Please help I am stuck!!!

The value for the side of rectangle XZ is equal 14, using the trigonometric ratios of cosine and sine of angles.

The trigonometric ratios concerns the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the triangle WYZ, the cosine of angle Y;

cos(Y) = 21/YZ {adjacent/hypotenuse}

YZ = [21/cos(Y)] {cross multiply}

Considering the triangle XYZ, the cosine of angle Y;

cos(Y) = YZ/28

YZ = 28 × cos(Y)

Therefore,

28cos(Y) = [21/cos(Y)]

cos²(Y) = 21/28 {cross multiply}

cos(Y) = √(21/28) {take the square root of both sides}

cos(Y) = 0.8660

Y = cos^(-1)(0.8660) {cross multiply}

Y = 30°

To get the side XZ, considering the triangle XYZ the sine of 30°;

sin30° = XZ/28 {opposite/hypotenuse}

by cross multiplication

XZ = 28 × sin30°

XZ = 14

Therefore, by proper application of the trigonometric ratios of cosine and sine of the angle for the given triangle, the side XZ = 14.

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Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

5 + 7 = 12 total fruits, which means that \(N = 12\)

7 apples, which means that \(k = 7\)

You receive 2 fruits, which means that \(n = 2\)

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182\)

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.

Answer:

dream

Step-by-step explanation:

why not

Answer:

Mine is 5 minute crafts

I love crafts, so ya. They are pretty popular

please give me brainiest :) !

Answer:10

Step-by-step explanation:

the first time in my class or must i forget abt u cos i always indoors and i know ukuthi im not strong so

In transformations, the Pre-Image is the original figure and the Image is the figure transformated.

In this case you can identify that the Pre-Image is the triangle ABC and the Image is the triangle A'B'C'.

Notice that the vertices of ABC are:

By definition, when the scale factor used in the dilation is between 0 and 1, the Image obtained is a reduction and, therefore, it is smaller than the Pre-Image. Since A'B'C' is smaller than ABC, then you can determine that ABC was dilated by this scale factor:

When a figure is reflected across the y-axis, the rule is:

If you dilate ABC by the scale factor shown above, and then you reflect it across the y-axis, the coordinates of the Image will be:

Notice that the coordinates of A'B'C' shown in the picture match with the vertices found above.

Therefore, the answer is: Option C.

The value of x is 34 degree.

The correct option is B.

We have the measure of arc = 68 degree

We know,

angle at Center = Arc

and, Angle on circle= Arc/2

So, Angle on Arc= 68/2

Angle on Arc= 34 degree

Thus, the value of x is 34 degree.

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Set A and Set R do not have one-to-one correspondence in terms of their elements. Therefore, the correct answer is no, because each element in set R is not represented in set A.

Set A is defined as the set of odd integers, while set R is defined as the set containing the elements 3, 7, 11, and 27. Since set R contains specific elements, it is not possible for every element in set A to be represented in set R.

For example, there are odd integers such as 5, 9, and 13 that are not included in set R. On the other hand, if the question was asking if set A is a subset of set R, then the answer would be no as well.

A subset relationship implies that every element in set A is also in set R, but since set R contains specific elements (3, 7, 11, 27), it does not include all the odd integers.

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Answer:

The first quartile is 99.5

Step-by-step explanation:

Answer:

(a) A 95% confidence interval for the population mean is [433.36 , 448.64].

(b) A 95% upper confidence bound for the population mean is 448.64.

Step-by-step explanation:

We are given that article contained the following observations on degrees of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

420, 425, 427, 427, 432, 433, 434, 437, 439, 446, 447, 448, 453, 454, 465, 469.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_n_-_1\)

where, \(\bar X\) = sample mean = \(\frac{\sum X}{n}\) = 441

            s = sample standard deviation = \(\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }\)  = 14.34

            n = sample size = 16

            \(\mu\) = population mean

Here for constructing a 95% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, \(\mu\) is ;

P(-2.131 < \(t_1_5\) < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 2.131) = 0.95

P( \(-2.131 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(2.131 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-2.131 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+2.131 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X -2.131 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X +2.131 \times {\frac{s}{\sqrt{n} } }\) ]

                                      = [ \(441-2.131 \times {\frac{14.34}{\sqrt{16} } }\) , \(441+2.131 \times {\frac{14.34}{\sqrt{16} } }\) ]

                                      = [433.36 , 448.64]

(a) Therefore, a 95% confidence interval for the population mean is [433.36 , 448.64].

The interpretation of the above interval is that we are 95% confident that the population mean will lie between 433.36 and 448.64.

(b) A 95% upper confidence bound for the population mean is 448.64 which means that we are 95% confident that the population mean will not be more than 448.64.

Answer:

20%

Step-by-step explanation:

if zero toppings is an option, then there would be 5 possibilities for toppings

0,1,2,3,or 4

the server randomly chose 3 toppings so that would be one out of 5 or 20%.

(If the server did not have the option to put zero toppings on then there would be only 4 options 1,2,3, or 4 toppings and the correct answer would be one out of 4 or 25%.)

Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.

By placing the given value in equation , we get u + v - 4u = (-20, 13)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

To evaluate u + v - 4u, we first need to find the vector 4u, which is obtained by multiplying the vector u by the scalar 4:

4u = 4(5,-2) = (20,-8)

Now, we can add u and v, and subtract 4u from the result:

u + v - 4u = (5,-2) + (-5,7) - (20,-8)

= (5 - 5 - 20, -2 + 7 + 8)

= (-20, 13)

Therefore, u + v - 4u = (-20, 13).

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9514 1404 393

Answer:

  Tn = (n/2)(n +1)

Step-by-step explanation:

The first differences are ...

  x -1, 6 -x, y -6, 15 -y

Then the second differences are ...

  (6 -x) -(x -1) = 1   ⇒   7 -2x = 1   ⇒   x = 3

  (y -6) -(6 -x) = 1   ⇒   x + y = 13   ⇒   y = 10

  (15 -y) -(y -6) = 1   ⇒   21 -2y = 1   ⇒   y = 10

Then the sequence is ...

  1, 3, 6, 10, 15, ...

which is the sequence of triangle numbers. The formula for the general term is ...

  Tn = (n/2)(n +1)

Answer:

Step-by-step explanation:

Here is a methode more general:

\(\Delta_{1,n}=u_{n+1}-u_{n}\\\\\Delta_{1,n+1}=u_{n+2}-u_{n+1}\\\\\\\Delta_{2,n}=\Delta_{1,n+1}-\Delta_{1,n}=u_{n+2}-u_{n+1}-(u_{n+1}-u_{n})\\=u_{n+2}-2*u_{n+1}+u_{n}=1\\\\\Delta_{2,n+1}=u_{n+3}-2*u_{n+2}+u_{n+1}=1\\\\\Delta_{2,n+1}-\Delta_{2,n}=u_{n+3}-3*u_{n+2}+3u_{n+1}-u_n=0\\\\Caracteristic\ equation: \ r^3-3r^2+3r-1=0=(r-1)^3\\\\u_n=k_1*1^n+k_2*n*1^n+k_3*n^2*1^n\\\\\)

\(\left\{\begin{array}{ccc}u_1&=&1\\u_2&=&x\\u_3&=&6\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}k_1+k_2+k_3&=&1\\k_1+2*k_2+4*k_3&=&x\\k_1+3*k_2+9*k_3&=&6\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}k_1&=&-3x+9\\\\k_2&=&4x-\dfrac{23}{2}\\\\k_3&=&-x+\dfrac{7}{2}\\\end {array}\right.\\u_n=-3x+9+(4x-\dfrac{23}{2})*n+(-x+\dfrac{7}{2})*n^2\\\\u_1=-3x+4x-x+9-\dfrac{23}{2} +\dfrac{7}{2} =1\\u_2=-3x+8x-4x+9-23 +14=x\\u_3=-3x+12x-9x+9-\dfrac{69}{2} +\dfrac{63}{2} =6\\\)

\(u_4=-3x+16x-16x+9-46 +56 =-3x+19=y\\u_5=-3x+20x-25x+9-\dfrac{115}{2} +\dfrac{175}{2} =-8x+39=15\\\\\Longrightarrow\ x=3\\k_1=-9+9=0\\k_2=4*3-\dfrac{23}{2} =\dfrac{1}{2}\\k_3=-3+\dfrac{7}{2} =\dfrac{1}{2}\\\\\\u_n=0+\dfrac{n}{2}+\dfrac{n^2}{2}=\dfrac{n*(n+1)}{2}\\\\Sequence\ is\ 1;3;6;10;15;...\\\)

Step-by-step explanation:

a. d = m/v

m = d × v

b. m = d × v

= 5.01g/cm × 1.2cm

= 6.012g

hopefully this makes sense

:)

The mass of pyrite sample in grams will be -  6.012 grams

We have a marble whose volume is 1.2 cubic centimeter and density is 5.01 g/cm. A relation - density d of a substance is given by the formula

d = m/v is also provided.

We have to determine its mass.

The solid state of matter has the highest density because the constituent particles are fixed and not allowed to move inside the solid. Moreover, they are bonded very close to each other.

According to the question -

Density - 5.01g/cm

Volume - 1.2cm.

Using the formula mentioned above, we get -

\($\rho = \frac{M}{V}\)

Rearranging the formula, we get -

M = ρV

M = 5.01 x 1.2 = 6.012 grams

Hence, the mass of pyrite sample in grams will be -  6.012 grams

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Answer:

9000

Step-by-step explanation:

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)

\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)

\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)

\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

The volume of a cube is given by the formula V = s^3, where s is the length of one of its sides. So, if the edge length of a cube is 3 inches, its volume would be:

V = 3^3 = 27 cubic inches

Answer: 4/33

Step-by-step explanation:

just divide

Answer:

The answer is 4/33.

Step-by-step explanation:

to get this you just have to divide.

you're welcome.

Answer:

a^2+B^2=c^2

Step-by-step explanation:

Step-by-step explanation:

(Hyp)² = (Base)² + (Height)²

C² = a² + b²

C= √a²+b²

This is the formula to find Hypotenuse of a right angled triangle

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

Step-by-step explanation:

(-1-5)/2 = -6/2= -3

(-5+9)/2 = 4/2 = 2

(-3, 2)