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Answer:

225

Step-by-step explanation:

Using the basic components of summation ∑

∑n = [tex]\frac{1}{2}[/tex] n(n + 1) and ∑1 = n

Thus

∑ (2n - 1) ← for n = 1 to 15

= ∑2n - ∑1

= 2∑n - ∑1

= 2 ([tex]\frac{1}{2}[/tex] n(n + 1)) - n

= n(n + 1) - n ← Evaluate for n = 15 ( the upper value )

= 15 × 16 - 15

= 240 - 15

= 225

Answer:

255

Step-by-step explanation:

Step-by-step explanation:

Given : If the hypotenuse of a 30-60-90 triangle has length 15 then the shorter leg has length  5.5 , 6.5 , 7.5.

To find : What is the length of the other leg and hypotenuse ?

Solution :

For a  30-60-90 triangle, sides are in the ratio  [tex]1:\sqrt{3}:2[/tex]

where, 1 is the shorter side,  

[tex]\sqrt{3}[/tex] the other side

and 2 the hypotenuse.

Short leg = 5.5

Other leg = [tex]5.5\times \sqrt3=5.5\sqrt3[/tex]

Hypotenuse = [tex]5.5\times 2=11[/tex]

Short leg = 6.5

Other leg = [tex]6.5\times \sqrt3=6.5\sqrt3[/tex]

Hypotenuse = [tex]6.5\times 2=13[/tex]

Short leg = 7.5

Other leg = [tex]7.5\times \sqrt3=7.5\sqrt3[/tex]

Hypotenuse = [tex]7.5\times 2=15[/tex]

Final answer:

In a 30-60-90 triangle with a hypotenuse of 15, the shorter leg has a length of 7.5, based on the ratio 1:√3:2.

Explanation:

If the hypotenuse of a 30-60-90 triangle has length 15, then to find the length of the shorter leg, we can use the properties of this special right triangle. In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2. In other words, if the shorter leg is 'x', the longer leg is 'x√3', and the hypotenuse is '2x'.

Since the hypotenuse is 15, we set '2x' equal to 15 and solve for 'x':

2x = 15

x = 15 / 2

x = 7.5

The shorter leg of the triangle has a length of 7.5.

The key characteristics of graph of f(x) = cosecx are, The range of the function is (−∞, −1]∪[1, ∞) and Asymptotes occurs every π, beginning at x = 0. So statements 1 & 3 are correct

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

Given that,

A trigonometric function,

f(x) = cosecx

The range of cosecx is (−∞, −1]∪[1, ∞)

At x = 0, it is approaching to infinity from both the sides

So, y intercept is not 1

At every π interval, it has Asymptotes

It never intersects the x axis, So x-intercept is not exist here

Hence, statements 1 & 3 are correct

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The graph of f(x)=cscx has a range of (−∞, −1]∪[1, ∞) , no y-intercept, and asymptotes at every multiple of \pi, but no x-intercepts.

The key characteristics of the graph of the function f(x)=cscx include the following:

This is because the cosecant function is the reciprocal of the sine function, which ranges from -1 to 1.

So, the cosecant function will take on all values that are less than -1 or greater than 1.

The sine function, which is the reciprocal of the cosecant, equals 0 at this point, and division by zero is undefined.

since cosecant is the reciprocal of sine, the function is undefined at these points;

so statement c is incorrect.

Option a., c., d.

Answer:

280

Step-by-step explanation:

360-80

Answer:

A-168

B-81

C-117

Step-by-step explanation:

you multiply all of the numbers together.

Answer:4/5

The required probability that the randomly picked counter is green is 4/5

According to the problem,

So, 16 green counters are the favorable cases.

∴ Required probability = 16/20 = 4/5

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Answer:

8, 9

Step-by-step explanation:

Since x > 7

This means that x cannot equal 7 but must be greater values than 7.

Thus 8 and 9 are solutions

Answer:

1) [tex]\frac{8\pi }{3}[/tex] or 8.38

2) [tex]\frac{9\pi }{8}[/tex] or 3.53

3) 4[tex]\pi[/tex] or 12.57

Step-by-step explanation:

The formula for arc length is [tex]2\pi r(\frac{angle}{360})[/tex]

1) 2[tex]\pi[/tex](4)× [tex]\frac{120}{360}[/tex]

2)[tex]2\pi (1.5)[/tex]×[tex]\frac{135}{360}[/tex]

3) [tex]2\pi(3)[/tex]×[tex]\frac{240}{360}[/tex]

Answer:

4 days

Step-by-step explanation:

268-112= 156    

156 divided by 39 = 4

Answer:

i think it is 4

Step-by-step explanation:

bc you do 268-112=156 then you take 156 and divide it by 39 and you end up getting 4.

Step-by-step explanation:

BC is tangent to the circle with center A at point C and AC is radius.

[tex] \therefore AC \perp BC\\

\therefore \angle ACB =90°\\[/tex]

Now by Pythagorean theorem:

[tex] AB^2 = AC^2 + BC^2 \\

\therefore AC^2 = AB^2-BC^2\\

\therefore x^2 = 17^2-14^2\\

\therefore x^2 =289-196\\

\therefore x^2 =93\\

\therefore x =\sqrt{93}\\

\therefore x =9.64365076\\

\huge \purple {\boxed {\therefore x = 9.64\: units}} [/tex]

message me! i have made an edited file of it finished <3

Answer:

Two hundred years = 2 century

4 decates= 40 years

36 months =3 years

96hours=4 days

6 months =26.071 weeks

Answer:

9. 21 days = 3 weeks (7 days in a week)

10. 200 years = 2 centuries (100 years in a century)

11. 4 decades = 40 years (10 years in a decade)

12. 36 months = 3 years (12 months in a year)

13. 96 hours = 4 days (24 hours in a day)

14. 6 months = 26 weeks (52 weeks in a year divided by 2)

15. 2 weeks

16. 50 years

17. 65 days

18. 110 weeks

19. hours

20. months

21. centuries

22. years  

Answer:

3.75

Step-by-step explanation:

3.75 you couldve used calculator :/

Answer:

3.75.

Step-by-step explanation:

15/4 = 3 with a remainder of 3. (3 3/4)

Then you make that into a decimal...

--> 3/4 is equal to 75 percent.

So 3.75..

Answer:

Take the coefficient of ''n'', divide it by 2, and raise it to the second power;

[tex]n^2+n+(\frac{1}{2})^2[/tex]

[tex]n^2+n+\frac{1}{4}=0[/tex]

[tex]=(n+\frac{1}{2} )^2[/tex]

Answer:

D or 4 square root 3

Step-by-step explanation:

using distance formula -12 square rooted - 2 square root 3 = -4squareroot3. So, after that you would square giving 48 then square root giving 4 square root 3. (-4 square root 2 and -32 square rooted cancel out giving 0)

Answer:

4.73

Step-by-step explanation:

4 8/11=4+8/11

=4/1+811

=(4/1×11/11)+8/11

=44/11+8/11=52/11

We know that

52/11

is the same as

52÷11

Then using

Long Division for 52 divided by 11

and rounding to a Max of 2 Decimal Places gives us

=4.73

Final answer:

The equivalent decimal to the mixed number 4 8/11 is 4.7273, achieved by dividing 8 by 11 to get 0.7273 and adding it to the whole number 4.

Explanation:

To write the mixed number 4 8/11 as a decimal, we need to convert the fractional part to decimal form and then add it to the whole number. To convert the fraction 8/11 to a decimal, we divide the numerator by the denominator using a calculator or long division.

Dividing 8 by 11 gives us approximately 0.7273. Now we add this decimal to the whole number 4 to get the decimal equivalent of the mixed number. The final result is 4.7273.

Remember that when rounding to four decimal places, if necessary, you look at the fifth decimal place to determine whether to round up or leave the fourth place as is. Since we do not have a fifth decimal place in this conversion, our four-decimal-place number is accurate as is.

Answer:

Step-by-step explanation:

mean=12.7413

median=6.75

mode=6

range=77

Answer:

mean=12.7413

median=6.75

mode=6

range=77

Step-by-step explanation:

Answer: 6x^2 + 17x + 12

Step-by-step explanation:

You multiply the two outside terms and the two inside terms then add

Answer:

135 grams

Step-by-step explanation:

Since there are 15 grams of powder in a 22oz serving, if you divide 198 by 22 you will get 9 total servings. If you multiply 15 by 9 you will get 135 total grams.

Answer:

adding salt makes the water freeze slower and evaporate slower too.

Step-by-step explanation:

While pure water freezes at 0°C (32°F), salt water needs to be colder before it freezes and so it usually takes longer to freeze. The more salt in the water, the lower the freezing point.

Answer:

Yes

Can I get brainliest

Answer:

Yes, I believe so.

Step-by-step explanation:

Answer:

31000 cm2

Step-by-step explanation:

Answer:

b=19

Step-by-step explanation:

2x(3x+5)+3(3x+5)= (3x+5)(2x+3)= 6x²+ 9x+10x+15=6x²+19x +15

6x² + 19x +15 = ax²+bx+c

a=6, b=19, c=15

Answer:

The answer is x-5 or "B" on edge

The longest line that can be drawn in a right rectangular prism (a box) is the diagonal from one corner to the opposite corner. This is called the space diagonal. It can be calculated using the Pythagorean theorem in three dimensions. In this case, the longest line is 16.8 cm.

The longest line that can be drawn in a right rectangular prism, also known as a box, is the diagonal drawn from one corner of the box to the opposite corner. This longest line is also known as the space diagonal of the box. To find the length of the space diagonal, we use the Pythagorean theorem in three dimensions, which is given by the formula d = √(l² + w² + h²), where l, w, and h are the length, width, and height of the box respectively.

In this case, the length l is 13 cm, the width w is 8 cm, and the height h is 7 cm. Thus, the length of the space diagonal is d = √((13 cm)² + (8 cm)² + (7 cm)²) = √(169 cm² + 64 cm² + 49 cm²) = √282 cm² = 16.8 cm. Therefore, the longest line segment that can be drawn in the box is 16.8 cm long.

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The longest line segment that can be drawn in the prism is approximately 16.79 cm long.

 First, we calculate the diagonal of the base of the prism, which is the rectangle with dimensions 13 cm by 8 cm.

The diagonal of this rectangle can be found using the Pythagorean theorem in two dimensions:

[tex]\[ d_{\text{base}} = \sqrt{l^2 + w^2} \][/tex]

[tex]\[ d_{\text{base}} = \sqrt{13^2 + 8^2} \][/tex]

[tex]\[ d_{\text{base}} = \sqrt{233} \][/tex]

 Next, we find the diagonal of the entire prism by considering the diagonal of the base and the height of the prism:

[tex]\[ d_{\text{prism}} = \sqrt{d_{\text{base}}^2 + h^2} \][/tex]

[tex]\[ d_{\text{prism}} = \sqrt{(\sqrt{233})^2 + 7^2} \][/tex]

[tex]\[ d_{\text{prism}} = \sqrt{282} \][/tex]

 Therefore, the longest line segment that can be drawn in the prism is the space diagonal, which is approximately:

[tex]\[ d_{\text{prism}} \approx \sqrt{282} \][/tex]

[tex]\[ d_{\text{prism}} \approx 16.79 \text{ cm} \][/tex]

 So, the longest line segment that can be drawn in the prism is approximately 16.79 cm long.

Answer:

[tex]-3.5[/tex]

Step-by-step explanation:

[tex] \frac{ - 5 - 2}{3 - 1} = \frac{ - 7}{2} = -3.5[/tex]

hope this helps you

Slope: [tex]-2/7[/tex]

Find the slope between your two points

[tex](x_{1} ,y_{1} )=(-5,3)\\(x_{2} ,y_{2} )=(2,1)[/tex]

Use the slope formula

[tex]y_{2} -y_{1} /x_{2} -x_{1}[/tex]

[tex]1-3/2--5[/tex]

[tex]-2/7[/tex]

Slope

[tex]-2/7[/tex]

Answer:

5

Step-by-step explanation:

30 years => 20

60 years => 10

90 years => 5

We will be left with 5 g of Cesium-137 after 90 years, given its half-life of 30 years and the initial quantity we have as 40 g.

Many elements tend to decompose over some time. The period over which an element reduces to half of itself in quantity is called the half-life of that substance.

The formula for the quantity of the element at a certain time t can be given as:

[tex]N_{t} = N_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}[/tex]

Where,

[tex]N_{t}[/tex] is the quantity of the element at time t,

[tex]N_{0}[/tex] is the initial quantity of the element,

[tex]{t_{1/2}[/tex] is the half-life of the element.

In the question, we are given that an element, Cesium-137 has a half-life of approximately 30 years.

We are asked to find the quantity of this element left after 90 years when we had an initial sample of 40 g.

To solve for the quantity left, we can use the formula for the quantity of the element at a certain time t can be given as:

[tex]N_{t} = N_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}[/tex]

Where,

[tex]N_{t}[/tex] is the quantity of the element at time t,

[tex]N_{0}[/tex] is the initial quantity of the element,

[tex]{t_{1/2}[/tex] is the half-life of the element,

by taking t = 90 years, [tex]N_{0}[/tex] = 40 g, [tex]{t_{1/2}[/tex] = 30 years, and [tex]N_{t}[/tex] = ?.

∴ [tex]N_{t} = N_{0}\left ( \frac{1}{2} \right )^{\frac{t}{t_{1/2}}}[/tex]

or, [tex]N_{t} = 40\left ( \frac{1}{2} \right )^{\frac{90}{30}}} g[/tex]

or, [tex]N_{t} = 40\left ( \frac{1}{2} \right )^{3}} g[/tex]

or, [tex]N_{t} = 40\left ( \frac{1}{8} \right ) g[/tex]

or, [tex]N_{t} = 5 g[/tex] .

∴ We will be left with 5 g of Cesium-137 after 90 years, given its half-life of 30 years and the initial quantity we have as 40 g.

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Answer:

3/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, convert 3/5 into 10ths.

3/5 = 6/10

Now, we know what 3/5 is equal to, we subtract.

9/10 - 6/10 = x

When we subtract, we get 3/10.

So that means, x =3/10

Hope this helps, have a great day, and stay safe.

How much do you owe?

Since each roommate will pay 20% of the $6,000 bill, you will owe 1 * 0.2 * 6000 = $1200.

What is 10% of the total repair bill?

10% of the total repair bill is 0.1 * 6000 = $600.

What will each roommate's 20% share be?

Each roommate's 20% share will be 0.2 * 6000 = $1200.

I hope this helps! Let me know if you have any other questions.