which angle corresponds with 3

Answer: one half

Step-by-step explanation:

Answer: None of these answers are correct.

Step-by-step explanation:

The triangles are congruent, meaning that by CPCTC, \(\angle BAC \cong \angle DE F\).

This means that as angles in a triangle add to 180 degrees,

\(60+45+x=180\\75+x=180\\x=105\)

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm

The sector area

The area of the sector is calculated as

Area = x/360 * πr²

Where

r² = 8² + 6²

So, we have

r² = 100

This means that

Area = 82/360 * π * 100

Evaluate

Area = 71.55

The triangle area

This is calculated as

Area = 0.5bh

So, we have

Area = 0.5 * 8 * 6

Evaluate

Area = 24

So, the area of the figure is

Figure = 24 + 71.55

Figure = 95.55

Hence, the area is 95.55

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Answer: x^2 -8x+9

Step-by-step explanation:

substitute  x-4 into f(x)

(x-4)^2 -5+2

expand brackets

x^-8x+16 -5+2

x^2-8x+13

Then substitute this answer into g(x)

x^2 -8x+13-4

=x^2-8x+9

Answer:

no

Step-by-step explanation:

Answer:

The answer is  C)140

The cost of wrapping both boxes would be = $1.13

Surface Area of a rectangular prism = 2 (lh +wh + lw )

where length = 0.6

width = 1

height =1.2

The surface area of Box A

= 2( 0.6×1.2+1×1.2+0.6×1)

= 2( 2.52)

= 5.04ft²

where length = 0.5

width = 1.6

height =1.6

Area = 2(0.5×1.6+1.6×1.6+0.5×1.6)

= 2(4.16)

= 8.32ft²

The total area of the boxes = 5.04+8.32 = 13.36

But 6.79 = 80 ft²

X = 13.36ft²

make X the subject of formula;

X = 13.36×6.79/80

X = 90.7144/80

X= $1.13

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Answer:

Step-by-step explanation:

A

a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimals). b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals). c. What is the 95% confidence interval for the population variance (to 2 decimals)

Answer:

A) x¯ = $1.33 million

B) σ = $0.9508 million

C) CI = ($0.74 million, $1.92 million)

Step-by-step explanation:

We are given the salary data as;

$2.2 million, $1.5 million, $0.5 million, $0.2 million, $2.4 million, $1.5 million, $2.7 million, $0.1 million, $2 million, $0.2 million

A) Population mean annual salary = $(2.2 + 1.5 + 0.5 + 0.2 + 2.4 + 1.5 + 2.7 + 0.1 + 2 + 0.2)/10 in millions

x¯ = $1.33 million

B) Formula for the standard deviation is;

√(Σ(x - x¯)²/n)

Thus, let's first find (x - x¯)² all in millions

>> (2.7 - 1.33)² = 1.37² = 1.8769

>> (2.4 - 1.33)² = 1.07² = 1.1449

>> (2.2 - 1.33)² = 0.87² = 0.7569

>> (2 - 1.33)² = 0.67² = 0.4489

>> (1.5 - 1.33)² = 0.17² = 0.0289

>> (1.5 - 1.33)² = 0.17² = 0.0289

>> (0.5 - 1.33)² = (-0.83)² = 0.6889

>> (0.2 - 1.33)² = (-1.13)² = 1.2769

>> (0.2 - 1.33)² = (-1.13)² = 1.2769

>> (0.1 - 1.33)² = (-1.23)² = 1.5129

Σ(x - x¯)² = 1.8769 + 1.1449 + 0.7569 + 0.4489 + 0.0289 + 0.0289 + 0.6889 + 1.2769 + 1.2769 + 1.5129

Σ(x - x¯)² = $9.041 million

Σ(x - x¯)²/n = $9.041/10 = $0.9041 million

standard deviation = √0.9041

σ = $0.9508 million

C) Critical value at a Confidence level of 95% is z = 1.96

Thus,formula for critical interval is;

CI = x¯ ± z(σ/√n)

CI = 1.33 ± 1.96(0.9508/√10)

CI = ($0.74 million, $1.92 million)

The exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

An exponential function is represented as:

\(y = b^x\)

The base is 3.

So, we have:

\(y = 3^x\)

It is stretched vertically by 2/3.

So, we have:

\(y = \frac23(3)^x\)

When reflected over the y-axis, we have:

\(y = \frac23(3)^{-x}\)

An asymptote of y = 2, makes the function becomes

\(y = \frac23(3)^{-x} + 2\)

Lastly, it passes through the point (0, 3.5).

So, we have:

\(y = \frac23(3)^{-x+h} + 2\)

This gives

\(3.5 = \frac23(3)^{-0+h} + 2\)

\(3.5 = \frac23(3)^{h} + 2\)

Subtract 2 from both sides

\(1.5 = \frac23(3)^{h}\)

Multiply by 3/2

\(2.25 = (3)^{h}\)

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in \(y = \frac23(3)^{-x+h} + 2\)

\(y = \frac23(3)^{-x+0.74} + 2\)

Hence, the exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

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Answer:

Give me heart and 5 stars

Step-by-step explanation:

Answer: 1, 2, and 4.

Step-by-step explanation: Each must be wider than the angle than a "L" has.

The rational numbers are given as follows:

To order the rational numbers, we must convert the fractions to decimal, dividing the numerator of the fraction by the denominator.

The conversion of each number is given as follows:

Hence they are ordered as follows:

7/15, 6/10, 5/3, 25/5.

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The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

Answer:

(2,-2)

Step-by-step explanation:

The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.

hope this helps :)

Answer:

--------------------------

From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:

The first line is given y = 1/2x - 3, equate both to get:

Then the value of y:

The solution is (2, - 2).

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = \(\frac{x^{2}y}{4} + \frac{y^3}{3}\) and Q = x

So the partial differentiation is

\(\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2\) and  \(\frac{\partial Q}{\partial x}\) = 1

By the Green's Theorem, work done by F is given as

W= \(\oint \vec{F}d\vec{r}\)

W= \(\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy\)

W= \(\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy\)

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr\)

and \(\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |\) = r

Thus;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr\)

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)

Answer:

31/10

Step-by-step explanation:

Answer:

5.006

Step-by-step explanation:

Answer:

The coordinates of the image will be: (15, -25)

Step-by-step explanation:

Given the point

A scale factor of 5 means that the new shape is five times the size of the original.

The coordinates of the image of (3,−5) after dilation by a scale factor of 5 centered at the origin can be obtained by multiplying the original coordinates of the object point by 5.

i.e.

(x, y) → (5x, 5y)

(3, -5) → (5×3, 5×(-5)) = (15, -25)

Therefore, the coordinates of the image will be: (15, -25)

Therefore, \((1.0001)^{38}\) ≈ 1.003800 to 6 decimal places.

E(1.0001) ≈ 0.000014 to 6 decimal places.

An algebraic expansion of powers of a binomial, a two-term polynomial, is provided by the binomial theorem, a mathematical theorem.

(a) To derive the result, we use the binomial theorem to expand \((1 + x)^k\):

\((1 + x)^k = C(k, 0) + C(k, 1)x + C(k, 2)x^2 + ... + C(k, k)x^k\)

where C(k, i) is the binomial coefficient. Consider only first two terms,

\((1 + x)^k\) ≈ \(C(k, 0) + C(k, 1)x = 1 + kx\)

where we have used the fact that C(k, 0) = 1 and C(k, 1) = k.

Using this approximation, we can estimate\((1.0001)^{38}\) as:

\((1.0001)^{38}\) ≈ (1 + 38 × 0.0001) = 1.0038

Therefore, \((1.0001)^{38}\) ≈ 1.0038 to 4 decimal places.

(b) Difference between the estimated and computed values \((1 + x)^k\) is

E(x) = \(| (1 + x)^k - (1 + kx) |\)

Using the approximation derived above, we can write:

E(x) ≈ \(| (1 + x)^k - (1 + kx) |\) ≈ |C(k, 2)x² + C(k, 3)x³ + ... + C(k, k)\(x^k\)|

For x = 1.0001 and k = 38, we have:

E(1.0001) ≈ |C(38, 2)(0.1001)² + C(38, 3)(1.0001)³ + ... + C(38, 38)(1.0001)³⁸|

Using a calculator or computer program, we can evaluate this expression to get: E(1.0001) ≈ 1.428 × 10⁻⁵ ≈ 0.00001428

Therefore, E(1.0001) ≈ 0.000014 to 6 decimal places.

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Answer:

1/3

Step-by-step explanation:

multiple of 4 is 4,8,12 and the multiple of 7 is 7,14 = 5/15=1/3

A game has a spinner with 15 equal sectors labeled 1 through 15, the value of P is mathematically given as

P=1/3

Question Parameter(s):

A game has a spinner with 15 equal sectors labeled 1 through 15.

Generally, the equation for the value of  P  is mathematically given as

P= multiple of 4and 7 /sample size

Where

Multiple of 4 is 4,8,12 and the multiple of 7 is 7,14

Therefore

P=5/15

P=1/3

In conclusion, The value of P is

P=1/3

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Answer:

60

Step-by-step explanation:

3/2t-16=4/3t-6

       +16      +16

3/2t=4/3t+10

      -4/3t

(t/6)6/1= 10(6/1)

t=60

Answer:

\(t=60\)

Step-by-step explanation:

To get both variables on one side, do the opposite of their current form and move them over (I'm not sure how else to explain this, so I'm just going to show you).

\(\frac{3}{2} t-16=\frac{4}{3} t-6\)

You see that the \(\frac{4}{3} t\) is positive, so you subtract it. The same goes for the -16 (do the opposite). You would add the -16 to the other side.

You need to do the opposite of them because only one number exists. If you move it, you need to cancel it out so that there is always only one of that number. (so when you add the -16 to the other side, the one on the left cancels out, but the same value (16) is still present on the right side and is added).

\(\frac{3}{2} t-\frac{4}{3} t=-6+16\)

Now you have this after moving like terms to their coinciding sides (you could do this any way, btw. It doesn't matter what order you add everything, so long as you get t on one side and by itself).

\(\frac{9}{6} t-\frac{8}{6}t =-6+16\\\frac{1}{6} t=10\\(\frac{6}{1} )(\frac{1}{6} t)=(\frac{6}{1} )(10)\\t=60\)

** Everything you do on one side, you need to do on the other side. This is a very important rule (and it goes hand in hand with the idea that there can only be one of each value, unless the exact same value appeared on both sides in the given equation).

Answer:

he made 6 2 point shots.

Step-by-step explanation:

here's why......... 3 times 1 is 3 and 3 times 4 is 12 in total that's 15 and 27-15 is 12 and 12 divided by 2 is 6.

Answer:

This is False

Step-by-step explanation:

Because if he made 3 1-point shots then 4 3-point shots, 3 multiplied by 1 is 3 and 4 multiplied by 3 is 12, and 12 multiplied by 3 is 36. So therefore he scored a total of 36 points. Thank me later :)

Answer:

x = 2

Step-by-step explanation:

The given point is (-2, 2).  A horizontal line passing through this point is x = 2.

The rule applied to obtain each vertex of the triangle DEF after the transformations is given as follows:

(x,y) -> 1/3(x - 3, y + 5).

The original coordinates of triangle DEF have the following format:

(x,y).

The dilation by a scale factor of 1/3 means that each of the coordinates is multiplied by 1/3, hence:

(x,y) -> 1/3(x,y).

The translation along the vector <-3,5> means that the x-coordinate is subtracted by 3 while 5 is added to the y-coordinate, hence:

(x,y) -> 1/3(x - 3, y + 5).

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The number which is not the part of the solution set to the inequality below is 27.

Given inequality is,

w - 10 ≤ 16

WE have to find the solution for the inequality.

Adding both side of the inequality with 10,

w - 10 + 10 ≤ 16 + 10

w ≤ 26

So the solution of the inequality consists of all the points which are less than or equal to 26.

So it contains 11, 15 and 26.

It does not contain 27.

Hence the solution does not contain 27.

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