A teacher has 1,425 marbles to divide equally among 9 groups of students to use in an experiment. What is the least number of marbles he could have left after the marbles are distributed?

Answer:

c) p = 3/q

Step-by-step explanation:

If 3 is divided by a smaller number "q", then it would result in a larger number "p".

Example:

1. Substitute 3 for "q"

3/3 = 1

q = 3

p = 1

2. Substitute 1 for "q"

3/1 = 3

q = 1

p = 3

When "q" decreased, "p" increased.

Step-by-step explanation:

c) p=3/q

i can confirm after 10.30

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

Explanation:

The fractions 2/3, 1/6 and 1/9 have the denominators 3, 6 and 9. The LCM is 18, so the LCD of the fractions is 18.

2/3 = 12/18 after multiplying top and bottom by 6

1/6 = 3/18 after multiplying top and bottom by 3

1/9 = 2/18 after multiplying top and bottom by 2

--------

The three original fractions 2/3, 1/6, and 1/9 are equivalent to 12/18, 3/18, and 2/18 in that exact order.

With the fractions all having the same denominator, we can add the numerators to place over the common denominator

12/18 + 3/18 + 2/18 = (12+3+2)/18 = 17/18

--------

After combining all of the shaded areas, we have 17/18 of the circle shaded in with 1/18 of the circle not shaded in.

You subtract 17/18 from 1 to get 1/18

1 - (17/18) = 18/18 - 17/18 = (18-17)/18 = 1/18

You could think of it like having 18 slices of cake total, and 17 are eaten by guests, so 18-17 = 1 is left over out of the 18 overall. So 1/18 of the cake hasn't been eaten.

The required fraction is 1/18, that is not covered.

A fraction is a numeral that represents a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

In the given spinner,

2/3 part is covered,

1/6 part is covered,

and 1/9 part is covered.

To determine the fraction of the portion that is not covered,

Let the not covered portion is x.

Since, Total value of circle = 1

2/3 + 1/6 + 1/9 + x = 1

(4 + 1)/6 + 1/9 + x = 1

5 / 6 + 1/9 + x = 1

(15 + 2) / 18 + x = 1

17/18 + x = 1

x = 1 - 17 / 18

x = 1 / 18

The portion of the circle that is not covered is 1/18.

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Answer:

The correct answer is;

ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency

Step-by-step explanation:

The given information are;

The point of intersection of GA ∩ TN = I

Segment TI is congruent to segment NI (Given)

Segment GI is congruent to segment IA (Given)

Angle ∠GIT is congruent to angle ∠AIN (Vertically opposite angles)

Therefore, we have;

Triangle, ΔGIT is congruent to triangle ΔNIA (Side Angle Side (SAS) rule of congruency)

Two triangles are said to be congruent by the Side Angle Side (SAS) rule of congruency,  when two of the sides and the included angle (the angle in between the two sides) of one of the triangle are equal to two sides and the included angle of the other triangle.

Therefore, the correct answer is ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency

Answer:

△GIT≅△AIN

By Rule: SAS

Answer:

Step-by-step explanation:goofy

Answer:

Step-by-step explanation:

You must show that this is a rational function.  As written, it is not such.

         -3x + 1

f(x) = ------------

           -x + 2

is a rational function; the horizontal line --------- indicates division.

If we let x grow large, the graph approaches the horizontal line y = 3, which we call "the horizontal asymptote."  There is a vertical asymptote at x = 2, which we know because the denominator will be zero at that x value.  The vertical intercept is

f(0) = 1/2, or (0, 1/2).

As x decreases towards negative infinity, the graph approaches the horizontal line (horizontal asymptote) y = 3.

Answer:

Step-by-step explanation:

The second answer choice correctly shows the result of multiplying functions m and n together.

Answer:

you can land on heads a possibility of 16 times

Step-by-step explanation:

Answer:

[tex]\huge\boxed{Second\ Number = 42}[/tex]

Step-by-step explanation:

Let the consecutive even numbers be x,x+2,x+4, x+ 6, x+ 8 and x+10

So, the given condition is:

x+x+2+x+4+x+6+x+8+x+10 = 270

6x + 30 = 270

Subtracting both sides by 30

6x = 270 - 30

6x = 240

Dividing both sides by 6

x = 40

So,

First Number = x = 40

Second Number = x+2 = 40+2 = 42

Third Number = x+4 = 40+4 = 44

Fourth Number = x+6 = 40+6 = 46

Fifth Number = x+8 = 40+8 = 48

Sixth Number = x+10 = 40+10 = 50

Answer:

22 I think

Step-by-step explanation:

Answer:

f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7

Step-by-step explanation:

The inverse of a function reverses the operations performed by the function  in the question such if f(x) = y, then we have, f⁻¹(y) = x, which reverses the operation of the first function.

The inverse of a function f(x) = 4·㏒₂(x - 7) is found as follows;

We have;

y = 4·㏒₂(x - 7)

We substitute x for y to get;

x = 4·㏒₂(y - 7)  which gives;

x/4 = ㏒₂(y - 7)

[tex]2^{\dfrac{x}{4} }[/tex] = y - 7

y = [tex]2^{\dfrac{x}{4} }[/tex] + 7

Therefore;

f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7.

Answer:

It goes over the goal post by 6 feet

Step-by-step explanation:

The football will be at the same x position as the goal when x = 40. When x = 40, y = -0.03 * 40² + 1.6 * 40 = 16. The height of the goal post can be represented by the equation y = 10. Since 16 > 10, the football goes over the goal post by 16 - 10 = 6 feet.

Answer:

  A number line with an open circle on 3, a closed circle on 5, and shading in between

Step-by-step explanation:

The solution to the first inequality is ...

  3x +1 > 10

  3x > 9 . . . . . subtract 1

  x > 3 . . . . . . divide by 3

__

The solution to the second inequality is ...

  4x ≤ 20

  x ≤ 5 . . . . . divide by 4

__

The solution set is then ...

  3 < x ≤ 5

This is represented by a graph with an open circle at 3, a closed circle at 5, and shading between.

Answer:

[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]

Step-by-step explanation:

From the way it is written, the [tex]x[/tex] is outside the square root. I will rewrite it as:

[tex]x\sqrt{5} =x\sqrt{3} +\sqrt{7}[/tex]

[tex]x\sqrt{5}-x\sqrt{3}=\sqrt{7}[/tex]

[tex]x(\sqrt{5} - \sqrt{3} )=\sqrt{7}[/tex]

[tex]$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2} $[/tex]

[tex]$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$[/tex]

[tex]$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2} $[/tex]

[tex]$x=\frac{\sqrt{35}+\sqrt{21}}{2} $[/tex]

Multiply denominator and numerator by 3

[tex]$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6} $[/tex]

Factor [tex]\sqrt{3}[/tex]

[tex]\sqrt{3} (\sqrt{105}+3 \sqrt{7})[/tex]

[tex]$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6} $[/tex]

Divide denominator and numerator by [tex]\sqrt{3}[/tex]

[tex]$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} } $[/tex]

Let's rewrite it again

[tex]$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} } $[/tex]

[tex]$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$[/tex]

It is already in the form [tex]$\sqrt{\frac{a}{b} } $[/tex]

Expanding the perfect square, we have

[tex]63+42\sqrt{15}+105[/tex]

[tex]$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12} $[/tex]

[tex]$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4} $[/tex]

Factor [tex]$\frac{7}{2} $[/tex]

[tex]$\frac{7}{2} (4+\sqrt{15} )$[/tex]

Therefore,

[tex]$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)} $[/tex]

[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]

Since there is two negative signs in the original equation, you need two negative signs in the equivalent one as well.

Because one of the negatives if before the fraction, it doesn't matter if the second negative is on the 13 or on the 12.

The answer is A.

For the next 25-year period,(CPI) is increased by only 1% due to Inflation and Stagnation.

What is Stagnation ?

Stagnation is a situation of slow economic growth and relatively high unemployment (which basically means that aggregate production is reducing and some of the inputs of the economy, such capital or labor, are unemployed) , accompanied by rising prices, or inflation.

In terms of national accounting, it means a reduction in gross domestic product (GDP), with inflation (rise in all prices in the economy).

In terms of aggregate demand and supply models, stagnation is the result of a contraction of aggregate supply, which ceteris paribus, results in lower levels of production and higher prices.

Many theories have tried to explain this phenomena. Common interpretations link stagnation with and increase of the cost of production in the economy (that might be generated by an increase of gasoline for example), and its implications in the production (lower production because of higher costs), consequently unemployment and a rise of prices due to the increase of cost.

Here, During a certain 25-year period, the consumer price index (CPI) increased by 99% and during the next 25-year period, it increased by only 1% which shows slow economic growth which can be due to Inflation and Stagnation.

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Answer:

[tex]93\frac{1}{3}[/tex] [tex]yd^{3}[/tex]

Step-by-step explanation:

The volume of a pyramid is:

[tex]V=\frac{lwh}{3}[/tex] (basically saying that you multiply the length, width, and the height together and then you divide that by 3)

Now, let's do the first part.

8 × 5 × 7 = 280

Now, let's divide.

280 ÷ 3 = 93 1/3

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a great day! :)

Answer:

[tex]\boxed{\sf 18\ problems = 22\ minutes}[/tex]

Step-by-step explanation:

Yan has finished = [tex]\frac{3}{5} of \ 45 \ maths \ problems[/tex]

Yan has finished = [tex]\frac{3}{5} * 45[/tex]

=> 3 * 9

=> 27 problems

Yan has problem left:

=> 45 - 27

=> 18 problems

1 problem = [tex]1 \frac{4}{5}[/tex] of a minute

1 problem = 1.2 minutes

18 problems = 1.2 * 18

18 problems = 21.6 minutes

18 problems ≈ 22 minutes

Answer:

[tex]\boxed{\sf 32 \ minutes}[/tex]

Step-by-step explanation:

Yan finished 3/5 of 45 math problems.

[tex]\frac{3}{5} \times 45=27[/tex]

Yan finished 27 math problems.

[tex]\sf 1\frac{4}{5} \ of \ a \ minute= 108 \ seconds=1.8 \ minutes[/tex]

Yan has [tex]45-27=18[/tex] problems left.

1 problem = 1.8 minutes

18 problems = [tex]1.8* 18=32.4[/tex] minutes

32.4 minutes to nearest minute will be 32 minutes.

Answer:

2 × 5

Step-by-step explanation:

We want to split the number 10 into its prime numbers.

A good way to start is divide the number by 2, if it's even. 10 is even, so we can divide by 2.

[tex]10\div2=5[/tex]

So the current factors are 2 and 5. We would keep going if one of these numbers was composite, but 2 and 5 or both prime numbers, so we can end the factorization here.

Therefore, the prime factorization of 10 is 2 × 5.

Hope this helped!

The prime factorization of 10 is 2 x 5.

Prime factorization is when you figure out the prime numbers that you can multiply together  to get a certain number.

To figure out the prime factors of 10, we begin by dividing it by the lowest prime number, which is 2. Because 10 can be divided evenly by 2, we can say that 10 is equal to 2 multiplied by 5.

The numbers 2 and 5 are special because they can only be divided by 1 and themselves. This makes them prime numbers. The prime factorization of 10 is the result of multiplying the prime factors 2 and 5 together.

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Answer:

$17

Step-by-step explanation:

If each ticket is $7 and there are 48 student multiply 7 and 48 to see how much the tickets were in total (336)

Now subtract 353 and 336 to see how much money is left (17)

Answer: -17?

Step-by-step explanation:

because 7*48= 336

then you would do 336-353= -17

which gave me the answer of -17

Answer:

x = 180 - [(180 - 3x) + (180 - 2x)]

Step-by-step explanation:

Start off by finding the angles of the triangle

Angle F = 180 - 3x

The angle across from I (which I will call I) = 180 - 2x

Angle G = 180 - (F + I)

Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G

Therefore x =  180 - (F + I) or otherwise said as:

x = 180 - [(180 - 3x) + (180 - 2x)]

I hope this is helpful :)

Answer:  1. A. y=17x

2.  $59.50

Step-by-step explanation:

1. In the table , it can be seen that as x increases y increases with the proportionality constant k = [tex]\dfrac{y}{x}=\dfrac{51}{3}=\dfrac{85}{5}=\dfrac{119}{7}=17[/tex],.

Equation of direct variation between  x and y : [tex]y=kx[/tex]

Put k= 17 , we get

[tex]y=17x[/tex] , which is the required equation.

So correct option is "A".

2. To find : The charge for renting a machine for 3.5 hours.

Put x= 3.5 in above equation , we get

[tex]y=17(3.5)=59.5[/tex]

Hence, the  charge for renting a machine for 3.5 hours is $59.50.

So correct option is "B".

Answer:

5

Step-by-step explanation:

-32=-7n-12+3n

-32=-7n+3n-12

-32=-4n-12

-4n=-32+12

-4n=-20

n=-20/-4

n=5

Answer:

[tex]n=5[/tex]

Step-by-step explanation:

[tex]-32=-7n-12+3n\\\text{Combine Like Terms}\\-32=-7n+3n-12\\-32=-4n-12\\\text{Isolate the Variable}\\-32+12=-4n-12+12\\-20=-4n\\\text{Divide each side by -4}\\n=5[/tex]

Answer:

f(x) is quadratic. g(x) and h(x) are linear.

Step-by-step explanation:

So we have the three functions:

[tex]f(x)=4x^2\\g(x)=1-x\\h(x)=32x[/tex]

Linear functions are polynomials in which the highest degree is 1.

Quadratic functions are polynomials in which the highest degree is 2.

And exponential functions usually have a variable in the exponent (e.g. 2^x).

For f(x), the highest degree is 2. Thus, f(x) is a quadratic function.

For g(x), the highest degree is 1 and there are no variables in the exponent. Thus, g(x) is a linear function.

Similarly, for h(x), the highest degree is 1 and there are no variables in the exponents, so h(x) is also a linear function.

Answer:

29

Step-by-step explanation:

using pemdas, you first need to solve 3² which is 9. Then you do what's in the parenthesis (4-1) which is 3. you'll first multiply 9 and 3 (27) add the 2 and there's your answer, 29.

Answer:

[tex]\boxed{y = -2}[/tex]

Step-by-step explanation:

Hey there!

To find y when x is -5 we go to -5 on the x-axis.

When at -5 find where the blue line is vertical to -5,

which is -2.

Hope this helps :)

Answer:

The first one

Step-by-step explanation:

This line is the best fit for the scatter plot because it touches a lot more points than the second

Answer:

The first line

Step-by-step explanation:

Hey there!

Well the first lie is a positive slope just like the dots whereas,

the second line is a negative slope.

Therefore, the first line is the line of best fit.

Hope this helps :)

Answer:

202m

Step-by-step explanation:

Please see attached picture for full solution.

Let x meters be the height of the building.

Answer:

7 units

Step-by-step explanation:

(number line:)

<- -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ->

         there are 7 units from 1 to -6 (you don't count the 0)

(I'm not sure if you understood my explanation, but I do am sure about the answer, so if there is something you didn't understand let me know, and which part are you confused about so I can help you out!)

Answer:

[tex]\huge\boxed{\sf 7\ units}[/tex]

Step-by-step explanation:

To find that how much far they are from each other, we can subtract both of them.

=> 1 - (-6)

=> 1 + 6

=> 7 units

So, they are 7 units apart from each other.

Answer:

Large herbivores, such as elephants and

giraffes, need to eat a lot. = Example

Their service is expedient - I'm amazed

by how fast they are!  Example, explanation

Jane is always very enthusiastic and

never negative or doubtful. = antonym

Carburetors, which feed fuel and air to

engines, are very important. = explanation

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[2×10*(-3) × (4×10*(4)] = 80

Step-by-step explanation:

First of all 0.002 is 10*(-3) and not 10(-2) , so you can eliminate the first 2 answers.

Second of all, according to the calculator the left equation is correct, while the right one isn't... so there you go

Glad to help :)

Answer:

x = 9x5 / 4

x = 45/4

(either one)

Step-by-step explanation:

[tex]\frac{4}{5}[/tex] = [tex]\frac{9}{x}[/tex]

Multiple known diagonals and divide by number opposite to unknown number (x).

Hope that helped!!! k

Answer:

(b) 4 x = 4 5 is the needed expression to solve for the value of x.

Step-by-step explanation:

Here, the given proportion is simplified as:

4/5=9/x

Now, to simplify any proportion of the form   the simplest way is cross multiplication.

So, cross multiplying  a/b=c/d -> ad=bc

Similarly cross multiplying 4/5=9/x, we get:

4 (x)  = (9) (5)