Maria is creating a round stained glass window like the one below. She needs to cut the dark pink glass to the correct size to fit into the frame. At what angle (x) should she cut the glass so that it fits if she knows the arc measure of a is 35º and the arc measure of b is 45º. What does x equal?

Answer:

There are two complex roots:

============

The standard form is:

Compared we can find values of the coefficients and the constant:

Substitute these values into quadratic formula:

     [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

and work out roots:

    [tex]x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4*1*10} }{2*1}=x=\dfrac{6\pm\sqrt{36-40} }{2}=\dfrac{6\pm2\sqrt{-1} }{2}=3 \pm i[/tex]

The solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)

The system of equations is given as

y=e^x+e^-x

y=5-x^2

See attachment for the graph of both equations

From the attached graph, the curve intersect at

(-1.189, 3.587) and (1.189, 3.587)

Hence, the solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)

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Hello and Good Morning/Afternoon:

Let's take this problem step by step:

Let's consider what the problem wants:

⇒ the value of (f-g)(y)

Let's consider what the problem gives us:

⇒ the value of f(y) and g(y)

Let's consider the relationship between f(y), g(y) and (f-g)(y)

 ⇒ [tex](f-g)(y)=f(y)-g(y)[/tex]

Let's solve for (f - g)(y)

 [tex]\hookrightarrow(f-g)(y) = f(y)-g(y) = 5y^2-2y+1-(-3y^2-y-2)\\=5y^2-2y+1+3y^2+y+2=8y^2-y+3[/tex]

Answer: 8y²- y + 3

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Applying the commutative law to our question, we have; 14 + ab = ab + 14

The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;

ab + cd = cd + ab

similarly, fg * jk = jk * fg

Applying the above commutative law to our question, we have;

14 + ab = ab + 14

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Answer:

$1.00 = 10 cent each

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

-14 1/9 is about -14.

-2 9/10 is about -3.

Multiplying these, we get (-14)(-3)=42.

Answer: 2/3

Step-by-step explanation:

The common denominator would be 3(x-1). Thus, you need to multiply the expression on the right by 3/3 to achieve a common denominator. Then you would have 3x/3(x-1).

The equation then is 2/3(x-1) = 3x/3(x-1)

You can cancel out the denominators now, and you have 2 = 3x, so x = 2/3

Answer:

A

Step-by-step explanation:

When sampling with replacement is used, an element that has already been chosen is put back into the sample frame and given the chance to be chosen again.

In the case of sampling without replacement, an element is eliminated from the sample frame after it has been chosen.

In this question, we are supposed to state the differences between sampling with replacement and sampling without replacement.

Generally speaking, sampling without replacement is more effective than producing representative samples using replacement sampling. It prevents the inclusion of the same population element in the sample several times.

By "drawing from a hat" or by using a computer program that simulates the same process, you select the sample at random using the lottery method.

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Answer:

V = 15 in.³

Step-by-step explanation:

The original cylinder has radius r and height h.

V = πr²h

Its volume is 30 in.³, so

πr²h = 30 in.³

The new cylinder has radius (1/2)r and height 2h.

Its volume is

V = π(r/2)²(2h)

V = πr² × 2h/4

V = πr²h/2

πr²h is the volume of the original cylinder, and it is 30 in.³.

V = 30 in.³/2

V = 15 in.³

Answer:

7 - 10

Step-by-step explanation:

Because it is -3 and 7 - 10 = -3

The probability that Ron will get by a pitch exactly once is 0.351912.

Given that out of 596 plate appearance Ron was hit 19 times from pitches.

We have to find the probability that ron was hit by pitches in 22 plate appearances.

The value of probability lies between 0 and 1. The formula of calculating proabability is number of items/ total items.

We can find the required probability through binomial distribution which is

n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex] where n is the number of trials and r is the successes.

Probability that Ron will be hit =19/596

=0.031

Probability that Ron will get hit by a pitch exactly once =P(X=1)

=[tex]22C_{1}(0.031)^{1} (1-0.031)^{21}[/tex]

=22!/1!21!*0.031*[tex](0.969)^{21}[/tex]

=22*0.031*0.516

=22*0.015996

=0.351912

Hence the probability that Ron will get hit by a pitch exactly once is 0.35.

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Answer:

Let j = number of shirts Jeff bought and s = the number of shirts Stephen bought.

a.) s + j = 15

b.) 2j - 3 = s

c.) Plug 2j -3 into the equation from question a.

2j -3 + j = 15

3j -3 = 15

3j = 18

j = 6

2j - 3 = s when j = 6

2(6) - 3 = s

s = 9

Jeff bought 6 shirts; Stephen bought 9 shirts.

d.) Jeff cost = 8.99(6) = $53.94

Stephen cost = 8.99(9) = $80.91

The wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

The distance between the two crests or troughs of the light wave is known as the wavelength of light.

The color of light is determined by its wavelength, and the pitch of sound is determined by its wavelength. The visible spectrum of light has wavelengths between around 700 nm (red) to 400 nm (violet). The range of audible sound wavelengths is roughly 17 mm to 17 m.

To calculate the wavelength of light, we use the equation:

[tex]$\lambda=\frac{c}{\nu}$[/tex]

where,

λ = wavelength of the light  

c = speed of light = [tex]$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex]

ν= frequency of light = [tex]$3 \times 10^{18} s^{-1}$[/tex]

Putting the above value in equation,

[tex]$\lambda=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{3 \times 10^{19} \mathrm{~s}-1}=1 \times 10^{-10} \mathrm{~m}$[/tex]

Hence, the wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

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Answer:

corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior

In the figure 10, the pair of angles are alternate interior angles.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

From the given figure,

1) corresponding angles

2) Adjacent angles (Supplementary)

3) Alternate interior angles

4) Allied angles (Same side interior)

5) Vertically opposite angles

6) Alternate exterior angles

7) corresponding angles

8) Alternate exterior angles

9) Vertically opposite angles

10) Alternate interior angles

Therefore, in the figure 10, the pair of angles are alternate interior angles.

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Answer:

ther will be 240 words in 4 1/4

Answer:

187 words.

Step-by-step explanation:

His rate of typing = 110 / 2 2/4

= 110 / 2.5

= 44 words / minute.

So in 4 1/4 minutes he will type

44 * 4 1/4

= 176 + 11

= 187 words.

Answer:

480

Step-by-step explanation:

First, lets solve for the area of the 3 rectangles in the prism

One can be found by doing 17*9. The other, 8*9, the last 15*9

Next, lets solve for the 2 triangles. This is found with...

1/2(8)(15). This turns out to be 60, and we multiply that by 2 since there are 2 of those triangles.

Add everything up:

72+153+135+120 = 480

Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage. In the given question, the percentage error is option b.  0.0772

Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage.

This can be expressed as;

percentage error = [tex]\frac{actual value - expected value}{actual value}[/tex] x 100%

Where the actual value is the accurate value, and the expected value is derived from the actual value.

Thus in the given question, it can be deduced that,

actual value = 625.483

expected value = 625.000

The difference between the two values = (625.483 - 625.000)

                                                  = 0.483

So that,

percentage error = [tex]\frac{0.483}{625.483}[/tex] x 100%

                   = 0.07722

percentage error = 0.0772

Therefore, the required percentage error is 0.0772 i.e option b.

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The child tickets were sold that day is 82.

Given the cost of child admission $6.30 and the cost of adult admission $9.80 and on Wednesday 144 tickets were sold for a total sales of $1124.20.

Let the child tickets are x and adult tickets are y.

On Monday, 144 tickets were sold for a total sales.

x+y=144              ........(1)

Total sales = $1124.20

Need to find the child tickets sold on Wednesday.

Total sales = 6.30x+9.80y

Total sales = $1124.20

So,6.30x+9.80y=1124.20                        .......(2)

Find the value of y from equation (1), we get

x+y-x=144-x

y=144-x

Now, we will substitute the value of y in equation (2) to find the value of x, we get

6.30x+9.80(144-x)=1124.20

Apply the distributive property that is a(b+c)=ab+ac, we get

6.30x+9.80×144-9.80x=1124.20

6.30x+1411.2-9.80x=1124.20

Combine the variable terms on left side, we get

1411.2-3.5x=1124.20

subtract 1411.2 from both sides, we get

1411.2-3.5x-1411.2=1124.20-1411.2

-3.5x=-287

Divide both sides with -3.5x, we get

-3.5x/(-3.5)=-287/(-3.5)

x=82

Therefore, 82 child tickets were sold on Wednesday when cost of child admission $6.30 and the cost of adult admission $9.80.

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The length of side VW is 7.5 cm

The given parameters are:

DE is 6 cm, EF is 7.5 cm, and DF is 5 cm

Since the two triangles are congruent, then it means that:

So, we have:

VW= EF

The side EF is

EF = 7.5 cm

So, we have:

VW = 7.5 cm

Hence, the length of side VW is 7.5 cm

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Answer:

660000

Step-by-step explanation:

The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true.

It should be noted that an inequality simply means a statement of an order relationship between two numbers and algebraic expressions.

From the information given, the equation illustrated is:

y < -0.2x² + 9x - 7.

63 < 0.2(10)² + (9 × 10) - 7

63 < 20 + 90 - 7.

63 < 103

In this case, the ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. This illustrates that the statement is true since sixty there is less than one hundred and three.

Therefore, this is true.

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Complete question:

The ordered pair (10,63) is a solution to the inequality y < -0.2x² + 9x - 7. Please select the best answer from the choices provided

True

False

The value of X that number of unit fails are 1/12.

According to the statement

we have a given that the there is a shipment of 60 highly sensitive accelerometer. And there is a testing of randomly 5 accelerometers.

And we have to find that the how much units that fails in the specifications.

So,

We find the value of X by use of Probability.

The probability that unit fails = number of units that chosen randomly / total units.

So, substitute the values in it then

The probability that unit fails = 5 / 60

The probability that unit fails = 1 / 12.

The probability that unit fails from 60 accelemoters  is 1 / 12.

So, The value of X that number of unit fails are 1/12.

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x² - 4x + 4 is the graphed parabola, so the correct option is D.

On the graph, we can see a parabola that opens upwards (then the leading coefficient is positive), and has a vertex at the point (2, 0).

Also, we can see that the y-intercept is y = 4, that means that the constant term of the parabola is 4.

The only option with a constant term equal to 4 is the last option:

y = (x - 2)*(x - 2) = x² - 4x + 4

So that is the graphed parabola.

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The contribution margin per unit is $ 1.50

The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.

One of the main components of break-even analysis is the idea of contribution margin.

Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.

According to the question,

Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)

                                        = $ 20

Selling Price per unit = $ 21.50

Thus, contribution margin per unit = $ (21.50 - 20)

                                                         = $ 1.50

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Answer:

60

Step-by-step explanation:

The yellow and green angles form a right angle, so the measures of those combined will be 90 degrees.

90 - 30 = 60

Answer: b. 125

Step-by-step explanation:

Find the square roots of each, and if the square root is a decimal, it is not a perfect square.

Square root of 81: 9

Square root of 49: 7

Square root of 100: 10

That leaves 125.

Answer:

Python will return:

True

Step-by-step explanation:

The math function ** is an exponent indicator.

The equation you made was:
[tex]2^2 =4[/tex]

When you run this in python, it will return as true.

It is run as a Boolean expression because you have already provided the answer to the expression with the "==" statement.

If you had provided an incorrect answer (setting it equal to any number other than 4), it would return False.

Answer:

37°

Step-by-step explanation:

Subtract angle IJL from angle IJK.

Surface area of the rectangular solid = 416 in.².

Volume = 480 in.³.

Surface area = 2(wl+hl+hw)

Volume = (length)(width)(height).

Given the following:

Length (l) = 12 in.

Width (w) = 10 in.

Height (h) = 4 in.

Surface area = 2(wl+hl+hw) = =2·(10·12+4·12+4·10) = 416 in.².

Volume = (12)(10)(4) = 480 in.³.

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