Kala's final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 82 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.

Answer:

Step-by-step explanation:

[tex]10 + {(2 \times 3)}^{2} \div 4 \times {( \frac{1}{2}) }^{3} [/tex]

To raise a product to a power, raise each factor to that power

[tex] = 10 + 4 \times 9 \div 4 \times {( \frac{1}{2} )}^{3} [/tex]

To raise a fraction to a power, raise the numerator and denominator to that power

[tex] = 10 + 4 \times 9 \div 4 \times \frac{1}{8} [/tex]

Any expression divided by itself equals 1

[tex] = 10 + 1 \times 9 \times \frac{1}{8} [/tex]

Any expression multiplied by 1 remains the same

[tex] = 10 + 9 \times \frac{1}{8} [/tex]

Calculate the product

[tex] = 10 + \frac{9}{8} [/tex]

Write all numerators above the common denominator

[tex] = \frac{80 + 9}{8} [/tex]

Add the numbers

[tex] = \frac{89}{8} [/tex]

Divide

[tex] = 11.125[/tex]

Hope this helps..

Best regards!!

Answer:

11 1/8

Step-by-step explanation:

Okay so I messed up big time. So I had to edit this! I am really sorry if you read mine before. I fixed mine. So this is the right answer. Sorry!

Answer:

b)

Step-by-step explanation:

Surface area of a cube = 6a²   , here a is the side of cube

When side is halved, side = a/2

Now, the surface area of new cube = 6* (a/2)²

                                                           = [tex]6*\frac{a^{2}}{4}=\frac{1}{4}*6a^{2}\\[/tex]

                                                            = one fourth of the cube

Answer:

s= 14

Step-by-step explanation:

The missing side is s

sin 30° = 7/s        switch s and sin 30°

s = 7/sin 30°

sin 30° is 0.5

so :

Answer:6/16 or 3/8

Step-by-step explanation:

I did it

Answer: 3/16

Step-by-step explanation:

Answer:

a) 20 students

b) 20 students

Step-by-step explanation:

a) From the given frequency table, we have to check the number of students that scored above 73.5 and add them up.

Therefore, the number of students that have grades above 73.5 are:

14 + 4 + 2 = 20 students

b) 75 falls in between 74 - 76 and we do not have the individual frequencies of the grades (74, 75, 76).

However, we can use the data we have from the table to make an assumption.

The number of students that have grades below 75 will be:

13 + 5 + 2 = 20 students

Answer:

The area of △ABC is equal to the area of △DEF

Step-by-step explanation:

On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).

How do the areas of triangle ABC and DEF compare? The area of △ABC is 1 square unit less than the area of △DEF. The area of △ABC is equal to the area of △DEF. The area of △ABC is 1 square unit greater than the area of △DEF. The area of △ABC is 2 square units greater than the area of △DEF.

Answer: The length of the sides of the triangle ABC are given below:

[tex]AB=\sqrt{(7-4)^2+(2-2)^2} =3\ unit\\\\BC=\sqrt{(4-7)^2+(6-2)^2} =5\ unit\\\\AC=\sqrt{(4-4)^2+(6-2)^2} =4\ unit[/tex]

The area of triangle ABC is given as:

Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 unit²

The length of the sides of the triangle DEF are given below:

[tex]DE=\sqrt{(4-(-2))^2+(-3-(-1))^2} =\sqrt{40} \ unit\\\\EF=\sqrt{(4-2)^2+(-1-(-3))^2} =2 \ unit\\\\DF=\sqrt{(4-(-2))^2+(-1-(-1))^2} =6 \ unit[/tex]

The area of triangle DEF is given as:

Area = 1/2 × base × height = 1/2 × 2 × 6 = 6 unit²

The area of triangle ABC is equal to 6 unit² and the area of triangle DEF is equal to 6 unit² , therefore The area of △ABC is equal to the area of △DEF

Answer:

b

Step-by-step explanation:

edge exam

Answer:

Axis of Symmetry: x = 3

Vertex: (3, 5)

Step-by-step explanation:

Use a graphing calc.

Answer:

3

Step-by-step explanation:

Answer: 15 teams

Step-by-step explanation:

Total number of games played in the tournament = 105

Number of participating teams = p

Each team plays against every other team , then the total number of games played by each team = (p - 1) , since a team can't play itself

To obtain total number of games played =

(Number of teams × number of games played) [p × (p-1)]

However, the teams played against each other only once :

Therefore, total number of games played:

[p × (p-1)] / 2

Since we've been given the total number of games played :

[p × (p-1)] / 2 = 105

p × (p-1) = 105 × 2

p × (p-1) = 210

p^2 - p = 210

p^2 - p - 210 = 0

p^2 - 15p + 14p - 210 = 0

p(p - 15) +14(p-15) = 0

(p - 15) = 0 or (p + 14) = 0

p = 15 or p = - 14

Number of teams can't be negative

Therefore p = 15

Number of teams = 15

Answer:

3/4

Step-by-step explanation:

Explanation:

List out the total number of outcomes = {1,2,3,4,5,6,7,8,9,10,11,12}

We have 12 items in this list.

From this list, highlight the outcomes that are less than 9. So we will have this smaller list of {1,2,3,4,5,6,7,8} which has 8 items in it.

There are 8 ways to get what we want (a number less than 9) out of 12 outcomes total

The probability is therefore 8/12 = 2/3

Answer:

(-2, -8/3)

Step-by-step explanation:

2(-2) - 6y = 12

-4 -6y = 12

-6y = 16

y = -16/6 = -8/3

Answer:

The speed is 74.0 miles per hour and the angle is 65.1° north-east

Step-by-step explanation:

We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.

Since the wind is moving south east, it is at 45 south of east or a bearing of 135.

Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles

Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles

The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles

The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles

The total vertical displacement of the plane is 176.64 miles - 42.43 miles =   134.21 miles

The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles

The direction of this displacement is thus

Ф = tan⁻¹(total vertical displacement/total horizontal displacement)

= tan⁻¹(134.21/62.43)

= tan⁻¹(2.1498)

= 65.05°

= 65.1° to the nearest tenth degree.

The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.

So the speed is 74.0 miles per hour and the angle is 65.1° north-east

146

Step-by-step explanation:

Given:

[tex]x - \dfrac{1}{x} = 12[/tex]

To Find:

[tex] \sf \: The \: value \: of \: {x}^{2} + \dfrac{1}{ {x}^{2} } [/tex]

How to find:

Just square both side, Solve as a equation and get the answer. Simple, Isn't it?

Solution:

See in attachment.

Answer:

146

Step-by-step explanation:

The answer of this question id 146 .

you can do this type of numericals by above process.

Answer:

15%

Step-by-step explanation:

Question:

The price of a jacket was slashed from Rs.960 to Rs.816.Then the rate of discount offered is​

Solution

Original price= Rs.960

Discount price= Rs.816

Difference in price=Original price - discount price

=Rs. 960 - Rs. 816

=Rs. 144

Percentage discount= Difference in price / Original price × 100

=Rs. 144 / Rs. 960 × 100

=0.15 × 100

=15%

The percentage discount =15% NOT 10% as you have written

Answer:

5

Step-by-step explanation:

Answer:

2,280

Step-by-step explanation:

Answer:

20 miles

Step-by-step explanation:

Given that :

When the car traveling north 'N' had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading east

Let the distance moved by the east bound car be e,

therefore, distance between the cars when the northbound car had traveled a distance of 15 miles = e + 5

Using Pythagoras rule:

(Hypotenus)^2 = (adjacent)^2 + (Opposite)^2

(e+5)^2 = 15^2 + e^2

(e+5)(e+5) = 225 + e^2

e^2 + 5e + 5e + 25 = 225 + e^2

e^2 + 10e + 25 = 225 + e^2

e^2 - e^2 + 10e = 225 - 25

10e = 200

e = 200 / 10

e = 20 miles

Check attached picture for solution diagram

Answer:

(0, –2)

Step-by-step explanation:

I am assuming that point 'B' is (-5 , 0).

The translation rule is: [tex](x,y)\rightarrow(x+5,y-2)[/tex].

Apply the rule to point 'B':

[tex]\frac{(-5,0)\rightarrow(-5+5,0-2)}{(x,y)\rightarrow(x+5,y-2)}\rightarrow\boxed{(0,-2)}[/tex]

B' should be (0, -2).

Answer:

Guy above me might be right but Im not sure. Im on the cumulative exam on edge.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the y intercept rewrite the equation in the above form

That's

4x - 2y =- 12

2y = 4x + 12

Divide both sides by 2

y = 2x + 6

comparing with the above formula the y intercept is 6

That's

(0 , 6)

The x intercept of a line the x coordinate on the line when y = 0

To find the x intercept let y = 0

That's

2x + 6 = 0

2x = - 6

Divide both sides by 2

x = - 3

The x intercept is - 3

That's

(- 3 , 0)

Hope this helps you

Answer:

the answer is x=-3 and y=6 so that means it is B.

4x-2y=-12

then; plug in 0 for x and then solve;

y=6

then do the same for the other side. plug in 0 for y and then solve.

x=-3

Hope this helps!

Answer:

1. 2.997

2. 29.93

Step-by-step explanation:

1. You gotta multiply the three sides given, to do this, they all have to be the same unit. Either convert them all to inches or feet then do the operation.

2. Same thing, gotta multiply all given values

Answer:

The second answer

Step-by-step explanation:

Remember rise over run since this is a negative line go down 4 and over to the right 3. Now you found your slope which is -4/3. To find the y intercept simply look at the y axis and look at where the line passes through it

Answer:

The answer is option C

The balance will be C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest,

then the interest amount earned is given by:

[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]

The formula will become

A (n) = 700 • (1 + 0.03)^(n – 1)

Where n = 5 years

A (5) = 700 • (1 + 0.03)^(5 – 1)

A (5) = 700 • (1 + 0.03)^(4)

Thus, the account balance at the beginning of 5 years or at the end of 4 years;

A (5)=700×(1+0.03)^(4)

A (5)=787.8

Hence, The answer is C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86.

Learn more about compound interest here:

https://brainly.com/question/11897800

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Answer:

(A) No solution

(B) One solution

(C) One solution

(D) One solution

(E) No solution

Please tell me if this is incorrect. I hope this helps!

Answer:

25 1/2 square meters remaining

Step-by-step explanation:

Total area of the pool deck=76 1/2 square meters

He painted 2/3 of the deck before stopping for lunch

Total painted=2/3 of 76 1/2

=2/3*153/2

=306/6

=51 square meters

Total remaining=Total area - total painted area

=76 1/2 - 51

=153/2 - 51

=153-102/2

=51/2

=25 1/2 square meters remaining

Answer: 148.5

Step-by-step explanation:

To find the area of this shape, comprised of a rectangle and a triangle, we can find the area of each shape and add them together.

The area of a triangle is 12⋅b⋅h. We are given the triangle's height, 13. The base of the triangle will be the same as the width of the rectangle, which we also know: 11. Now we can calculate the area of the triangle:

A = 1/2⋅b⋅h

A = 12⋅11⋅13

A = 71.5

Now we can find the area of the rectangle, which is l⋅w. The width of the rectangle is 11, which is the same as the base of the triangle; the length is 7:

A =l⋅w

A = 7⋅11

A = 77

Finally, we can add together the area of the triangle and the rectangle to find the total area:

A = 71.5 + 77 = 148.5

The total area of the front of a house will be 148.5.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangle has a width = 11

The triangle's height = 13

The rectangle's height = 7

Now,

Since, The base of the triangle will be the same as the width of the rectangle.

Hence, The area of rectangle = 7 x 11

                                              = 77

And, The area of triangle = 1/2 x 11 x 13

                                      = 71.5

Thus, The total area of the front of a house = 77 + 71.5

                                                                  = 148.5

Therefore, The total area of the front of a house will be 148.5.

Learn more about the rectangle visit:

https://brainly.com/question/398984

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Answer:

165

Step-by-step explanation:

we solve this by sum over the possible symmetry groups of the colorings.

1.If the board has 90 degree rotational symmetry, then all four squares are the same color. There are 5 such boards.

2. If the board has 180 degree rotational symmetry (but not 90 degree), then it has to be a 2-color checkerboard pattern. There are ⁵c₂=10 such boards.

All the remaining boards have no rotational symmetry. We can count these boards by taking all possible colorings, subtracting the ones counted above, and dividing by four (since each of these boards corresponds to four colorings). The result is (54−2×10−5)÷4=600÷4=150.

so, total number of boards= 5+10+150= 165.

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

Since he needs beans to sell. The common sense constraints would be that both x and y need to be equal to or greater than 0, otherwise he wouldn’t have anything to sell.

The answer is the last choice

Answer:

x>=0, and

y>=0

Step-by-step explanation:

Let

x = pounds of house blend he sells/makes every day

y = pounds of exoted blend he makes/sells every day

constraint for costa rican beans

x/2 + y/4 <= 200 ...............(1)

constraint for Ethiopian beans

x/2 + 3y/4 <=330..................(2)

Total weight per day

x+y <= 200+330 = 530............(3)

common sense constraints, cannot have negative weight for coffee

x>=0, and

y>=0

Answer:

1. 30

2. 18

3. 460

4. 3

Step-by-step explanation:

According to the hierarchy of operations, we first need to solve {},[] or () (starting by the inner ones). Then the multiplications and divisions and lastly we will add and subtract. Therefore we have:

(i) (45 x 2) ÷ [ 28 – { 14 + 9 } ]

(90) ÷ [ 28 – { 14 + 9 } ] solved the ()

(90) ÷ [ 28 – { 25 } ]  solved the {}

(90) ÷ [ 3 ] solved the  []

30.      

ii) 72 ÷ [ 23 – { 4 + ( 3 x 5 ) }]

72 ÷ [ 23 – { 4 + ( 15 ) }]  solved the ()

72 ÷ [ 23 – {19) ] solved the {}

72 ÷ 4 solved the []

18

(iii) 102 + 13 × 8 + 125 ÷ 5 × 10

102 + 104 + 25 x 10 Solved the first multiplication and division

102 +104 + 250 Solved the multiplication

460  

(iv) 57 ÷ [ { ( 10 + 5) - 3 × 2 } + 10 ]

57 ÷ [ { 15 - 3 × 2 } + 10 ] solved the inner ()

57 ÷ [ { 15 - 6 } + 10 ]  solved the multiplication

57 ÷ [ 9 + 10 ] solved the {}

57 ÷ 19 solved the []

3

Answer:

-2

Step-by-step explanation:

Hello,

First of all, let's check the denominator.

[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]

Now, let's see the numerator.

[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]

So we cannot factorise the numerator with (x+2) or (x-3)

Then, -2 and 3 are the the discontinuities of the expression.

There is only -2 in the list, this is the correct answer.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you