Kevin correctly answered 75% of 32 test questions. How many more questions would Kevin have to answer correctly to get more than 80% correct?

Answer:

  3000

Step-by-step explanation:

The multiplier associated with each percentage change (p) is (1 +p). We can use this fact to relate the original number to the modified number.

__

Let x represent the original number. Then the discounted number is ...

  x(1 -20%)(1 -25%)(1 -20%) = x(0.8)(0.75)(0.8) = 0.48x

After those discounts, the increased number is ...

  (0.48x)(1 +20%)(1 +25%)(1 +20%) = (0.48x)(1.2)(1.25)(1.2) = 0.864x

The difference from the original is ...

  x - 0.864x = 408

  0.136x = 408 . . . . simplify

  x = 3000 . . . . . . . divide by the coefficient of x

The original number was 3000.

Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The measure of the other leg of the triangle is 5.1961 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Let the length of the other leg can be represented by x.

Given the hypotenuse of a right triangle measures 6 cm and one of its legs measures 3 cm. Therefore, the measure of the other legs can be written as,

Hypotenuse² = 3² + x²

6² = 3² + x²

36 = 9 + x²

x² = 27

x = √27

x = 5.1961

Hence, the measure of the other leg of the triangle is 5.1961 units.

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Answer:

The circumference is 6.3 in

The circumference of the circle is given by the equation C = 6.3 inches

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the circumference of the circle be represented as C

Now , the equation will be

Let the radius of the circle be r = 1 inch

Now , circumference of circle = 2πr

Substituting the values in the equation , we get

The circumference of the circle C = 2 ( 3.14159 ) x 1

On simplifying the equation , we get

The circumference of the circle C = 6.3 inches

Hence , the circumference of the circle is 6.3 inches

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A cylinder is a three-dimensional structure formed by two parallel circular bases connected. The height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

Given the volume of the cylinder is 1250 cm³, and the radius of the cylinder is 8 cm. Therefore, the volume of the cylinder can be written as,

[tex]\text{Volume of the cylinder} = \pi r^2h[/tex]

[tex]1250 = \pi \times (8)^2 \times h\\\\h = 6.217\rm\ cm[/tex]

Hence, the height of the can that has a volume of 1250 cm³ if the radius is 8 cm is 6.217 cm.

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Answer:

2340

Step-by-step explanation:

4590*.51=2340.9

Because you can not have .9 people, you round down to 2340

2341 students are in the freshman class.

Percentage is defined as ratio expressed as a fraction of 100.

Total no. of students in the freshman Economics majors = 4590

51% students of a university's freshman class,

Let x no. of students in the freshman class,

x = 51/100×(4590)

x = 0.51×(4590)

x = 2340.9

x = 2340.9 ≈ 2341

Hence, 2341 students are in the freshman class.

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The sequence is recursively defined by

[tex]\begin{cases}a_1 = 1 \\ a_2 = 2 \\ a_n = a_{n-1} a_{n-2} & \text{for } n \ge 3\end{cases}[/tex]

By this definition,

[tex]a_{n-1} = a_{n-2} a_{n-3} \implies a_n = a_{n-2}^2 a_{n-3}[/tex]

[tex]a_{n-2} = a_{n-3} a_{n-4} \implies a_n = (a_{n-3} a_{n-4})^2 a_{n-3} = a_{n-3}^3 a_{n-4}^2[/tex]

[tex]a_{n-3} = a_{n-4} a_{n-5} \implies a_n = (a_{n-4} a_{n-5})^3 a_{n-4}^2 = a_{n-4}^5 a_{n-5}^3[/tex]

[tex]a_{n-4} = a_{n-5} a_{n-6} \implies a_n = (a_{n-5} a_{n-6})^5 a_{n-5}^3 = a_{n-5}^8 a_{n-6}^5[/tex]

and so on.

Recall the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, 21, …}, where the next term in the sequence is the sum of the previous two terms. If [tex]F_n[/tex] is the n-th Fibonacci number, then continuing the pattern above we would arrive at

[tex]a_n = {a_2}^{F_{n-1}} {a_1}^{F_{n-2}} = 2^{F_{n-1}}[/tex]

Notice that the sequence of positive powers of 2 leaves a periodic sequence of residues mod 10 :

[tex]2 \equiv 2 \pmod{10}[/tex]

[tex]2^2 \equiv 4 \equiv 4 \pmod{10}[/tex]

[tex]2^3 \equiv 8 \equiv 8 \pmod{10}[/tex]

[tex]2^4 \equiv 16 \equiv 6 \pmod{10}[/tex]

[tex]2^5 \equiv 2 \times 2^4 \equiv 2 \times 6 \equiv 2 \pmod{10}[/tex]

[tex]2^6 \equiv 2^2 \times 2^4 \equiv 4 \times 6 \equiv 4 \pmod{10}[/tex]

and so on; the period of this sequence of residues is 4.

The period of [tex]F_n[/tex] taken mod 4 is 6 :

[tex]\{1, 1, 2, 3, 5, 8, \ldots\} \equiv \{1, 1, 2, 3, 1, 0, \ldots\} \pmod 4[/tex]

(This follows from the "properties" section in the link in comment. In this case, π(4) = 3/2 × 4 = 6.)

It follows that

[tex]34 \equiv 4 \pmod 6 \implies F_{34} \equiv 3 \pmod 4 \implies 2^{F_{34}} \equiv 2^3 \equiv 8 \pmod{10}[/tex]

which means the last digit of [tex]a_{35}[/tex] is 8.

-7/6 = - 1.167 in simplest form

Answer:

Step-by-step explanation:

You cant simply this into fraction but you can simplify it to decimal form

which is - 1.17 round off

Answer:

Where is the picture????

Answer:

C) 15, 20, 25

Step-by-step explanation:

If you plug this in pythagorean theorem, it works. The others don't.

Answer: Max. Max has a 49% chance of getting a 1 or 2 when Josie only has a 33% chance of getting a green block

............................................................................

Answer:

d) 190,172,154

Step-by-step explanation:

208-18=190

190-18=172

172-18=154

Answer:

5x^2 - 4x - 3 = 0

Step-by-step explanation:

For the equation

ax^2 + bx + c = 0

the  roots are   [-b +/- √(b^2 - 4ac)] / 2a

So comparing the terms to the values in the question:

a = 5

b = -4

c = -3

The expansion of the series is 2 + 6 + 8 + 10

The summation expression is given as:

[tex]\sum\limits^4_{n=1} 2(n + 1)[/tex]

When n = 1, we have:

2(n + 1) = 2(1 + 1)  = 4

When n = 2, we have:

2(n + 1) = 2(2 + 1)  = 6

When n = 3, we have:

2(n + 1) = 2(3 + 1)  = 8

When n = 4, we have:

2(n + 1) = 2(4 + 1)  = 10

So, we have:

[tex]\sum\limits^4_{n=1} 2(n + 1) = 2 + 6 + 8 + 10[/tex]

Hence, the expansion of the series is 2 + 6 + 8 + 10

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Answer:

The correct option is actually d. 4 + 8 + 16 + 32

Step-by-step explanation:

Answer:

d = 306 m

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (10, 20) and (x₂, y₂ ) = (280, 164) ← house and beach coordinates

d = [tex]\sqrt{(280-10)^2+(164-20)^2}[/tex]

   = [tex]\sqrt{270^2+144^2}[/tex]

   = [tex]\sqrt{72900+20736}[/tex]

   = [tex]\sqrt{93636}[/tex]

   = 306 m

Answer:

The distance from Francesca's house to the beach is 306 meters.

Step-by-step explanation:

Use the Pythagorean Theorem to find the straight-line distance from Francesca's house to the beach.

Step 1 Find the length of the horizontal leg.

The length of the horizontal leg is the absolute value of the difference between the x- coordinates of the points (280,20) and (10,20).

|280 - 10| = 270

The length of the horizontal leg is 270 meters

Step 2 Find the length of the vertical leg.

The length of the vertical leg is the absolute value of the difference between the y- coordinates of the points (280,164) and (280,20)

|164 - 20| = 144

The length of the vertical leg is 144 meters.

Step 3 Let a = 270 and b = 144. Let c represent the length of the hypotenuse. Use the Pythagorean Theorem to find c.

a² + b² = c²

270² + 144² = c² Substitute into the formula.

72900 + 20736 = c² Simplify.

93636 = c² Add.

√93636 = c Take the square root of both sides.

306 = c Simplify.

The distance from Francesca's house to the beach is 306 meters.

Area of base

Area of one triangle side

Area of 4 sides

TSA

20+25=45ft²

Answer:

C)  45 ft²

Step-by-step explanation:

Formulae

Area of a square = x²  (where x is the side length)

Area of a triangle = 1/2 × base × height

The surface area of a square pyramid comprises:

⇒ area of square base = 5² = 25 ft²

⇒ area of triangular face = 1/2 × 5 × 2 = 5 ft²

⇒ Total surface area = area of square base + 4 triangular areas

                                   = 25 + 4(5)

                                   = 25 + 20

                                   = 45 ft²

Answer:

7x - 30

Step-by-step explanation:

5x -2(15-x)

Distribute -2 to the parenthesis

= 5x -30 +2x

Combine like terms

7x-30

Answer:

-1

Step-by-step explanation:

m= -1

Slope Formula: (y2 - y1) / (x2 - x1)

Point 1 = (4, 3)

Point 2 = (11, -4)

Slope = (-4 - 3) / (11 - 4) = -7 / 7 = -1

Answer: slope = -1

Hope this helps!

The correct roots of this equation is:

x = 10

y = 6

– This equation is a value substitution system. To solve it, we will: add the terms equal to x, with the sums of the equality.

2x + y = 26

x - y = 4

2x + x = 26 + 4

3x = 30

x = 30/3

x = 10

– Now, let's "take" the first equation of the system, and we'll calculate it, replacing x with its value.

2x + y = 26

2 . 10 + y = 26

20 + y = 26

y = 26 - 20

y = 6

Therefore, the roots of this equation or system is:

x = 10

y = 6

Answer:

Step-by-step explanation:

Remark

You have an isosceles triangle. That means that the angles opposite the marked sides are equal. So mark the angle on the lower left of the triangle as 50 degrees.

The solution to problem depends on the fact that the sum of the two inside angles of the triangle (each of which is marked as 50 degrees) not supplementary to the exterior angle, are still equal to the exterior angle.

Givens

<1 = 50 degrees

<2 = 50 degrees

Exterior angle = 15x + 25   Substitute the givens into the equation

Equation

<1 + <2 = 15x + 25

Solution

50 + 50  = 15x + 25                       Combine the left side

100 = 15x + 25                               Subtract 25 from both sides

100 - 25 = 15x + 25 - 25                Combine

75 = 15x                                          Divide both sides by 15

75/15 = 15x/15                      

5 = x

Answer

<1 = 50 degrees

<2 = 50 degrees

15x + 25 = 75 + 25 = 100

If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.

Then the perimeter of the preimage, the original triangle, before its

dilation will be

Let c be the perimeter of the original triangle.

Then we have

[tex]\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67[/tex]

Then the perimeter of the original triangle is 66.67 units.

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Table 3 will fit snugly in the corner of the room.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

From the given data we will check the value of the diagonal by applying the Pythagorean theorem.

So by using the Pythagorean theorem:-

D ²  =    L²   +   W²

D²   =    ( 2.4 )²  +  ( 3.2 )²

D²   =    ( 5.76   +    10.24 )  =   16

D     =   √16   =  4  feet

Therefore table 3 will fit snugly in the corner of the room.

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Answer:

Table 3.

Step-by-step explanation:

Person above is correct, I'm takin the test!!

Answer:

i think its D.

Step-by-step explanation:

i just counted

Answer:

8x^2 2y^3

Step-by-step explanation:

Answer:

22 degrees F

Step-by-step explanation:

[tex]20--2=20+2[/tex]

Subtracting a negative number makes the sign positive, so 20 + 2 = 22 degrees F.

Answer:

100

100 is not an odd number, its higher than 90 but not 100

and 100-100=0

Step-by-step explanation:

Hope it helps

Answer:

9.5 feet

Step-by-step explanation:

Area of square garden = side length²

⇒ 90 = l²

⇒ l = √90

⇒ l = 3√10

⇒ l = 9.5 feet (nearest tenth)

The length of one side lies between the whole numbers 9 and 10.

Answer:

9 and 10

side length = 9.5 ft (nearest tenth)

Step-by-step explanation:

Area of a square = s²  (where s is the side length)

Therefore, if the square garden measures 90 ft², the length of one side will be √90.

To find the two whole numbers that √90 lies between, find the perfect square either side of 90.

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...

Therefore, 90 lies between 81 and 100:  

⇒ 81 < 90 < 100

Square root the numbers:

⇒ √81 < √90 < √100

⇒ 9 < √90 < 10

Therefore, the length of one side of Grandma's garden is between 9 and 10.

To estimate √90 to the nearest tenth, find the difference between the three numbers:

[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]

As 90 is almost in the middle of 81 and 100,

⇒ √90 = 9.5 (nearest tenth)

According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.

Answer:

(-3, -2)

Explanation:

Coordinates are represented in the form of (x, y)

To know the x coordinates see the value on the x-axis.

To know the y coordinates see the value on the y-axis.

From there we can identify:

A = (x, y) = (-4, 4)

B = (x, y) = (2, 2)

C = (x, y) = (0, -5)

D = (x, y) = (-3, -2) ← Required answer.

Answer:

D

Step-by-step explanation:

um well just based on what its asking for it wants a sentence that uses both.

Answer:

C

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we know in our case

b(b+12) = 189 cm²

b² + 12b - 189 = 0

let's try to solve this by completing the square.

that means we try to find the expression

(b + k)² + c

that is equal to

b² + 12b - 189

(b + k)² + c = b² + 2kb + k² + c = b² + 12b - 189

so,

2k = 12

k = 6

and then

k² + c = -189

6² + c = -189

36 + c = -189

c = -225

(b + 6)² - 225 = 0

(b + 6)² = 225

b + 6 = 15

b = 9

so, the baseline b = 9 cm.

the height b+12 = 9+12 = 21 cm.