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Elan Coil [88]
3 years ago
10

There are 20 children in the cast of a class play,

Mathematics
1 answer:
puteri [66]3 years ago
3 0
D would be your answer
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Olivia flips a two-sided counter and then spins a spinner with six equal-size sections labeled 1 through 6. One side of the coun
Novay_Z [31]

Answer:

12

Step-by-step explanation:

A 2 - sided counter ; (red, yellow)

A spinner (1,2,3,4,5,6)

Number of trials = 80

P(red and number > 3) :

P(red) = 1/2 ;

P(number >3) : numbers greater Than 3 = (4, 5, 6)

Hence, P(number <3) = 3 /6 = 1/2

Theoretical probability = 1/2 *1/2 = 1/4

Expected number of outcomes :

1/4 * number of trials

1/4 * 80 = 20

Experimental outcome :

Relative frequency = number of outcomes / number of trials

Relative frequency = 2/5

Hence,

2/5 = number of outcomes / 80

Cross multiply :

160 = number of outcomes * 5

Number of outcomes = 160 /5 = 32

Actual outcomes = 32

Difference between actual and expected :

32 - 20 = 12

7 0
3 years ago
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.​
Naily [24]

Answer: 1436 units cubed (3.14) or 1437 units cubed (π)

Step-by-step explanation:

answer depends on if you substitute in 3.14 for π or not

8 0
3 years ago
For the function f(x)=ax^3+bx^2-5x+9, determine the values of a and b so that f(-1)=12 and f'(-1)=3
Alecsey [184]

If

<em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² - 5<em>x</em> + 9

then

<em>f '(x)</em> = 3<em>ax </em>² + 2<em>bx</em> - 5

Given that <em>f</em> (-1) = 12 and <em>f</em> '(-1) = 3, we get the system of equations

-<em>a</em> + <em>b</em> + 5 + 9 = 12

3<em>a</em> - 2<em>b</em> - 5 = 3

or

-<em>a</em> + <em>b</em> = -2

3<em>a</em> - 2<em>b</em> = 8

Multiply through the first equation by 2 and add it to the second one to eliminate <em>b</em> and solve for <em>a</em> :

2(-<em>a</em> + <em>b</em>) + (3<em>a</em> - 2<em>b</em>) = 2(-2) + 8

-2<em>a</em> + 2<em>b</em> + 3<em>a</em> - 2<em>b</em> = -4 + 8

<em>a</em> = 4

Substitute this into the first equation above to solve for <em>b</em> :

-4 + <em>b</em> = -2

<em>b</em> = 2

4 0
3 years ago
Tara received 28 out of 35 points on her last math test. What percentage score did the teacher record in her grade book for Tara
ZanzabumX [31]

Answer:

80%

Step-by-step explanation:

28/35 = 0.8

Divide. Convert a decimal to a percent by multiplying times 100.

0.8 × 100 = 80

Tara earned an 80%

You could use a calculator as described above or using mental math or pencil and paper:

28/35 = 4/5

Simplify.

4/5 = 8/10 = 80/100

Percent means per hundred, change 28/35 to hundredths as above.

Tara (still) gets an 80%.

4 0
2 years ago
10) Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangen
lora16 [44]
Those two angles are congruent.

_____
The angles are corresponding parts of congruent triangles (CPCT). Triangles OBA and OCA are right triangles congruent by the HL postulate. The "H" is segment OA. The "L" is the radius, OB or OC. Of course the angles at B and C are 90° as with any radius and tangent line.
5 0
3 years ago
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