Nadiya determines that there are no fractions equivalent to StartFraction 2 Over 10 EndFraction with a denominator greater than 10, but less than 20, that have a whole number numerator and denominator. Is Nadiya correct?
Yes, Nadiya is correct. By multiplying the numerator and denominator by 2, the first fraction equivalent to StartFraction 2 Over 10 EndFraction is StartFraction 4 Over 20 EndFraction.
Yes, Nadiya is correct. By multiplying the whole fraction by any whole number, each equivalent fraction will continue to have a denominator of 10.
No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to StartFraction 2 Over 10 EndFraction by 3 and arrive at the equivalent fraction StartFraction 3 Over 15 EndFraction.
No, Nadiya is incorrect. She could add any number between 1 and 8 to the numerator and denominator and arrive at an equivalent fraction with a denominator greater than 10 but less than 20.

Answer:

216.

Step-by-step explanation:

These numbers are perfect cubes starting with 2^3.

2^3, 3^3,  4^3,  5^3 so the next one is 6^3, which is 216.

Answer:

x = 11.5 hours

Step-by-step explanation:

Set up a proportion:

[tex]\frac{460}{8}[/tex] = [tex]\frac{661.25}{x}[/tex]

661.25/460 = 1.4375

Multiply 8 by 1.4375 to find x:

8(1.4375) = 11.5

x = 11.5 hours

Answer:

The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6

Step-by-step explanation:

We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.

n/5 ≥ 11

Multiply by 5 on both sides.

n ≥ 55

Now, let's do the second one.

-3y ≤ -18

Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)

y ≥ 6

Answer:  BC = 10

======================================================

Work Shown:

The term "collinear" means all points fall on the same straight line.

Point B is on segment AC.

Through the segment addition postulate, we can say

AB+BC = AC

This is the idea where we glue together smaller segments to form a larger segment, and we keep everything to be a straight line.

Apply substitution and solve for x

AB+BC = AC

2x-12+x+2 = 14

3x-10 = 14

3x = 14+10

3x = 24

x = 24/3

x = 8

Then we can find the length of BC

BC = x+2

BC = 8+2

BC = 10

--------

Note that AB = 2x-12 = 2*8-12 = 16-12 = 4

and how AB+BC = 4+10 = 14 which matches with AC = 14

Therefore we have shown AB+BC = AC is true to confirm the answer.

Collinear points are points on the same line.

The value of BC is 10

Since points A, B and C are on the same line, where B is between points A and C.

So, we have:

[tex]AC = AB + BC[/tex]

Substitute values for AC, AB and BC

[tex]14 = 2x - 12 + x + 2[/tex]

Collect like terms

[tex]2x +x =14 + 12 - 2[/tex]

[tex]3x =24[/tex]

Divide both sides of the equation by 3

[tex]x =8[/tex]

Substitute 8 for x in BC = x + 2

[tex]BC =8 + 2[/tex]

[tex]BC =10[/tex]

Hence, the value of BC is 10

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Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

The time will be t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable the dependent variable.

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum.

We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground.

The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

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Answer:

[tex]1035[/tex]

Step-by-step explanation:

(63756×60)/(70×5280)

=1035

Answer:

There is only one solution set.

Step-by-step explanation:

The set can contain any number of solutions or none.

This is all I know, hope it helps.

Answer:

525 dollars

Step-by-step explanation:

simple interest yearly ( year 11 does not count because the question asking at the amount at the  beginning of year 11)

interest=300*0.075*10= 225

the amount in the account : 300+225=525 dollars

Answer: 4

Step-by-step explanation:

We know that a plane is 2 dimensional surface that extends infinitely far.

The number of points required to define a plane = 3

Here , we have 4 points A, B, C, and D.

So, the number of possible combinations of 3 points to make a plane from 4 points = [tex]C(4,3)[/tex]

[tex]=4[/tex]            [ [tex]C(n,n-1)=n[/tex] ]

Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.

Answer:

B. 15 days

Step-by-step explanation:

A=10=1/10 of the job

B=12=1/12 of the job

A+B+C=4=1/4 of the job

A+B

=1/10 + 1/12

=10+12/120

=22/120

=11/60

(A+B+C) - (A+B)

=1/4 - 11/60

=5 - 11/60

=4/60

=1/15

It would take C alone 15 days to finish the job

Hey there! I'm happy to help!

If we have 6 red marbles and 4 blue marbles, we have 10 total marbles.

First, we have the probability that a marble we draw is red, which is 6/10. This simplifies to 3/5.

If this happens, there are only 5 red marbles left and 9 total ones. So, the probability of drawing a red one again is 5/9.

We multiply these two probabilities together to see the probability of them both happening.

[tex]\frac{3}{5} *\frac {5}{9}= \frac{1}{3}[/tex]

The probability that both marbles are red is 1/3.

Have a wonderful day! :D

Answer:

Step-by-step explanation:

Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.

the total surface of the cone A = πrs+πr² and the volume is expressed as

V = 1/3πr²h

For the surface area of the cone;

Given parameters

radius = 8 cm and slant height s = 15 cm

Total surface area A = π(8)(15) + π(8)²

A = 90π+64π

A = 154π

If π = 3.14

A = 154(3.14)

A = 483.56cm²

A = 483.6cm²

Hence the total surface area of the cone to the nearest tenth is 483.6cm²

For the volume of the cone;

V = 1/3πr²h

Using pythagoras theorem to get the height of the cone;

l² = h²+r²

h² = l²-r²

h² = 15²-8²

h² = 225-64

h² = 161

h = √161

h = 12.69cm

V = 1/3π* (8)² * 12.69

V =  1/3π* 64 * 12.69

V =  1/3*3.14* 64 * 12.69

V = 2550.1824/3

V = 850.06 cm³

V = 850.1 cm³

Hence, the volume of the cone is  850.1 cm³ to the nearest tenth.

Answer:

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Step-by-step explanation:

Long division:

13  33

13*2 = 26

33 - 26 = 7

we have: 33/13 = 2 r7

we know that we can rewrite the remainder as 7/13

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Answer:

15.60 times 100 divided by 390=4%

Step-by-step explanation:

The required sales tax rate percentage is 4%.

The sales tax for an item was $15.60 and it cost $390 before tax. To find the sales tax rate. Write your answer as a percentage.

the percentage is defined as, the composition of something out of whole inbounds of 100.example 10% of 150 = 10 * 150/100
                                                                = 15
It shows that 10 percent of 150 is 15.

sales tax = $15.60
cost = $390
To get the sales tax percentage we have to find out the tax composition of tax to the cost. So,
Sale tax percent = sale tax/cost  * 100
                            = 15.60/390   * 100
                            = 0.04 * 100
                            = 4 %

Thus, the required sales tax rate percentage is 4%.

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Answer:

18 square centimeters

Step-by-step explanation:

Notice that if e is the midpoint of the side CB, and angle [tex]\angle x = 45^o[/tex], then this rectangle is in fact two squares of side 3 cm put together. therefore, side CD has a length of 6 cm, and as a result, the area of the figure is given by the product base times height = 6 x 3 = 18 [tex]cm^2[/tex]

Answer:

(B)  18

Step-by-step explanation:

The angle x is 45 degrees.  Since it is bisecting a 90 degree angle, the angle on the other side is 45 degrees.

90 - 45 = 45

Since AB is 3, DC is 3.  Since the right triangle DC is 45-90-45, the other side, CE, will also be 3.  Since CE is half of the side of the rectangle, multiply it by 2 to get 6.  The sides of the rectangle are 3 and 6.  Use the formula for area of a rectangle to solve.

A = lw

A = (6)(3)

A = 18

The answer is B.

(x-p)(x-q)

y(x-q) .... let y = x-p

yx - yq ... distribute

x(y) - q(y)

x(x-p) - q(x-p) ... replace y with x-p

x^2 - px - qx + pq .... distribute

x^2 + (-p-q)x + pq

The last expression is in the form ax^2+bx+c with a = 1, b = -p-q and c = pq

The constant term is the term without any variable x attached to it (either x or x^2), so the constant term is pq

Answer:

'y', "addition", '9'.

Step-by-step explanation:

The variable is an unknown value in an algebraic equation or expression. It is represented by a letter.

'y' would be the variable in the given equation.

The operation in the expression is addition. The '+' sign represents addition, which means 9 and 'y' would be added together to get the sum.

Constants are terms in a expression or equation that contains no variables. This means that constants are only numbers.

'9' would be the given constant in the expression.

Hope this helps.

Answer:

y

+

9

Step-by-step explanation:

Answer:

6 quarts

Step-by-step explanation:

8 bags

--------

2 quarts

Multiply top and bottom by 3

8*3 bags

--------

2*3 quarts

24 bags

--------------

6 quarts

Answer:

6

Step-by-step explanation:

2 quarts of iced tea = 8 tea bags.

x quarts of Iced tea = 24 tea bags

=> 2/8 = x/24

=> Multiply the extremes and means

=> 8x = 48

=> 8x / 8 = 48 / 8

=> x = 6

6 quarts of iced tea can be made with 24 tea bags.

Answer:

25

Step-by-step explanation:

5^2

This is 5 multiplied by itself 2 times

5*5

25

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

Answer:

The two polynomials are:

(x + 1) and (x² + x)

Step-by-step explanation:

A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.

Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.

So,

Let's multiply both numerator and denominator by (x + 1) to get;

(x + 1)/(x(x + 1))

This gives; (x + 1)/(x² + x)

Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.

Answer:

6 3/5

Step-by-step explanation:

33/5 = 6 R3

Answer:

6.6

Step-by-step explanation:

33÷5=6.6

33 divided by 5equal

Answer:

0 miles- $50

1 mile- $53

2 miles- $56

3 miles-$59

Step-by-step explanation:

you add $3 to the original 50 as you go each mile.

Answer:

63/125

Step-by-step explanation:

Turn the decimal .504

=> 504/1000

=> 504/1000 = 252/500

=> 252/500 = 126/250

=> 126/250 = 63/125

=> 63/125 cannot be simplified anymore.

So, 63/125 is the simplified fraction of .504

Answer:

C) 1

Step-by-step explanation:

First half:

Invert and multiply

x²/y²*y³/x²=x²y³/y²x³=y/x

Second half:

Invert and multiply

1/y*x/1=x/y

Combine

y/x*x/y=xy/xy=1

Answer:

c = 152

Step-by-step explanation:

c/8+5 = 24

Subtract 5 from each side

c/8+5-5 = 24-5

c/8 = 19

Multiply each side by 8

c/8*8 = 19*8

c =152

Answer:

D. 152

Step-by-step explanation:

First, subtract 5 from both sides:

c/8 + 5 = 24

c/8 = 19

Multiply both sides by 8:

c = 152

So, the correct answer is D, 152