Need help with this math question

Among the provided options, the number of siblings is an example of a discrete random variable. This is because it represents a countable quantity. The other options are examples of continuous random variables.

In the context of statistics, a discrete random variable is one that can take on a countable number of distinct values. Examples include the number of books in a backpack or the number of siblings a person has. These are variables that can be counted, rather than measured.

From the options provided, the one that represents a discrete random variable is the number of siblings. This is because the number of siblings is a countable quantity. The other options including the hours worked at a job, the weight of a child, or the length of a fish represent continuous random variables because they are measured rather than counted.

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Among the options given, the number of siblings is an example of a discrete random variable. Discrete random variables have countable values obtained from counting, not measuring. Therefore, examples like number of siblings where counts are involved are discrete.

In the realm of probability and statistics, discrete and continuous are two classifications for random variables. They differ in the way that their possible values are characterized or measured. We can summarize it as follows: discrete random variables are countable, while continuous random variables are uncountable, bearing values that are brought about through measurement.

In the options given - hours worked at a job, weight of a child, number of siblings, length of a fish - the one that best represents an example of a discrete random variable is the number of siblings. This is an example of a discrete random variable because it involves counting (you count the number of siblings) and not measuring.

It's important to understand that the type of a random variable, whether it's discrete or continuous, depends on how it's defined. For instance, number of miles you drive to work is considered discrete as you count the miles. However, if it's the distance you drive to work, it's measured and is considered a continuous random variable.

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bearing in mind that arcs get their angle measurement from the central angle they're in.

since point C is the center of the circle, then ∡ACB is a central angle, containing the arcAB, and since arcAB = 36° = ∡ACB.

To find the arithmetic sequence, we can first find it's common difference by deducting the first term by the second term:

-7-(-15)

=-7+15

=8

Therefore the common difference is 8, and to find the remaining terms we can add 8 for the respective terms.

T(4) = 1+8 =9

Therefore the answer is c)9,17,25,33.

Hope it helps!

Answer: c) 9,17,25,33

Step-by-step explanation:

Use the equation [tex]a_n=a_1+d(n-1)[/tex]

Where "n" is the nth term,  [tex]a_1[/tex] is the first term, "d" is the common difference and "n" is a integer greater than zero.

Find the common diference "d":

[tex]d=(-7)-(-15)\\d=8[/tex]

Then we know that:

[tex]a_1=-15\\d=8\\[/tex]

Since we need to find the next four terms and we know three terms then:

 For [tex]n=4[/tex]:

[tex]a_4=-15+8(4-1))=9[/tex]

For [tex]n=5[/tex]:

[tex]a_5=-15+8(5-1))=17[/tex]

For [tex]n=6[/tex]:

[tex]a_6=-15+8(6-1))=25[/tex]

For [tex]n=7[/tex]:

[tex]a_7=-15+8(7-1))=33[/tex]

Answer:

50

Step-by-step explanation:

105+x+25=180

   x+130  =180

            x=50

the value of x is 50°

The angle made by a straight line is 180 degrees. This is a fundamental property of a straight line. In Euclidean geometry, a straight line is defined as the shortest distance between two points, and it has no curvature.

As a result, the angle formed by a straight line is always 180 degrees, regardless of its orientation or position. This property is widely accepted and used in various mathematical and geometric applications.

We know that angle made by straight line is 180°

∠EAB + ∠BAC + ∠CAD = 180°

x° + 105°+ 25° = 180°

x° + 130° = 180°

x° = 180° - 130°

x° = 50°

Therefore, the value of x is 50°

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Answer:

Explanation:

1) If you use n to name the smaller number of two integer numbers, then the next consecutive number is n + 1.

2) The product of those two numbers is n × (n + 1) = n (n + 1).

3) Half of that product is n (n + 1) / 2.

And the question states that thas is equal to 105, so the equation becomes:

4) n (n + 1) / 2 = 105

Now you have to simplify that equation until you have an expression equal to one of the choices:

5) Simplification:

And that is the first choice, so you have your answer.

Answer:

n² + n - 210 = 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\text{If set of order pairs belongs to a linear function, then}\\\\(x_1,\ y_1),\ (x_2,\ y_2),\ (x_3,\ y_3)\\\\\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_3-y_2}{x_3-x_2}\\\\=========================[/tex]

[tex]A)\\(-5,\ 16),\ (-1,\ 4),\ (3,\ -8),\ (7,\ -20)\\\\\dfrac{4-16}{-1-(-5)}=\dfrac{-12}{4}=-3\\\\\dfrac{-8-4}{3-(-1)}=\dfrac{-12}{4}=-3\\\\\dfrac{-20-(-8)}{7-3}=\dfrac{-12}{4}=-3\\\\\bold{CORRECT}[/tex]

[tex]B)\\(5,\ 16),\ (1,\ -4),\ (-3,\ -8),\ (-7,\ -20)\\\\\dfrac{-4-16}{1-5}=\dfrac{-20}{-4}=5\\\\\dfrac{-8-(-4)}{-3-1}=\dfrac{-4}{-4}=1\\\\\bold{INCORRECT}[/tex]

[tex]C)\\(-4,\ 16),\ (-1,\ 4),\ (2,\ -8),\ (6,\ -20)\\\\\dfrac{4-16}{-1-(-4)}=\dfrac{-12}{3}=-4\\\\\dfrac{-8-4}{2-(-1)}=\dfrac{-12}{3}=-4\\\\\dfrac{-20-(-8)}{6-2}=\dfrac{-12}{4}=-3\\\\\bold{INCORRECT}[/tex]

[tex]D)\\(5,\ -16),\ (1,\ -4),\ (-3,\ 8),\ (-7,\ -20)\\\\\dfrac{-4-(-16)}{1-5}=\dfrac{12}{-4}=-3\\\\\dfrac{8-(-4)}{-3-1}=\dfrac{12}{-4}=-3\\\\\dfrac{-20-8}{-7-(-3)}=\dfrac{-28}{-4}=7\\\\\bold{INCORRECT}[/tex]

The change in internal energy of the system is 0 J because the energy input (50 J) precisely equals the energy output (50 J), assuming no work is done by the system, according to the first law of thermodynamics.

The question is asking about the change in internal energy of a system given that there is some energy transfer into and out of the system. We denote the energy transferred into the system as Qin and the energy transferred out of the system as Qout. For this question, Qin is 50 J and Qout is 50 J.

The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Qin) minus the work done by the system (W) and the heat leaving the system (Qout). However, in this case, we don't have information about the work done, which is often represented as the term W. If we assume no work is done, the equation simplifies to ΔU = Qin - Qout.

Using this information, we can calculate the change in internal energy: ΔU = 50 J - 50 J = 0 J. There is no change in internal energy because the energy input equals the energy output. Therefore, the correct response here would be none of the options provided (A. 20 J, B. 30 J), but instead, it would be 0 J.

Answer:

  about 1099 pounds

Step-by-step explanation:

The weight of the truck is directed downward. It is countered by a force normal to the plane of the hill and one that is parallel to the plane of the hill. The question is asking about this latter force.

The magnitude of the force parallel to the hillside required to keep the truck stationary is ...

  (2600 lb)·sin(25°) ≈ 1098.81 lb ≈ 1099 lb

The probabilities for each outcome of the number of heads are:

- Probability of 0 heads: [tex]\( P(0) = \frac{4}{80} = 0.05 \)[/tex]

- Probability of 1 head: [tex]\( P(1) = \frac{8}{80} = 0.10 \)[/tex]

- Probability of 2 heads: [tex]\( P(2) = \frac{36}{80} = 0.45 \)[/tex]

- Probability of 3 heads: [tex]\( P(3) = \frac{20}{80} = 0.25 \)[/tex]

- Probability of 4 heads: [tex]\( P(4) = \frac{12}{80} = 0.15 \)[/tex]

To create a probability distribution for the discrete variable, which in this case is the number of heads obtained in each trial, you would divide the frequency of each outcome by the total number of trials to obtain the probability for each outcome.

Based on the information provided:

- There were 80 trials.

- The frequency for 0 heads is 4.

- The frequency for 1 head is 8.

- The frequency for 2 heads is 36.

- The frequency for 3 heads is 20.

- The frequency for 4 heads is 12.

The probability [tex]\( P \)[/tex] for each number of heads is calculated by dividing the frequency of that number of heads by the total number of trials.

So, for each number of heads [tex]\( x \)[/tex]:

[tex]\[ P(x) = \frac{\text{Frequency of } x}{\text{Total number of trials}} \][/tex]

The probabilities for each outcome of the number of heads are:

- Probability of 0 heads: [tex]\( P(0) = \frac{4}{80} = 0.05 \)[/tex]

- Probability of 1 head: [tex]\( P(1) = \frac{8}{80} = 0.10 \)[/tex]

- Probability of 2 heads: [tex]\( P(2) = \frac{36}{80} = 0.45 \)[/tex]

- Probability of 3 heads: [tex]\( P(3) = \frac{20}{80} = 0.25 \)[/tex]

- Probability of 4 heads: [tex]\( P(4) = \frac{12}{80} = 0.15 \)[/tex]

Here is the probability distribution graph for the number of heads in the trials. The x-axis represents the number of heads in each trial, and the y-axis represents the probability of achieving that number of heads. Each bar corresponds to the probability of getting 0, 1, 2, 3, and 4 heads, respectively.

Answer:

C) $26.00

Step-by-step explanation:

No. of hours needed to be paid for = 25 - 1 = 24 (First hour is free)

Cost of next 10 hours = $30 x 10 = $300

No. of hours left to be paid for = 24 - 10 = 14

Cost of last 14 hours = $664 - $300 = $364

Discounted hourly rate = $364 / 14 = $26

Answer:

The answer is Median.

Step-by-step explanation:

Answer:

15 units

Step-by-step explanation:

I just took this geometry test with the same question. Its 15

Answer:

159.12

Step-by-step explanation:

find the amount with taxe (Ax1.02)

add all of them up together

then divide by 5

Answer:

159.12

Step-by-step explanation:

find the amount with taxe (Ax1.02)

add all of them up together

then divide by 5

[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=25\pi \end{cases}\implies 25\pi =4\pi r^2 \\\\\\ \cfrac{25\pi }{4\pi }=r^2\implies \cfrac{25}{4}=r^2\implies \sqrt{\cfrac{25}{4}}=r\implies \cfrac{\sqrt{25}}{\sqrt{4}}=r\implies \cfrac{5}{2}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \frac{5}{2} \right)^3}{3}\implies V=\cfrac{4\pi \cdot \frac{125}{8}}{3}\implies V=\cfrac{\frac{500\pi }{8}}{~~\frac{3}{1}~~} \\\\\\ V=\cfrac{500\pi }{8}\cdot \cfrac{1}{3}\implies V=\cfrac{500\pi }{24}\implies V=\cfrac{125\pi }{6}\implies V\approx 65.45[/tex]

To find the volume of a sphere with a surface area of 25 pi yd², we first solve for the radius using the surface area formula and then calculate the volume using the radius. The calculated volume is approximately 65.45 yd³.

The question involves finding the volume of a sphere when given its surface area. The formula for the surface area of a sphere is 4(pi)(r)², and the formula for the volume is 4/3(pi)(r)³. Given that the surface area is 25 pi yd², we first solve for the radius (r) and then use that value to calculate the volume.

1. Start with the surface area formula: 25 pi = 4(pi)(r)².

2. Solve for r²: r² = 25/4.

3. Then, take the square root to find r: r = √(25/4) = 2.5 yd.

4. Finally, use the radius to find the volume: Volume = 4/3(pi)(2.5)³ = 65.45 yd³ (approximately).

Answer: 1st Blank: Product

2nd Blank: Sum

3rd Blank: Years

I'm sorry I get this wrong, please tell me if it is wrong.

Answer:

Product, sum, and years

Step-by-step explanation:

The compound interest formula is -

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where P = 250

r = 1.8% or 0.018

n = 2 (semiannually)

t = t

The given scenario can be modeled as:

[tex]250(1+\frac{0.018}{2})^{2t}[/tex]

We have to fill in the blanks:

The expression is the PRODUCT of the amount initially deposited($250) and the SUM of one and the rate of increase(1.8%) raised to the number of compounding period and YEARS (2t).

Answer:

All the real numbers.

Step-by-step explanation:

We have that x≥-1 or x<2.

The 'or' means that it can be one value or another: [-1, +∞) U (-∞, 2) = ℝ. Then, the solution to the compound inequality is All the real numbers. In set notation: ℝ.

Final answer:

The compound inequality x ≥ -1 or x < 2 is satisfied by all real numbers between -1 and 2, inclusive on the -1. The solution set can be expressed as -1 ≤ x < 2 and visualized on a number line, including all numbers from -1 to just below 2.

Explanation:

To solve the compound inequality x ≥ -1 or x < 2, we need to consider the two parts of the inequality separately and then find the union of their solutions. The first inequality, x ≥ -1, represents all real numbers greater than or equal to -1. The second inequality, x < 2, represents all real numbers less than 2. Since any real number that satisfies either condition is part of the solution set, we find that the entire set of real numbers between -1 and 2, inclusive on the -1, satisfies the compound inequality.

To visualize this, we can plot the solution on a number line. The number -1 will be included in the solution set (as indicated by a closed circle or bracket), and extend to the right, towards infinity. Simultaneously, we will plot the solution for the second inequality, which starts from negative infinity and continues to the number 2, not including 2 (indicated by an open circle or parenthesis). The overlap of these two ranges gives us the final solution set for the inequality.

The solution to the compound inequality is therefore all real numbers that are greater than or equal to -1 or less than 2, which can be expressed simply as -1 ≤ x < 2.

Percentage is related to 100 and tells us how much we have of a quantity compared to another one. Suppose you have 100 cars and want to know how much cars are in red color. If 70 cars are red, then 70 percent of the cars are red. In general, we can find the percentage of a number following the steps:

For this example, let's take number 200 and the percentage 20%:

STEP 1: Multiply the number by the percentage:

200 x 20 = 4000

STEP 2: Now divide the number by 100:

400/100 = 40

STEP 3: If necessary., round to the desired precision.

To calculate the percentage of a number, divide the part by the whole and multiply by 100.

The percentage of a number is a measure of the proportion that a given quantity represents in relation to a whole, expressed as a fraction of 100. It's commonly used to express portions, ratios, and comparisons. For example, 25% of 100 is 25.

To calculate the percentage of a number, you can use the formula: (part/whole) * 100. Start by dividing the part by the whole, then multiply the result by 100. For example, if you want to find 25% of 80, you would divide 25 by 100 to get 0.25, then multiply 0.25 by 80 to get 20. So, 25% of 80 is 20.

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Answer:

the answer is b, 5.

Step-by-step explanation:

you don't even have to pay attention the denominators of the equation. If you plug in 5 for x in the numerators of the equation. so 8 times 8=40 + 2 times 5=10. basically do 8 times 5 + 2 times 5 it = 50. Because 8 times 5 = 40, and 2 times 5= 10. 40 + 10 =50.

Answer:

  ±1/5, ±1, ±11/5, ±11

Step-by-step explanation:

Potential rational roots of 5x² -7x +11 will be of the form ...

  (divisor of 11)/(divisor of 5)

so will include ...

  ±1/5, ±1, ±11/5, ±11

Answer:

0.003981 . . . . moles per liter

Step-by-step explanation:

The concentration of H+ ions in the acid will be ...

10^(-2.4) ≈ 0.003981 . . . . moles per liter

The concentration of H+ ions in the base will be ...

10^-11.2 ≈ 0.000 000 000 006310 . . . . moles per liter

To a few decimal places, the difference is ...

0.003981 . . . . moles per liter

_____

The two numbers differ by about 9 orders of magnitude, so the value of the difference between the larger and the smaller is essentially the value of the larger number. The smaller one, by comparison, can be considered to be zero (for subtraction purposes).

Final answer:

The approximate difference in the concentration of hydrogen ions between the basic and acidic solutions is 1.58 × 10^-9.

Explanation:

The pH scale is a logarithmic scale that describes the acidity or basicity of a solution. A pH difference of 1 between two solutions corresponds to a difference of a factor of 10 in their hydrogen ion concentrations.

Given that a basic solution has a pH of 11.2 and an acidic solution has a pH of 2.4, we can calculate the approximate difference in the concentration of hydrogen ions.

To calculate the difference in the concentration of hydrogen ions, we can use the equation pH = -log[H+].

For the basic solution with a pH of 11.2:

pH = -log[H+]

11.2 = -log[H+]

Using the logarithmic scale, we can calculate the concentration of hydrogen ions:

H+ = 10^-pH

H+ = 10^-11.2

H+ ≈ 6.31 × 10^-12

For the acidic solution with a pH of 2.4:

pH = -log[H+]

2.4 = -log[H+]

Using the logarithmic scale, we can calculate the concentration of hydrogen ions:

H+ = 10^-pH

H+ = 10^-2.4

H+ ≈ 0.004

Therefore, the approximate difference in the concentration of hydrogen ions between the two solutions is:

6.31 × 10^-12 / 0.004 ≈ 1.58 × 10^-9

Answer:

  A.  x ≈ 9/8

Step-by-step explanation:

We can see that left side > right side at x=1 and left side < right side at x=2. So, the solution is between x=1 and x=2.

As a first approximation, we can choose x = 3/2. Left side ≈ 0.73, right = 3.5

The solution is between x=1 and x=3/2.

For the 2nd approximation, we choose x = 5/4. Left ≈ 1.28, right = 2.25

The solution is between x=1 and x=5/4.

For the 3rd approximation, we choose x = 9/8. Left ≈ 1.62, right ≈ 1.63

The solution is between x=1 and x=9/8. The next estimate will be 17/16.

Our third estimate of the solution is 9/8.

Answer:

The common difference is 3

Step-by-step explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant called the common difference

we have

[tex]5,8,11,14[/tex]

so

[tex]a1=5[/tex]

[tex]a2=8[/tex]

[tex]a3=11[/tex]

[tex]a4=14[/tex]

[tex]a2-a1=8-5=3[/tex]

[tex]a3-a2=11-8=3[/tex]

[tex]a4-a3=14-11=3[/tex]

therefore

The common difference is 3

Answer:

  2 2/3 hours

Step-by-step explanation:

The total of the given outage lengths is ...

  (1/4) + (2/3) + (1 3/4) = (1/4 + 1 3/4) + 2/3

  = 2 + 2/3 = 2 2/3

The water was off for 2 2/3 hours.

Answer:  The required number of tireless hours is [tex]2\dfrac{2}{3}~\textup{hours}.[/tex]

Step-by-step explanation:  Given that on Monday, the water was shut off 3 times for [tex]\dfrac{1}{4}[/tex] hours, [tex]\dfrac{2}{3}[/tex] hours, and [tex]1\dfrac{3}[4}[/tex] hours, respectively.

We are to find the tireless number of hours for which the water was off.

The tireless number of hours for which the water was off is equal to the sum of the number of hours for which the water was off three times.

Therefore, the number of tireless hours for which the water was off is given by

[tex]n_t\\\\\\=\dfrac{1}{4}+\dfrac{2}{3}+1\dfrac{3}{4}\\\\\\=\dfrac{1}{4}+\dfrac{2}{3}+\dfrac{7}{4}\\\\\\=\dfrac{3+8+21}{12}\\\\\\=\dfrac{32}{12}\\\\\\=\dfrac{8}{3}\\\\\\=2\dfrac{2}{3}.[/tex]

Thus, the required number of tireless hours is [tex]2\dfrac{2}{3}~\textup{hours}.[/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2\implies A=2121.8[/tex]

Answer:

No, because 3(2)+3 not equal to 15

Step-by-step explanation:

let the goals of Skylar be x

goals of wyatt be y

y=2x

x+y=15

3x=15

x=5

y=10

An equation is formed of two equal expressions. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the goal scored by Skylar and Wyatt be x and y respectively. Now, given Wyatt scored 2 times as many goals as Skylar. Therefore,

y = 2x

Also, Together they scored 15 goals. Therefore,

x + y = 15

x + 2x = 15

3x = 15

x = 5

Thus, Skylar and Wyatt have scored 5 and 10 goals respectively.

Hence, the correct option is A.

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Answer:

The answer in the procedure

Step-by-step explanation:

we know that

Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilation's) can be found that map one figure onto another.  

In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that

Circle 1 is centered at (5,8) and has a radius of 8 centimeters

Circle 2 is centered at (1,-2) and has a radius of 4 centimeters

step 1

Move the center of the circle 1 onto the center of the circle 2

the transformation has the following rule

(x,y)--------> (x-4,y-10)

so

(5,8)------> (5-4,8-10)-----> (1,-2)

center circle 1 is now equal to center circle 2  

The circles are now concentric (they have the same center)

step 2

A dilation is needed to decrease the size of circle 1 to coincide with circle 2

scale factor=radius circle 2/radius circle 1-----> 4/8----> 0.5

radius circle 1 will be=8*scale factor-----> 8*0.5-----> 4 cm

radius circle 1 is now equal to radius circle 2  

therefore

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

Answer:

  eight more than a fifth of a number

Step-by-step explanation:

k/5 is one-fifth of a number. When 8 is added to it, the result is ...

  eight more than a fifth of a number

_____

There is no multiplication by 5, so any phrasing with "five times" is incorrect.

The one-fifth multiplier is applied only to k, not to any sum.

Answer:

Part A)

scientific notation ------> [tex]2.56*10^{11}\ bits[/tex]

standard notation ----->  [tex]256,000,000,000\ bits[/tex]

Part B)

scientific notation ------> [tex]5.12*10^{11}\ bits[/tex]

standard notation ----->  [tex]512,000,000,000\ bits[/tex]

Part C)

scientific notation ------> [tex]1.28*10^{11}\ bits[/tex]

standard notation ----->  [tex]128,000,000,000\ bits[/tex]

Part D)

scientific notation ------> [tex]6.4*10^{10}\ bits[/tex]

standard notation ----->  [tex]64,000,000,000\ bits[/tex]

Part E)

scientific notation ------> [tex]3.2*10^{11}\ bits[/tex]

standard notation ----->  [tex]320,000,000,000\ bits[/tex]

Step-by-step explanation:

we know that

[tex]1\ Gigabyte=1*10^{9}\ bytes[/tex]

[tex]1\ byte=8\ bits[/tex]

therefore

[tex]1\ Gigabyte=8*10^{9}\ bits[/tex]

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{32}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=32*8*10^{9}\\ \\x=256*10^{9}\ bits\\ \\x=2.56*10^{11}\ bits[/tex]

scientific notation ------> [tex]2.56*10^{11}\ bits[/tex]

standard notation ----->  [tex]256,000,000,000\ bits[/tex]

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{64}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=64*8*10^{9}\\ \\x=512*10^{9}\ bits\\ \\x=5.12*10^{11}\ bits[/tex]

scientific notation ------> [tex]5.12*10^{11}\ bits[/tex]

standard notation ----->  [tex]512,000,000,000\ bits[/tex]

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{16}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=16*8*10^{9}\\ \\x=128*10^{9}\ bits\\ \\x=1.28*10^{11}\ bits[/tex]

scientific notation ------> [tex]1.28*10^{11}\ bits[/tex]

standard notation ----->  [tex]128,000,000,000\ bits[/tex]

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{8}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=8*8*10^{9}\\ \\x=64*10^{9}\ bits\\ \\x=6.4*10^{10}\ bits[/tex]

scientific notation ------> [tex]6.4*10^{10}\ bits[/tex]

standard notation ----->  [tex]64,000,000,000\ bits[/tex]

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

so

using proportion

[tex]\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{40}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=40*8*10^{9}\\ \\x=320*10^{9}\ bits\\ \\x=3.2*10^{11}\ bits[/tex]

scientific notation ------> [tex]3.2*10^{11}\ bits[/tex]

standard notation ----->  [tex]320,000,000,000\ bits[/tex]

Answer:

Part A)

scientific notation ------> 2.56*10^{11}\ bits2.56∗10

11

bits

standard notation -----> 256,000,000,000\ bits256,000,000,000 bits

Part B)

scientific notation ------> 5.12*10^{11}\ bits5.12∗10

11

bits

standard notation -----> 512,000,000,000\ bits512,000,000,000 bits

Part C)

scientific notation ------> 1.28*10^{11}\ bits1.28∗10

11

bits

standard notation -----> 128,000,000,000\ bits128,000,000,000 bits

Part D)

scientific notation ------> 6.4*10^{10}\ bits6.4∗10

10

bits

standard notation -----> 64,000,000,000\ bits64,000,000,000 bits

Part E)

scientific notation ------> 3.2*10^{11}\ bits3.2∗10

11

bits

standard notation -----> 320,000,000,000\ bits320,000,000,000 bits

Step-by-step explanation:

we know that

1\ Gigabyte=1*10^{9}\ bytes1 Gigabyte=1∗10

9

bytes

1\ byte=8\ bits1 byte=8 bits

therefore

1\ Gigabyte=8*10^{9}\ bits1 Gigabyte=8∗10

9

bits

Part A

Theresa and her brother, Ruben, are getting phones that each have 32 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation

we know that

Each phone have 32 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{32}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=32*8*10^{9}\\ \\x=256*10^{9}\ bits\\ \\x=2.56*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

32

bits

Gigabytes

x=32∗8∗10

9

x=256∗10

9

bits

x=2.56∗10

11

bits

scientific notation ------> 2.56*10^{11}\ bits2.56∗10

11

bits

standard notation -----> 256,000,000,000\ bits256,000,000,000 bits

Part B

Theresa’s parents, Cal and Julia, are getting phones that each have 64 gigabytes of storage. How many bits of storage come with each phone? Type your answer in both scientific and standard notation.

we know that

Each phone have 64 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{64}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=64*8*10^{9}\\ \\x=512*10^{9}\ bits\\ \\x=5.12*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

64

bits

Gigabytes

x=64∗8∗10

9

x=512∗10

9

bits

x=5.12∗10

11

bits

scientific notation ------> 5.12*10^{11}\ bits5.12∗10

11

bits

standard notation -----> 512,000,000,000\ bits512,000,000,000 bits

Part C

Because they are getting four new phones, the family also gets two free tablets. Each tablet has 16 gigabytes of storage. How many bits of storage come with each tablet?

we know that

Each tablet have 16 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{16}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=16*8*10^{9}\\ \\x=128*10^{9}\ bits\\ \\x=1.28*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

16

bits

Gigabytes

x=16∗8∗10

9

x=128∗10

9

bits

x=1.28∗10

11

bits

scientific notation ------> 1.28*10^{11}\ bits1.28∗10

11

bits

standard notation -----> 128,000,000,000\ bits128,000,000,000 bits

Part D

Theresa talked her parents into getting SD cards for her phone and her brother’s phone. Inserting an SD card into a phone gives it more storage. They both get 8-gigabyte SD cards. How many bits of storage come with each SD card? Type your answer in both scientific and standard notation

we know that

Each SD card have 8 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{8}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=8*8*10^{9}\\ \\x=64*10^{9}\ bits\\ \\x=6.4*10^{10}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

8

bits

Gigabytes

x=8∗8∗10

9

x=64∗10

9

bits

x=6.4∗10

10

bits

scientific notation ------> 6.4*10^{10}\ bits6.4∗10

10

bits

standard notation -----> 64,000,000,000\ bits64,000,000,000 bits

Part E

With their plan, the family also gets access to storage on the cloud. They can store a total of 40 gigabytes on the cloud. How many bits of storage do they get on the cloud? Type your answer in both scientific and standard notation

we know that

The cloud have 40 gigabytes of storage

so

using proportion

\begin{gathered}\frac{1}{8*10^{9}}\frac{\ Gigabytes}{\ bits} =\frac{40}{x}\frac{\ Gigabytes}{\ bits}\\ \\x=40*8*10^{9}\\ \\x=320*10^{9}\ bits\\ \\x=3.2*10^{11}\ bits\end{gathered}

8∗10

9

1

bits

Gigabytes

=

x

40

bits

Gigabytes

x=40∗8∗10

9

x=320∗10

9

bits

x=3.2∗10

11

bits

scientific notation ------> 3.2*10^{11}\ bits3.2∗10

11

bits

standard notation -----> 320,000,000,000\ bits320,000,000,000 bits

d = 25 ft

ω = (45º) ⁄ 2 = 22.5º

sin(ω) = R ⁄ d

                sin(22.5º) = R ⁄ 25

R = 9.57 feet

Diameter = 2R

Diameter = 2 • (9.57)

Diameter = 19.1 feet

Diameter = 19 feet (when rounded)

Answer:

20

Step-by-step explanation:

did it on study island