Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
(1.5, 2.85)
O (1.05, 3.3)
(-1.2, -1.05)
O(-2.4, -2.1)

Answer:

11. ∠ABC = 96°

12. (x – 2)² + (y + 3)² = 4

Step-by-step explanation:

11. The inscribe angle (the angle inside the circle, ∠ABC) is equal to half of the outer circle.

∠ABC = 1/2∠AC

∠ABC = 1/2(192°) = 96°

12. The general equation for a circle is: (x – h)² + (y – k)² = r², where

h and k are the center of the circle (h, k), and r is the radius.

Look at the graph, the circle is centered at (2, -3), so

h=2

k=-3

and the radius of the circle is 2, so

r=2

Plug it all back into the equation:

(x – h)² + (y – k)² = r²

(x – (2))² + (y – (-3))² = (2)²

(x – 2)² + (y + 3)² = 4

This is right angle trig. We know that...

cos(18°) x hypotenuse = 100

hypotenuse = 100/cos(18°)

hypotenuse = 105.15 meters approx.

Because they want the height of the tree we want "sin(18°) x hypotenuse".

sin(18°) x 105.15 = 32.5 meters approx.

answer: 32.5 meters approx.

The required height of the tree is 32.5 meters.

Given that,
A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees.  To estimate the height h of the tree to the nearest tenth of a meter.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
let the height of the tree be x, and the slant height from the foot of the person to the top of the tree be h,
according to the question,
base length = 100
cos 18 = 100 / h
h = 105.14
Now,
sin 18 = x / h
sin 18 = x / 105.14
x = 32.5 meters

Thus, the required height of the tree is 32.5 meters.

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Answer:

[tex]Sin(Cos^{-1} (14x))=\sqrt{1-196x^2}[/tex]

Step-by-step explandation:

First of all, from the figure we can define the cosine and sine functions as

[tex]Cos(theta)=\frac{adjacent }{hypotenuse }[/tex]

[tex]Sin(theta)=\frac{Opposite}{hypotenuse }[/tex]

And by analogy with the statement:

[tex]14x=\frac{adjacent }{hypotenuse }[/tex]

Which can be rewritten as:

[tex]\frac{14x}{1}=\frac{adjacent }{hypotenuse }[/tex]

You have then that, for the given triangle, the values of the adjacent and hypotenuse sides, are then given by:

:

Adjacent=14x

Hypotenuse=1

And according to the Pythagorean theorem:

[tex] Opposite=\sqrt{1-(14x)^2}[/tex]

Finally, by doing:

[tex]Cos^-1(14x)=theta[/tex]

We have that:

[tex]Sin(Cos^{-1} (14x))=Sen(theta)=\frac{Opposite}{hypotenuse}=\frac{\sqrt{1-(14x)^2}}{1}=\sqrt{1-(14x)^2}[/tex]

The expression [tex]\( \sin(\cos^{-1}(14x)) \)[/tex] is equivalent to the expression [tex]\[ \sqrt{1 - 196(x)^2} \][/tex].

To express [tex]\( \sin(\cos^{-1}(14x)) \)[/tex] using a right triangle, we proceed as follows:

1. Understand the expression:

[tex]\( \cos^{-1}(14x) \)[/tex] denotes the angle [tex]\( \theta \)[/tex] such that [tex]\( \cos(\theta) = 14x \)[/tex].

We are required to find [tex]\( \sin(\theta) \)[/tex].

2. Use a right triangle:

Let's consider a right triangle where:

One of the acute angles is [tex]\( \theta \)[/tex].

Assume [tex]\( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{14x}{1} \)[/tex]

To find the opposite side (let's call it [tex]\( \sqrt{1 - (14x)^2} \))[/tex], we use the Pythagorean identity:

[tex]\[ \sin(\theta) = \sqrt{1 - \cos^2(\theta)} = \sqrt{1 - (14x)^2} \][/tex]

[tex]\[ \sin(\cos^{-1}(14x)) = \sqrt{1 - (14x)^2} \][/tex]

[tex]\[ \sin(\cos^{-1}(14x)) = \sqrt{1 - 196(x)^2} \][/tex]

Answer:

A is a function/B is not.

Step-by-step explanation:

A, there are 1 x value for 1 y value.

B, is not a function because for 1 x value, there are 2 y values.

Answer:

See below.

Step-by-step explanation:

Graph A is a function because it passes the vertical line test. You could draw a vertical line anywhere on the graph which will only pass through the graph at one point. It is a many-to-one relation.

Graph B is not a function because some vertical lines will pass through the graph at  2 points. It is a one-to-many relation.,

One-to-one and many-to-one relations are functions  but one-to-many are not functions.

Answer:

Step-by-step explanation:

If CD is a diameter of circle S, then CD goes through circle S at point S.  CS is a radius, and so is DS.  That means that they are the same length.  That also means that S is the midpoint of CD.  We can use the midpoint formula and the 2 points we are given to find the other endpoint, D.

[tex](-\frac{2}{3},\frac{3}{4})  =(\frac{\frac{4}{9}+x }{2},\frac{-\frac{5}{9}+y }{2})[/tex]

To solve for x, we will use the x coordinate of the midpoint; likewise for y.  x first:

[tex]-\frac{2}{3}=\frac{\frac{4}{9}+x }{2}[/tex]

Multiply both sides by 2 to get rid of the lowermost 2 and get

[tex]-\frac{4}{3}=\frac{4}{9}+x[/tex]

Subtract 4/9 from both sides to get

[tex]x=-\frac{16}{9}[/tex]

Now y:

[tex]\frac{3}{4}=\frac{-\frac{5}{9}+y }{2}[/tex]

Again multiply both sides by that lower 2 to get

[tex]\frac{3}{2}=-\frac{5}{9}+y[/tex]

Add 5/9 to both sides to get

[tex]y=\frac{37}{18}[/tex]

And there you go!

[tex]D(-\frac{16}{9},\frac{37}{18})[/tex]

Answer:

The Inequality [tex]s > 768\ mi/hr[/tex] is true at which a moving object creates a sonic boom.

Step-by-step explanation:

Given:

Speed of Sound = 768 miles per hour

Also Given:

When an object travels faster than the speed of sound, it creates a sonic boom.

We need to find the inequality which is true only for speeds (s) at which a moving object creates a sonic boom

So We can say;

When;

[tex]s < 768\ mi/hr[/tex]  ⇒ Normal sound no sonic boom (false)

[tex]s = 768\ mi/hr[/tex]  ⇒ speed of sound but no sonic boom (false)

[tex]s > 768\ mi/hr[/tex]  ⇒ sonic boom is created (True)

Hence The Inequality [tex]s > 768\ mi/hr[/tex] is true at which a moving object creates a sonic boom.

Answer:

The number of tiles are covered by the painting are 12.

Step-by-step explanation:

Consider the provided information.

The painting is covering up some of the tiles on the wall as shown below:

Here it is given that there are 28 squares tiles on the wall.

Total tiles = Number of tiles covered by the painting - uncovered tiles

28 =  Number of tiles covered by the painting - 16

Number of tiles covered by the painting = 28 - 16

Number of tiles covered by the painting = 12

Hence, the number of tiles are covered by the painting are 12.

The person can roll the die in 1512 different ways to get 3 fours, 5 sixes, and 1 two in 9 rolls.

When rolling a standard six-sided die, there are 6 possible outcomes for each roll. To find the number of ways the person can get 3 fours, 5 sixes, and 1 two in 9 rolls, we can use the concept of combinations. The number of combinations of getting 3 fours, 5 sixes, and 1 two from 9 rolls is calculated by multiplying the number of ways to choose the positions of the fours, sixes, and two, and then multiplying it by the probability of each outcome.

To calculate this, we can use the formula for combinations:

C(n, r) = n! / ((n - r)! x r!)

Using this formula, we can find the number of ways to choose the positions of the fours, sixes, and two:

Finally, we can multiply these numbers together to find the total number of ways:

Total number of ways = 84 x 6 x 3 = 1512

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√57 = 7.549

Round to 7.5

Answer:

7.5

Step-by-step explanation:

7.549

Answer:

W = (P - 2L)/2 = (28- 2*8)/2 = 6

Where W is the width, P is the perimeter and L is the length of the garden.

Step-by-step explanation:

Since the equations are not given, i will try to come up with the similar equation than the ne that was the correct option in this exercise.

You can obtain the perimeter of a rectangle by summing the length of its four sides. Thus, the perimeter of the garden, lets call it P, is 2W + 2L, where W denotes the width and L the length. Since Nancy knows the perimeter, in order to calculate the width she can substract from it 2L (which is also known), and divide by 2 to obtain W, thus

W = (P - 2L)/2

If we reemplace P by 28 and L by 8, we obtain

W = (28-8*2)/2 = (28-16)/2 ) = 12/2 = 6.

Answer: $0

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 1 year

P = $450

R = 4.5%

Therefore

I = (450 × 4.5 × 1)/100

I = 2025/100

I = 20.25

For compound interest,

Initial amount deposited into the account is $450 This means that the principal,

P = 450

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 4.5%. So

r = 4.5/100 = 0.045

It was compounded for just a year. So

t = 1

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 450 (1+0.045/1)^1×1

A = 450(1.045) = $470.25

Compound interest = 470.25 - 450 = 20.25

The difference is 20.25 - 20.25 = 0

Answer:

$0

Step-by-step explanation:

There is no difference between the simple interest and compound interest at the end of one year.

Answer:

E. 800%

Step-by-step explanation:

Since,

u = 8d/h²      __________ eqn (1)

Now, density (d) is doubled and usage (h) is halved.

Hence the new life (u'), becomes:

u' = 8(2d)/(0.5h)²

u' = 8(8d/h²)

using eqn (1), we get:

u' = 8u

In percentage,

u' = 800% of u

In words, the percentage increase in useful life of the equipment is 800%.

Answer: E. 800%

Step-by-step explanation:

The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h^2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment.

Assuming d = 1 and h = 1, then

u = (8 × 1)/1^2 = 8

If the density of the underlying material is doubled and the daily usage of the equipment is halved, it means that

d = 2 and h = 1/2 = 0.5, therefore,

u = (8 × 2)/0.5^2 = 16/0.25 = 64

64/8 = 8

The percentage increase in the useful life of the equipment is

8 × 100 = 800%

Answer:

Step-by-step explanation:

[tex]log_{a}(13)=4\\so~ a^{4}=13[/tex]

To calculate the desired sample size with a 98% confidence level and 0.65-hour margin of error, we use the appropriate formula for sample size calculation in statistics, which leads us to a required sample size of 98 bacteria.

In this case, we are trying to determine the appropriate sample size using statistical methodology. To calculate this, we can use the formula for the sample size which is n = (Z∗σ/E)^2. Here, 'Z' is the z-value corresponding to the desired confidence level (for 98% confidence, Z score or z-value is 2.33), σ is the standard deviation (which is 4.8 hours in this case), and 'E' is the desired margin of error (0.65 hours).

Substituting these values into the formula gives: n = (2.33∗4.8/0.65)^2. After simplifying this calculation, we get n = 97.46. However, we can't have a fractional part of a sample, so we round up to the nearest whole number which is 98. So, you would need a sample size of 98 bacteria in order to achieve a 0.65-hour margin of error at a 98% confidence level.

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Answer:

Step-by-step explanation:

Let x represent the number of milliliters of 6.5% vinegar required. Then the total amount of acetic acid in the mix is ...

  6.5%·x + 5%(200 -x) = 6%·200

  1.5x = 200 . . . . . . . . . . . . . multiply by 100, subtract 1000

  x = 200/1.5 = 133 1/3 . . . . mL of 6.5% vinegar

  200-x = 66 2/3 . . . . . . . . . mL of 5% vinegar

Answer:

20hours

Step-by-step explanation:

Jack can complete the painting in 30hours. The fraction he can paint per hour is thus 1/30

Trainee can complete the painting in 45hours, the fraction he can paint per hour is 1/45

If they are working together, the fraction that can paint in an hour is :

1/45 + 1/30 = 5/90 = 1/18

Now we know they can paint 1/18 of the room in an hour, the number of hours needed to completely paint the room is thus 1/1/18 = 18 hours

Rounding up answer to the nearest tenth is 20hours

Answer:

[tex]\frac{4x}{2x+y} +\frac{2y}{2x+y}=2[/tex]

Step-by-step explanation:

Given:

The expression to simplify is given as:

[tex]\frac{4x}{2x+y} +\frac{2y}{2x+y}[/tex]

Since, the denominator is same, we add the numerators and divide it by the same denominator. This gives,

[tex]\frac{4x+2y}{2x+y}[/tex]

Now, we simplify further by factoring out the common terms from the numerator and denominator if possible.

We observe that, 2 is a common factor to both [tex]4x\ and\ 2y[/tex]. So, we factor out 2 from the numerator. This gives,

[tex]\frac{2(2x+y)}{2x+y}[/tex]

Now, the term [tex]2x+y[/tex] is common in both the numerator and denominator. Hence, [tex]\frac{2x+y}{2x+y}=1[/tex]

So, the simplified form is:

[tex]=2\times \frac{2x+y}{2x+y}\\\\=2\times 1\\\\=2[/tex]

Answer:

The required equation is given by,

2 + [tex]\frac {13x}{4}[/tex] = [tex]\frac {1}{2} + \frac {11y}{2}[/tex]

Step-by-step explanation:

Let, each jar of  Liam's paint contains x quarts of paint.

Then, Liam's solution contains,

2 + [tex]3\dfrac {1}{4} \times x[/tex]  quarts of paint  or,

2 + [tex]\frac {13x}{4}[/tex] quarts of paint

and,

let, each jar of Evan's paint  contains, y quarts of paint.

Then, Evan's solution contains,

[tex]\frac {1}{2} + 5 \dfrac {1}{2} \times y[/tex] quarts of paint or,

[tex]\frac {1}{2} + \frac {11y}{2}[/tex] quarts of paint

now, according to the question,

the required equation is given by,

2 + [tex]\frac {13x}{4}[/tex] = [tex]\frac {1}{2} + \frac {11y}{2}[/tex]

To find an equation that represents the volume of paint mixed by Liam and Evan, we assume that 1 jar equals 1 quart. By adding the quarts of paint each person uses, we get the equation 2 + 3 1/4 = 1/2 + 5 1/2, meaning they both used the same total volume of paint.

To find the equation that represents the situation, we need to equate the total volume of paint used by Liam to the total volume used by Evan. We know that Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint. Evan, on the other hand, uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. Assuming that 1 jar is equivalent to 1 quart, we can simply add the volumes for Liam and Evan:

Liam's total volume = 2 quarts (yellow) + 3 1/4 quarts (blue)

Evan's total volume = 1/2 quart (yellow) + 5 1/2 quarts (red)

Since they end up with the same volume of paint, we have the equation:

2 + 3 1/4 = 1/2 + 5 1/2

To solve for quarts, simplify both sides:

5 1/4 = 6

This equation represents the volumes of paint mixed by Liam and Evan.

Answer:

(1) P=4a+4

(2) P=2a+4[tex]\sqrt{42}[/tex]a

Step-by-step explanation:

Well, let us call longer side b, shorter side a and diagonal d. The perimeter of a rectangle is 2*(a+b). Let us write this formula as P=2*(a+b)

In (1) it is stated that b=a+2. Hence, the perimeter of the rectangle is P=2*(a+b). In terms of b, let us write (a+2). So P=2*(a+a+2)=4a+4.

In (2) it is stated that d/a=13 or d=13a. From Pythagorean theorem d^2=a^2+b^2. Hence, b^2=168a^2 or b=2[tex]\sqrt{42}[/tex]a. Finally, P=2*(a+b)=2*(a+2[tex]\sqrt{42}[/tex]a)=2a+4[tex]\sqrt{42}[/tex]a

Answer:

36 minutes long

Step-by-step explanation:

6.82 = 2.5 + 0.12m

4.32 = 0.12m

36 = m; 36 minutes long.

Answer:

B. 36.

Step-by-step explanation:

Substituting 6.82 for m:

6.82 = 2.5 + 0.12m

0.12 m = 6.82 - 2.5

0.12m = 4.32

m = 4.32 / 0.12

m = 36 minutes.

Some degenerate parabola cases form a single straight line, while other cases form one pair of parallel lines.

A degenerate hyperbola forms two lines that intersect at the vertex of the cone. We can rule out choice B.

A degenerate circle is a single point, so we can rule out choice C.

A degenerate ellipse is also a single point. Any circle is an ellipse (but not the other way around). We can rule out choice D.

Answer:

Explanation:

a). Description of what Brian did wrong.

Brian did not solve the inequality correctly. It seems he made several wrong steps:

b). Your work solving the inequality:

        - x < 3 - 2

        -x < 1

       x > - 1

Then the solution of the inequality is all the real numbers greater than - 1.

c). The correct solution graphed on a number line

d). The correct solution in set notation.

Three valid forms indicating the solution in set notation are:

Both the colon (:) and the straight bar (|) mean "such that".

Answer:

C

Step-by-step explanation:

The average speed can be obtained by adding the distances together and dividing by the total amount of time.

The total distance the man traveled from A to D is the addition of the distance from A to B plus the distance from B to C plus the distance from C to D. This is mathematically equal to 145 + 160 + 115 = 420 miles.

Dividing 420 miles by 6 = 70 miles per hour

Answer:

equation : 2x = 8

solution : x = 4

Step-by-step explanation:

let the number be x

"the sum of a number and itself "

= sum of x and x

= x + x

= 2x

"the sum of a number and itself  is 8"

2x = 8

solving the equation, divide both sides by 2

2x = 8

x = 8/2

x = 4

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

[tex]P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92[/tex]

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of [tex]P(A\cap B\cap C\cap D)[/tex].

If two events X and Y are independent, then

[tex]P(X\cap Y)=P(X)\times P(Y)[/tex]

Assume the probability of one part working does not depend on the functionality of any of the other parts.

[tex]P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)[/tex]

Substitute the given values.

[tex]P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92[/tex]

[tex]P(A\cap B\cap C\cap D)=0.7559226[/tex]

[tex]P(A\cap B\cap C\cap D)\approx 0.756[/tex]

Therefore, the probability that the machine works properly is 0.756.

Final answer:

The probability that the machine works properly is found by multiplying the probabilities of all four components working: P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513, or 75.13%.

Explanation:

To find the probability that the machine works properly, we need to calculate the probability that all four components, A, B, C, and D, are working. Since the functionality of each component is independent, we can find this combined probability by multiplying the individual probabilities together.

The probability of A working is P(A) = 0.93, B working is P(B) = 0.93, C working is P(C) = 0.95, and D working is P(D) = 0.92. So the probability of the machine working is:

P(Machine works) = P(A) * P(B) * P(C) * P(D) = 0.93 * 0.93 * 0.95 * 0.92 = 0.7513

Therefore, the probability that the machine works properly is 0.7513, which is 75.13%.

Good morning,

Answer:

Step-by-step explanation:

V = h × (base area)

  = 12 × (π×r²)

then 192π = 12π×r²

Then 192 = 12×r²

Then r² = 192÷12 = 16

Then r = √16 = 4.

:)

To find the length of the curve defined by $y=\dfrac{1}{3}(x^2+2)^{3/2}$ over the interval $1\leq x\leq 4$, we must integrate the square root of the sum of 1 and the square of the derivative of our function from 1 to 4.

To begin with, we want to find the derivative of our function. In other words, we need to compute $dy/dx$.

The derivative, with the Chain Rule gives us:
$y' = \dfrac{1}{3} \cdot \dfrac{3}{2} \cdot 2x \cdot (x^2+2)^{1/2}$
Simplifying gives:
$y' = x \cdot (x^2+2)^{1/2}$

Next, we substitute $y'$ into the formula for finding the length of a curve:

$L = \int_{a}^{b}\sqrt{1+(y')^2}dx$

We should note that $a = 1$ and $b = 4$ here. We substitute $y'=x \cdot (x^2+2)^{1/2}$ and obtain:

$L = \int_{1}^{4}\sqrt{1+(x \cdot (x^2+2)^{1/2})^2}dx$

We can now evaluate the integral, where we will square the entire derivative and add 1 as being under the square root.

So, finally, evaluating this integral gives us the length of the curve, which in this case is 24.

Therefore, the length of the curve $y=\dfrac{1}{3}(x^2+2)^{3/2}$ over the interval $1\leq x\leq 4$ is 24.

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Answer:

b. Continuous

Step-by-step explanation:

Continuous variable is a variable that can take on any value between its minimum value and its maximum value. A continuous variable is a type of quantitative variable used to describe data that is measurable while Discrete variables are countable in a finite amount of time. Now, justifying whether the gallons of gasoline pumped by a filling station during a day is continuous or discrete. The number of gallons of gasoline pumped by a filling during during a day is a continuous variable because it has a measurable volume which can take value from the minimum to maximum values of the total volume of gasoline the filling station have in the storage tank.

The number of gallons of gasoline pumped by a filling station in a day is a Continuous variable because it can take on an infinite number of values between any two given points.

The number of gallons of gasoline pumped by a filling station during a day is a Continuous variable. Continuous variables are numerical variables that have an infinite number of values between any two values. A continuous variable can be numeric or date/time. For instance, the number of gallons pumped, which can take on possibly infinite values ranging from zero upwards, is a continuous variable.

In contrast, a Discrete variable is a variable whose value is obtained by counting. A Qualitative (or categorical) variable is a variable that can be put into categories, but the numbers placed on the categories have no numerical meaning. An Attribute is a specific domain within qualitative data, like a sub-category.

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Answer:

She sold 14 new plans to earn $680 last week.

Step-by-step explanation:

$400 + 20(x) = $680

Take 400 away from total cost. So, 680 - 400 = 280.

Now, divide 280 by 20, and x = 14.

The equation would be $400 + 20(14) = $680

Answer:

AD is congruent to RS

Step-by-step explanation:

we know that

If two figures are congruent, then its corresponding sides and its corresponding angles are congruent

In this problem

If

ABCD≅PQRS

then

Corresponding angles

∠A≅∠P

∠B≅∠Q

∠C≅∠R

∠D≅∠S

Corresponding sides

AB≅PQ

BC≅QR

CD≅RS

AD≅PS