Find each value to 4 decimal places. Include Step by step

a) sin 36°
b) cos 14°
c) tan 86°

Answer:

-8

Step-by-step explanation:

1/2 times 10 is 5. and a negative times a negative is a positive, so you have a positive 12, which becomes 5+12-25, which is -8

x ^2 + y ^2 = 9   =>   y = y(x) = ± √(9 - x ^2)

Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by y(x), which is

√(9 - x ^2) - (- √(9 - x ^2)) = 2 √(9 - x ^2)

The area of each square section is the square of this length,

(2 √(9 - x ^2)) = 4 (9 - x ^2) = 36 - 4x ^2

We get the whole solid for -3 ≤ x ≤ 3, so integrating gives a volume of

\(\displaystyle\int_{-3}^3(36-4x^2)\,\mathrm dx=\boxed{144}\)

Answer:

A is the answer

Step-by-step explanation:

if its wrong than its C

The volume of a prism is given by the formula:

Where w is the width, l is the length and h is the height of the prism. In this case, we are dealing with a square prism, which means that the base of the prism is a square, as you know, the length and width of a square are the same, thus l=w, then we get:

To find the area of the prism, we have to find the area of each face and then sum them up.

the faces are either a rectangle or a square, for this kind of figures the area equals the length times the width of the figure:

Then, for the top and bottom faces, the area is:

For the right and left faces, we have:

For the front and back faces we have:

By summing up these areas, we get:

Where we added 2 times each area because opposite areas have the same area (like the bottom and top faces, both areas are equal)

Now that we have two expressions, for the area and the volume of the prism, we need to write an equation of S as a function of w, this means that we have to find an expression to calculate S with only one variable appearing (w) so far in our formula of S we have the variables w and h, then we need to find the way of writing h as a function of w and then replace it into the formula of S.

If we take the formula of the volume, replace 125 in^3 for V and then solve for h, we get:

Now let's substitute this expression into the formula of S, like this:

Then, the equation of S as a function of w is:

Ellie's growth rate is 2.4 pounds per month.

To find Ellie's growth rate in pounds per month, we divide the change in weight by the time period. Let's calculate it using the given information:

Determine the change in weight:

Change in weight = 0.6 pounds

Determine the time period:

Time period = 0.25 months

Calculate the growth rate:

Growth rate = Change in weight / Time period

Substituting the values:

Growth rate = 0.6 pounds / 0.25 months

To divide by a fraction, we multiply by its reciprocal:

Growth rate = 0.6 pounds * (1 / 0.25 months)

Simplifying the fraction:

Growth rate = 0.6 pounds * 4 months

Multiplying:

Growth rate = 2.4 pounds per month

Therefore, Ellie's growth rate is 2.4 pounds per month. This means that, on average, she gains 2.4 pounds every month.

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Answer:

Vertex = (-1, 2)  

Maximum

Step-by-step explanation:  

The middle point of the graph is at x coordinate -1 and the point is at the top while the graph slopes down so it is a maximum point and not a minimum point.

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Answer:

\(7x + 2 = 8x + 5 \\ collecting \: like \: terms \: \\ 7x - 8x = 5 - 2 \\ - 1x = 3\)

(ecuacion primer grado para hoy. ). what does this mean..

Answer:

Recopilar términos semejantes

Answer: The x intercept is (11/2)

Step-by-step explanation:

Answer: The smaller piece is 750m long.

Step-by-step explanation:

let the smaller piece be x

so

150m + x + x = 1650

150 + 2x = 1650

or, 2x = 1500

so, x = 750 m

The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.

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14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer:

x = 8

each side is 74

Step-by-step explanation:

set two sides equal to each other

see image

Answer:

21, 7

Step-by-step explanation:

1st number = x, 2nd number = y

Given x + 3y = 42    (1)

find maximum value of xy.

Multiply by x on (1), get

x^2 + 3xy = 42x

3xy = -x^2 + 42x = -(x^2 - 42x)

Make a perfect square,

3xy = -(x^2 - 42x + 21^2) + 21^2

3xy = 21^2 - (x - 21)^2

Note (x - 21)^2 is non-negative, so when x = 21, the right hand side has a maximum value of 21^2, so xy is a maximum.

Use (1) and x = 21, we get 21 + 3y = 42, 3y = 21, y = 7

Hence, the two positive real numbers are 21 and 7

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.

According to the information provided:

55% of the team does not like to run.

Of those who do not like to run, 70% enjoy cycling.

Of those who enjoy running, 80% also enjoy cycling.

To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.

Percentage of athletes who do not like to run and enjoy cycling:

= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)

= 55% * 70% = 38.5%

Percentage of athletes who enjoy running and enjoy cycling:

= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)

= (100% - 55%) * 80% = 45% * 80% = 36%

Total percentage of athletes who enjoy cycling:

= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling

= 38.5% + 36% = 74.5%

Therefore, the correct answer is:

74.5%

Answer:

57,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know from the property of 30°x60°x90° right triangle:

We see AC = 2*BC, therefore:

Correct choice is B

The ratio of angles is directly proportional to the ratio of sides

The ratio of sides here is 1:1/2:1

Now

\(\\ \sf\longmapsto 2x+x=90°\)

\(\\ \sf\longmapsto 3x=90\)

\(\\ \sf\longmapsto x=30\)

Answer:

Mean = 75

Median = 80

Mode = 85

The mode

Step-by-step explanation:

Given the data :

45 45 50 50 55 60 70 75 75 80 80 85 85 85 85 90 95 95 95 100

Rearranged data :

45, 45, 50, 50, 55, 60, 70, 75, 75, 80, 80, 85, 85, 85, 85, 90, 95, 95, 95, 100

The mean score :

ΣX / n ; n = sample size = 20

ΣX = 1500

Mean = 1500 / 20 = 75

Mode = most frequently occurring = 85 ( frequency of 4)

Median = 0.5(n + 1)th term

Median = 0.5(20 + 1)th term

Median = 0.5(21) th term

Median = 10.5th term = (10 + 11)th term / 2

Median = (80 + 80) / 2 = 160 / 2 = 80

2.) The mode

The probabilities are given as follows:

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 104.2, \sigma = 87.9, n = 48, s = \frac{87.9}{\sqrt{48}} = 12.69\)

The probability is the p-value of Z when X = 129.6 subtracted by the p-value of Z when X = 85.2, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (129.6 - 104.2)/87.9

Z = 0.29 has a p-value of 0.6141.

\(Z = \frac{X - \mu}{\sigma}\)

Z = (85.2 - 104.2)/87.9

Z = -0.22 has a p-value of 0.4129.

Hence:

0.6141 - 0.4129 = 0.2012 = 20.12%.

For the sample mean, we use the standard error, hence:

\(Z = \frac{X - \mu}{s}\)

Z = (129.6 - 104.2)/12.69

Z = 2 has a p-value of 0.9772.

\(Z = \frac{X - \mu}{s}\)

Z = (85.2 - 104.2)/12.69

Z = -1.5 has a p-value of 0.0668.

Hence:

0.9772 - 0.0668 = 0.9104 = 91.04%.

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Answer:

the answer is $53

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

We need to know about scale factor to solve the problem. Matthew's mark last term was 50%.

It is given that Matthew's marks increased by a factor of 3/2 this term. This means that whatever marks Matthew had received in his previous term, it was increased by 3/2 this term. If we consider his original marks to be x, then we can get the increased marks by multiplying x by 3/2. We know that the new marks is 75%, we need to find the value of x.

3x/2=75

x=75x2/3=25x2=50

Therefore the marks Matthew received in the previous term is 50%.

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Answer: equilateral triangle ANP inscribed in circle C, regular hexagon AMNBPQ inscribed in circle C

Step-by-step explanation:

By looking through our choices, we can eliminate which choices could be wrong and which choices could be right.

Δ MNQ does form a triangle, however, it DOES NOT form a equilateral triangle.

Δ ANP does form a triangle and it is ALSO an equilateral triangle.

Hexagon AMNBPQ does form a hexagon and it is ALSO a regular polygon as we can see all the sides and angles within the polygon are congruent to one another.

MNPQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.

ANBQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.

1274 divided by 14 equals 91, see attachment below

Answer:

rate of change is a #

Step-by-step explanation:

Answer:

2)  Minimum = 15
     Lower Quartile = 19
     Median = 30.5
     Upper Quartile = 45
     Maximum = 62

3)  Minimum = 82
     Lower Quartile = 89
     Median = 99.5
     Upper Quartile = 112.5
     Maximum = 120

Step-by-step explanation:

A box and whisker plot (also known as a "box plot"), is a graph displaying the distribution of a set of data based on a five number summary.

\(\hrulefill\)

Given data set:

To calculate the values of the five-number summary, order the given data values from smallest to largest:

There are 10 data values in the data set, so this is an even data set.

As there are an even number of data values, the median is the mean of the middle two values, 30 and 31:

\(\sf Median=\dfrac{30+31}{2}=30.5\)

The lower quartile is the median of the data points to the left of the median. Therefore:

The upper quartile is the median of the data points to the right of the median. Therefore:

Therefore, the five-number summary of the given data set is:

To draw the box-and-whisker plot (see attachment 1):

\(\hrulefill\)

Given data set:

To calculate the values of the five-number summary, order the given data values from smallest to largest:

There are 12 data values in the data set, so this is an even data set.

As there are an even number of data values, the median is the mean of the middle two values, 99 and 100:

\(\sf Median=\dfrac{99+100}{2}=99.5\)

The lower quartile is the median of the data points to the left of the median. As there is an even number of data points to the left of the median, the lower quartile is the mean of the middle two values, 88 and 90:

\(\sf Lower\;Quartile=\dfrac{88+90}{2}=89\)

The upper quartile is the median of the data points to the right of the median. As there is an even number of data points to the right of the median, the upper quartile is the mean of the middle two values, 110 and 115:

\(\sf Upper\;Quartile=\dfrac{110+115}{2}=112.5\)

Therefore, the five-number summary of the given data set is:

To draw the box-and-whisker plot (see attachment 2):