When she first purchased it, Soledad's computer had 500 GB of hard drive space. After six months, there
were only 407 GB available. Enter and solve an equation to find the amount of hard drive space that
Soledad used in the first six months. Uses as your variable.
- 500
The equation is
She has used
GB of memory

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

74 fishes

Step-by-step explanation:

Total number of people = 1672

Let us represent:

Number of people over the age of 50 = a

Number of people below the age of 50 = b

People over the age of 50 she gave = 16 fish

People below 50 she gave = 96 fish. Only 3/4 of the over 50s collected their salmon

= 3/4a collected fish = 0.75a

If a should collect = 96 fishes

0.75a =

Cross Multiply

=0.75a × 96 fishes/ a

= 72 fishes

Therefore, 3/4 of the over 50s collected 72 fishes.

1/8 of the under 50s collected their fish.

= 1/8b collected fish = 0.125b

If b people should collect = 16 fishes

0.125b people =

Cross Multiply

0.125b × 16 fishes/b

= 2 fishes.

Therefore, the total number of fishes shared

= 72 fishes + 2 fishes

= 74 fishes

Answer:

\(P = (-5,5)\)

Step-by-step explanation:

Let the segments be A and B

\(A = (-9,3)\)

\(B = (1,8)\)

\(m:n = 2:3\)

Required

Determine the endpoints after it is divided into ratios.

Let the point be represented with P

The formula to use is:

\(P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

Where

\(A = (-9,3)\)  ----- \((x_1,y_1)\)

\(B = (1,8)\) ------ \((x_2,y_2)\)

So:

\(P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

\(P = (\frac{2 * 1 + 3 * -9}{2 + 3},\frac{2 * 8 + 3 * 3}{2 + 3})\)

\(P = (\frac{-25}{5},\frac{25}{5})\)

\(P = (-5,5)\)

Rational square roots: √225, √81, √576, √36, √441, √324

Irrational square roots: √300, √120, √12, √50, √200

Let's determine whether each square root is rational or irrational:

√225 = 15. This is a rational number since it can be expressed as a fraction of two integers (15 = 15/1).

√300 ≈ 17.32050808. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√120 ≈ 10.95445115. This is also an irrational number for the same reasons as above.

√81 = 9. This is a rational number since it can be expressed as a fraction of two integers (9 = 9/1).

√576 = 24. This is a rational number since it can be expressed as a fraction of two integers (24 = 24/1).

√36 = 6. This is a rational number since it can be expressed as a fraction of two integers (6 = 6/1).

√12 ≈ 3.464101615. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√441 = 21. This is a rational number since it can be expressed as a fraction of two integers (21 = 21/1).

√50 ≈ 7.071067812. This is an irrational number for the same reasons as above.

√324 = 18. This is a rational number since it can be expressed as a fraction of two integers (18 = 18/1).

√200 ≈ 14.14213562. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

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Answer:

26 shots.

Step-by-step explanation:

60% of 42 is 25.2 but you can't make .2 of a shot so you have to round up.

Answer:

B. ∃x (x2<1)

Step-by-step explanation:

When we take X = 0 and Placing it in each option as follow

A.

∃x (3x=1)

∃x (3(0)=1)

∃x (0=1)

Which is not true

B.

∃x (x2<1)

∃x ((0)2<1)

∃x (0<1)

Which is true

C.

∀x (x2=1)

∀x ((0)2=1)

∀x (0=1)

Which is not true

D.

∃x (x2<0)

∃x ((0)2<0)

∃x (0<0)

Which is not true.

Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

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Thank you! :))

Transformations known as rigid motions involve moving but not resizing an image. Dilation is the only transformation that is not a rigid motion. A transformation that alters a figure's size is called a dilation.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location. Transformations may be divided into four categories: translation, rotation, reflection, and dilation. A metamorphosis is a significant alteration in appearance or form. Your life may change as a result of a significant occasion like getting your driver's license, enrolling in college, or getting married. An extreme, radical change is called a transformation.

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The value of PQ that divides PS in the ratio of 2:1:2 is 14 units.

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

The ratio of PQ: QR: RS is equal to 2:1:2. If PS = 35, hence:

PQ = [(2) / (2 + 1 + 2)] * PS = (2/5) * 35 = 14

The value of PQ that divides PS in the ratio of 2:1:2 is 14 units.

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Answer:

See Picture. I made a 100.

Step-by-step explanation:

Weekly- $17253.46

Daily- $17254.01

Continuously- $17254.11

Monthly- $17251.29

Semi-annually- $17237.36

Quarterly- $17245.69

Compound interest is the addition of interest on the interest of the principal amount.

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

\(A = P(1+ \dfrac{r}{n})^{nt}\)

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46\)

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55\)

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

\(A = Pe^{rt}\)

Substitute the values, we will get,

\(A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45\)

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23\)

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36\)

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7\)

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Answer:

10

Step-by-step explanation:

12/2=6+4=10

Answer:

It cannot be used to assess individual renal function or degree of obstruction. Sulfadiazine stones are also difficult to visualize on CT because of relatively low attenuation. It is relatively expensive.

Answer:

(3,5)

Step-by-step explanation:

Mid-point = (1i+2j+5i+8j)/2

=(6i+10j)/2

=3i+5j

=(3 5)

Answer:

hope this is correct

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer is 3 2/5. ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer:

3\(\frac{2}{5}\)

Step-by-step explanation:

5 × 3 = 15

2 remains

Answer:

90-62=28

28+38=66

90-66=24

in 15 seconds they are 24 meters lower

Write the system of equations.

let x be number of male students

let y be number of female students

the number of students can be modeled by the equation

the number of female students can be modeled by the equation

insert the second equation into the first equation

solve the equation for x

use the number of x into the second equation to find y

prove that the results is correct with the first equation

Answer:

\(\displaystyle y = -3x + 9\)

Step-by-step explanation:

First, find the rate of change of the line:

\(\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-6 + 3}{-1 + 2} = m \hookrightarrow \frac{-3}{1} = m \\ \\ \boxed{-3 = m}\)

_______________________________________________

Now plug all the information into the Slope-Intercept Formula. It does not matter which ordered pair is chosen:

\(\displaystyle 3 = -3[2] + b \hookrightarrow 3 = -6 + b; 9 = b \\ \\ \boxed{\boxed{y = -3x + 9}} \\ \\ OR \\ \\ 6 = -3[1] + b \hookrightarrow 6 = -3 + b; 9 = b \\ \\ \boxed{\boxed{y = -3x + 9}}\)

I am joyous to assist you at any time.

Answer:

to much math

Step-by-step explanation:

The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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Answer:

-5/3

Step-by-step explanation:

trust me bro

Answer:

Use desmos

Step-by-step explanation:

Basically it is a graphing calculator put your points

Answer:

21.44 All you need to do is divide the 2.68 by 2 then multiply it by 16

Answer:

-1 is the next one ithink

Answer:

- 2

Step-by-step explanation:

Add 5 From Both Sides

Simplify

Subtract 9x from both sides of the equation

Simplify

Divide both sides of the equation by the same term

Simplify

Solution

Answer:

\(x=-2\)

Step-by-step explanation:

Step-by-step on how to solve it is in the picture below ↓

Hope this helps! :)

Answer:

$0.91

Step-by-step explanation:

Given:

If one pound of Parmesan cheese costs $14.60, to find the cost of a one-ounce portion, simply divide the cost of one pound by 16:

\(\implies \textsf{1 ounce portion}=\dfrac{\$14.60}{16}=\$0.9125=\$0.91\;\sf (nearest \; cent)\)

Therefore, the standard portion cost for a one-ounce portion of Parmesan cheese is $0.91 (nearest cent).

Answer:

39916800

Step-by-step explanation:

1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10 × 11

By rearranging the triangles side by side and making sure the triangles vertices touches each other. The image below is formed

What you notice : The image formed by placing the triangle side by side with the vertices touching each other is that, the shape formed is a trapezium.

a) If the triangles are cut out at equal proportion, then the angles are equal and the the triangles are equiangular; the angles are 60 degrees each

b) If the triangles are not cut out equally, then the greatest number of right angle that we can get in a triangle is one (1) and the greatest number of obstuse angle in a triangle is one (1)

Reason:

The sum of the three angles of a triangle is 180 degrees, of which if one angle is 90 degrees (right angle) then the other two angles will be less than 90 degrees each, as their sum will give 90 degrees

Also if one of the three angles is an obtuse angle ( say 115 degrees) then the other two angles will be acute angles each.

Answer:

Acute

Step-by-step explanation:

two of the angles are acute and the other is right.