In a math class with 28 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 19 students who completed the assignment. There were 15 students who passed the test and also completed the assignment. What is the probability that a student passed the test given that they completed the homework

Answer:

k = ±2√5 + 3

Step-by-step explanation:

[tex]k=3+2\sqrt5\ or\ k=3-2\sqrt5[/tex]

[tex]k^2-6k=11[/tex]

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[tex]k^2-6k+(6\times\frac{1}{2})^2=11+(6\times\frac{1}{2})^2[/tex]

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[tex]k^2-6k+3^2=11+3^2[/tex]

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[tex](k-3)^2=11+3^2[/tex]

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[tex](k-3)^2=11+9[/tex]

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[tex](k-3)^2=20[/tex]

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[tex]k-3=\sqrt{20}\ or\ k-3=-\sqrt{20}[/tex]

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                                 [tex](k-3=\sqrt{20})[/tex]

[tex]k=\sqrt{20}+3\\ k=2\sqrt{5}+3[/tex]

____________________________________________________

                               [tex](k-3=-\sqrt{20})[/tex]

[tex]k=\sqrt{20}+3\\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

[tex]k=2\sqrt{5}+3\ or\ k=-2\sqrt{5}+3[/tex]

_____________________________________________________

I hope this helps you

:)

Answer:

8.5 cm

Step-by-step explanation:

volume = height × area of base

since this a square, area of base = x²

so 289 = 4 × x²

x² = 289 ÷ 4

x² = 72.25

so x = √72.25

x = 8.5cm

hope this helps

Answer:320 cubic cm

Step-by-step explanation:  if you  multiply 16x20m  you get 320  cm

Answer:

yes your answer is 45 degree

Answer:

105°

Step-by-step explanation:

There 360° in a circle, so...

360°-150°-105°=105°

check: 150°+105°+105°= 360°

[Answer] 105°

To find the better buy divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound.

The cost price per pound is the amount of money required to buy one pound of a brand or goods.

To find the cost price per pound, divide the total amount of cost of the goods to the total number of goods.

At one farmer’s market, bananas cost $0.80 per pound.

At another farmer’s market, bananas are sold in 5-pound bags for $4. 50 per bag. To compare it with first market price, divide the 5 pound bags with $4.50.

The cost of one bag in this market is,

[tex]C=\dfrac{4.50}{5}\\C=0.5625[/tex]

As this cost is less, thus, the cost of this market for one banana is less than the first market and so this is the better buy.

Hence, to find the better buy divide 4.50 by 5 to find the unit rate for the 5-pound bag, and compare that number to $0. 80 per pound.

Learn more about the cost price per pound here;

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here's the solution ~

As we know, we can calculate the circumference of a circle in terms of its diameter as :

[tex]\qquad \sf  \dashrightarrow \:c = \pi d[/tex]

where, c = circumference and d = diameter

And also, circumference of circle is terms of radius (r) is :

[tex]\qquad \sf  \dashrightarrow \:c = 2\pi r[/tex]

Now, let's move on to questions ~

[tex]\qquad \sf  \dashrightarrow \:3.14 \times 5.9 [/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx18.53 \: ft[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex] \qquad \sf  \dashrightarrow \: \approx10.048 \: ft[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:3.14 \times 6.1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx19.15 \: ft[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:2×3.14 \times 3.7[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx2×11.62 \: m[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx23.24 \: m[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:2×3.14 \times 6.2[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx2× 19.47 \: units[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx38.94 \: m[/tex]

・ ．━━━━━━━†━━━━━━━━━．・

[tex]\qquad \sf  \dashrightarrow \:2×3.14 \times 5.1[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx2×16.01 \: ft[/tex]

[tex]\qquad \sf  \dashrightarrow \: \approx \: 32.02m[/tex]

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Answer:

The roots you found should be [tex](3x-4)(x+1)=0[/tex], which shows that [tex]x = \frac{4}{3} \\ x=-1[/tex]

Step-by-step explanation:

You likely messed up when trying to one or both of the roots back into the equation.

Answer:

Step-by-step explanation:

To solve for x and y, take advantage of the relationships between angles and diagonals in a rhombus. Each diagonal bisects the vertex angle, and the acute angles in each right triangle are complementary.

__

The angles created by the diagonal at the lower left vertex are congruent:

  y° = 21°

__

The angles x° and y° are complementary:

  x° = 90° -21°

  x° = 69°

Answer:

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).

Answer:

1

Step-by-step explanation:

[tex] \tan( \frac{5\pi}{4} ) \times \frac{\pi}{180} = 1.19[/tex]

The question wants in radian, not in degrees since using the unit circle. Hope this helps

Answer:

a) 1

Step-by-step explanation:

Tan 5pi/4: 1

Tan (-5pi/4): -1

Tan 5pi/4 in degrees: tan (225°)

The length of the dilated line segment is 80 units.

Dilation is the increase or decrease in the size of a figure or object.

The segment with endpoints (10,40) and (70,120) is dilated by a factor of 4/5 to get (8, 32) and (56, 96).

The distance between points (8, 32) and (56, 96) is:

[tex]Distance = \sqrt{(96-32)^2+(56-8)^2} =80\ units[/tex]

The length of the dilated line segment is 80 units.

Find out more on dilation at: https://brainly.com/question/10253650

The amount of orange that Manny and Josh have leftover after eating lunch is 1.

A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

Oranges Manny has left = 1 - 4/9 = 5/9

Oranges Josh has left = 1 - 5/9 = 4/9

Oranges they both have left = 5/9 + 4/9 = 1

To learn more about subtraction of fractions, please check: https://brainly.com/question/915789

Answer:

20 square units

Step-by-step explanation:

as its a square, we just add all the sides together. like a+b+c+d..

5+5+5+5=20 units

distance : 15 units

coordinates :  (7,0) and (-8, 45)

slope:

[tex]\sf \rightarrow \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\sf \rightarrow \dfrac{45-0}{-8-7}[/tex]

[tex]\sf \rightarrow -3[/tex]

equation:

[tex]\hookrightarrow \sf y - 0 = -3(x-7)[/tex]

[tex]\hookrightarrow \sf y = -3x+21[/tex]

the y-intercept of this function:

[tex]\hookrightarrow \sf y = -3(0)+21[/tex]

[tex]\hookrightarrow \sf y =21[/tex]

distance between both y-intercept :

The fraction of the game that Daniel's team scores 2 or more runs is 1/4 of the game.

A box plot is used to study the distribution and level of a set of scores. Scores are distributed into 4 groups. Each group has a value of 25%

The first quartile, is the first line on the box. The first quartile represents 1/4 of the score.

To learn more about box plots, please check: https://brainly.com/question/27215146

Answer:

Volume: 37.7cm3

It will melt in 21 minutes.

Step-by-step explanation:

Volume of a sphere: 4/3 x pi x r^2

4/3 X pi x 3^2 = 37.7cm3

37.7/1.8=20.943 minutes

Answer:

Five feet

Step-by-step explanation:

H = A ÷ L

H = 65 ÷ 13

H = 5 ft

Answer:

A (0,3)

Step-by-step explanation:

The Y-intercept is where X equals 0  

When X equals zero, Y equals 3.

Answer:

22 feet

Step-by-step explanation:

The area of a circle is π · r².

So, step one is to figure out the radius, so taking that equation, we can say π · r² = 121π.

Divide both sides by π to get r² = 121

Then, you take the square root of both sides to leave r = 11.

The diameter is twice as long as the radius, so multiply 11 · 2 to get 22.

The diameter is 22 feet long.

Answer:

  234 square millimeters

Step-by-step explanation:

You want the area of the irregular polygon shown.

There are always several ways you can find the area of a figure like this. In the attachment we have shown extensions of the vertical and horizontal lines that will divide the figure into a triangle and two rectangles.

The triangle has a base of 12 mm and a height of 13 mm. Its area is ...

  A = 1/2bh

  A = 1/2(12 mm)(13 mm) = 78 mm²

The upper rectangle has a width of 8 mm and a length of 14 mm. Its area is ...

  A = LW

  A = (14 mm)(8 mm) = 112 mm²

The lower rectangle has a width of 4 mm and a length of 11 mm. Its area is ...

  A = (4 mm)(11 mm) = 44 mm²

The area of the figure is the sum of the areas of its parts:

  total area = triangle area + upper rectangle + lower rectangle

  total area = 78 mm² + 112 mm² + 44 mm² = 234 mm²

The area of the figure is 234 square millimeters.

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Answer:

17.5

Step-by-step explanation:

The area for a triangle is (base*height)/2 this means

(5*7)/2 = 17.5 units^2

Answer:

Step-by-step explanation:

base = b = 5 units

height = h = 7 units

[tex]\bf \boxed{\text{Area of triangle = $\dfrac{1}{2}bh$}}[/tex]

                           [tex]=\dfrac{1}{2}*5*7\\\\\\=\dfrac{35}{2}\\\\\\= 17.5 \ square \ units[/tex]

Answer:

6x - 8x + 4 + 36 - 9x

= 40 - 11x

Considering the double line graph, it is found that a good prediction for eighth grade enrollment in 2010 is of 165.

It states that:

In 2009, there were 150 students enrolled in the 8th grade, hence an estimate for 2010 should be of about 165 or 170 students.

More can be learned about graphs at https://brainly.com/question/24808124

Answer:

165

Step-by-step explanation:

Answer:

the 1/2w +22 one is a binomial

Step-by-step explanation:

a binomial is a equation with one two separate numbers AFTER simplifcation. so "1+1" is not a binomial because its equal to just 2, but "1 + x" is a binomial because its simplifed

Definition of a trapezoid: a quadrilateral with one pair of parallel sides

Thus PQRS is a trapezium because Line PQ is parallel to line SR

Hope that helps!

Answer:

C. $104

Step-by-step explanation:

First, we need to figure out what percent $120 is of $1500.

120 ÷ 1500 = 0.08 = 8%. So, $120 is 8% of $1500, and this is the percentage that'll be used to calculate Sunday's commission.

0.08 (8%) × 1300 = 104

Thus, you earned $104 on Sunday.

Step-by-step explanation:

For this problem, we need to use the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.

This gives us that the equation of the circle is (x-1)^2 + (y-1)^2 = 25.

The function [tex]y = -5t^2 + 125[/tex] of the nickel is quadratic function

It will take 5 seconds for the coin to hit the ground

The function is given as:

[tex]y = -5t^2 + 125[/tex]

When the nickel hits the ground, the value of the function is:

y = 0

So, we have:

[tex]-5t^2 + 125 = 0[/tex]

Subtract 125 from both sides

[tex]-5t^2 =- 125[/tex]

Divide both sides by -5

[tex]t^2 =25[/tex]

Take the square root of both sides

[tex]t = 5[/tex]

Hence, it will take 5 seconds for the coin to hit the ground

Read more about quadratic functions at:

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