In the house, m∠ 1 = 45⁰. Find the measure of ∠ 2.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 500\\ P=\textit{initial amount}\dotfill &3300\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=years \end{cases}[/tex]

[tex]500 = 3300(1 - 0.75)^{t} \implies \cfrac{500}{3300}=0.25^t\implies \cfrac{5}{33}=0.25^t \\\\\\ \log\left( \cfrac{5}{33} \right)=\log(0.25^t)\implies \log\left( \cfrac{5}{33} \right)=t\log(0.25) \\\\\\ \cfrac{\log\left( \frac{5}{33} \right)}{\log(0.25)}=t\implies 2\approx t\qquad \qquad \textit{to be exact, about 1 year and 131 days}[/tex]

Answer:

x = 45

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 3x + 90 + 90 = 360

4x + 180 = 360 ( subtract 180 from both sides )

4x = 180 ( divide both sides by 4 )

x = 45

None. The discriminant of the quadratic equation is [tex]b^{2}[/tex]-4ac = [tex]11^{2}[/tex] - 4(1)(18) = 121 - 72 = 49, which is not a perfect square.

A perfect square is a number that can be expressed as the product of two equal integers. For example, 9 is a perfect square because it can be written as 3 x 3.

The zeros of this quadratic function can be found by setting the equation equal to 0 and solving for x.

0 = [tex]x^{2}[/tex] + 11x + 18

To solve for x, we can use the quadratic formula:

x = [-b ± √([tex]b^{2}[/tex] - 4ac)]/2a

Substituting in our values from the equation above, we get:

x = [-11 ± √([tex]11^{2}[/tex] - 4(1)(18))]/2(1)

x = [-11 ± √(-63)]/2

Since the square root of a negative number is not a real number, there are no zeros.

Therefore, the answer is None.

So, there are no real solutions.

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Answer:

Step-by-step explanation:

The expression 36 divided by s = 4 can be solved for s by dividing both sides of the equation by 36:

36/s = 4

Dividing both sides of the equation by 4:

s = 36/4 = 9

So, the value of s that makes the equation true is 9. This means that if you divide 36 by 9, the result will be 4.

Answer:

97 R=26

Step-by-step explanation:

the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.

94.68 cm

The formula for circumference of a circle is C = 2πr, where r is the radius of the circle. Therefore, to find the circumference of the circle, we need to first calculate the radius.

The area of the circle is given as A = πr2.

Therefore, we can rearrange this equation to solve for the radius, which is

r = √(A/π)

Plugging in the given area, A = 3.14, we get

r = √(3.14/π) = √(3.14/3.14) = 1

Now, we can use the circumference formula to calculate the circumference, which is

C = 2πr = 2π(1) = 2π × 3.14 = 6.28 × 3.14 = 19.4568

Therefore, the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.

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The value of x in function cos(3pi/2+2x/3)=1/2 is  x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

We are given;

6sinx=5, 6cosx=7, sin2x=0, sin(x+pi/3)+1=0, cos(2x/3-pi/4)=[tex]\sqrt{2} /2[/tex], cos2x-1=0, 2sin3x=-1, cos(3pi/2+2x/3)=1/2

Now,

1. 6sinx=5

sinx=5/6

x=0.98511078

2. sin2x=0

x=n*pi/2

3. sin(x+pi/3)+1=0

x-intercept= (pi/6+2n*pi)

y-intercept= (0, [tex]\sqrt{3}[/tex]/2 -1)

4. cos(2x/3-pi/4)=[tex]\sqrt{2}/2[/tex]

x= (pi/4+n*pi, pi+n*pi)

6. cos2x-1=0

x=n*pi

7. 2sin3x=-1

x= 7pi/18 + 2pi*n/3, 11pi/18+2pi*n/3

8. cos(3pi/2+2x/3)=1/2

x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n

For any value of integer n

Therefore, the answer of trigonometric function will be x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

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The total number of socks are n, 3 of which are red. when 2 socks are chosen randomly from the box, the probability of both socks being red is 1/2 so the value of n is 4.

The information given by question is

Total number of socks = n

Number of red socks   = 3

when 2 socks are chosen randomly from the box

Probability of both socks being red = 1/2

Ways of choosing 2 socks from n = [tex]_nC_2[/tex]

Ways of choosing 2 red socks from 3 = [tex]_3C_2[/tex]

Probability of both socks being red = [tex]\frac{_3C_2}{_nC_2}[/tex]

  [tex]\frac{6}{n(n-1)}[/tex] = [tex]\frac{1}{2}[/tex]

  12 = n² - n

n² - n -12 = 0

n² - 4n + 3n - 12 = 0

n(n - 4) + 3(n - 4) = 0

(n - 4)(n + 3) = 0

n = 4 or -3

Ignore negative value, therefore n = 4

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Answer:

4:5

Step-by-step explanation:

Answer:

80% shining

20% not shining

1 4/5 bags of dog food will last the LPS for approximately 8 and 3/10 days, or 8.3 days.

The Logan pet store uses 9/10 of a bag of dog food every day, which means they need 9/10 * 1 bag = 9/10 bags of dog food per day. To determine how many days 1 4/5 bags of dog food will last,

we need to divide the total amount of dog food by the amount used per day: 1 4/5 bags / (9/10 bags/day) = (9/10)*(18/5) / (9/10) = 18/5 days. Therefore, 1 4/5 bags of dog food will last for 18/5 days.

One 4/5 bags of dog food will last the Logan Pet Store (LPS) for approximately 8 and 3/10 days. This is because if the LPS uses 9/10 of a bag of dog food every day, then they are using 9/10 * 5/5 = 9/10 bags of dog food per day. If we divide 1 4/5 bags of dog food by 9/10 of a bag per day, we get (1 4/5) / (9/10) = (18/5) / (9/10) = 18/5 * 10/9 = 20/9 days. Therefore, 1 4/5 bags of dog food will last the LPS for approximately 8 and 3/10 days, or 8.3 days.

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Answer: =x^4+7x^3+7x^2-3x+19

Step-by-step explanation:

= 10x^3 -x^2 +6x +3 +x^4 -3x^3 +8x^2-9x+16

Step 1. Group like-terms. x^4+10x^3-3x^3-x^2+8x^2+6x-9x+3+16

Step 2. Add similar elements. x^4+7x^3-x^2+8x^2+6x-9x+3+16

Step 3. Keep adding similar elements. x^4+7x^3+7x^2+6x-9x+3+16

Step 4. Add similar elements, again. x^4+7x^3+7x^2-3x+3+16

Step 5. Final adding elements. x^4+7x^3+7x^2-3x+19

On solving the provided question, we can say that Length of rectangle = 50 m and Area of rectangle = 300 m.sq and the breadth of the garden is 6 m.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Length of rectangle = 50 m and Area of rectangle = 300 m.sq

Since, Area of rectangle = length x breadth

Therefore, Breadth = 300/6

Thus, the breadth of the garden is 6 m.

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A bone fragment that has 10% of the parent Pb-210 remaining with half-life of Pb-210 is 22 years, the bone fragment is approximately 51 years old.

To determine the age of the bone fragment, you need to calculate the number of half-lives that have elapsed since the bone was formed. The age of the bone can be calculated using the formula:

age = number of half-lives * half-life

To calculate the number of half-lives, you need to determine how much of the original Pb-210 has decayed. If a bone fragment has 10% of the parent Pb-210 remaining, then 90% has decayed.

You can calculate the number of half-lives by taking the natural logarithm of the ratio of the remaining amount of Pb-210 to the original amount:

number of half-lives = ln(0.10) / ln(0.5)

Using the half-life of Pb-210, which is 22 years, you can now calculate the age of the bone fragment:

age = number of half-lives * 22 years

Substituting the values and calculating the number of half-lives and the age of the bone fragment, you get:

number of half-lives = ln(0.10) / ln(0.5) = 2.302

age = number of half-lives * 22 years = 51.064 years

So, the bone fragment is approximately 51 years old.

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We can tell that Mike thought the difference would be 72, but it is actually 72.74 by rounding off.

A number is simplified when it is rounded off, preserving its value while moving it closer to the next number.

It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.

When numbers are rounded off, the important numbers are kept.

To determine how to round a number, look at the next digit in the appropriate position; if it is less than 5, round down, and if it is greater than 5, round up.

So, Mike determined 79 to be 79.44 and 7 to be 6.7, so he determined the difference as follows:

79 - 7 = 72

Actual numbers that vary are:

79.44 - 6.7 = 72.74

Therefore, we can tell that Mike thought the difference would be 72, but it is actually 72.74 by rounding off.

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Correct question:

Mike estimated the difference of 79.44 and 6.7 by rounding each number to the nearest whole. What was Mike's estimate, and what is the actual difference of the numbers? Enter your answers in the boxes. Mike estimated the difference to be. The actual difference is __.

The following data represent the dividend yields of a random sample of 28 publicly traded stocks. The five number summary is: 0, 0.185, 0.72, 2.30, 3.58

The term "trade shocks" refers to changes in the amount of commodities and services exchanged globally as well as in international pricing that result in net profits or losses from trade. It has to do with changes in international marketplaces that frequently occur independently of national influences. Conventional wisdom is that terms-of-trade shocks are a significant contributor to business cycles in developing and underdeveloped nations. This viewpoint is founded in great part on the examination of calibrated business-cycle models.

(a) From the given table it is shown that,

0,3.58,0.37/2, (0.69+0.85)/2, (2.11 + 2.49)/2

The five number summary is: 0, 0.185, 0.72, 2.30, 3.58

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Answer: 56 yards

Step-by-step explanation:

4 + 7 + 5 = 16

128 / 16 = 8 yards

7 is the highest ratio in the set so

7 x 8 yards = 56 yards

Answer: -8x - 19

Step-by-step explanation:

Distribute: 5-8(x+3) = 5-8x-24

5-8x-24= -19 - 8x

= -8x - 19

Answer:

-8x - 19

Step-by-step explanation:

1. Rearrange terms: 5 - 8 (3 + x)
2. Distribute terms: 5 - 8 ( x + 3) = 5 - 8x - 24

3. Subtract the numbers: 5 - 8x - 24 = -19 - 8x

4. Rearrange terms again: -19 - 8x to -8x - 19

5. Here's your answer! Hope this helped :)

Answer:

3(x)+4-8

find x.

Step-by-step explanation:

Answer:

your mom a cow your dad left for milk

Answer:

5

6

2,5

this is how I got the answer

The probability of drawing one blue marble on the first draw is 4/10. Since we do not replace the marble, there are only 9 marbles left in the bag, so the probability of drawing a green marble on the second draw is 2/9.

The probability of drawing one blue marble and one green marble is the product of the probabilities of each event:

(4/10) x (2/9) = 8/90 = 4/45

Therefore, the probability of drawing one blue marble and one green marble is 4/45.

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The probability distribution function of Y is the set of all probabilities P(Y), for all possible values of Y[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]. Option E is correct.

Let Y be the discrete random variable that counts the number of face cards in a seven-card hand drawn from a standard 52-card deck. The possible values for Y are 0, 1, 2, 3, 4, 5, 6, and 7.

The number of ways to get Y face cards in a seven-card hand is given by the binomial coefficient C(7, Y), where C(7, Y) represents the number of combinations of 7 things taken Y at a time.

The probability of getting Y face cards in a seven-card hand is given by:

[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]

where [tex](12/52)^Y[/tex] represents the probability of drawing Y face cards and [tex](40/52)^{(7-Y)}[/tex] represents the probability of drawing the remaining 7-Y cards from the 40 non-face cards.

Thus, the probability distribution function of Y is the set of all probabilities P(Y), for all possible values of Y:

[tex]P(Y) = (C(7, Y) * (12/52)^Y * (40/52)^{(7-Y)} /C(7, 52)[/tex]

Y = 0, 1, 2, ..., 7

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the equation for the line perpendicular will be y = -5x +11.

What is the equation straight line?

The formula for a straight line is generally expressed as Y = mx + c, where m stands for the slope and c for the y-intercept. In geometry, it is the straight-line version of the equation that is most usually utilised. A straight-line's equation can be expressed in a variety of forms, including point-slope form, slope-intercept form, general form, standard form, etc. An infinitely long straight line has two dimensions and is a geometrical object with two ends. The equations for a straight line that are used the most frequently are y = mx + c and axe + by = c. Point-slope, slope-intercept, standard, general, and other forms are more variations.

The given line is y = x/5 +3

the slope is m = 1/5

So the slope of the perpendicular line will be -5

So the equation of line will be y-3 = m1(x-1)+3

y-3 = -5x+5+3

y = -5x +11

Hence the equation for the line will be y = -5x +11.

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Answer:

Non-linear

Step-by-step explanation:

y = 10/x is non-linear!

Because a linear equation is an equation of a straight line, which means the degree of a linear equation must be 0. In this case, the degree of variable y is 1; the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not linear.

The solution for the given equation is C) [tex]x=\frac{-1+-\sqrt{33} }{4}[/tex]

What does a quadratic function mean?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other words, a "polynomial function of degree 2" is a quadratic function.

The formula for the solution of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is

[tex]x=\frac{-b+-\sqrt[2]{b^{2}-4ac } }{2a}[/tex].

So, the solution for the equation [tex]2x^{2} +x-4=0[/tex] is

[tex]x=\frac{-1+-\sqrt[2]{1^{2}-4*2*(-4) } }{2*2}\\x=\frac{-1+-\sqrt[2]{1+32 } }{4}\\x=\frac{-1+-\sqrt{33} }{4}[/tex]

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Answer:

Step-by-step explanation:

when does this come into play? what year??

Answer:

Step-by-step explanation:

To graph the equation 3y = -6x - 12, we can start by finding the x and y intercepts.

The x-intercept is the point where y = 0, so we can substitute 0 for y in the equation:

3y = -6x - 12

3 * 0 = -6x - 12

0 = -6x - 12

12 = -6x

x = -2

So the x-intercept is (-2, 0).

The y-intercept is the point where x = 0, so we can substitute 0 for x in the equation:

3y = -6x - 12

3y = -6 * 0 - 12

3y = -12

y = -4

So the y-intercept is (0, -4).

Now that we have the x and y intercepts, we can plot the points on the graph and draw a line that passes through both points. This line will be the graph of the equation.

In this case, the graph of the equation 3y = -6x - 12 is a downward sloping line that passes through the points (-2, 0) and (0, -4).