Find the slope-intercept equation of the tangent line to the graph of f(x)=x^2 at (-3,9).

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]

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]

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

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.

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

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.

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:

  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:

The correct statements that are true to functions are :

These above two can be explained as : We write a function as y = f(x), where x is the independent variable, and y is dependent as it depends on x values.

Rest all options are incorrect.

Answer:

The correct options are:

Option A: All functions have a dependent variable.

Option B: All functions have an independent variable.

Option E: A horizontal line is an example of a functional relationship.

Step-by-step explanation:

Consider the provided information.

Function: A function is a relationship where each input has only one output.

Which is denoted by "y=f(x)" where x is input value, also the variable x is independent and y is dependent.

Each input value has exactly one output value vice versa is not true.

Vertical line test: A equation is said to be a function if all vertical lines intersect the graph at most once.

Now consider the provided options:

Option A: All functions have a dependent variable.

This option is true, by the above definition of function.

Option B: All functions have an independent variable.

This option is true, by the above definition of function.

Option C: The range of a function includes its domain.

This option is false.

Understand this with the help of an example:

Consider the function [tex]y=x^2[/tex]

The range of the function is [0,∞) and domain of the function (-∞,∞).

Here range doesn't contains the domain.

Thus this option is wrong.  

Option D: vertical line is an example of a functional relationship.

The equation of the vertical line is x=a where a can be any real number.  

We have different values of y for a unique x also the function fails the vertical line test.

Thus the option D is False.

Option E: A horizontal line is an example of a functional relationship.

The equation of horizontal line is y=a where a can be any real number.

For each input has only one output also it satisfy the vertical line test. We will have same value of y for any x.  Which satisfy the property of function.

Thus this option is true.

Option F: Each output value of a function can correspond to only one input value by definition of function.

Understand this with the help of an example:

Consider the function y=a

The function has same output value for each input value. Which is the contradictory to the option's statement.

Thus, this option is false.

The correct options are:

Option A: All functions have a dependent variable.

Option B: All functions have an independent variable.

Option E: A horizontal line is an example of a functional relationship.

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).

8 days ago is -8 and the time was 24 minutes

9 days ago is -9 and the time was 18 minutes.

The time 2 days ago was halfway in between.

Add the two times together and divide by 2:

24 + 18 = 42 / 2 = 21 minutes

The coordinate is at (-2,21)

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

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:

Option A (48 yards).

Step-by-step explanation:

The perimeter of any shape other than the ellipse is given by:

Perimeter = Sum of all sides.

Since there are two pairs of lines and both lines in the pair are congruent in each other in a rectangle, the formula can be updated as:

Perimeter of a rectangle = 2L + 2W; where L is the length and W is the width.

The perimeter of the fence around the rectangular pool is 108 feet and the width of the pool is 6 feet. The length can be calculated by plugging in the values in the above equation:

108 = 2L + 2(6).

2L = 108 - 12.

L = 96/2.

L = 48 feet.

So Option A is the correct answer!!!

The length of the fence in yards, if he uses all 108 feet of material, is 48 feet if Mason has 108 feet of material to build a fence around a rectangular pool on his property.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

Mason has 108 feet of material to build a fence around a rectangular pool on his property.

As we know,

Perimeter = Sum of all sides.

The perimeter of a rectangle (P) = 2L + 2W

Here L is the length and W is the width.

P = 109 feet

W = 6 feet

108 = 2L + 2(6)

2L = 108 - 12

L = 96/2

L = 48 feet.

Thus, the length of the fence in yards, if he uses all 108 feet of material, is 48 feet if Mason has 108 feet of material to build a fence around a rectangular pool on his property.

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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

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:

  ±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:

B

Step-by-step explanation:

Answer:

The answer is Median.

Step-by-step explanation:

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.

For this case we have that there are a total of 14 male students and a total of 16 female students. Thus, there is a total of 30 students distributed in the four categories.

On the other hand, we have a total of 8 Junior students.

Then, the probability of selecting a student Junior is [tex]\frac {8} {30} * 100 = 26.67[/tex]

Rounding off we have 27%

Answer:

27%

The probability that the student is junior to the nearest whole percent is 27%

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

The total outcome will be the total number of students (both male and female)

Total outcome = 4+6+2+2+3+4+6+3

Total outcome = 30

Since we are to find the probability that the student is a junior.

Total Juniors = 2 + 6 = 8

Expected outcome = 8

Probability that the student is junior = 8/30

Express as a percentage:

[tex]Pr(Juniors)=\dfrac{8}{30} \times 100\%\\ Pr(Juniors)=\dfrac{800}{30}\\ Pr(Juniors)=26.66\%\\[/tex]

Hence the probability that the student is a junior is 27%.

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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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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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I think it is A because the numbers decreased

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:

15 units

Step-by-step explanation:

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

Answer:

The coordinate would be (-1, -1)

Step-by-step explanation:

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

The value of x is 20.1036 given that x³=8125. This can be obtained by using prime factorization.

The number 8125 can be written as factors of primes as,

8125 = 5×5×5×5×13

x³ = 5×5×5×5×13

Take cube roots on both sides,

⇒ x = ∛5×5×5×5×13

x = 5∛5×13

x = 5 × 4.02072 ⇒ x = 20.1036

Hence the value of x is 20.1036 given that x³=8125.

Learn more about roots here:

brainly.com/question/27863878

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To solve the equation x^3 = 8125 for x, we need to take the cube root of both sides of the equation. The cube root of a number y, denoted as y^(1/3), is a number which, when raised to the power of 3, gives y.
So, let's calculate the cube root of 8125:
First, we can factor 8125 into its prime factors to help simplify the cube root:
8125 = 5 * 1625 = 5 * 5 * 325 = 5 * 5 * 5 * 65 = 5 * 5 * 5 * 5 * 13   (Since 65 = 5 * 13)
Now that we have the prime factorization of 8125, we can group the factors into triples:
8125 = (5 * 5 * 5) * 13
Notice that there are three 5s in one group and a leftover 13 that cannot form a triple.
The cube root of a product of factors is the product of the cube roots of those factors, so taking the cube root of both sides of the equation gives us:
x = (5 * 5 * 5)^(1/3) * 13^(1/3)
x = 5 * 13^(1/3)
Because 13 is a prime number and cannot be broken down any further, it does not have a rational cube root. As a result, 13^(1/3) is an irrational number and cannot be represented exactly as a fraction. However, we can write the exact answer as:
x = 5 * 13^(1/3)
To find an approximate rational representation, we can look for a fraction that is close to the cube root of 13. Since we cannot do this exactly without a calculator, we can only leave our final answer like this, with the understanding that the cube root of 13 remains irrational.
In conclusion, the exact result, in simplest form without using an irrational-to-rational conversion (which would not be exact), is:
x = 5 * 13^(1/3)