Find the missing angle. 60° 80° 90° 200

Answer:

a=108;b=36;c=72

Step-by-step explanation:

Answer:

a = 108°

b = 36°

c = 72°

Step-by-step explanation:

Note : the sum of the interior angles of a regular pentagon = 540°

Then

The measure of one interior angle of a reg pentagon =540/5 = 108°

Therefore a = 108°

c = 180 - 108 = 72°

SRT is a new isosceles triangle then :

[tex]b=\frac{180-108}{2} = \frac{72}{2} =36[/tex]

Answer:

3

Step-by-step explanation:

The N1, N6 and N8 national highways meet in Bloemfontein,

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Answer:

P(king or diamond) = P(king) + P(diamond) - P(king and diamond) P(king or diamond) = (4/52) + (13/52) - (1/52) P(king or diamond) = 16/52 Page 5 P(king or diamond) = 4/13.

Answer:

4a^2+48a+288+(fraction)1800/a-6

Step-by-step explanation:

The distribution of y is [tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]

The given parameters are:

Probability of success, p = 60%

Sample size, n = 5

The distribution of y is represented as:

[tex]P(y) = ^nC_y * p^y * (1 - p)^{n-y}[/tex]

So, we have:

[tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]

Hence, the distribution of y is [tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]

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Answer:

Step-by-step explanation:

Parabola:

   [tex]\sf f(x) =\dfrac{-1}{2}x^2+7x - 5\\\\a = \dfrac{-1}{2} \ ; b = 7 \ ; \ c = -5[/tex]

[tex]\sf x = \dfrac{-b}{2a}\\\\x =\dfrac{-7}{2*\dfrac{-1}{2}}\\\\ = \dfrac{-7}{-1}[/tex]

x = 7

Now, to find the y-value substitute this in the equation

               [tex]\sf f(x) = \dfrac{-1}{2}*7^2+7*7-5\\\\ =\dfrac{-49}{2}+49-5\\\\ = \dfrac{-49}{2}+44\\\\ = \dfrac{-49}{2}+\dfrac{88}{2}\\\\= \dfrac{39}{2}[/tex]

[tex]\boxed{Vertex(7 ,\dfrac{39}{2})}[/tex]

b) The value of a is negative. So, the parabola is open down words and the maximum value is given by the y-coordinate of the Vertex.

             [tex]\sf \boxed{Maximum \ value= \dfrac{39}{2}}[/tex]

[tex]\sf c) Range = [\dfrac{39}{2}, -infinity)[/tex]

Answer:

(a) (7,39/2)

(b) Maximum, 39/2

(c) y ≤ 39/2

(d) Increase when x < 7 and decrease when x > 7

Step-by-step explanation:

Given the parabola:

[tex]\displaystyle \large{f(x)=-\dfrac{1}{2}x^2+7x-5}[/tex]

( A ) Find the vertex

In order to find the vertex, let’s use calculus for this one. Recall the power rules for differentiation:

Power Rules

[tex]\displaystyle \large{f(x)=x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant)}}[/tex]

Derivative Definition

Derive the parabola:

[tex]\displaystyle \large{f'(x)=-\dfrac{1}{2}(2)x^{2-1} + 7(1)x^{1-1} -0}\\\\\displaystyle \large{f'(x)=-x+7}[/tex]

Since vertex has slope = 0 —> e.g f'(x) = 0:

[tex]\displaystyle \large{0=-x+7}\\\\\displaystyle \large{-x=-7}\\\\\displaystyle \large{x=7}[/tex]

Substitute x = 7 in f(x):

[tex]\displaystyle \large{f(7)=-\dfrac{1}{2}(7)^2+7(7)-5}\\\\\displaystyle \large{f(7)=-\dfrac{1}{2}(49)+49-5}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+44}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+\dfrac{88}{2}}\\\\\displaystyle \large{f(7)=\dfrac{39}{2}}[/tex]

Therefore, the vertex is at (7,39/2)

( B ) Determine if max or min then find the value

Since the parabola opens downward then there only exists maximum value. The maximum value is the y-value of vertex at x-value of vertex. Henceforth:

( C ) Find range

For parabola, range is minimum value </≤ y </≤ maximum value. We know that parabola has maximum value of 39/2 but no minimum value so we can just ignore it then we’d have:

[Note: < and > are for open-dot meaning the value will not be included —> e.g x > 4 means 4 isn’t included in.]

( D ) Find the interval when function is increasing and when it’s decreasing

For parabola, the function will increase only if f'(x) or slope > 0 and will decrease only f'(x) < 0.

We know, from part A that the derivative is:

[tex]\displaystyle \large{f'(x)=-x+7}[/tex]

Therefore, when f'(x) > 0 —> e.g -x + 7 > 0:

[tex]\displaystyle \large{-x+7 > 0}\\\\\displaystyle \large{-x > -7}\\\\\displaystyle \large{x < 7}[/tex]

When f'(x) < 0 —> e.g -x + 7 < 0:

[tex]\displaystyle \large{-x+7 < 0}\\\\\displaystyle \large{-x < -7}\\\\\displaystyle \large{x > 7}[/tex]

Therefore, the function will increase when x < 7 and will decrease when x > 7.

Answer:

arc BX = central angle BCX

inscribed BNX = 1/2 of central angle BCX

inscribed BNX = 1/2 of arc BX

Step-by-step explanation:

arc BX = central angle BCX

inscribed BNX = 1/2 of central angle BCX

inscribed BNX = 1/2 of arc BX

The circumference of the circle that Jason drew is gotten as; 62.80 inches

Since Jason lifted the pen and pulled the chain as far as it would reach before drawing a circle, then it means that;

radius of circle; r = 10 inches

Formula for circumference is;

C = 2πr

Thus;

C = 2 * 3.14 * 10

C = 62.80 inches

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The measure of each angle is 43.25 and 46.75

The attached image represents the missing piece in the question.

From the image, we can see that:

3x - 13 + 5x - 47 = 90 ---- complementary angles

Evaluate the like terms

8x = 150

Divide by 8

x = 18.75

Substitute x = 18.75 in the given angles

3x-13 = 3 * 18,75 - 13 = 43.25

5x -47 = 5 * 18.75 - 47 = 46.75

Hence, the measure of each angle is 43.25 and 46.75

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Answer:

[tex]\boxed{\sf \dfrac{14}{95}}[/tex]

Explanation:

Black ribbons = 8 ribbons

Green ribbons = 12 ribbons

Total ribbons: 12 + 8 = 20 ribbons

[tex]\sf Probability = \dfrac{Favorable \ Outcomes}{Total \ Possible \ Outcomes}[/tex]

For Lila:

[tex]\sf Lila \ picks \ black \ : \ \dfrac{8}{20}[/tex]

Left black ribbons: 8 - 1 = 7 black ribbons

Left total ribbons: 20 -1 = 19 total ribbons

For Jessica:

[tex]\sf Jessica \ picks \ black \ : \ \dfrac{7}{19}[/tex]

Probability that they both pick black ribbons:

[tex]\sf \rightarrow \dfrac{8}{20} \ x \ \dfrac{7}{19}[/tex]

[tex]\sf \rightarrow \dfrac{14}{95}[/tex]

Answer:

See below ~

Step-by-step explanation:

Perimeter

Area

Answer:

(amounts could be:)

Katia: $3.50

Mateo: $1.75

Step-by-step explanation:

Remember that a quarter = $0.25, 4 quarters = $1.00

after an hour of playing games in the arcade, Katia has $1.75 more than Mateo

lets say that Katia has (random amount)$3.50(14 quarters) and Mateo has $1.75 less than that.

$3.50 - $1.75 = $1.75

Out of all 252 twelfth graders, 114 rode in a car to school

The proportion of students that rode in a car is given as:

p = 45.24%

So, the number of students that rode in a car is:

Students = 45.24% * 252

Evaluate the product

Students = 114.008

Approximate

Student = 114

Hence, 114 rode in a car to school

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Answer:

5.75

Step-by-step explanation:

If

1 box = 8 tomatoes

x boxes = 46 tomatoes

1 = 8

x = 46

You cross multiply giving you

8x = 46×1

8x = 46

8x/8 = 46/8

x = 5.75

For the basket with 4 different types of marbles, there are  4,096 combinations in which we can select 6 marbles (in order).

Here we need to identify the number of selections. We have 6 selections (assuming that order matters).

Now we need to find the number of options for each of these. We know that there are 4 different colors of marbles, then for each selection, we have 4 options:

The total number of combinations is given by the product between the numbers of options, so we have:

C = 4*4*4*4*4*4 = 4,096 combinations.

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Answer:

1. Find the prime factorization of each number.

2. Write each number as a product of primes, matching primes vertically when possible.

3. Bring down the same numbers in each column and the remaining numbers in each column.

4. Multiply the factors to get the LCM.

for example the lcm of 24 and 36

= 24 = (2 × 2 × 2 × 3) = 2^3 × 3^1

 and 36 = (2 × 2 × 3 × 3) = 2^2 × 3^2

LCM(24, 36) = 2^2 × 3 × 2 × = 72

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The relative frequency table is:

Class         Frequency  Relative frequency

40 - 50         4                     0.1

50 - 60          6                     0.15

60 - 70           11                     0.18

70 - 80            9                     0.23

80 - 90              7                    0.18

90 - 100             3                   0.08

The relative frequency measures how often a value appears relative to the sum of the total values. The class width is 10. The class width is the difference between the upper and lower boundary (e.g. 100 - 90).

Frequency is the number of times the numbers in the class interval appear in the data set. Relative frequency is the frequency of a class interval divided by the total frequency of the data set.

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Answer:

question is not correct

Step-by-step explanation:

3(x+2)=11+3x+5

3x+6=11+3x+5, once 3x is subjected from both sides it becomes unsolvable

Answer: Infinite solution

Step-by-step explanation: 3x + 6 = 11 + 3x - 5

                                             -3x

6 = 11 - 5

6 = 6

Answer: 1 What???

Step-by-step explanation:

The answer will be option D which is to Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9.

Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of sample is important in an experiment, that is, to carry it out in a random way.

Given that:-

A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded.

Assign the homework questions the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9. These represent the questions that will be graded.

Hence the answer will be option D which is to Assign the homework questions to the numbers 0–9. Use a random number table to select the first three unique numbers between 0 and 9.

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Answer:

Step-by-step explanation:

Answer:

i agree with the other anwser!!

Step-by-step explanation:

The answer is C.

Step-by-step explanation:

I can't explain but I literally just did this question and I got it right

Expand 13 as 10 + 3.

10 = 2×5, so

13 = 2×5 + 3×1

or

13 = 2×5¹ + 3×5⁰ = 23₅

Answer:

6

Step-by-step explanation:

The ratio of boys to girls is 2:5

let the number of boys be 2x -------(i)

and number of girls be 5x

and the total number of students is 21

therefore we know that..

2x+5x = 21

on solving for x,

7x=21

x= 21/7

x=3

now, by putting the value of x in (i),

2x = 2×3 = 6

therefore, there are 6 boys in the classroom.

you find the no. of girls similarly.

hope it helps !!...

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