In ΔCDE, the measure of ∠E=90°, DC = 97, CE = 72, and ED = 65. What ratio represents the sine of ∠C?

Answer:

0.1296

Step-by-step explanation:

9/25 = 0.36

0.36 squared = 0.1296

The length of the rope must be, at least, 5.9 meters.

The rope will allow the sheep to move in an almost perfect circle (except for the part where the shed is) so we will have 3/4 of a circle.

So here we just need to find the length L of the rope such that:

10 yd² = (3/4)*pi*L^2

Where (3/4)*pi*L² is the area of 3/4 of a circle of radius L.

and pi = 3.14

Solving for L we will get:

L = √( 10 yd²*(4/3*3.14)) = 6.4 yd

Writting this in meters, we will get:

1 yd = 0.9144 m

then:

L = 6.4* 0.9144 m = 5.9m

The rope must be at least 5.9 meters long.

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Answer:

25:35

Step-by-step explanation:

5 + 7 = 12

60 ÷ 12 = 5

5 × 5 = 25

5 ×7 = 35

ratio = 25:35

Answer:

$338/20 = $16.90

Answer:

[tex]\$16.90 \textrm{ per hour}[/tex]

Step-by-step explanation:

To solve this, we simply have to divide the total amount of money that Taylor earned by the number of hours that she worked for.

[tex]\dfrac{\$338.00}{20 \textrm{ hr}} = \$16.90 \textrm{ per hr}[/tex]

The probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

When events A and B are independent, the probability of them occurring together is the product of their individual probabilities.

P(A and B) = P(A) * P(B) = 0.31 * 0.76 = 0.2356

P(A|B) = P(A and B) / P(B) = 0.2356 / 0.76 = 0.31 (It is same as P(A) because events A and B are independent)

P(B|A) = P(A and B) / P(A) = 0.2356 / 0.31 = 0.76 (It is same as P(B) because events A and B are independent)

P(A or B) = P(A) + P(B) - P(A and B) = 0.31 + 0.76 - 0.2356 = 0.8144

Therefore, the probability of (A and B) is 0.2356, the conditional probability of (A|B) is 0.31, the conditional probability of (B|A) is 0.76, and the probability of (A or B) is 0.8144.

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In addition to the 3-digit numbers shown, the letters A, B, C, and D each represent a unique single digit. out of the  following e.19  could be the sum of A+B+C+D.

To find the sum of A, B, C, and D, we first need to add the 3-digit numbers ABC and DBC. To do this, we can use the standard column addition method. Starting from the right column, we add the single digits A and D together to get the one digit of the sum. Moving to the left column, we add the two-digit numbers BC and BC, which adds up to 180.

Then, we add the single digits B and C together to get the tens digit of the sum. Finally, we add the two-digit numbers AC and DC together to get the hundreds of digits of the sum. When we put all the digits together, we get the sum of A, B, C, and D to be 850. Since 850 is not one of the given answers, we look for the nearest option. The nearest option is 19, which is the answer to this question.

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Answer:

answer is b second which is -6

The cost of painting the room walls with two coats of paint would be $84.38

To determine the cost of painting the room walls with two coats of paint, you would need to know the total square footage of the walls you are planning to paint. Once you have that information, you can calculate the total cost by multiplying the number of gallons of paint required by the cost per gallon. For example, if the room has 800 square feet of walls, you would need 2.28 gallons of paint (800/350 = 2.28) and the total cost would be $84.38 (2.28 x $36.50). If you want to know the cost of one coat, you will need to divide that number by 2.

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The solution to the system of equations is (0, -5) or (4, 3).

What is the system of equations?

A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.

To solve the system of equations, we'll substitute the second equation into the first:

x^2 + (2x - 5)^2 = 25

Expanding the square in the second equation:

x^2 + 4x^2 - 20x + 25 = 25

5x^2 - 20x = 0

5x(x - 4) = 0

So x = 0 or x = 4.

For x = 0:

y = 2x - 5 = -5

For x = 4:

y = 2x - 5 = 3

Hence, the solution to the system of equations is (0, -5) or (4, 3).

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Answer:

Area for triangle : Area =  1⁄2× base × height

Area for square : Area = base × height

Step-by-step explanation:

Answer:the final answer is 7

Step-by-step explanation:

On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles  in order to make renting from Company B a better deal

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

so, we have -

Company A charges =  $35 per day

plus =  $0.45 per mile.

Company B charges =  $60 per day

plus  = $0.25 per mile.

McCall would need to drive 126 miles  in order to make renting from Company B a better deal

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The probability that we observe a sum of 5 or 9 before a sum of 7 is 7/18

The term probability is referred as the number of ways of achieving success. the total number of possible outcomes

Here we have given that we roll a pair of standard dice until the sum of the two numbers on which they land is 5 or 7 or 9.

As we all know that the sample space for the rolling of two dice that is the pair of dice is written as n(s) = 36

Then the probability of getting the sum of 5 is written as,

=> 4/36

Similarly, the probability of getting sum of 7 is written as,

=> 6/36

And the probability of getting sum of 9 is written as,

=> 4/36

Then the total probability is calculated as,

=> 14/36

When we simplify this one then we get,

=> 7/18

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Answer:

Step-by-step explanation:

The sum of a geometric sequence can be found using the formula

Sn = a₁ (1 - rⁿ⁻¹)/ (1 - r)

where a₁ is the first term, r is the common ratio, and n is the number of terms.

In this case, a₁ = -8, r = -3, and n = 10.

Plugging these values into the formula, we get

Sn = -8 (1 - (-3)⁹⁻¹) / (1 - (-3))

Sn = -8 (1 + 3⁹) / 4

Sn = -8 (1 + 19683) / 4

Sn = -8 × 19684 / 4

Sn = -4920

a)  It is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.

b)It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05)  ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.

Now, According to the question:

Part (a) Step 1: Given Information

Given, p = 0.097

Formula used:

The expected value

μ = 1/p

Part (a) Step 2: Simplification

The number of independent trials required until first success is distributed geometrically.

A geometric distribution's expected value is

μ = 1/p = 1/0.097 = 10.3039

Hence, it is expected that to examine about 10.3039 invoices until you achieve your first success, which is an invoice starting with an 8 or 9.

Part (b) Step 1: Given Information

Given, p = 0.097

Formulae to be used

Geometric probability:

P(X = k) = [tex]q^k^-^1p = (1-p)^k^-^1p[/tex]

Addition rule:

P(A ∪ B) = P(A) + P(B)

Complement rule:

P(A°) = P(not A) = 1 - P(A)

Part (b) Step 2: Simplification

Consider, p = 0.097

Compute the binomial probability definition at k = 1, 2,and3....40  :

P(X = 1) = [tex](1 - 0.097)^1^-^1(0.097)[/tex] = 0.097

Using the complement rule:

P(X ≥ 40) = 1 - P(X ≤ 39) = 1 - 0.9813 = 0.0187 = 1.87%

It has been discovered that the likelihood of achieving the first success on the 40th invoice or after it is small (less than (0.05)  ), This demonstrates that the occurrence is unlikely to occur, and hence there is sufficient convincing evidence that the invoice amounts are not genuine.

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The given question is incomplete, The complete question is:

Using Benford's law According to Benford's law (Exercise 15, page 377), the probability that the first digit of the amount of a randomly chosen invoice is an 8 or a 9 is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8 or a 9 .

a. How many invoices do you expect to examine before finding one that begins with an 8 or 9 ?

b. In fact, the first invoice you find with an amount that starts with an 8 or 9 is the 40 th invoice. Does this result provide convincing evidence that the invoice amounts are not genuine? Calculate an appropriate probability to support your answer.

Answer:

[tex]\mathrm{A.\;\;\boxed{V = \dfrac{m}{D}}}\\\\\\\\\mathrm{B.\;\;\boxed{8.8496\;cm^3}}[/tex]

Step-by-step explanation:

Object density formula is
[tex]D = \dfrac{m}V}\\[/tex]

with the variables defined as in the question

A.

B.

The weight of a piece of luggage that can be checked in, given the use of w to represent the weight, is W < 45.

The statement given is that, " each piece of luggage to be checked in must weigh less than 45 pounds. "

What this means is that the mass of each luggage should not be up to 45 pounds. The weight of the luggage should not be more than 45 pounds and it should not be equal to 45 pounds.

If the weight of luggage was said to be equal or less, then the symbol of equal or less than, which is ≤ would have been used.

However, the weight should be less than 45 pounds and with the weight being w, the expression would be:

W < 45

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The rest of the question is:

Use W to represent the weight (in pounds) of a piece of luggage that can be checked in

A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square. To find the length of the side of the octagon, we can use the Pythagorean theorem to calculate the length of the hypotenuse of the isosceles right triangle.

In an isosceles right triangle, the two legs have the same length and the hypotenuse is the side opposite the right angle. Since the square has sides of length 2000, half of the side of the square is the leg of the isosceles right triangle.

So the leg of the isosceles right triangle is 2000/2 = 1000.

Applying the Pythagorean theorem to find the hypotenuse of the isosceles right triangle:

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

c = sqrt(1000^2 + 1000^2)

c = sqrt(1000000)

c = 1000*sqrt(2)

So the length of each side of the octagon is 1000sqrt(2)

Answer:

sin x + cos x = [tex]\sqrt{2}[/tex]

Step-by-step explanation:

given

tan x = 1 , then

x = [tex]tan^{-1}[/tex] (1) = 45°

the exact values of both sin45° and cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin x + cos x

= sin45° + cos45°

= [tex]\frac{1}{\sqrt{2} }[/tex] + [tex]\frac{1}{\sqrt{2} }[/tex]

= [tex]\frac{2}{\sqrt{2} }[/tex]

rationalise the denominator by multiplying numerator/ denominator by [tex]\sqrt{2}[/tex]

= [tex]\frac{2(\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }[/tex]

= [tex]\frac{2\sqrt{2} }{2}[/tex]

= [tex]\sqrt{2}[/tex]

The equation of the line is y = -3x + 5.

To find the equation of a line that passes through two points and is perpendicular to the equator, we need to calculate the slope of the line that passes through the two points first.

The slope of the line passing through (1,10) and (1,10) is 0. This means that the line is perpendicular to the equator, whose slope is undefined.

Next, we need to calculate the y-intercept. If we assume that the line passes through the point (1,10), then the y-intercept is 10.

Finally, we can use the slope and the y-intercept to write the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0 and the y-intercept is 10, so the equation of the line is y = 0x + 10, which simplifies to y = 10.

Since the slope of the line is 0, we can also write the equation of the line in the form y = -3x + b, where b is the y-intercept. In this case, the y-intercept is 10, so the equation of the line is y = -3x + 10, which simplifies to y = -3x + 5.

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Tom's pencil is longer than Ellen's pencil with (3x+10)cm

Subtraction is one of the four arithmetic operation along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 minus 2 peaches, this means that 5 peaches with 2 taken away, resulting in a total of 3 peaches.

Ellen's pencils length = 2x+15

Tom's pencil length = 5x+25

Tom's pencil will be longer than Ellen's with;

(5x + 25 ) - (2x+15)

= 5x + 25 -2x - 15

collect like terms

5x -2x +25-15

3x +10

therefore Tom's pencil is longer than Ellen's pencil with ( 3x+10) cm

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Answer:

wouldn't this be 4,2?

Step-by-step explanation:

i remember doing this in school last year and dilation means you would multiple the coordinates by what ever the dilation factor was, in this case its 2.

The value of x is 15 units.

What are Corresponding  Angles ?

When two parallel lines are intersected by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).

For instance, angle p and angle w are the comparable angles in the image below.

Step-by-step explanation:

In the given triangle RSQ and ΔRST it is given that

∠RTS ≅ ∠SRQ ≅ 90°

∠RSQ is common in two triangles Δ RSQ and Δ RST.

Therefore two angles are equal so both the triangles are common.

From this property we opposite sides of the corresponding angles will be in the same ratio.

SR/SQ = ST/SR

x/(9 + 16) = 9/x

By cross multiplication on each side of the equation

x² = 25×9 = 225

x = √225 = 15

Therefore measurement of x is 15 units.

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The average rate of change of a function over an interval is the total change in the function's output (or y-value) divided by the total change in the function's input (or x-value) over that interval.

Given the function h(x) = 1/8 x^3 - x^2, the average rate of change over the interval -2 < x < 2 is:

(h(2) - h(-2)) / (2 - (-2))

First, we have to find h(2) and h(-2) by substituting these values in the function:

h(2) = 1/8 (2)^3 - (2)^2 = 1/8 * 8 - 4 = 0.5

h(-2) = 1/8 (-2)^3 - (-2)^2 = 1/8 * -8 - 4 = -4.5

So, the average rate of change is:

(0.5 - (-4.5)) / (2 - (-2)) = 5 / 4 = 1.25

Therefore, the average rate of change of h over the interval -2 < x < 2 is 1.25

Answer:

x + y ≥ 6 (Melissa exercises for at least 6 hours per week)

x ≤ 11 (Melissa spends at most 11 hours doing cardiovascular work)

y ≤ 4 (Melissa spends at most 4 hours on weight training)

To graph this region, you can plot the constraints on the x-y coordinate plane and shade the area that satisfies all of them.

The first constraint x+y>=6 can be represented by the line y = -x +6

The second constraint x<=11 can be represented by the line y = 11

The third constraint y<=4 can be represented by the line y = 4

The shaded area will be the region that is above and to the right of the line y = -x + 6, below the line y = 11 and below the line y = 4.

Kind of hard to shade a graph without having it in front of me. Hope this helps!

Answer:

livirav737 has provided the correct answer first.

I am merely providing the graph

Step-by-step explanation:

Plotted using online graphing tool Geogebra

The heavily shaded region with ABCD as its corners represents the region corresponding to all 5 inequalities

Note
Though not explicitly stated

You must also have the two additional constraints

x ≥ 0, y ≥ 0

These are called non-negativity constraints to ensure that x and y are not negative. The number of hours exercised on each platform cannot be less than 0

In this particular case, these are not necessary but standard practice is to include them whenever you have a system of inequalities with non-negative variables

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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He encourages them to remain brave and steadfast, and emphasizes the importance of unity and solidarity in order to achieve victory.

In the Leon, King Leonidas uses the to rally his troops and to inspire them to fight for freedom. He uses it to explain the importance of fighting for freedom and the consequences of failing to do so. He emphasizes the importance of remaining brave and steadfast, and speaks of the need for unity and solidarity in order to achieve victory. He also uses the Maka to explain the importance of having faith in the gods and themselves, and trust that the gods will grant them victory. King Leonidas’ use of the Maka is much more complex than a ceremonial purpose, as he is using it to motivate and teach his troops. He speaks of the need to stay united and to fight for freedom, which is something that is larger than any one individual. He stresses the importance of having faith in the gods, as well as in each other, and that by doing so, victory can be achieved.

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No, absolute value functions do not pass the vertical line test.

The vertical line test is a way to determine if a graph represents a function. A graph represents a function if and only if no vertical line intersects the graph more than once.

An absolute value function is defined as:

y = |x|

The graph of this function is a V-shape, with the vertex at the origin. The graph of the function is defined for all x-values, but the graph is not a function because a vertical line can intersect the graph at two points, one for x and the other for -x, for example if the vertical line x=2, it will intersects the graph at (2,2) and (2,-2), thus it does not pass the vertical line test.

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The coordinate pair of the given solution of the system would be= (g, h) (1,-8).

Substitution equation is defined as the equation that can be solved when a value is being solved and substituted for the other missing value to be gotten.

4g + h = -4 ---->. eq 1

12g + 2h = -4 ----> eq 2

Make h the subject of formula;

h = -4 - 4g -----> eq 3

Substitute equation 3 into equation 2;

12g + 2( -4 - 4g) = -4

12g - 8 -8g = -4

4g -8 = -4

4g = -4 +8

4g = 4

g = 4/4= 1

Solve for g = 1 in equation 1;

4(1) + h = -4

4 + h = -4

h = -4-4

h = -8

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Answer:

  214.9°

Step-by-step explanation:

You want to know the angle of rotation that moves a point on a circle of 16 inch radius a distance of 5 feet.

The relation between the length of an arc and the central angle in radians is ...

  s = rθ

The distance of 5 ft is equal to 60 inches, so we have ...

  60 = 16θ

Solving for θ gives ...

  θ = 60/16 = 15/4 . . . . radians

The angle in radians can be converted to an angle in degrees by multiplying it by 180°/π:

  15/4 radians = (15/4)·(180°/π) ≈ 214.9°

The wheel turned through an angle of about 214.9°.