\\\\\Rightarrow 3x=69\\\\\Rightarrow x=\dfrac{69}{3}\\\\\Rightarrow x=23.[/tex]

And, from equation (i), we get

[tex]23+y=60\\\\\Rightarrow y=60-23\\\\\Rightarrow y=37.[/tex]

Thus, the required number of quarters is 23 and that of dimes is 37.

Final answer:

Jacob has 23 quarters and 37 dimes. We use a system of linear equations with two unknowns representing the number of quarters (q) and dimes (d) to determine the quantities by solving for q and d.

Explanation:

To solve the question of how many quarters and dimes Jacob has, we need to use a system of linear equations. The unknowns in this system represent the number of quarters and dimes. Let's define q as the number of quarters and d as the number of dimes Jacob has. Therefore, we have two equations:

The total number of coins: q + d = 60

The total value of coins: 0.25q + 0.10d = 9.45

Solving the system of equations, we begin by multiplying the second equation by 100 to get rid of decimals, resulting in 25q + 10d = 945. We can use either substitution or elimination to solve for q and d. Let's use the elimination method:

Multiply the first equation by -10 and add it to the second equation to eliminate d.

-10q - 10d = -600

(25q + 10d) + (-10q - 10d) = 945 + (-600)

15q = 345

q = 345 / 15

q = 23

Now that we have the number of quarters, we can find the number of dimes:

Substitute q = 23 in the first equation.

23 + d = 60

d = 60 - 23

d = 37

Hence, Jacob has 23 quarters and 37 dimes.

Simplify. Assume that no denominator is equal to zero.

Answers

Answer:

The answer is C, 3³.

Step-by-step explanation:

When you're dividing integers with exponents, you subtract the two exponent (and when multiplying them, you add them instead.)

In this case, you subtract 7 from 10 which gives you 3.

Answer:

[tex]\frac{3^{10}}{3^7}=3^3[/tex]

Step-by-step explanation:

The [tex]3^{10}[/tex] means we have ten copies of 3 on top; the [tex]3^{7}[/tex] means we have seven copies of three underneath.

[tex]\frac{3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3}{3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3}[/tex]

We have three extra 3's, and they are on top.

[tex]\frac{3\cdot 3\cdot 3}{1} =3^3[/tex]

Therefore,

[tex]\frac{3^{10}}{3^7}=3^3[/tex]

We can also use the The Quotient Rule for Exponents,

For any non-zero number x and any integers a and b [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

[tex]\frac{3^{10}}{3^7}=3^{10-7}=3^3[/tex]

For most answers, you will simply enter your numeric answer directly into the space provided to the right of the equal sign. Answer the following question by typing the numeric answer into the answer box. If you have a gross of items, you have 144 items. If you buy a gross of eggs, how many dozen eggs do you have? Express your answer in dozens. Do not enter the units; they are provided to the right of the answer box.

Answers

Answer:

  12

Step-by-step explanation:

144 = 12×12 = 12×(1 dozen) = 12 dozen

A gross is equal to 144 items. So, if you have a gross of eggs, you would have 12 dozen eggs.

A gross is equal to 144 items. Since there are 12 items in a dozen, to find how many dozen eggs you have in a gross, you divide 144 by 12. This gives you a total of 12 dozen eggs.

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The Order of Magnitude for the total length of 6 cars, which average 8 feet

each, is ______

Answers

Answer:

The Order of Magnitude is 1

Step-by-step explanation:

If

N=a*10^{b}

b is the order of magnitude

Total length = 6 * 8 feet= 48 feet=4.8*10^1 feet

Answer:

The order of magnitude of length is 2.

Step-by-step explanation:

Since we are given the total number of cars is 6 and the length of each car is 8 feet hence the length of 6 cars equals

[tex]Length=6\times 8=48[/tex]

Now by definition of order of magnitude we know it is the smallest power of 10 by which a number can be represented.

Mathematically order of magnitude of 'N' is given by 'b'

[tex]N=a\times 10^{b}\\\\with\\\\\frac{\sqrt{10}}{10}\leq a<\sqrt{10}[/tex]

Hence we can write

[tex]48=0.48\times 10^{2}[/tex]

Since the power of 10 is 2 hence the order of magnitude of 48 feet is 2.

The monthly demand for a product is normally distributed with mean = 700 and standard deviation = 200.

1. What is probability demand will exceed 900 units in a month?

2. What is probability demand will be less than 392 units in a month?

Answers

Answer:  a)  0.1587  b)  0.0618

Step-by-step explanation:

Let x be the random variable that  represents the monthly demand for a product.

Given : The monthly demand for a product is normally distributed with mean = 700 and standard deviation = 200.

i.e. [tex]\mu=700[/tex]   and  [tex]\sigma=200[/tex]

a) Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponds to x= 900 will be :

[tex]z=\dfrac{900-700}{200}=1[/tex]

Now, by using the standard normal z-table , the probability demand will exceed 900 units in a month :-

[tex]P(z>1)=1-P(z\leq1)=1-0.8413=0.1587[/tex]

Hence, the probability demand will exceed 900 units in a month=0.1587

a) Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponds to x=  392 will be :

[tex]z=\dfrac{ 392-700}{200}=-1.54[/tex]

Now, by using the standard normal z-table , the probability demand will be less than 392 units in a month :-

[tex]P(z<-1.54)=1-P(z<1.54)=1-0.9382=0.0618[/tex]

Hence, the probability demand will be less than 392 units in a month = 0.0618

Final answer:

The probabilities requested can be found by calculating the z-scores for the given values and then using a standard normal distribution table to locate the associated probability.

Explanation:

To find the probability that the monthly demand for a product will exceed 900 units when the mean demand is 700 units and the standard deviation is 200 units, we need to calculate the z-score and then use the standard normal distribution table.

The z-score is calculated by the formula:

Z = (X - μ) / σ

Where:

X is the value of interest (900 units in this case).μ (mu) is the mean of the distribution (700 units).σ (sigma) is the standard deviation of the distribution (200 units).

Thus, the z-score for 900 units is:

Z = (900 - 700) / 200 = 1

Using standard normal distribution tables or software, we find the probability associated with a z-score of 1.

For the second question, the z-score for 392 units is calculated in the same way:

Z = (392 - 700) / 200 = -1.54

Again, using standard normal distribution tables or software, we find the probability associated with a z-score of -1.54.

It is important to understand that these probabilities represent the area under the curve of the normal distribution from the z-score to the end of one tail.

A team of 4 golfers scored 69,73,70, and 74 on the first round on a
par 72 course. They reduced their team score by 3 on the second
round.
a) How many strokes above or below par was the team score on the
first round?

Answers

Answer: There are 2 strokes below par that the team has scored in the first round.

Step-by-step explanation:

Since we have given that

Scores of a team

69, 73, 70 and 74

on the first round on a part 72 course.

Now, we need to find the number of strokes above or below the par.

So, we will compare all the scores with 72.

So,

69-72 = -3(below par)

73-72 = 1 (above par)

70-72= - 2 (below par)

74-72 = 2 ( above par)

So, Number of strokes above or below par is given by

[tex]-3+1-2+2\\\\=-2[/tex]

Hence, there are 2 strokes below par that the team has scored in the first round.

The following question has two parts. First, answer part A. Then, answer part B.

The numbers below follow a pattern.

0.007 0.07 0.7. 7 ____ ______

Part A
What are the next two numbers in the pattern? Drag the numbers into the boxes.

70 700 7,000 70,000

0.007 0.07 0.7 7 ____ _____

Part B
Which is the relationship between the terms in the pattern above? Drag a number to the box.

1,1000 1,100 1.10 1000 10 100

Each term is _____ times as great as the term to its left.

Answers

Part A) 70 and then 700
Part B) 10

In part A, the next two numbers in the pattern are 70 and 700. In part B, the relationship between the terms in the pattern is that each term is 10 times as great as the term to its left.

Part A:

The pattern in part A involves multiplying each number by 10. Starting with 0.007, we multiply it by 10 to get 0.07. Then, we multiply 0.07 by 10 to get 0.7. Next, we multiply 0.7 by 10 to get 7. So, the next two numbers in the pattern are 70 and 700.

Part B:

The relationship between the terms in the pattern above is that each term is 10 times as great as the term to its left. For example, 0.07 is 10 times greater than 0.007, and 0.7 is 10 times greater than 0.07. This pattern continues, with 7 being 10 times greater than 0.7 and so on.

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How many colchicine tablets, each containing 600 mcg, may be prepared from 30 g of colchicine?

Answers

Answer:

50,000 tablets may be prepared from 30g of colchicine

Step-by-step explanation:

This problem can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

First Step:

The first step is knowing how many g are in a tablet.

Each gram has 1,000,000 mcg. So:

1g - 1,000,000 mcg

xg - 600 mcg

1,000,000x = 600

[tex]x = \frac{600}{1,000,000} = 0.0006[/tex]

Each tablet has 0.0006g

Final step:

How many tablets may be prepared from 30g of colchicine?

1 tablet - 0.0006g

x tablets - 30g

0.0006x = 30

[tex]x = \frac{30}{0.0006}[/tex]

x = 50,000

50,000 tablets may be prepared from 30g of colchicine

A sample of households in a community is selected at random from the telephone directory. In this community, 2% of households have no telephone, 14% have only cell phones, and another 25% have unlisted telephone numbers. The sample will certainly suffer from

A. nonresponse.
B. false responses.
C. undercoverage.
D. None of the above.

Answers

Answer:

under coverage

Step-by-step explanation:

From the given information we can say that 2% of households have no telephone, 14% have only cell phones, and another 25% have unlisted telephone numbers. Since, the facility is available some part of population and not available to the whole population so, clearly its an examples under coverage.

Imagine that Amy counted 60 numbers per minute and continued to count nonstop until she reached 19,000. Determine a reasonable estimate of the number of hours it would take Amy to complete the counting. It will take Amy approximately (Type a whole number.) hours to count to 19,000.

Answers

Final answer:

At a rate of 60 numbers per minute, Amy would need approximately 5.28 hours to count to 19,000. Rounding to the nearest whole number gives a final estimate of 6 hours.

Explanation:

To answer the question, we'll need to estimate the time Amy would take to count to 19,000. She is counting at a frequency of 60 numbers per minute. This rate is constant throughout her counting.

Therefore, we need to divide the total number of numbers she is counting, which is 19,000, by the rate at which she is counting, which is 60 numbers per minute. The result is approximately 316.67 minutes. To convert this to hours, we divide by 60 (as there are 60 minutes in an hour). That gives us approximately 5.28 hours. Because the question asks for a reasonable whole number estimate, we can round this number up to give us a final answer of 6 hours.

Learn more about Time Estimation here:

https://brainly.com/question/28579204

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The product of 2 more than a number and 10 is 36 more than 8 times the number. What is the number?

Answers

Here's my step-by-step explanation:

Whenever you see the phrase "a number" in a problem like this, then they want you to use a variable. Let's use n for number and translate from English to Algebraic.

- The product of 2 more than a number and 10 is 36 more than 8 times the number.

- The product of 2 more than n and 10 is 36 more than 8 times n.

- The product of 2 + n and 10 is 36 + 8n.

- (2 + n)(10) is 36 + 8n.

- (2 + n)(10) = 36 + 8n

Let's solve.

(2 + n)(10) = 36 + 8n

20 + 10n = 36 + 8n

10n - 8n = 36 - 20

2n = 16

n = 8

Hope this helps, let me know if I made a mistake or if you have any questions!

Write down all elements of the set {XER: X3 -x = 0).

Answers

Answer:

The elements of given set are -1, 0 and 1.

Step-by-step explanation:

The given set is

[tex]\{x\in R:x^3-x=0\}[/tex]

We need to find all the elements of given set.

The given equation is

[tex]x^3-x=0[/tex]           .... (1)

Solve this equation o find the value of x.

Taking out common factors.

[tex]x(x^2-1)=0[/tex]

Using zero product property,

[tex]x=0[/tex]

[tex]x^2-1=0[/tex]

[tex]x^2=1[/tex]

[tex]x=\pm 1[/tex]

All rational and irrational numbers are real numbers.

On solving equation (1) we get x = -1, 0, 1. All these numbers are real number. So, the elements of given set are -1, 0 and 1. The set is defined as

{ -1, 0, 1}

Therefore, the elements of given set are -1, 0 and 1.

If the area of square 1 is 250 units squared, and the area of square 3 is 120 units squared, what is the area if square 2? Explain your reasoning.

Answers

Answer:

The area of square 2 is 130 units square

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The area of a square is

[tex]A=b^{2}[/tex]

where

b is the length side of the square

Let

b1 ----> the length side of square 1

b2 ----> the length side of square 2

b3 ----> the length side of square 3

Applying the Pythagoras Theorem

[tex]b1^{2}=b2^{2}+b3^{2}[/tex] -----> equation A

we have

[tex]A1=250\ units^2[/tex]

[tex]A3=120\ units^2[/tex]

Remember that

[tex]A=b^{2}[/tex]

so

[tex]A1=b1^2=250\ units^2[/tex]

[tex]A3=b3^2=120\ units^2[/tex]

substitute in the equation A and solve for b2^2

[tex]250=b2^{2}+120[/tex]

[tex]b2^{2}=250-120[/tex]

[tex]b2^{2}=130[/tex]

[tex]A2=b2^{2}[/tex]

therefore

The area of square 2 is 130 units square

Solve for b.
b +3(3 - 2b) = 1 - 2(b + 1)

Answers

Answer:

b+3(3-2b)=1-2(b+1)  

One solution was found :

                  b = 10/3 = 3.333

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

               b+3*(3-2*b)-(1-2*(b+1))=0  

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (b+(3•(3-2b)))-(1-2•(b+1))  = 0  

Step  2  :

Equation at the end of step  2  :

 (b +  3 • (3 - 2b)) -  (-2b - 1)  = 0  

Step  3  :

Equation at the end of step  3  :

 10 - 3b  = 0  

Step  4  :

Solving a Single Variable Equation :

4.1      Solve  :    -3b+10 = 0  

Subtract  10  from both sides of the equation :  

                     -3b = -10

Multiply both sides of the equation by (-1) :  3b = 10

Divide both sides of the equation by 3:

                    b = 10/3 = 3.333

One solution was found :

                  b = 10/3 = 3.333

Step-by-step explanation:

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