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adell [148]
3 years ago
11

Catherine 168 pieces of gum playing at a bean bag toss in the county fair at school she gave three to every student in her math

class she has 8 remaining how many students are in her class
Mathematics
1 answer:
Drupady [299]3 years ago
7 0

Givens

Let the number of students in the class be x

Let the number of pieces of gum she gave out be 3x

Equation

3x + 8 = 168 This will not work out evenly. Let's try x - 1. The reason for that is because she may not give out anything to herself.

3(x - 1) + 8 = 168      This doesn't work either.

Well we have to choose. It's a rounding problem.

3x + 8 = 168     Subtract 8 from both sides.

3x = 168 - 8      Combine

3x = 160           Divide by 3 on both sides.

x = 160 / 3

x = 53.333333333

Since that can't be, we could say there were 53 students.

3x

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.
mario62 [17]

Answer:

(x-7)^2+(y-5)^2=1

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

<u>Center of the circle:</u>

  • The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)

(x_m, y_m) = (7,5)

This is the center coordinate of our circle.

<u>Radius: </u>

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}

r = \sqrt{(6-7)^2+(5-5)^2}

r = \sqrt{1^2}

r = 1

<u>Equation of the circle: </u>

The equation is written as:

(x-a)^2+(y-b)^2=r^2

here, (a,b) are the center points of the circle

in our case this is (a,b)=(x_m,y_m)=(7,5)

and r = 1

(x-7)^2+(y-5)^2=1^2

(x-7)^2+(y-5)^2=1

This is the equation of the circle!

3 0
3 years ago
Someone explain it please
Alina [70]

9514 1404 393

Answer:

  ∠A = 44°

Step-by-step explanation:

In order to find the measure of angle A, you need to know the value of the variable x. This means you need some relation that you can solve to find x.

Happily, that relation is "the sum of angles in a triangle is 180°." This means ...

  84° +(x +59)° +(x +51)° = 180°

  (2x + 194)° = 180° . . . collect terms

  2x = -14 . . . . . . . . . . divide by °, and subtract 194

  x = -7 . . . . . . . . . . . .divide by 2

Now, the measure of angle A is ...

  ∠A = (x +51)° = (-7 +51)°

  ∠A = 44°

4 0
3 years ago
PLZ HELP<br> (3x+3/4x) - (6+1/2) = 4x<br> Solve for x
goldfiish [28.3K]

x=-26 is the final anwser :)

5 0
3 years ago
15 POINTS WITH BRAINLIEST!!! TIMED TEST HELP!!!
podryga [215]

Answer:

D

Step-by-step explanation:

since it's a multiplication consider the two factors one by one

cubic root of y^6 = y^(6/3) = y^2

cubic root of 8x^3= 2x^(3/3)= 2x

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6 0
3 years ago
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct resul
o-na [289]

Answer:

H0:p= 0.80                 H1: p< 0.80  one tailed test

Step-by-step explanation:

We state the null and alternative hypotheses as that the results are 80 % against the claim that the results are less than 80%.

H0:p= 0.80                 H1: p< 0.80  one tailed test

p2= 0.8 , p1= 74/97= 0.763

q1= 1-0.763= 0.237    q2= 0.2

The level of significance is 0.05 .

The Z∝= ±1.645 for ∝= 0.05

The test statistic used here is

Z= p1-p2/ √pq/n

Putting the values:

Z= 0.763 -0.8 / √ 0.8*0.2/97

z= -0.037/ 0.0406

z= -0.9113

The Z∝ = ±1.645 for ∝= 0.05 for one tailed test.

As the calculated value  does not fall in the critical region  we fail to reject the null hypothesis. There is not sufficient evidence to support  the claim that such polygraph results are correct less than 80% of the time.

Using the normal probability table.

P (Z <  -0.9113)= 1- P(z= 0.9311) = 1- 0.8238= 0.1762

If P- value is smaller than the significance level reject H0.

0.1762> 0.005  Fail to reject H0.

8 0
3 years ago
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