Let Events A & B be described as follows: P(A) = watching a movie P(B) = going out to dinner The probability that a person will watch a movie is 62% and the probability of going out to dinner is 46%. The probability of watching a movie and going out to dinner is 28.52% Are watching a movie and going out to dinner independent events? No, because the P(A) + P(B) ≠ P(A and B). Yes, because the P(A) + P(B) is greater than 100%. No, because the P(A)P(B) ≠ P(A and B). Yes, because the P(A)P(B) = P(A and B).

Answer:

x =23/14

If we want to change it to a mixed number

x = 1 9/14

Step-by-step explanation:

42x – 5 = 64

Add 5 to each side

42x – 5+5 = 64+5

42x = 69

Divide each side by 42

42x/42 = 69/42

x = 69/42

Divide the top and bottom by 3

x =23/14

If we want to change it to a mixed number

x = 1 9/14

Answer:

d)4

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

Answer:

720

Step-by-step explanation:

We are given the following permutation problem to solve:

[tex] _ 6 P _ 6 [/tex]

We know that the number of possibilities to choose an ordered set of [tex] r [/tex] objects from a total of [tex]n[/tex] objects is given by:

[tex] _ n P _ r = \frac { n ! } { ( n - r ) ! } [/tex]

Substituting the given values, n = 6, r = 6:

[tex] _ 6 P _ 6 = \frac { 6 ! } { ( 6 - 6 ) ! } [/tex] = 720

ANSWER

Point-slope form:

[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]

Slope-intercept form:

[tex]y= -\frac{3}{5} x + \frac{9}{5}[/tex]

EXPLANATION

The graphed line passes through

[tex](-2,3) \: \: and \: \: (3,0)[/tex]

The slope of this line is determined using

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

We substitute the points to get;

[tex]m = \frac{0 - 3}{3 - - 2} [/tex]

[tex]m = -\frac{3}{5} [/tex]

The point-slope formula is:

[tex]y-y_1 = m(x - x_1)[/tex]

Substitute the first point and slope to get:

[tex]y - 3 = -\frac{3}{5} (x - - 2)[/tex]

[tex]y - 3 = -\frac{3}{5} (x + 2)[/tex]

To find the slope-intercept form, we expand to get:

[tex]y= -\frac{3}{5} x - \frac{6}{5} + 3[/tex]

[tex]y= -\frac{3}{5} x + \frac{9}{5} [/tex]

Answer:

Slope

[tex]m=-\frac{3}{5}[/tex]

point-slope form

[tex]y=-\frac{3}{5}(x-3)[/tex]

slope-intersection form

[tex]y=-\frac{3}{5}x+1.8[/tex]

Step-by-step explanation:

The equation of a line in the point-slope form has the following formula:

[tex]y-y_0 = m (x-x_0)[/tex]

Where m is the slope and [tex](x_0, y_0)[/tex] is a point belonging to the line.

The equation of a line in the slope-intersection form has the following formula:

[tex]y = mx + b[/tex]

Where b is the intersection of the line with the y axis.

To calculate the slope of the line knowing 2 points we use the following formula:

[tex]m=\frac{y_1-y_0}{x_1-x_0}[/tex]

In this case:

[tex]x_0 =3\\y_0=0\\x_1=-2\\y_1=3[/tex]

So

[tex]m=\frac{3-0}{-2-3}[/tex]

[tex]m=-\frac{3}{5}[/tex]

So the equation of a line in the point-slope form

[tex]y-0 =-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}(x-3)[/tex]

The equation of a line in the slope-intersection form is:

[tex]y-0=-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}(x-3)[/tex]

[tex]y=-\frac{3}{5}x+\frac{9}{5}[/tex]

[tex]y=-\frac{3}{5}x+1.8[/tex]

with [tex]b=1.8[/tex]

Answer: Option C

Step-by-step explanation:

By definition, a relation is considered a function if and only if for each input value x there is only one associated output y value.

To verify if the graph of a relation is a function, trace on the graph vertical lines parallel to the y axis. If one of these vertical lines cuts the graph in 2 or more points, then the relationship is not a function

By definition, a function is considered a one-to-one function if and only if there is no equal output value and, for two different input values.

For example, the following ordered pairs do not correspond to a one-to-one function, because the output value y = 6 is associated with two input values ​​x = 1 and x = 3

(1, 6) (3, 6)

To verify if the graph of a relation is a function, draw on the graph horizontal lines parallel to the x axis. If one of these horizontal lines cuts the graph in 2 or more points, then the relationship is not a one-to-one function.

When you draw vertical lines on the plot shown, you will see that they always intersect at a single point. Therefore the relationship is a function

When drawing horizontal lines on the displayed graph you will notice that they always intersect at a single point. Therefore the function is a one-to-one function

the answer is C

Answer:

A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. ... The first one is a translation rule.

Final answer:

In a glide reflection, the translation occurs first, moving the figure along a straight line, followed by a reflection over a line parallel to the translation vector, resulting in a figure that has been moved and potentially reoriented.

Explanation:

In a glide reflection, a transformation that combines a translation with a reflection, the proper sequence is important. The translation part comes first, where the figure is slid along a straight line called the translation vector. After the figure has been moved, the second step is the reflection over a line parallel to the vector of the translation. This two-step process results in a final image that has the same size and shape as the original figure but is in a different position and may have a different orientation.

Imagine a point undergoing a glide reflection. Initially, it is translated along a vector, and then it is reflected across a line that is parallel to the direction of translation. The end result is that the point has 'glided' to a new location, as if it had slid across a mirror placed at an angle to its original path.

Answer:

5 but its probaly not right bc im just looking for pointsStep-by-step explanation:

Answer:

parameter

Step-by-step explanation:

Answer:

276.75

Step-by-step explanation:

Deposit 1230. paying 2.25 % 10 yrs.

the interest is 276.75 and the amount is 1506.75

Answer:

The answer to the first question is $276.75     and the answer to the second question is $4882.50

Step-by-step explanation:

Johnny deposited $1230 in a savings account at 2.25 percent interest. How much interest will the account earn in 10 years?

To solve this, we simply use the simple interest formula;

Simple Interest = PRT / 100

where p is the principal, R is the rate and T is the time (in years)

In this question principal = $1230  rate = 2.25   and time = 10

We can now plug the variables into the formula;

Simple Interest = PRT / 100

                           =$1230  × 2.25× 10    /     100

                             = $27675  / 100

                              = $276.75

Therefore, the amount of interest earn in 10 years is  $276.75

Will got an insurance check of $4500 after a car accident. He deposited it into a savings  account at 1.7 percent interest for five years. What was the total amount of money in the  account after five years?

We can also solve this second part of the question using the simple interest formula, here;

principal = $4500

Rate =1.7

Time =5

We will now insert our values into the simple interest formula, thus;

Simple Interest = PRT / 100

                          =$4500 × 1.7 × 5   / 100

                          =$38250 / 100

                          =$382.50

Simple interest =$382.50

Total amount = $4500 + $382.50

                      =$4882.50

Therefore, the total amount in the account after five years is $4882.50

Answer:

B.

Step-by-step explanation:

the denominator you want is 16 so 4(4) is 16, which makes 3(4) 12 so 12/16. 7/16 is already perfect. 8(2) is 16 therefore 5(2) is 10 which makes 10/16.

Answer: both are 21/29

Step-by-step explanation:

Use SOHCAHTOA so the opposite/hypotenuse for P is 21/29 and the adjacent/hypotenuse for Q is also 21/29

Answer:

  see below

Step-by-step explanation:

A proportional relationship has a graph that always goes through the origin. This fact by itself eliminates all the wrong answers.

A slope of 2/3 means the rise is 2 for each horizontal run to the right of 3. The two given points are 2 vertical units and 3 horizontal units apart, demonstrating a slope of 2/3.

The z-score for a student who scored 75 on the test with an average of 80 and a standard deviation of 6 is approximately -0.833, indicating the score is 0.833 standard deviations below the mean.

To calculate the z-score for a student who scored 75 on a history test, we can use the z-score formula:

[tex]Z = \( \frac{X - \mu}{\sigma} \)[/tex]

Where:

X is the raw score (75 in this case)

[tex]\( \mu \)[/tex] is the mean score (80)

[tex]\( \sigma \)[/tex] is the standard deviation (6)

Inserting the values, we get:

[tex]Z = \( \frac{75 - 80}{6} \) = \( \frac{-5}{6} \) = -0.833\[/tex]

The z-score for a student who earned 75 on the test is approximately -0.833, rounded to the nearest thousandth. This z-score indicates that the student's score is about 0.833 standard deviations below the mean

Answer:

A

Step-by-step explanation:

y = 2x² + 8x + 3

Complete the square:

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) + 3 - 2(4)

y = 2(x + 2)² - 5

So the vertex is at (-2, -5).  The graph must be Graph A.

Graph A has its vertex at (-4, -5). Then the correct option is A.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The parabolic expression is given below.

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

y = 2(x² + 4x + 4) - 8 + 3

y = 2(x + 4)² -5

The vertex of the parabola is at (-4, -5).

Graph A has its vertex at (-4, -5). Then the correct option is A.

Then the graph of the parabola is given below.

More about the parabola link is given below.

https://brainly.com/question/8495504

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Answer:

81

Step-by-step explanation:

3 digits ^4 number options

3^4=81

Answer:

The missing coefficient of the x-term of the product (-x-5)2 is 10.

Step-by-step explanation:

Through whole square formula.

(-x-5)2 = (-x)^2 -2(-x)(5)+(5)^2

=x^2+10x+25

Therefore, the missing coefficient of the x-term of the product is 10

Answer:

10

Step-by-step explanation:

The given expression is

[tex](-x-5)^2[/tex]

We need to find the coefficient of x.

According to the property of algebra.

[tex](a-b)^2=a^2-2ab+b^2[/tex]

In the given expression a=-x and b=5.

Substitute a=-x and b=5 in the above formula.

[tex](-x-5)^2=(-x)^2-2(-x)(5)+(5)^2[/tex]

On further simplification we get

[tex](-x-5)^2=x^2+10x+25[/tex]

Coefficient of x is a multiplicative factor of x.

Therefore, the coefficient of x is 10.

There are a total of 2,000 students in the school.

1.) There are 540 students in the 6th grade. 540 is only 27% of students compared to the total. To find the total students in the whole school, we divide 540 by 27%.

2.) We first change 27% into a decimal by moving the point two times to the left. (Rule to change the percent into a decimal)

27% = .27

3.) Before we divide, we remove the decimal by moving the decimal two times to the right and so do we to 540.

.27 = 27

540. = 54000.

4.) Now we have 54000 divided by 27 which give us the answer of 2,000.

Hope this Helps!!!

Please Mark as Brainliest!!!

Answer:

2,000 students are in school i do not know if it’s decimals because decimals are like % percentage but ok 2,000 is my answer I hope this helped

Answer:

B).  (2, –23)

Well this person made it easy by literally saying the answer...

Step-by-step explanation:

Hope this helps!!  Also heart and rate if you found this answer helpful!!

The correct option is, (B) (2, –23).

Learn more about  coordinates here:

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Answer:

{2, 2, -6}

Step-by-step explanation:

synthetic division is one of the easier ways of determining whether or not a given number is a root of a polynomial.  Here we're told that -6 is a root.  Let's go through the steps of synthetic division:  keep in mind that if there is no remainder (that is, the remainder is zero), then the divisor (such as -6) is a zero of the polynomial.

The coefficients of f(x)=x^3+2x^2-20x+24 are {1, 2, -20, 24}.

Setting up synthetic div.:

       -6   )   1    2    -20    24

                      -6     24    -24

             ----------------------------

                 1    -4       4     0

Here the remainder is zero (0), so it is safe to assume that -6 is a zero of the original polynomial.

We can continue with synth. div. to determine the remaining zeros of the original function  f(x)=x^3+2x^2-20x+24.   The coefficients {1,  -4,  4} represent the quadratic x^2 - 4x + 4.  Let's check whether the factor 2 of 4 is indeed a zero:

2   )   1    -4    4

               2   -4

    -----------------

       1      -2    0

Here the remainder is zero.  Thus, 2 is a zero of f(x)=x^3+2x^2-20x+24.  Notice that the remaining coefficients are {1, -2}; they represent x - 2 = 0, so the third root is 2.

Thus, the zeros of f(x)=x^3+2x^2-20x+24 are {2, 2, -6}

Answer: C (600 - 28w < 300)

I know this because: I took the E2020 test

Answer:

Answer: C (600 - 28w < 300)

Step-by-step explanation:

Answer:

a = -4

b = 6

Step-by-step explanation:

See attached

Answer:

a=-4 and b=6

Step-by-step explanation:

[tex]\frac{a}{x-8} +\frac{b}{x+4} =\frac{2x-64}{(x-8)(x+4)}[/tex]

First, add the fractions by finding the common denominator.

In this case, (x-8)(x+4).

[tex]\frac{a(x+4) + b(x-8)}{(x-8)(x+4)} =\frac{2x-64}{(x-8)(x+4)}[/tex]

Therefore, the numerators are equal:

[tex]a(x+4) + b(x-8) =2x-64[/tex]

Simplify:

[tex]ax+4a + bx-8b =2x-64\\(a+b)x+4a-8b=2x-64[/tex]

Now match the coefficients.

[tex]a+b=2, 4a-8b=-64[/tex]

Solve the system of equations.  I'll use substitution, but you can also use elimination if you prefer.

[tex]4a-8b=-64\\a-2b=-16\\(2-b)-2b=-16\\2-3b=-16\\-3b=-18\\b=6\\a=-4[/tex]

Therefore, a=-4 and b=6.

Answer:

b

Step-by-step explanation:

Using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 1)

d = [tex]\sqrt{(4+1)^2+(1-4)^2}[/tex]

  = [tex]\sqrt{5^2+(-3)^2}[/tex]

  = [tex]\sqrt{25+9}[/tex] = [tex]\sqrt{34}[/tex] → b

Answer:

  $1,000 at 2%; $1,800 at 4%

Step-by-step explanation:

Let x represent the amount invested at 2%. Then x+800 was invested at 4% and the total interest earned was ...

  x·2% + (x+800)·4% = 92

  x·6% + 32 = 92 . . . . . . . . . simplify

  x·0.06 = 60 . . . . . . . . . . . . subtract 32; write 6% as a decimal

  x = 60/0.06 = 1000 . . . . . divide by the coefficient of x

$1000 was invested at 2%; $1800 was invested at 4%.

Final answer:

The angle 237° is located in the third quadrant since it is between 180° and 270°.Therefore, the correct answer to the question is:

D. III

Explanation:

The question asks in which quadrant the angle 237° is located. To determine the quadrant of an angle in standard position (angle measured from the positive x-axis), we use the following information:

Angles from 0° to 90° are in the first quadrant.

Angles from 90° to 180° are in the second quadrant.

Angles from 180° to 270° are in the third quadrant.

Angles from 270° to 360° are in the fourth quadrant.

Since 237° is between 180° and 270°, it is located in the third quadrant. Therefore, the correct answer to the question is:

D. III

Answer:

  4 cm

Step-by-step explanation:

You have done all of the parts except the final division.

  13 = 3.25x

  13/3.25 = x = 4 . . . . . divide both sides by 3.25

The missing base measure of the enlarged trapezoid is 4 cm.

Answer:

4 CM

Step-by-step explanation:

Answer: [tex]7m^5-3m^3-3[/tex]

Step-by-step explanation:

You can observe that you need to subtract the polynomial [tex](6m^5 + 3 - m^3 -4m)[/tex] and the polynomial [tex](-m^5 + 2m^3- 4m + 6)[/tex].

It is important the remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]

Then, the first step is to distribute the negative sign:

[tex](6m^5 + 3 - m^3 -4m)-(-m^5 + 2m^3- 4m + 6)=\\=6m^5 + 3 - m^3 -4m+m^5-2m^3+ 4m- 6[/tex]

And finally you must add the like terms. Then:

[tex]=7m^5-3m^3-3[/tex]

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\\ 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]

The solutions obtained are Part (A) 2.75 × 10¹¹ bits of storage, Part (B) 5.50 × 10¹¹ bits of storage ,Part (C) 1.37 × 10¹¹ bits of storage, Part (D) 6.87 × 10¹⁰ bits of storage, Part (E)  3.44 × 10¹¹ bits of storage.

Phone and Tablet Storage Measurement

Let's break down each part of the question to help Theresa and her family understand the storage capacity in bits.

Part A

Theresa and Ruben's phones each have 32 gigabytes (GB) of storage. To find the number of bits:

→ Convert gigabytes to bytes: 32 GB = 32 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits (since 1 byte = 8 bits): 32 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 32 × 1024 × 1024 × 1024 × 8 = 274,877,906,944 bits.

→ In scientific notation, this is approximately 2.75 × 10¹¹ bits.

Part B

Cal and Julia's phones each have 64 gigabytes (GB) of storage:

→ Convert gigabytes to bytes: 64 GB = 64 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 64 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 64 × 1024 × 1024 × 1024 × 8 = 549,755,813,888 bits.

→ In scientific notation, this is approximately 5.50 × 10¹¹ bits.

Part C

The family gets two free tablets with 16 gigabytes (GB) of storage each:

→ Convert gigabytes to bytes: 16 GB = 16 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 16 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 16 × 1024 × 1024 × 1024 × 8 = 137,438,953,472 bits.

→ In scientific notation, this is approximately 1.37 × 10¹¹ bits.

Part D

Theresa and Ruben each get 8-gigabyte (GB) SD cards:

→ Convert gigabytes to bytes: 8 GB = 8 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 8 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 8 × 1024 × 1024 × 1024 × 8 = 68,719,476,736 bits.

→ In scientific notation, this is approximately 6.87 × 10¹⁰ bits.

Part E

The family gets 40 gigabytes (GB) of cloud storage:

→ Convert gigabytes to bytes: 40 GB = 40 × 1024 × 1024 × 1024 bytes.

→ Convert bytes to bits: 40 × 1024 × 1024 × 1024 × 8 bits.

→ Calculate the value: 40 × 1024 × 1024 × 1024 × 8 = 343,597,383,680 bits.

→ In scientific notation, this is approximately 3.44 × 10¹¹ bits.

Answer:

  the last choice shown here: F'(0, -4), G'(-3, -1), H'(-2, 2), I'(0, -2)

Step-by-step explanation:

The translation vector tells you that the new coordinates are found by adding -4 to each of the old coordinates. When you realize that the answer choices differ in their values for H' and I', you can conclude that you only need to find one of those to determine the correct answer.

  H' = H + (-4, -4) = (2-4, 6-4) = (-2, 2) . . . corresponds to the last choice shown

_____

When you subtract 4 from each of the coordinates of the other points, you find they also match the last answer selection.

Final answer:

The translation of the figure along the vector ⟨−4,−4⟩ results in the vertices F'(0,-4), G'(-3,-1), H'(-2,2), and I'(0,-2).

Explanation:

The student is asking about a translation of a geometric figure in the coordinate plane. To translate a figure, we add the translation vector to each vertex of the figure. In this case, the translation vector is ⟨−4,−4⟩, which means we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate of each vertex of the figure.

Therefore, the translated figure will have vertices F'(0,-4), G'(-3,-1), H'(-2,2), and I'(0,-2).

Answer:

[tex]\sqrt[6]{200}[/tex]

Step-by-step explanation:

First of all, you need to know that you cannot multiply those radicals without having a common index (the little number outside the radical that sits in the curve of the radical).  One is a 3 and the other, without being stated outright, is understood to be a 2.  BUT we can make them like.  The index of a radical is the denominator of the exponential equivalent.  

[tex]\sqrt[3]{5}=5^{\frac{1}{3}}[/tex] and

[tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]

See how the indexes are now the denominators of the rational exponents.  We can make them like by finding the LCM of 3 and 2...which is 6:

[tex]5^{\frac{1}{3}}=5^{\frac{2}{6}}[/tex] and

[tex]2^{\frac{1}{2}}= 2^{\frac{3}{6}}[/tex]

Now that the indexes are like, we rewrite them as radicals again:

[tex]\sqrt[6]{5^2}*\sqrt[6]{2^3}[/tex] which, simplified, is

[tex]\sqrt[6]{25}*\sqrt[6]{8}[/tex]

Now we can find the product which is

[tex]\sqrt[6]{200}[/tex]

The product of ∛5 ×√2 is approximately 2.41. The correct option is b) [tex]\sqrt[6]{200}[/tex], which matches the calculated value.

To find the product ∛5 × √2, we first take the cube root of 5 (∛5) and then multiply it by the square root of 2 (√2).

∛5 ≈ 1.71 (approximately, rounded to two decimal places)

√2 ≈ 1.41 (approximately, rounded to two decimal places)

Now, let's calculate the product:

∛5 × √2 ≈ 1.71 × 1.41 ≈ 2.41 (approximately, rounded to two decimal places)

Now, let's check the options:

a. [tex]\sqrt[6]{10}[/tex] ≈ 1.72 (approximately, rounded to two decimal places)

b. [tex]\sqrt[6]{200}[/tex] ≈ 2.41 (approximately, rounded to two decimal places) <-- Matches our calculated value.

c. [tex]\sqrt[6]{500}[/tex] ≈ 2.80 (approximately, rounded to two decimal places)

d.[tex]\sqrt[6]{100000}[/tex] ≈ 5.62 (approximately, rounded to two decimal places)

The correct answer is option b)[tex]\sqrt[6]{200}[/tex].

To know more about product:

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Answer:

sqrt(5)

Step-by-step explanation:

Honestly think this person means to find the magnitude of the vector.  You can use dot product here, the vector with itself... But that isn't the last step.

v dot v=4+1=5

and so |v|=sqrt(5)

Answer:

It doesn't. x = 22 271 201

Step-by-step explanation:

You are going to need a calculator no matter how you do it.

[tex]x =19 169 000 \times e^{0.15}[/tex]

(a) The direct method

[tex]x = 19 169 000\times 2.718 281 828^{0.15} = 19 169 000 \times 1.161 834 243 = 22 271 201[/tex]

(b) The indirect method

[tex]\ln \left (19 169 000\times 2.718 281 828^{0.15} \right ) = \ln(19 169 000) + 0.15 = 16.768 805 + 0.15 = 16.918 804\\\\e^{16.918 804} = 22 271 201[/tex]

For this case we must indicate the graph corresponding to the following equation:

[tex]y = 2e ^ x[/tex]

Then, we evaluate the equation for[tex] x = 0[/tex]

[tex]y = 2e ^ 0[/tex]

We have by definition, any number raised to zero results in 1.

So:

[tex]y = 2[/tex]

Now we evaluate the equation for x = -1

[tex]y = 2e ^ {-1}\\y = \frac {2} {e}\\y = 0.736[/tex]

We already have two points to graph:

[tex](0,2)\\(-1,0.736)[/tex]

Observing the options, we realize that the correct option is option C.

It should be noted that graphs A and D, by definition, do not correspond to the exponential function.

Answer:

Option C