Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:

Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below

Answer:

  z = 0.80

Step-by-step explanation:

You want the value of z such that p(-z < X < z) = 0.5762 for a normal distribution.

The area outside the region of interest will be split evenly between the two tails. That is, the lower tail will hold (1 -0.5762)/2 = 0.2119 of the area of the distribution. The required value of z will be the magnitude of the Inverse CDF function for this value.

The attached calculator shows the required value of z is about 0.80.

Answer:

(7) AB is a tangent , (8) AB is not a tangent

Step-by-step explanation:

the angle between a tangent and the radius is 90°

if AB is a tangent then Δ ABC is right with hypotenuse AC

using Pythagoras' identity

the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.

if AC² = AB² + BC² , then AB is a tangent to the circle

(7)

AC² = 34² = 1156

AB² + BC² = 30² + 16² = 900 + 256 = 1156

since AC² = AB² + BC² , then AB is a tangent to the circle

(8)

AC² = 28² = 784

AB² + BC² = 21² + 20² = 441 + 400 = 841

since AC² ≠ AB² + BC² , then AB is not a tangent to the circle

Answer: $105,000

Step-by-step explanation:

$140,000-25%deposit =$105,000

Answer:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735...

Step-by-step explanation:

The volume of the solid with a hole in the shape of a rectangular prism passing through the center of a cylinder with a radius of 10 yards is approximately 1410 cubic yards, rounded to the nearest ten.

The cylinder with the hole can be viewed as the difference of two solids: the cylinder and the rectangular prism. The volume of the cylinder is given by the formula V_cyl = π[tex]r^2h[/tex], where r is the radius and h is the height.

The height of the cylinder is equal to the height of the rectangular prism that passes through its center. The height of the rectangular prism is given as 12 yards, which is also the diameter of the cylinder. Therefore, the height of the cylinder is h = 12/2 = 6 yards.

The volume of the cylinder is therefore V_cyl = π[tex](10)^2(6)[/tex] = 600π cubic yards.

The rectangular prism has a length of 20 yards, a width of 10 yards, and a height of 12 yards. Therefore, its volume is V_prism = 20 × 10 × 12 = 2400 cubic yards.

The volume of the solid with the hole is then:

V = V_cyl - V_prism = 600π - 2400 = 600(π - 4) ≈ 1412.2 cubic yards.

Therefore, the volume of the solid is approximately 1410 cubic yards.

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a) [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex] series has sum of 20.

What is sum?

In mathematics, the sum of a series is the result obtained by adding together all the terms in a sequence of numbers.

The series that has a sum of 20 is [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex].

To see why, we can use the formula for the sum of an infinite geometric series:

[tex]S = \frac{a}{(1-r)}[/tex]

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, the first term is:

[tex]a = 5(\frac{3}{4} )^0 = 5[/tex]

And the common ratio is:

[tex]r = \frac{3}{4}[/tex]

So, the formula becomes:

[tex]S = \frac{5}{(1-\frac{3}{4} )}[/tex]

Simplifying the denominator, we get:

[tex]S = \frac{5}{\frac{1}{4}}[/tex]

Multiplying by the reciprocal, we get:

S = 20

Therefore, the sum of the series is 20, which means that the series [tex]$\sum\limits_{n=1}^{\infty} 5\left(\frac{3}{4}\right)^{n-1}$[/tex]

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The given expression can be written in scientific notation as 1.8 x 10² To obtain this, we first divide 2,520,000 by 14,000 to get 180. Then, we express this as 1.8 x 10² by moving the decimal point two places to the left and adding an exponent of 2.

For expressing very big or very small numbers in scientific notation, the number is written as the product of a number between 1 and 10 and a power of 10

To convert a number to scientific notation, first express it in the form a x 10^b, where a is a number between 1 and 10, and b is an integer.

Then, move the decimal point in a to obtain a number between 1 and 10, and add an exponent to 10 that corresponds to the number of places you moved the decimal point.

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Answer:

1 c

2 d

3 a

4 b

5 e

Step-by-step explanation:

scale factor > 1 => expansion

scale factor < 1 => contraction

scale factor = 1 => no change

scale factor is (-) => opposite site

Answer:

Step-by-step explanation: Multiply all numbers and add all then divided by the lowest

Let x be the scale factor.

Then, the ratio of the areas of the two triangles is x².

We are given that the larger triangle has an area of 360 square meters and the smaller triangle has an area of 2.5 square meters. So we can set up the equation:

x²(2.5) = 360

Solving for x, we get:

x = sqrt(360/2.5)

x = sqrt(144)

x = 12

Therefore, the scale factor is 12:1. Answer: 12:1.

The probabilities of the events and their values are shown below

The total number of marbles in the bag is 13, with 6 blue, 2 green, and 5 red.

P(Blue or Green) represents the probability of selecting a blue or green marble on the first pick.

This is calculated as follows:

P(Blue or Green) = P(Blue) + P(Green)

= 6/13 + 2/13

= 61.5%

P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, with replacement.

Therefore:

P(Blue and Green) = P(Blue) * P(Green)

= (6/13) * (2/13)

= 7.1%

P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, without replacement.

Therefore:

P(Blue and Green) = P(Blue) * P(Green)

= (6/13) * (2/12)

= 7.7%

P(Blue) represents the probability of selecting a blue marble on the first pick.

This is simply the proportion of blue marbles in the bag:

P(Blue) = 46.2%

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a) The total cost for renting a compact car for eight days is as follows for each plan:

b) It is more economical to take the weekly rental plan than the daily rental plan.

Each plan's total rental cost is determined using multiplication or addition.

For instance, the total cost for the daily plan is a product of the daily rental cost and the number of days the car is rented.

The total cost for the weekly plan is an addition operation since the car is rented for 7 days (weekly cost) and 1 day (daily cost).

                               Day                  Week

Rental cost per      $48                   $312

1 week = 7 days

Total rental cost for

8 days                $384 ($48 x 8)     $360 ($312 + $48)

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The distance walked by Dario from to reach comic book store is 1.4 miles.

Displacement and distance are two terms that, while they appear to imply the same thing, have quite different definitions and meanings. Displacement is the measurement of "how much space an item has covered while it has been in motion," whereas distance is the indication of "how much ground an object has covered during its motion." Let's examine the distinction between displacement and distance in this essay.

For the given route we have:

House to jewelry store:

0.2 - (-0.5) = 0.2 + 0.5 = 0.7 miles.

Jewelry store to bank:

0.6 - 0.2 = 0.4 miles.

Bank to comic book store:

-0.5 -(-0.8) = -0.5 + 0.8 = 0.3 miles.

House to comic book store:

0.7 + 0.4 + 0.3 = 1.4 miles.

Hence, the distance walked by Dario from to reach comic book store is 1.4 miles.

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The complete question is:

Answer:

Step-by-step explanation:

Let's start by setting up two variables to represent the number of pounds of type A and type B coffee used in the blend. Let:

x be the number of pounds of type A coffee used

3x be the number of pounds of type B coffee used (since there were three times as many pounds of type B used as type A)

The total cost of the blend is given as $796.00, so we can set up an equation based on the cost of each type of coffee and their respective amounts:

5.95x + 4.65(3x) = 796

Simplifying and solving for x, we get:

5.95x + 13.95x = 796

19.90x = 796

x = 40

Therefore, 40 pounds of type A coffee were used in the blend. To find the number of pounds of type B coffee, we can substitute x = 40 into our expression for the number of pounds of type B:

3x = 3(40) = 120

Therefore, 120 pounds of type B coffee were used in the blend.

(a)The transformed vertices would be:

W' = (1, -3)

X' = (-3, 0)

Y' = (1, -2)

(b)The transformed vertices would be:

W' = (-0, 1)

X' = (4, 4)

Y' = (-0, 2)

a) Reflection: To reflect the triangle across the y-axis, we simply need to negate the x-coordinates of each vertex.

The transformed vertices would be:

W' = (-0, 1)

X' = (4, 4)

Y' = (-0, 2)

The reflected triangle would be W'X'Y'.

b) Translation: To translate the triangle by the vector (1, -4), we add (1, -4) to the coordinates of each vertex.

The transformed vertices would be:

W' = (1, -3)

X' = (-3, 0)

Y' = (1, -2)

The translated triangle would be W'X'Y'.

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[tex]\Large\textbf{Please give complete questions}[/tex]

Answer:

12

Step-by-step explanation:

The absolute extrema for the given function occurred at the critical points for Interval  [0, 2π] is 3.

The point wherein the minimum or maximum value of the function is reached is known as the absolute extremum (also global extremum) of the function in the given interval.

The absolute extremum, or point equivalent to the highest or least value in the entire function, is frequently the interval specified, which is the domain of the function.

The given function :

y = 3 cos x,

Differentiate the function with respect to 'x'.

y' = -3 sin x

Find the critical point , by y = 0

-3 sin x = 0  

x = sin ⁻¹ (0)

Interval  [0, 2π]

So, critical points are: x = 0,π, 2π

Now, evaluate function by putting the critical points;

y(0) = 3 cos 0 = 3

y(π) = 3 cos π = 0

y(2π) = 3 cos 2π = 3

Thus, absolute extrema for the given function occurred at the critical points 0 and 2π that is 3.

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The measures of the numbered angles in the rhombus include the following:

In Mathematics and Geometry, a rhombus can be defined as a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal). Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees).

This ultimately implies that, the opposite sides of a rhombus are parallel and the sum of all the four (4) interior angles is equal to 360 degrees.

m∠3 + 90° + 31° = 180°

m∠3 + 121° = 180°

m∠3 = 180° - 121°

m∠3 = 59°

m∠3 ≅ m∠6 ≅ m∠4 = 59°

Since opposite angles are equal, we have:

m∠1 ≅ m∠5 = 31°

Since the two (2) diagonals bisect each other at right angles (90 degrees), we have:

m∠2 = 90°

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The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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Answer:

Step-by-step explanation:

explain you question more i cant understand if i could i would help

Answer: a/ c/ d and e

Step-by-step explanation:

Using equations,

A: y=-x²+6x-5

y=3

3=-x²+6x-5

y=0

B: (x-2) (x-4) =0

C: x-2=0 OR x-4=0

D: x=2 OR x=4

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, etc.

Y=-x²+6x-5

Y=3

Using substitution:

3 = - x²+6x- 5

x²- 6x+8 = 0

Now factor your equation:

x²- 6x+8 = 0

⇒ x² -2x - 4x + 8 = 0

⇒ x (x-2) -4(x-2) = 0

⇒ (x- 2) (x-4) =0

Identify the x-values of the solutions:

x-2=0 or x-4 =0

x=2 or x=4

Identify the solution to the system:

x=2       y=3 and

x=4       y=3

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Approximately 106.79 mg of Tylenol remain in Courtney's body after 4 hours.

What is the capacity of taking medication?

When someone takes medication, it is important to understand how long the medication remains in their system. This can help ensure that the medication is effective and prevent unwanted side effects. In this case, Courtney has taken 250mg of Tylenol to relieve a headache. We are asked to find out how much of the Tylenol remains in her body after 4 hours.

To answer this question, we can use the formula A=250(.73)ⁿ, where A represents the amount of Tylenol remaining in the body after n hours. The value 250 represents the initial amount of Tylenol Courtney took, and 0.73 represents the percentage of Tylenol that is eliminated from the body per hour.

When we substitute n=4 into the formula, we get A= 250(.73)⁴. This means that after 4 hours, approximately 106.79 mg of Tylenol remain in Courtney's body. This calculation assumes that Courtney has not taken any additional Tylenol during this time period.

It is worth noting that individual factors such as age, weight, and metabolism can affect how long a medication remains in someone's system. Additionally, taking medications with other substances, such as alcohol or other medications, can also impact the body's ability to eliminate the medication. Therefore, it is always important to follow the advice of a medical professional and carefully read medication labels and instructions.

A = 250(.73)ⁿ

A = 250(.73)⁴ (substituting n=4)

A ≈ 106.79

In conclusion, we can calculate that after 4 hours, approximately 106.79 mg of Tylenol remains in Courtney's body. It is important to remember that medication elimination can vary based on individual factors, and it is always best to consult a healthcare professional if you have any concerns about medication use or potential side effects.

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Answer:

x=-5, y=-2

Step-by-step explanation:

2x+4y=-18                (1)

5x-10y=-5                 (2)

apply 5×(1)+2×(2)

10x+20y=-90      (3)

10x-20y=-10   (4)

by adding (3) and (4)

20x=-100

x=-5

put the value of x in  (1)

we get 2×(-5)+4y=-18

⇒y=-2

After solving the given equations, the value of x and y are -5 and -2 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, we have the equations:

2x+4y=-18                (1)

5x-10y=-5                 (2)

Apply as follows: 5×(1)+2×(2)

10x+20y=-90      (3)

10x-20y=-10   (4)

After adding (3) and (4):

20x=-100

x=-5

Insert the value of x in  (1) as follows:

We obtain: 2×(-5)+4y=-18

⇒y=-2

Therefore, after solving the given equations, the value of x and y are -5 and -2 respectively.

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Answer: 16

Step-by-step explanation: Solve the parentheses inside first, which should be (3 + 5) (3 - 1). Solve the inside which the answer would be (8) (2). Multiply after (2x8) to get the answer 16

hope it helps!!

Answer: D. y=-x+7

Step-by-step explanation: For example,

(-1,8)

x= -1

y=8

-(-1) = 1

1 + 7 = 8