origami is the Japanese art of paper folding the diagram below represents an unfolded paper kabuto a samuri warriors helmet which of the following are pairs of congruen segments? check all that apply ​

Answer:

x = 16

y = 11

Step-by-step explanation:

Let the larger number = x

Let the smaller number = y

x  - y = 5

x = 2*y - 6

Put the second equation into the first. Substitute for x

2y - 6 - y = 5                          

combine

y - 6 = 5

and 6 to both sides.

y - 6 + 6 = 5 + 6

Combine

y = 11

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

Find x

x - y = 5           Substitute for y

x - 11  = 5          Add 11 to both sides.

x - 11+11=5+11

x = 16

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=23.9\\ h=100 \end{cases}\implies V=\cfrac{\pi (23.9)^2(100)}{3} \\\\\\ V=\cfrac{57121\pi }{3}\implies V\approx 59816.97\implies \stackrel{\textit{rounded up}}{V=59817} \\\\[-0.35em] ~\dotfill[/tex]

now, for the second one, we know the diameter is 10, thus its radius is half that or 5.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ V=225 \end{cases}\implies 225=\cfrac{\pi (5)^2 h}{3}\implies 225=\cfrac{25\pi h}{3} \\\\\\ \cfrac{225}{25\pi }=\cfrac{h}{3}\implies \cfrac{9}{\pi }=\cfrac{h}{3}\implies \cfrac{27}{\pi }=h\implies 8.59\approx h\implies \stackrel{\textit{rounded up}}{8.6=h}[/tex]

About 2 and a half hours

Answer:

A sphere

Step-by-step explanation:

A sphere is a round three dimensional object with no sharp corners or vertexes.  Since a basketball fits this criteria, it is a sphere.

210. she has 210 ways to choose 6 friends from the list of 10 to sit at the table closest to the head table no matter the order.

This is a problem of combinations and can be solved using the equation [tex]nC_{k}=\frac{n!}{k!(n-k)!}[/tex], where n! and k! is the factorial of a number. The factorial is defined in principle as the product of all positive integers from 1 (ie, natural numbers) to n.

She has a list of 10 friends and we want to know in how many ways she can choose 6 friends.

Using the combinations equation, with n = 10 and k = 6:

[tex]10C_{6}=\frac{10!}{6!(10-6)!}=\frac{10!}{6!(4!)}=\frac{10.9.8.7}{4.3.2.1}=\frac{5040}{24} =210[/tex]

Answer:

It's actually right and scalene

Step-by-step explanation:

Since there is a ninety degree angle, it isn't obtuse or acute because the angle is a right angle. And since all the side lengths are different, it must be scalene in comparison to isoceles or equilateral.

The given triangle is Right angled triangle and Scalene triangle i.e. option A and E.

Triangle is a two dimensional shape having three side and sum of all angles is equals to .

We have,

A triangle with,

Angles of 90°, 53°, 37° and

Sides 3, 4, 5.

So,

We know that,

When a triangle have any angle equals to 90° then it is a Right angled triangle.

Now,

When a triangle have any three sides unequal and all three angles are of different measures, then it is Scalene triangle.

So,

From the above mentioned statements we can say that triangle is Right angled and Scalene triangle.

Hence, we can say that the given triangle is Right angled triangle, Scalene triangle.

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The focus point of the parabola is (2,-2).

ANSWER

[tex](2,- 1)[/tex]

EXPLANATION

The given parabola is

[tex]y = \frac{1}{4} {x}^{2} - x - 1[/tex]

We need to write this parabola in the vertex form by completing the square,

[tex]y = \frac{1}{4} ( {x}^{2} - 4x) - 1[/tex]

[tex]y = \frac{1}{4} ( {x}^{2} - 4x + 4) - \frac{1}{4} \times 4 - 1[/tex]

[tex]y = \frac{1}{4} (x - 2 )^{2} - 2[/tex]

[tex] {(x - 2)}^{2} = 4(y + 2)[/tex]

The vertex is

(2,-2)

The focal length is

[tex]p = 1[/tex]

The focus is

[tex](2,-2 + 1)[/tex]

[tex](2,- 1)[/tex]

To determine how long it will take for $10,000 to triple with a continuous compounded interest rate of 5.5%, we use the continuous compound interest formula. Solve the equation for t by taking the natural logarithm of both sides and dividing by the interest rate, which yields t = ln(3) / 0.055.

The subject at hand deals with Continuous Compound Interest. The formula used to calculate this is A = Pe^(rt), where A is the final amount, P is the initial principal, r is the yearly interest rate and t is the time in years.

In this case, the initial principal P is $10,000, the final amount (A) we want is $30,000 (because we want to triple the money), and the rate r is 5.5% or 0.055 as a decimal. We want to find t.

Plugging into the formula, we get 30000 = 10000 * e^(0.055t). Dividing both sides by 10000 yields 3 = e^(0.055t). If we take the natural log (ln) of both sides, the equation simplifies to ln(3) = 0.055t. Finally, solving for t, we get t = ln(3) / 0.055.

This will give you the number of years it'll take for the money to triple at an interest rate of 5.5% compounded continuously.

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Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio, hence

[tex]a_{8}[/tex] = 6 × [tex](-1/3)^{7}[/tex] = 6 × - [tex]\frac{1}{3^{7} }[/tex] = 6 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{2}{729}[/tex]

Answer:

-1/2

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

    = (1-2)/(3-1)

    = -1/2

The slope is -1/2

Answer:

The slope is -1/2.

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{1-2}{3-1}=\frac{2}{-1}=-\frac{1}{2}[/tex]

[tex]\Large\textnormal{Therefore, the slope is -1/2.}[/tex]

it is 8/15 because if you count all the groups it is 15 and if you count all the numbers 1 it is 8 which is 8/15

To determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of a data set, you need to follow these steps:

1. Order the Data Set: Arrange the data set in ascending order.

2. Minimum and Maximum: Identify the smallest and largest values in the ordered data set.

3. Median (Q2): This is the middle value of the data set. If there is an odd number of observations, it is the middle one. If there is an even number of observations, it is the average of the two middle values.

4. First Quartile (Q1): This is the median of the first half of the data (the lower 50%). If the number of observations is odd, do not include the median in this half.

5. Third Quartile (Q3): This is the median of the second half of the data (the upper 50%). If the number of observations is odd, do not include the median in this half.

Let's consider an example data set to illustrate these steps:

Example Data Set: 3, 7, 8, 5, 12, 14, 21, 13, 18

1. Order the Data Set: 3, 5, 7, 8, 12, 13, 14, 18, 21

2. Minimum and Maximum:

  - Minimum = 3

  - Maximum = 21

3. Median (Q2):

  - Since there are 9 data points (odd number), the median is the 5th value.

  - Median = 12

4. First Quartile (Q1):

  - The lower half of the data (excluding the median) is: 3, 5, 7, 8

  - Median of this lower half = (5 + 7) / 2 = 6

5. Third Quartile (Q3):

  - The upper half of the data (excluding the median) is: 13, 14, 18, 21

  - Median of this upper half = (14 + 18) / 2 = 16

So, the five-number summary for the example data set is:

- Minimum = 3

- First Quartile (Q1) = 6

- Median (Q2) = 12

- Third Quartile (Q3) = 16

- Maximum = 21

The answer is c.4a4

Answer:

Step-by-step explanation:

I am very good at Pythagorean theorem I did it this year. So A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17

To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific

Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²

Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.

Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.

I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.

Answer:

a) i) No

ii) Probability of drawing a diamond and then spade without replacement is 0.0637.

b) i) Yes

ii) Probability of drawing a diamond and then spade with replacement is 0.0625

Step-by-step explanation:

Part a) Without replacement:

i) Are these events independent?

No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.

ii) Determine the probability of drawing a diamond and then a spade without replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after taking diamond = 52 -1 =51

Spades = 13

Probability of drawing a spade  = 13/51

Probability of drawing a diamond and then spade = 13/52 * 13/51

= 169/2652

=0.0637

So, Probability of drawing a diamond and then spade without replacement  is 0.0637

Part b) With replacements

i) Are these events independent?

Input Yes or No:

Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.

ii) Determine the probability of drawing a diamond and then a spade with replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after replacing diamond = 52

Spades = 13

Probability of drawing a spade  = 13/52

Probability of drawing a diamond and then spade = 13/52 * 13/52

= 169/2704

=0.0625

So, Probability of drawing a diamond and then spade with replacement is 0.0625

The first two events are not independent, with a probability P = 0.0637

The second pair of events is independent, and the probability is P = 0.0625

First, all the cards on the deck have the same probability of being randomly drawn, which will be p = 1/52.

A) Now, if Lacy first draws a diamond card, now the number of cards in the deck are less (now there are 51 cards on the deck). So the probability of drawing now a spade is larger than before. Then the first two events are not independent.

The probability of drawing a diamond card at first is:

P = 13/52 (because there are 13 diamonds and a total of 52 cards).

The probability of drawing a spade after is:

Q = (13/51)

The joint probability is the product of the individual probabilities, this will give:p = P*Q = (13/52)*(13/51) = 0.0637

B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).

The probability of drawing a diamond is:

P = 13/52

Now we replace the diamond card drawn.

The probability of drawing a spade will be:

Q = 13/52

The joint probability is:

p = P*Q = (13/52)^2 = 0.0625

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Answer:

A triangle

Step-by-step explanation:

If you slice open all of these shapes you will see a circle except the triangle.

Answer:

A triangle because the other shapes are to do with circles.

Answer A.

Answer:

Step-by-step explanation:

i) Recursive rule is

[tex]a_{n+1} =a_n-10[/tex]

2) Explicit rule for the sequence is

this is arithmetic sequence with a = -1 and d = 15

Hence

[tex]a_n=-1+15(n-1)\\a_n=15n-16[/tex]

3) [tex]P(A and B) = \frac{2}{25} (\frac{5}{6} )\\=\frac{1}{15}[/tex]

4) Sample men = total/no of entries

=[tex]\frac{409}{10} =40.9[/tex]

=41

Answer:

[tex]17.4\ years[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=?\ years\\ P=\$3,000\\ r=0.04\\n=12\\ A=\$6,000[/tex]  

substitute in the formula above  

[tex]\$6,000=\$3,000(1+\frac{0.04}{12})^{12t}[/tex]  

[tex]2=(\frac{12.04}{12})^{12t}[/tex]  

Applying log both sides

[tex]log(2)=log[(\frac{12.04}{12})^{12t}][/tex]  

[tex]log(2)=(12t)log[(\frac{12.04}{12})][/tex]  

[tex]t=log(2)/[(12)log(\frac{12.04}{12})]=17.4\ years[/tex]  

the figure is four sided so it a heptagon

for a heptagon, the sum of all interior angles is 900°

i.e. x+(x+50°)+(x+50°)+(x+50°)+×+×+(x+50°)=900°

or, 7x+200°=900°

or, 7x=700°

or, x= 100°

Answer:

The value of x = 100 ⇒ answer B

Step-by-step explanation:

* Lets study how to find the sum of the interior angles of any polygon

- We can find the sum of the measures of the interior angles of any

 polygon using the rule (n - 2) × 180°, where n is the number of its

 sides or its angles

* Now lets solve the problem

- The polygon has 7 sides and 7 angles

- The measure of three angles of them is x°

- The measure of four angles of them is (x + 50)°

∵ The sum of the interior angles = (n - 2) × 180°

∵ n = 7

∴ The sum of the interior angles = (7 - 2) × 180° = 5 × 180° = 900°

∵ Three angles each measured x°

∵ Four angles each measured (x + 50)°

∴ 3(x°) + 4(x + 50)° = 900° ⇒ simplify it

∴ 3x + 4(x) + 4(50) = 900 ⇒ add the like terms

∴ 3x + 4x + 200 = 900 ⇒ add the like terms

∴ 7x + 200 = 900 ⇒ subtract 200 from both sides

∴ 7x = 700 ⇒ divide both side by 7

∴ x = 100

* The value of x = 100

Step-by-step explanation:

v= 1/2x1 3/7

v= 7/8 units 3

Answer:

Final answer is [tex]\frac{5}{36}[/tex].

Step-by-step explanation:

Given that two 6-sided number cubes are rolled. Now we need to find about what is the possibility of rolling a sum of 8​.

From the sample space, you can see that there are total 36 possible outcomes.

out of those outcomes, there are only 5 outcomes that has sum = 8

which are {(2,6), (3,5), (4,4), (5,3), (6,2)}.

Hence probability of rolling a sum of 8 [tex]=\frac{5}{36}[/tex].

Hence final answer is [tex]\frac{5}{36}[/tex].

Answer:

(6 , 7.25)

Step-by-step explanation:

Given in the question coordinates (-4,-9) and (21,31.625)

x1 = -4

y1 = -9

x2 = 21

y2 = 31.625

Ratio

a : b

2 : 3

Formula to use

x = x1 + [tex]\frac{a}{a+b}[/tex](x2-x1)

y = y1 + [tex]\frac{a}{a+b}[/tex](y2 -y1)

Plug values on the formula

x = -4 + [tex]\frac{2}{2+3}(21+4)[/tex]

x = 6

y = -9 + [tex]\frac{2}{2+3}(31.625+9)[/tex]

y = 7.25

Co-ordinates of the point which divide the line into 2:3 is

(6 , 7.25)

Final answer:

To divide a line segment with endpoints (-4, -9) and (21, 31.625) in a 2:3 ratio, we use the section formula to find the partition point, which is (21, 7.25).

Explanation:

The student is asking how to find the point that divides a line segment in a particular ratio, which is a common problem in coordinate geometry. Given the end points of the line segment at (-4,-9) and (21, 31.625) and the ratio of 2:3, we can use the section formula to find the required point.

Here's how we do it step by step:

Applying the formula, the coordinates of the point (x, y) are:

x = (-4×3 + 21×2)/5 = (63 + 42)/5 = 105/5 = 21

and

y = (-9×3 + 31.625×2)/5 = (-27 + 63.25)/5 = 36.25/5 = 7.25

Therefore, the coordinates of the partitioning point are (21, 7.25).

Answer:

the real answer is about 0.80

Step-by-step explanation:

so it is asking you about what proportion of the population has a favorite social network, and you see that there is a category that is a no favorite and site A B and C are the sites that are favorites. You add 0.24 + 0.30 + 0.26          and you get 0.80. And that is how you get 0.80

Answer:

Answer is D 82.4%  

Step-by-step explanation:

Got it right on the test :)

The probability of on-time arrival in class given that the subject is biology is 82.4%

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

From the definition, the probability is the ratio of total favourable outcome to total outcome.

From the data table, the probability of on-time arrival in class given that the subject is biology:

= 82.4%

Thus, the probability of on-time arrival in class given that the subject is biology is 82.4%

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1 and 5 are the same angle, so if added together equal 100, then each angle is 50 degrees.

Angle 1 and angle 2 make a straight line which means they need to equal 180 degrees.

Angle 2 = 180 - 50 = 130 degrees.

Answer:

angle 2= 130

Step-by-step explanation:

180-50=130

Let D = difference between mean and median of data.

Mean = (22 + 8 + 10 + 18 + 12 + 20)/6

Mean = 90/6

Mean = 15

Let m = median

m = 8, 10, 12, 18, 20, 22

m = (12 + 18)/2

m = 30/2

m = 15

D = M - m

D = 15n- 15

D = 0

Answer:

2 44⁄125 [2,352] → Product

507⁄5000 [0,1014] → Product

6 3⁄625 [6,0048] → Product

9 → Quotient

1½ [1,5] → Quotient

2700 → Quotient

Step-by-step explanation:

Treat the decimals as whole numbers by moving the decimal marks all the way to the end of each decimal first, evaluate, then move the decimal mark back to the left the number of times as you started on for both decimals in total.

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

X will equal 8 and y would equal 3

The solution to the system of equations -2x + 9y = 11 and -5x + 2y = -34 is found using the elimination method. The solution is x = 8 and y = 3.

The system of equations provided appears to be:

To solve this system, we can use the method of substitution or elimination. In this case, we'll use the elimination method. First, we want to manipulate the equations so that when we add them together, one of the variables gets eliminated.

Let's multiply the first equation by 5 and the second equation by 2:

Now, we subtract the second equation from the first:

-10x + 45y - (-10x + 4y) = 55 - (-68)

Which simplifies to:

41y = 123

Divide both sides by 41 to find the value of y:

y = 123 / 41 = 3

Now, substitute y = 3 into one of the original equations to solve for x. We'll use the first equation:

-2x + 9(3) = 11

-2x + 27 = 11

-2x = 11 - 27

-2x = -16

Divide both sides by -2:

x = -16 / -2 = 8

The solutions to the system of equations are x = 8 and y = 3.

Answer:

Eric's weekly salary is $680.77

Step-by-step explanation:

$35,400 divided by the number of weeks in a year, Which is 52. 52/35,400=680.77

Answer: He can predict 16 balls

Step-by-step explanation:

Answer:

16 balls; c

Step-by-step explanation: