A purse contains 5-cent coins and 10-cent coins worth a total of $1.05. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse? HELP PLEASE WITH WORK

Answers

Answer 1

Let f and t represent the numbers of 5- and 10-cent coins in the purse. (We expect these numbers to be positive integers.)
.. 5f +10t = 105 . . . . . . current value
.. 10f +5t = 215 . . . . . . value if numbers are swapped

Multiply the first equation by -2 and add to the second.
.. -2(5f +10t) +(10f +5t) = -2(105) +215
.. -15t = 5
.. t = -1/3

No such coin arrangement is possible.

_____
If you simply add the two original equations, you get
.. 15(t + f) = 320
.. t + f = 21 1/3 . . . . . There are 21 1/3 coins in the purse.

Taking that at face value, we find the average coin value is
.. 1.05/21.3333... = 4.921875¢ . . . . less than the value of a nickel

There is no combination of nickels and dimes that will make the average value of a single coin be less than 5¢. (The average value must be between 5¢ and 10¢.)

Answer 2

Answer:

The other person should be correct

Step-by-step explanation:

Related Questions

What is the measure of angle z in this figure?

Enter your answer in the box.

z = ___°

Answers

Hello!

I've attached a photo for reference.

Lines A and B form straight angles, which measure 180 degrees. That means that -

m∠x + m∠y = 180°
m∠y + m∠z = 180°
m∠z + 43° = 180°
43° + m∠x = 180°

Since you're trying to find z, use the solvable equation with z in it:

m∠z + 43° = 180°
180 = z + 43
137 = z

Answer:
m∠z = 137°

what is the probabilaty getting a sum of 7 if you rolled a pair of dice?

Answers

There are 36 possible outcomes when we throw a pair of fair six-sided dice.
Out of these, six {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} give a sum of 7.
Therefore the probability of rolling a sum of 7 is 6/36=1/6

Which shows how the distributive property can be used to evaluate 7×84/5?

Answers

Well you have nothing here, so I'll take a guess.
84/5 gives 16 4/5. I don't know how much saving in work there is in doing this but you could do this.

7 ( 16 + 4/5)
You still have to do something with 28/5 when you get done, but it is one way to do it.

Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.20.2, 0.30.3, and 0.50.5, respectively. what is the standard deviation of this customer's book purchases?

Answers

E [x] = Expected value of X
μ = average
σ = standard deviation
V (X) = Variance
σ = (V(X)) ^ 0.5
E [X] = X * P (x)
Assuming that the number of books purchased is a discrete random variable with mean μ = E [X]
Then the variance of X can be written as V (X) = E [X-μ]^2
We started finding the average μ
μ = 0 * 0.20 + 1 * 0.30 + 2 * 0.50
μ = 1.3
Once the average is found, we can calculate the value of the variance
V (X) = 0.20 * (0-1.3) ^ 2 + 0.30 * (1-1.3) ^ 2 + 0.50 * (2-1.3) ^ 2
V (X) = 0.61
Now we know that from the variance the standard deviation can be obtained by doing:
σ = (V (X)) ^ 0.5
Finally
σ = 0.781

The standard deviation of the customer's book purchases is 0.72.

The standard deviation of a discrete probability distribution can be calculated using the following formula:

σ = √(p[tex](x - \mu)^2[/tex])

where:

σ is the standard deviation

p(x) is the probability of the event x

μ is the mean of the distribution

In this case, the probabilities of the customer purchasing 0, 1, or 2 books are 0.2, 0.3, and 0.5, respectively. So, the mean of the distribution is:

μ = (0 * 0.2) + (1 * 0.3) + (2 * 0.5) = 1.2

The standard deviation is then:

σ = √([tex](0 - 1.2)^2 (0.3)^2[/tex] + [tex](1 - 1.2)^2 (0.3)^2[/tex] + [tex](2 - 1.2)^2 (0.5)^2)[/tex] = 0.72

So, the standard deviation of the customer's book purchases is 0.72.

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what is 0.080 as a fraction

Answers

Answer:

To write 0.080 as a fraction you have to write 0.080 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.080 = 0.080/1 = 0.8/10 = 8/100

So your final answer is: 0.080 as a fraction equals 8/100

Step-by-step explanation:

The decimal number 0.080 as a fraction is A = 2/25

Given data:

The decimal number is represented as 0.080

Step 1: Count the number of decimal places in the given decimal. So, there are three decimal places.

Step 2: Write the decimal as the numerator of the fraction. The decimal 0.080 becomes the numerator 80.

Step 3: Determine the denominator of the fraction. Since there are three decimal places, the denominator should be 10 raised to the power of the number of decimal places. So, the denominator is 10³ = 1000.

Putting it all together, 0.080 as a fraction is 80/1000.

Dividing both the numerator and denominator by 40:

80 ÷ 40 / 1000 ÷ 40 = 2/25

Hence, 0.080 as a simplified fraction is 2/25.

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Andy and alex both decided to order prints of their photos. Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints. He paid a total of $32.50 for his photos. Alex paid 20$ for 20 small 4x6 inch prints and 8 large 8x10 inch prints. How much do the small and large sized prints cost

Answers

Final answer:

To find the cost of small and large prints, we create two equations based on Andy's and Alex's orders and solve for the two variables. The small 4x6 inch prints cost $0.50 each, and the large 8x10 inch prints cost $1.25 each.

Explanation:

To solve how much small and large sized prints cost, we can set up a system of linear equations based on the information given:

Andy's order: 40 small prints and 10 large prints for $32.50Alex's order: 20 small prints and 8 large prints for $20.00

Let s represent the cost of a small 4x6 inch print, and let l represent the cost of a large 8x10 inch print. We can then form the equations:

40s + 10l = 32.5020s + 8l = 20.00

By dividing the first equation by 2, we get:

20s + 5l = 16.25

Subtracting the second equation from this result gives:

(20s + 5l) - (20s + 8l) = (16.25 - 20)-3l = -3.75l = 1.25

With the cost of a large print found, we can plug this back into the second equation to find the cost of a small print:

20s + 8(1.25) = 2020s + 10 = 2020s = 10s = 0.50

Therefore, the cost of a small 4x6 inch print is $0.50 and a large 8x10 inch print is $1.25.

You track fuel accounts for q shipping line. One vessel consumes 2 1/2 tons of fuel per day during transport. About how many fuel in tons should the vessel consume during 15-day transport?

Answers

For this case, the first thing we must do is rewrite the expression:
2 1/2
Rewriting we have:
2.5 ton / day
The total amount after 15 days is:
(2.5) * (15) = 37.5 Ton
Rewriting we have:
37 1/2 Ton
Answer:
the vessel should consume 37 1/2 Ton during 15-day transport

With a short time remaining in the day a delivery driver has to make deliveries at 5 locations among the 6 locations remaining. How many different routes are possible

Answers

The delivery driver has to make deliveries at 5 locations among the 6 locations. This means the order of the probability is important because the route he will take from A to B is different with A to C.
So, you need to use permutation for this problem. The calculation would be:
6P5= 6!/ (6-5)!= 720 different routes

Final answer:

To find the number of different routes the delivery driver can take to make the deliveries at 5 out of 6 locations, we can use the concept of permutations.

Explanation:

To find the number of different routes the delivery driver can take, we can use the concept of permutations. Since the delivery driver has to make deliveries at 5 out of the remaining 6 locations, we need to calculate the number of ways to arrange these locations.

We can use the formula for permutations to find the number of different routes:

nPr = n! / (n - r)!

Using this formula, we can calculate the number of different routes as:

6P5 = 6! / (6 - 5)! = 6! / 1! = 6 × 5 × 4 × 3 × 2 × 1 / 1 = 720

Therefore, there are 720 different routes the delivery driver can take to make the deliveries.

a paragraph of; compare savings and investments

Answers

Your "savings" are usually put into the safest places or products that allow you access to your money at any time. Examples include savings accounts, checking accounts, and certificates of deposit. At some banks and savings and loan associations your deposits may be insured by the Federal Deposit Insurance Corporation. When you "invest," you have a greater chance of losing your money than when you "save." Unlike the Federal Deposit Insurance Corporation; insured deposits, the money you invest in securities, mutual funds, and other similar investments is not federally insured. You could lose your "principal," which is the amount you've invested. Which is true, even if you purchase your investments through a bank. But when you invest, you also have the opportunity to earn more money than when you save. There is a tradeoff between the higher risk of investing and the potential for greater rewards.

Grace has 2 cups of strawberries and plans to divide this amount into equal parts to make 3 strawberry pies. What fraction of a cup of strawberries will be used for each pie?

Answers

The whole number of cups 2 will be divided by 3 pies leaving a fraction of
[tex] \frac{2}{3} [/tex]
cups for each individual pie.

Number of cups of Strawberries are there for 3 pies =2

Now we apply unitary method here to find how many strawberries are need for 1 pie.

Number of cups of Strawberries required for 1 pie = 2/3

Answer: So Grace would require 2/3 cups of Strawberries for making one pie.

Determine the x-intercept of 5x -6y =10

Answers

5x-6y=10

This is a linear equation...

A typical linear equation is written in the form
y=mx+c

Where m=gradient
And c=intercept

So all you have to do is to express y in terms of x "make y the subject of the formula"

Therefore 5x-6y=10

6y=5x-10
Divide through by 6

6y/6 = 5x/6 - 10/6

The intercept here is = - 10/6
Gradient = 5/6-----the coefficient of x....

Hope this helped.....???

a puppy pen is 4 square feet wide and 5 feet long. is 21 square feet of fabric large enough to make a mat for the pen? Explain

Answers

yes because the area of the puppy pen is only 20 hope this helps!

Yes, length times width equals the area of a square or rectangle. so 4 feet times 5 feet is 20 feet squared, so you will have some fabric left over.

A gardener plants a bed of flowers such that he plants twenty day lilies in the first row, twenty-six day lilies in the second row, and thirty-two day lilies in the third row. He continues to plant lilies in the bed with this pattern for a total of twelve rows. How many day lilies did he plant?

Answers

he planted 92 of those because 12 times 6 is 72 and 72 plus 20 is 92 therefore the answer is 92

There are 86 lilies he did plant in 12th row of the garden.

What is Arithmetic Sequence?

Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Here, The number of lilies plants in first, second third,..., and last row are respectively.

20,26,32,........

the number of rows of lilies plants is 12.

The sequence 20,26,32,........ is an A.P. with first term a =20, common difference d = 6 and n =12

formula for nth term.

∴aₙ = a+(n−1)d

aₙ=20+ (12-1).6

aₙ = 20 + 11 X 6

aₙ = 86

Thus, there are 86 lilies he did plant in 12th row of the garden.

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Michael will be travelling out of town for business. During his travel, he is scheduled to have 4 dinners, 5 lunches, and 3 breakfasts. His employer will pay him for these meals at the following rate: $ 22.65 for dinner, $ 10.95 for lunch, and $ 6.53 for breakfast.

Answers

one dinner = 22.65
4 dinners = 22.65 x 4 = $90.60

one lunch = 10.95
5 lunches = 10.95 x 5 = $54.75

one breakfast = 6.53
3 breakfasts = 6.53 x 3 = 19.59

Total = $90.60 + $54.75 + $19.59 = $164.94

Which number line represents the solution set for the inequality-4(x+3)<-2-2x

Answers

Final answer:

The inequality -4(x+3)<-2-2x simplifies to x > -5. Therefore, the number line representing this solution should shade the values greater than -5, thus, highlighting that x is any value greater than -5.

Explanation:

Let's solve the inequality -4(x+3)<-2-2x step by step:

Distribute -4 through (x+3) to get -4x-12<-2-2x. Add 4x to both sides to isolate x, which leads to -12 < 2x - 2. Finally, add 2 to both sides to isolate x to get -10 < 2x or equivalently, x > -5.

As a result, the number line that represents this solution is one where the values greater than -5 are shaded. This means the value of x is anything greater than -5. Any number line visualization should start at -5 and include everything to the right of that point.

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factor, x^4y+8x^3y-6x^2y^2-48xy^2

Answers

Hey there Ruben!

[tex]\boxed{\boxed{((((x^4)*y)+((8*(x^3))*y))-((6*(x^2))*(y^2)))-(24*3xy^2)}} \\ \\ (let's \ simplify \ some \ number's \ down) \\ \\ \boxed{\boxed{ ((((x4)*y)+((8*(x3))*y))-((2*3x2) *y2))-(24*3xy2)}} \\ \\ \\ Pull \ out \ like \ factors : \\ \\ \boxed{\boxed{ x4y + 8x^3y - 6x2y^2 - 48xy^2 = xy * (x3 + 8x^2 - 6xy - 48^y) }} \\ \\ \\ (TAKE \ NOTICE) \swarrow\swarrow\swarrow\swarrow \swarrow\swarrow\swarrow\swarrow\swarrow\swarrow \\ \\ \\ [/tex]

[tex]\boxed{\boxed{\boxed{ (((((x^4)*y)+(23x^3*y))-(2*3x2y2))}}} \\ \\ \\ \boxed{\boxed{\boxed{-(24*3xy2))-xy*(x3+8x2-6xy-48y) = \boxed{0}}}}}[/tex]

I hope this helps you!

the answer is xy(x+8)(x^2-6y)

see attached picture for steps:

find the surface area of the toolbox

Answers

787.2 inches squared

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5

Answers

Solve for x over the real numbers:
x^2 - 4 x = 5

Subtract 5 from both sides:
x^2 - 4 x - 5 = 0

x = (4 ± sqrt((-4)^2 - 4 (-5)))/2 = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2:
x = (4 + sqrt(36))/2 or x = (4 - sqrt(36))/2

sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (4 + 6)/2 or x = (4 - 6)/2

(4 + 6)/2 = 10/2 = 5:
x = 5 or x = (4 - 6)/2

(4 - 6)/2 = -2/2 = -1:

Answer: x = 5 or x = -1

Answer:

x = 5 or x = -1

Step-by-step explanation:

x^2 – 4x = 5

Solve it by completing the square method

In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it

-4/2 = -2

square it (-2)^2 = 4

Now add 4 on both sides

x^2 – 4x +4 = 5+4

x^2 – 4x +4 = 9

Now factor the left hand side

(x-2)(x-2)=9

(x-2)^2 = 9

Take square root on both sides

x-2 = +-3

x-2 = 3 , so x= 5

x-2 = -3, so x= -1

Zakai cuts a piece of birthday cake as shown below.

What is the volume of the piece of cake?

Answers

A= (B*h)/2
A=10*18/2
A=90
V=A*H
V=90*6
V=540

What is the mean of the values in the stem-and-leaf plot? Enter your answer in the box.Key: 2|5 means 25

Enter your answer in the box.

Key: 2|5 means 25

A stem-and-leaf plot with a stem value of 1 with leaf values of 5 and 8, a stem value of 2, a stem value of 3, a stem value of 4 with a leaf value of 6, a stem value of 5 with leaf values of 0, 0, 0, 0, 7, a stem value of 6, a stem value of 7, a stem value of 8, and a stem value of 9.

Answers

The stem and leaf plot represents the numbers 15, 18, 46, 50, 50, 50, 50, 57. To find the mean, add these up (336) and divide by the number of data points (8). The mean is 42.

The mean of the values in the stem-and-leaf plot is 42.

To find the mean of the values in the stem-and-leaf plot, we first need to interpret the plot correctly. Here's the stem-and-leaf plot description:

Stem | Leaves

1 | 5, 8

2 |

3 |

4 | 6

5 | 0, 0, 0, 0, 7

6 |

7 |

8 |

9 |

Let's list the individual values from the plot:

- From stem 1: Leaves are 5 and 8

- From stem 4: Leaf is 6

- From stem 5: Leaves are 0, 0, 0, 0, 7

Now, we calculate the mean (average) of these values.

Step-by-step calculation:

1. List of values:

- Values from stem 1: 15, 18

- Values from stem 4: 46

- Values from stem 5: 50, 50, 50, 57

2. Count the number of values:

- There are 2 values from stem 1, 1 value from stem 4, and 5 values from stem 5.

- Total count = 2 + 1 + 5 = 8

3. Calculate the sum of all values:

- Sum = 15 + 18 + 46 + 50 + 50 + 50 + 50 + 57

- Sum = 336

4. Calculate the mean:

- Mean = Sum / Count

- Mean = 336 / 8

- Mean = 42

Therefore, the mean of the values in the stem-and-leaf plot is [tex]{42} \).[/tex]

The perimeter of a quilt is 34 ft. If the quilt is 8 ft long, what is the area

Answers

2l + 2w = 34 (l = 8) (Problem)
2 x 8 = 16 (Finding out the length)
16 + 2w = 34 (Problem with the length)
-16 -16 (Using the subtraction property of equality to isolate the variable)
2w = 18 (New problem)
/2 /2 (Using division property of equality)
w = 9. (Width is found)

9 x 8 = 72. The area is 72 squared feet.

34-(8x2)=18
18÷2=9
8x9=72

Solve and plot your answer on the number line below: 7.08 + 2x=15.96

Answers

7.08 + 2x =15.96
-7.08. -7.08
-------------------------
2x=8.88 divide each by 2

X=4.44
You would plot it in between 4 and 5 but on one of the line marks depending on what there value are

Jorge is standing at a horizontal distance of 25 feet away from a building. his eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65, how high is the window washer above the ground

Answers

we know that
tan 65°=y/25------------> y=tan 65°*25 ( distance of the washer at the eye level)
[the window washer high above the ground]=[(tan 65°)*25+5.5]
[the window washer high above the ground]=[53.61+5.5]=59.11 ft

the answer is 59.11 ft

The given family of functions is the general solution of the differential equation on the indicated interval. find a member of the family that is a solution of the initial-value problem. y = c1e4x + c2e−x, (−∞, ∞); y'' − 3y' − 4y = 0, y(0) = 1, y'(0) = 2

Answers

Try this option (see the attachment), if it is possible check result in other sources.

Solution:

The given differential equation is,

[tex]y=C_{1}e^{4 x}+C_{2}e^{-x}[/tex]------(A)

Differentiating once,with respect to x,

[tex]y'=4C_{1}e^{4 x}-C_{2}e^{-x}[/tex]-------(1)

Differentiating again with respect to x,

[tex]y"=16C_{1}e^{4 x}+C_{2}e^{-x}[/tex]-------(2)

Equation (1) + Equation (2)

y' +y" [tex]=20 C_{1}e^{4 x}[/tex]

[tex]C_{1}=\frac{y'+y"}{20e^{4 x}}[/tex]

4 ×Equation (1) - Equation (2)

4 y'- y"[tex]=-5 C_{2}e^{-x}[/tex]

[tex]C_{2}=\frac{4y'-y"}{-5e^{-x}}[/tex]

Substituting the value of [tex]C_{1},C_{2}[/tex] in A,we get

[tex]y=\frac{y'+y"}{20}+\frac{4 y'-y"}{-5}\\\\ 20 y=y'+y"-16 y'+4 y"\\\\ 20 y=-15 y'+5y"\\\\ 4 y+3 y'-y"=0[/tex]

As, y(0)=1 , and y'(0)=2, gives

[tex]C_{1}+C_{2}=1\\\\ 4C_{1}-C_{2}=2[/tex]

gives , [tex]5C_{1}=3\\\\ C_{1}=\frac{3}{5}\\\\ 5 C_{2}=2\\\\ C_{2}=\frac{2}{5}[/tex]

So, member of the family that is a solution of the initial-value problem, [tex]y=C_{1}e^{4 x}+C_{2}e^{-x}[/tex] is

[tex]5 y=3 e^{4 x}+2 e^{-x}[/tex]

A stained glass window is shaped like a semicircle the bottom edge of the window is 36 inches long what is the area of the stained glass window

Answers

check the picture below.

so, if the semi-circle has a diameter of 36, then the radius is half that, or 18

[tex]\bf \textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2}\quad \begin{cases} r=radius\\ -----\\ r=18 \end{cases}\implies A=\cfrac{\pi 18^2}{2}\implies A=\cfrac{324\pi }{2} \\\\\\ A=162\pi [/tex]

Hdc produces microcomputer hard drives at four different production facilities (f1, f2, f3, and f4) hard drive production at f1, f2, f3, and f4 is 20%, 25%, 15%, and 40%, respectively. quality control records indicate that 1.5%, 2%, 1%, and 3% of the hard drives are defective at f1, f2, f3, and f4, respectively.
a. if a defective hdc hard drive is picked at random, what is the probability that it was produced at f2?
b. if a defective hdc hard drive is picked at random, what is the probability that it was produced at f4?
c. if an hdc hard drive is picked at random, what is the probability that it is non-defective? g

Answers

a. Probability defective hard drive from F2 ≈ 0.3226.

b. Probability defective hard drive from F4 ≈ 0.7742.

c. Probability non-defective hard drive ≈ 0.9785.

To solve this problem, we can use Bayes' theorem, which states:

[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]

Where:

- [tex]$ P(A|B) $[/tex] is the probability of event A happening given that event B has occurred.

- [tex]$ P(B|A) $[/tex] is the probability of event B happening given that event A has occurred.

- [tex]$ P(A) $[/tex] and [tex]$ P(B) $[/tex] are the probabilities of events A and B, respectively.

Let's solve each part of the problem:

a. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F2?

Let:

- A be the event that the hard drive is defective.

- B be the event that the hard drive was produced at F2.

We need to find [tex]$ P(B|A) $[/tex], the probability that the hard drive was produced at F2 given that it is defective.

[tex]$\begin{aligned} & P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\ & P(A \cap B)=P(A \mid B) \times P(B)=0.02 \times 0.25=0.005 \\ & P(A)=P(A \cap F 1)+P(A \cap F 2)+P(A \cap F 3)+P(A \cap F 4) \\ & P(A)=0.015 \times 0.20+0.02 \times 0.25+0.01 \times 0.15+0.03 \times 0.40=0.0155 \\ & P(B \mid A)=\frac{0.005}{0.0155} \approx 0.3226\end{aligned}$[/tex]

b. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F4?

We need to find [tex]$ P(F4|A) $[/tex], the probability that the hard drive was produced at F4 given that it is defective.

[tex]\[ P(F4|A) = \frac{P(A \cap F4)}{P(A)} \][/tex]

[tex]\[ P(A \cap F4) = P(A|F4) \times P(F4) = 0.03 \times 0.40 = 0.012 \][/tex]

[tex]\[ P(F4|A) = \frac{0.012}{0.0155} \approx 0.7742 \][/tex]

c. If an HDC hard drive is picked at random, what is the probability that it is non-defective?

Let P(non-defective) = P(non-defective at F1) + P(non-defective at F2) + P(non-defective at F3) + P(non-defective at F4)

P(non-defective) = [tex](1 - 0.015) \times 0.20 + (1 - 0.02) \times 0.25 + (1 - 0.01) \times 0.15 + (1 - 0.03) \times 0.40[/tex]

P(non-defective) = [tex]0.985 \times 0.20 + 0.98 \times 0.25 + 0.99 \times 0.15 + 0.97 \times 0.40[/tex]

P(non-defective) = 0.197 + 0.245 + 0.1485 + 0.388 = 0.9785

So, the probability that an HDC hard drive picked at random is non-defective is approximately [tex]$ 0.9785 $[/tex].

How many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code?

Answers

Note that powers of 2 can be written in binary as

[tex]2^0=1_2[/tex]
[tex]2^1=10_2[/tex]
[tex]2^2=100_2[/tex]

and so on. Observe that [tex]n+1[/tex] digits are required to represent the [tex]n[/tex]-th power of 2 in binary.

Also observe that

[tex]\log_2(2^n)=n\log_22=n[/tex]

so we need only add 1 to the logarithm to find the number of binary digits needed to represent powers of 2. For any other number (non-power-of-2), we would need to round down the logarithm to the nearest integer, since for example,

[tex]2_{10}=10_2\iff\log_2(2^1)=\log_22=1[/tex]
[tex]3_{10}=11_2\iff\log_23=1+(\text{some number between 0 and 1})[/tex]
[tex]4_{10}=100_2\iff\log_24=2[/tex]

That is, both 2 and 3 require only two binary digits, so we don't care about the decimal part of [tex]\log_23[/tex]. We only need the integer part, [tex]\lfloor\log_23\rfloor[/tex], then we add 1.

Now, [tex]2^9=512<1024=2^{10}[/tex], and 999 falls between these consecutive powers of 2. That means

[tex]\log_2999=9+\text{(some number between 0 and 1})[/tex]

which means 999 requires [tex]\lfloor\log_2999\rfloor+1=9+1=10[/tex] binary digits.

Your question seems to ask how many binary digits in total you need to represent all of the numbers 0-999. That would depend on how you encode numbers that requires less than 10 digits, like 1. Do you simply write [tex]1_2[/tex]? Or do you pad this number with 0s to get 10 digits, i.e. [tex]0000000001_2[/tex]? In the latter case, the answer is obvious; [tex]1000\times10=10^4[/tex] total binary digits are needed.

In the latter case, there's a bit more work involved, but really it's just a matter of finding how many number lie between successive powers of 2. For instance, 0 and 1 both require one digit, 2 and 3 require two, while 4-7 require three, while 8-15 require four, and so on.

Final answer:

To represent the decimal numbers from 0 to 999 in binary code, we require 10 bits. This is determined by finding the binary equivalent of the largest number, 999, which necessitates at least 10 powers of 2 (from [tex]2^0 \ to \ 2^9[/tex]).

Explanation:

To determine how many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code, we need to find the binary equivalent of the largest number in that range, which is 999. In binary, this would require the highest power of 2 that is less than or equal to 999. The largest power of 2 less than 999 is 512 (29), and we continue to add powers of 2 to represent the number:

512 (29)
256 (28)
128 (27)
64 (26)
32 (25)
16 (24)
8 (23)
4 (22)
2 (21)
1 (20)

Adding these up, we see that we need at least 10 bits to represent the number 999 in binary, because adding powers of 2 from 20 to 29 will give us the required range. Therefore, we need 10 bits to represent any number from 0 to 999 in binary.

ASAP Select the statement that correctly describes the expression below.

(2x+5)^2
a) the sum of the square of 2 times x and 5

b)the square of the sum of 2 times x and 5

c)the square of 2 times the addition of x and 5

d)the sum of 2 times x and the square of 5

Answers

I believe it is b)the square of the sum of 2 times x and 5

Answer:

Option B

Step-by-step explanation:

The given expression is ( 2x + 5)²

We have to form a statement to describe the expression given.

(2x + 5)² square of sum of 2 times x and 5

Option B is the correct answer.

Please help me out with #8 surface area and please explain

Answers

Well I certainly understand why you are having grief. I wonder what we know about this thing? The bottom triangle is easy enough to figure out, but are the lines leading up to it parallel? If they are then 5.2 is not correct, or the right
angle symbol is meant to connect to the vertical line closest to us.
What's all the writing to the left and right. What does it say?

Finally what do you know? Can you find area using Heron's Formula for area. I'm going to hold off saying much. You can put a remark somewhere. The magic editor will pick it up and tell me you've done it.

How many outcomes are there in the sample space for rolling 1 die?

Answers

Answer:

Step-by-step explanation:

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