given;, angle 2 = angle 4. angle 2 = 110
prove angle 3 = 70​

Answer:

1260.04

Step-by-step explanation:

The formula for compound interest is:

A = P(1+\(\frac{r}{n}\)\()^{nt}\) where A is the final amount, P is the initial principal balance, r is the interest rate, n is the number of times interest applied per time period and t is the number of time periods elapsed. Since the deposit was compounded annually, just like the interest, we can omit the n in the equation.

Applying the formula to question:

800(1+\(\frac{2.88}{100}\)\()^{16}\) = 1260.04 (rounded off to nearest cent since it's money)

The ratio of pounds of dark clothes to pounds of white clothes is 3:1, which is option A

To find the ratio of pounds of dark clothes to pounds of white clothes, we need to divide the pounds of dark clothes by the pounds of white clothes.

Given that Corey has 12 lbs of dark clothes and 4 lbs of whites.

So, the ratio of pounds of dark clothes to pounds of white clothes = 12/4.

Simplifying this ratio, we get:

Ratio of pounds of dark clothes to pounds of white clothes = 3/1

Therefore, the ratio of pounds of dark clothes to pounds of white clothes is 3:1, which is option A.  

This means that for every 3 pounds of dark clothes, Corey has 1 pound of white clothes. Ratios are a way to compare two quantities, and they can be expressed in different ways, such as in fraction or in the form of a colon. In this case, the ratio is 3:1, which means that for every 3 pounds of dark clothes, there is 1 pound of white clothes.

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Answer:

The Probability of both happening is 0.304.

Step-by-step explanation:

P(A) × P(B)

=  0.76 × 0.4

=  0.304

The graph with the same end behavior is the one in option C.

The given function has a numerator with a negative leading coefficient and an odd degree, while the denominator is a quadratic polynomial.

It will mean that as x tends to negative infinity, the function tends to infinity, and as x tends to positive infinity, the function tends to negative infinty, that is the end behavior of the given function.

The graph with that end behavior is the same one than in option C.

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Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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He is incorrect because he should have 6 factors of 9.

Answer:

I think he is incorrect because 3x3 x 3x2 only equals 0.16. So I think it is answer 3.

Step-by-step explanation:

Answer:

Me please

Step-by-step explanation:

I like ice cream :D

Answer:

I do!!! Please may I get it? If someone else asked and you chose them that's fine!

Step-by-step explanation:

(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest.

- •Trix•

( Yes I know my - •Trix• thingy is not my user but its what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)

Answer:

1/2

Step-by-step explanation:

11/3 divided by 2/3

=5.5

11/3 divided by 2/3 , the quotient is 5 and remainder is 1.

The divisor is the integer that divides a given number. The resultant number is sometimes referred to as the quotient. The residual is the number that the divisor leaves after partially dividing the original integer.

Let,  first number is x and second number is y

On dividing given two number

Division=x/y

\(x/y=\frac{11/3}{2/3}\)

\(x/y=11/2\)

It is given that the quotient for dividing two numbers is 5.

Using,

Dividend = Divisor x Quotient + Remainder

Here,

Dividend =11

Divisor =2

Quotient =5

On, substituting these values to get Remainder

11=2 x 5+ Remainder

Remainder=1

Thus, remainder is 1.

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The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Complete question is;

Katie just opened a checking account at the bank. Within the first month, she deposited three checks for $21.68, $42.09, and $65.44. She withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.

Write Katie’s withdrawals as negative rational numbers and her deposits as positive rational numbers.

Answer:

Deposits are; +21.68, +42.09, and +65.44.

Withdrawals are; -4.64, -23.11, and -9.78

Step-by-step explanation:

We are told that the deposits are;

$21.68, $42.09, and $65.44.

Now, she withdrew $4.64 for new pencils, $23.11 for earbuds, and $9.78 for movies from her account in the same month.

We are told to write Katie’s withdrawals as negative rational numbers and her deposits as positive rational numbers.

A rational number is a number that can be expressed as the ratio of two integers. In this question, by inspection, all the given values for deposits and withdrawals can be expressed as the ratio of 2 integers.

Thus;

Deposits are; +21.68, +42.09, and +65.44.

Withdrawals are; -4.64, -23.11, and -9.78

A random sample and a non-random sample for this situation are given below:

This refers to the statistical population where there is an equal chance of being selected by members of a population.

Hence, we can see that a random sample and a non-random sample for this situation are given above and this shows that each of them have equal chances of being selected (random sampling)

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Answer: y = -0.5x +1

Step-by-step explanation:

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Answer:

The required equations are

\((-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0\) and

\((-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0\).

Step-by-step explanation:

The given parametric equation of the line, \(L\), is \(x=5+t, y=6, z=-2-3t,\) so, an arbitrary point on the line is \(R(x,y,z)=R(5+t, 6, -2-3t)\)

The vector equation of the line passing through the points \(P(-5,7,-8)\) and \(R(5+t, 6, -2-3t)\) is

\(\vec P + \lambda \vec{(PR)}=0\)

\(\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((5+t-(-5))\hat i + (6-7)\hat j +(-2-3t-8)\hat k\right)=0\)

\(\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+t)\hat i -\hat j +(6-3t)\hat k\right)=0\;\cdots (i)\)

The given equation can also be written as

\(\frac {x-5}{1}=\frac {v-6}{0}=\frac{z+2}{-3}=t \; \cdots (ii)\)

The standard  equation of the line passes through the point \(P_0(x_0,y_0,z_0)\) and having direction\(\vec v= a_1 \hat i +a_2 \hat j +a_3 \hat k\) is

\(\frac {x-x_0}{a_1}=\frac {y-y_0}{a_2}=\frac{z-z_0}{a_3}=t \;\cdots (iii)\)

Here, The value of the parameter,\(t\), of any point \(R\) at a distance \(d\) from the point, \(P_0\), can be determined by

\(|t \vec v|=d\;\cdots (iv)\)

Comparing equations \((ii)\) and \((iii)\)

The line is passing through the point \(P_0 (5,6,-2)\) having direction \(\vec v=\hat i -3 \hat k\).

Note that the point \(Q(5,6,-2)\) is the same as \(P_0\) obtained above.

Now, the value of the parameter, \(t\), for point \(R\) at distance \(d=3\) from the point \(Q(5,6,-2)\) can be determined by equation \((iv)\), we have

\(|t(\hat i -3 \hat k)|=3\)

\(\Rightarrow t^2|(\hat i -3 \hat k)|^2=9\)

\(\Rightarrow 10t^2=9\)

\(\Rightarrow t^2=\frac {9}{10}\)

\(\Rightarrow t=\pm \frac {3}{\sqrt {10}}\)

Put the value of \(t\) in equation \((i)\), the required equations are as follows:

For \(t= \frac {3}{\sqrt {10}}\)

\((-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +\left(6-3\times \frac {3}{\sqrt {10}})\hat k\right)=0\)

\(\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0\)

and for \(t= -\frac {3}{\sqrt {10}}\),

\((-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\left (-\frac {3}{\sqrt {10}}\right))\hat i -\hat j +(6-3\times \left(-\frac {3}{\sqrt {10}}\right)\hat k\right)=0\)

\(\Rightarrow  (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0\)

The entered responses are correct

Write out the points from the given information to see the nature of the ellipse as follows:

The sum of the given geometric sequence to 2 dp is 936.00

To get the sum of a geometric sequence, we will use the formula for calculating the sum to infinity of the sequence as shown:

\(S_\infty=\frac{1}{1-r}\)

a is the first term

r is the common ratio

Given the sequence  S = 0.936 + 0.935 + ... + 0.92 + 0.9 + 1

a = 0.936

r = 0.935/0.936 = 0.998

Substitute into the formula

\(S_\infty=\frac{0.936}{1-0.999}\\S_\infty=\frac{0.936}{0.001}\\S_\infty=936\)

Hence the sum of the given geometric sequence to 2 dp is 936.00

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The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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Answer:

\(a = 6m/s^2\)

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

\(a\ \alpha\ \frac{1}{m}\)

Convert variation to equality

\(a = \frac{F}{m}\); Where F is the constant of variation (Force)

Make F the subject of formula;

\(F = ma\)

When mass = 4kg; Acceleration = 15m/s²

\(F = 4 * 15\)

\(F = 60N\)

When mass = 10kg; Substitute 60 for Force

\(F = ma\)

\(60 = 10 * a\)

\(60 = 10a\)

Divide both sides by 10

\(\frac{60}{10} = \frac{10a}{10}\)

\(a = 6m/s^2\)

Hence, the acceleration is \(a = 6m/s^2\)

The book value of the automobile at the end of 3 years is $13,000.

The straight-line method is method of depreciation that allocates the same depreciation expense each year.

Straight line depreciation expense = (Cost of asset - Salvage value) / useful life

($32,500 - 0) / 5 = $6,500

Total depreciation in 3 years = $6,500 x 3 = $19,500

Book value = cost of the automobile - total depreciation

$32,500 - $19,500 = $13,000

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Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: air pressures of properly inflated sports balls.

Average recommended psi Tolerance

(pounds per square inch)

Soccer ball 12.05 ±3.55

Basketball 8.00 ±0.5  

Volleyball  4.44 ±0.18

Each recommendation is expressed like the "average air pressure" ± "standard deviation of the recommended air pressure" so if you express it in inequality it will be:

X[bar]-S ≤ X ≤ X[bar]+S

So for each ball type, you can write it as:

Soccer ball

12.05-3.55 ≤ X ≤ 12.05+3.55

8.5 ≤ X ≤ 15.6

Basketball

8.00-0.5  ≤ X ≤ 8.00+0.5

7.5  ≤ X ≤ 8.5

Volleyball

4.44-0.18 ≤ X ≤ 4.44+0.18

4.26 ≤ X ≤ 4.62

I hope this helps!

Answer:

Step-by-step explanation:

This is what I got!

Part I:

Soccer ball: | x – 12.05 | ≤ 3.55  

Basketball: | x – 8 | ≤ 0.5  

Volleyball: | x – 4.44 | ≤ 0.18

Part II:

Basketball: | x – 8 | > 0.5

Part III:

Basketball:

| x – 8 | ≤ 0.5

x – 8 ≤ 0.5

x ≤ 8.5

x – 8 ≥ 0.5

x ≥ 7.5

7.5 ≤  x ≤ 8.5

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

Answer:

A property of a function is that it gives one output for an input

if a function gives one output for an input, it is a function and otherwise it is not a function otherwise

here, we can see that we have 2 outputs for the input '6'. therefore, it is NOT a function

We can write a proportion.

44:3 = 12:m

~Simplify

44m = 36

~Divide 44 to both sides

m = 36/44 or 9/11 minutes

Best of Luck!

Answer: 0.818 minutes

Step-by-step explanation:

You would normally divide 44/3 to see how many plates are washed per minute, but if you reverse it, 3/44 then you will know how much time is spent washing each plate which is 0.068181. Multiply that by 12 and there’s your answer

An inequality that represents the state's hourly wage requirement include the following: C. m ≥ $9.25 per hour.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Assuming the variable m represent the state's hourly wage requirement. Additionally, each interval on the number line represent 0.25 per hour.

Since the shaded circle (dot) is located at point 9.25 and the arrows points or increases to the right, an inequality that represents the state's hourly wage requirement is m ≥ $9.25 per hour.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Given:

From the given y = x³, it has changed to f(x) = x³ + 1

Adding a value to the y-intercept of a function will result for its graph to shift upward.

In this case, since we added 1 (+1) to the formula, this will add 1 to all the y values of the graph. Therefore for the first part of the question, the answer would be "It would add one to all the y-values"

Next, since we know that adding a y-intercept will move the graph upwards, the answer for the second part would be "It will shift all points up one."

To make it even more clearer, here is an example.

To conclude this, the answer to the first part would be ""It would add one to all the y-values"

S