Find the value of x in the figure below

Answer:

pi/3, 5pi/3

Step-by-step explanation:

We can see that when cosine is at 1/2, the angle measures are pi/3 degrees and 5pi/3 degrees. You can use a unit circle to find this. You can also find arccos(1/2), but that will only give you the value pi/3, not 5pi/3.

We can plug these in to find that they are indeed equal to 1/2.

The x-value that corresponds to a y-value of 1/2 between π and 2π is π/3.

Here, we have,

To find the x-value that corresponds to a y-value of 1/2 between π and 2π for the equation y = cos(x), we can use the inverse cosine function (also known as arccosine or cos⁻¹).

The inverse cosine function will give us the angle whose cosine is a specific value.

In this case, we want to find the angle whose cosine is 1/2.

Using the inverse cosine function, we can write the equation as:

x = arccos(1/2)

To solve this equation, we need to evaluate the inverse cosine of 1/2. In general, the inverse cosine of a value returns an angle between 0 and π (180 degrees). In this case, we are interested in finding an angle between π and 2π.

The value of arccos(1/2) is π/3.

Therefore, the x-value that corresponds to a y-value of 1/2 between π and 2π is π/3.

It's important to mention that the cosine function is periodic, so there are multiple x-values that can correspond to a y-value of 1/2. In this case, we have chosen the x-value that lies between π and 2π.

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Answer:

  x = 50

  y = 65

Step-by-step explanation:

The marked sides show you that the triangle is isosceles. That means the base angles, y° and 65°, are congruent.

  y = 65

__

The sum of the angles in a triangle is 180°.

  65° +65° +x° = 180°

  x° = 180° -130° = 50° . . . . . . subtract 130°

  x = 50

At least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.

The given parameters;

The number of gummy bear bags needed to share 5 gummy bears to each person is calculated as follows;

let the number of gummy bears bag = x

[tex]\frac{9x}{8} = 5\\\\9x = 40\\\\x = \frac{40}{9} \\\\x = 4.4[/tex]

Thus, at least 5 bags of gummy bear bags are needed for each person to get 5 gummy bears.

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Answer:

87/103

Step-by-step explanation:

An actual two-by-two table is a tabular representation containing two rows and two columns.

Mathematically, the set-up of the two-by-two table for this data can be computed as:

Tested                  True Positive for cancer   True Negative    Total

Predicted Positive         800                            3200                 4000

Predicted Negative        100                            95900              96000

Total                                900                            99100              100000  

The prevalence rate of prostate cancer in this population is:

[tex]\mathbf{ =\dfrac{900}{100000}}[/tex]

[tex]\mathbf{ =\dfrac{9}{1000}}[/tex]

= 9 per thousand.

The calculation of the sensitivity of this screening is as follows:

[tex]\mathbf{=\dfrac{TP}{TP+PN_1}}[/tex]

where;

∴

[tex]\mathbf{=\dfrac{800}{800+100}}[/tex]

= 0.889

= 88.9%

The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.

The calculation of the specificity  of this screening is as follows:

[tex]\mathbf{=\dfrac{PN_2}{PN_2+TN}}[/tex]

where;

∴

[tex]\mathbf{=\dfrac{95900}{95900+3200}}[/tex]

= 0.9677

= 96.77%

The interpretation shows that 96.7% of an actual negative is correctly identified as such.

The positive predicted value of the screening test is computed as:

[tex]\mathbf{= \dfrac{TP}{TP + TN}}[/tex]

[tex]\mathbf{= \dfrac{800}{800 + 3200}}[/tex]

= 0.2

= 20%

The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.

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Answer:

length (l) = 14 feet

breadth (b) = 7 feet

height (h) = 7 feet

so, volume of the

rectangular moving

van = l*b*h

=14feet * 7feet *7feet

= 686 cubic feet

Answer: 7 weeks

Step-by-step explanation:

Let x represent number of weeks

Let y represent the total amount

Amount = Paycheck deposited * number of weeks + Initial amount

y = 125x + 475

Number of weeks until she has $1350

1350 = 125x + 475

125x+475-475=1350-475

125x=875

x=7

Therefore, the student will have $1350 in her bank account after 7 weeks

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:

y+3=-1/2(x-2)

We can simplify this to

y= -1/2x-2

We can then check the point of intersection:

-1/2x-2=2x+3

-5=2.5x

x=-2

we can plug this in to the first equation to get y=2(-2)+3=-1

So the point of intersection of the circle and the tangent line is (-2,-1)

Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.

[tex]\sqrt{(-2-2)^{2}+(-1-(-3))^{2} } =\sqrt{(-4)^{2}+2^{2} } =\sqrt{20} =2\sqrt{5}[/tex]

The radius of the circle is [tex]2\sqrt{5}[/tex]

For Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

The line y=2x+3 is tangent to the circle with center (2,-3)

The distance from the center of the circle to the line is equal to the radius of the circle.

The distance from a point (x₁, y₁) to a line Ax + By + C = 0 is given by the formula:

d = |Ax₁+ By₁ + C| /√A² + B²

The equation of the line is y = 2x + 3, which can be written in the form Ax + By + C = 0 as (-2)x + y - 3 = 0.

d = |-2(2) + (-3) - 3| / √(-2)² + 1²

d=10/√5

The radius of the circle is equal to the distance from the center to the tangent line, which is:

radius = 10/√5

Hence, for Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5

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Answer:

sugar is bad so just use cream

Step-by-step explanation:

sugar can increase the risk of weight gain, diabetes, tooth cavities, and more.

hope this helps

Answer:

It is 7 whole

Step-by-step explanation:

3/15 is 5 without anything left plus the 3 is 7

3,400 at 10%

600 at 15%

This is the answer.

Answer:

+2 • (25y + 29)/5

Step-by-step explanation:

Answer: 4509

8,140-3,631

= 4509

Answer:

-4+-3+2-3

Step-by-step explanation:

Answer:

Danny's offer is cheaper

Step-by-step explanation:

Danny is offering 36$ for 4 hours meaning you would do 36÷4=9 (9$ per hour)

Martin is offering 54$ for 3 hours so 54÷3=18 (18$ per hour)

Or the faster way of finding why is Danny is offering more hours for cheaper

Hope this helps

Answer:

16

Step-by-step explanation:

261 - 256 - 251

-5 by step

to 50th term there is 49 -5's from 261.

261 + 49.(-5) = 261 - 245 = 16

Answer:

16

Step-by-step explanation:

The sequence appears to be an arithmetic sequence. To find the 50th term we should create a general formula for the sequence.

General formula of an arithmetic sequence: [tex]a_n=a_1+(n-1)d[/tex]

where An = nth term, a1 = first term , n = number of terms and d = common difference.

The first term is 261 so a1 = 261

The common difference appears to be -5

( 256 - 261 = -5 ) and ( 251 - 256 = -5 )

so d = -5

We want to find the 50th term so n = 50

We then plug all of this in to get the 50th terms

Formula : [tex]a_n=a_1+(n-1)d[/tex]

a1 = 261 , n = 50 and d = -5

[tex]a_n=261 + (50-1)-5[/tex]

subtract 1 from 50

[tex]a_n=261+(49)(-5)[/tex]

multiply 49 and -5

[tex]a_n=261-245[/tex]

subtract 245 from 261

[tex]a_n=16[/tex]

The 50th term is 16

=======================================================

Explanation:

The ratio we want is in the format green:red:total which means we list the number of green first, then the number of red next, then the number total last. The order is very important. This is because we'll simply list the numbers without saying the color name or "total". So the reader will imply what the numbers refer to, based on this order mentioned.

We have:

The ratio of green to red to total is 70:50:162

To reduce the ratio, we divide all three parts of that ratio by the GCF 2

The ratio 70:50:162 fully reduces to 35:25:81 which is the final answer.

This says that for every 35 green marbles, we have 25 red marbles and 81 total marbles.

Answer:A. y=1.5x

Step-by-step explanation:

x represents the number of twizzlers

1.5 represents the the price that you have to pay for each Twizzlers

And y represents the total cost

Answer:

what's thequestion?

Step-by-step explanation:

Answer:

$2421.95

Step-by-step explanation:

To calculate the final value from compound interest, we can use the formula

A = P(1+r/n)^(nt), where A represents the final amount, P is the initial amount, r is the rate, n is the number of times compounded per time period, and t is the amount of time.

Here, P is 2000, 1.2% is the rate (to convert to a decimal, we can divide by 100 to get 0.012), n = 2 because it is compounded semi-annually, and 16 is the number of years, or t. Plugging these in, we get

2000(1+0.012/2)^(2*16) = 2421.95

Answer:

The perimeter of the rectangle is 3.5 m or 350 cm.

Hope you could get an idea from here.

Doubt clarification - use comment section.

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

Step-by-step explanation:

no why? cause the guy bought 2 shirts for 19 dollors each where was he at nikes?  on average a shirt cost 15 bucks but 19? yeah no

Answer:

A

Step-by-step explanation:

20% of 60 is 12

Hope that helps

Answer: this is 4

Step-by-step explanation: A+b=2+2=4

Answer:

e = 2

Step-by-step explanation:

7(2e - 1) - 3 = 6 + 6e

14e - 7 - 3 = 6 + 6e

14e - 10 = 6 + 6e

14e - 6e - 10 = 6

8e - 10 = 6

8e = 6 + 10

8e = 16

8e/8 = 16/8

e = 2

Recheck:

7(2e - 1) - 3 = 6 + 6e

7(2(2) - 1) - 3 = 6 + 6(2)

7(4 - 1) - 3 = 6 + 12

7(3) - 3 = 18

21 - 3 = 18

18 = 18 ✅

Answer:

t = 17.5 f = 12

Step-by-step explanation:

If MNOP is a square, you know that each angle is going to be 90°. To solve, let's first set each equation equal to 90°:

[tex]90 = 4t + 20[/tex]

and

[tex]90 = 7f + 6[/tex]

Then solve both equations:

[tex]90 = 4t + 20 \\ 70 = 4t \\ 17.5 = t[/tex]

and

[tex]90 = 7f + 6 \\ 84 = 7f \\ 12 = f[/tex]

I hope that helps!

Answer:

m∠DEB = _70_°

m∠BCD= _110_°

m∠EAB= _73_°​

Step-by-step explanation:

To find ∠DEB:

Take the angle of ∠EDC, which is 110°. We know the total degree in a triangle is 180°. So, we do 180° - 110° to get 70°.

To find ∠BCD:

Because EBCD is an isosceles trapezoid, this means that ∠D and ∠C both have the congruent angles. Since we know ∠EDC is 110°, this means that ∠C is also 110°.

To find ∠EAB:

We know that m∠ABC is 133° and ∠DEA is 114°. However, both angles count both the triangle and trapezoid. Previously we figured out that ∠DEB is 70°. We'll take the angle of ∠DEA and subtract the angle of ∠DEB from it, which gets us 44°. To figure out the angle of ∠B, we take the angle of ∠ABC and subtract 70° or the angle of ∠DEB, which gets us 63°. Now we take the total degree of a triangle, 180° and minus both 44° and 63° from it, which is 73°.

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