MATHEMATICS MIDDLE SCHOOL

How would I write these problems?

Answers

Answer 1

Answer:

21) Total number of cups: 26

6) Solution of the equation: x = -12

7) Father's age: 40

4) Distance driven: 400 miles

Step-by-step explanation:

21)

Let's call:

$h=10 cm$ the height of each cup

$H=30 cm$ the total height available in the dispenser

We are told that each cup added to the stack add a height of

$\Delta h = 0.8 cm$

We can therefore solve the problem by writing the following equation:

$H=h+N\Delta h$

which means that the total height available (H) is filled by the height of one cup (h) + the number of additional cup multiplied by 0.8.

Solving for N:

$N=(H-h)/(\Delta h)=(30-10)/(0.8)=25$

And including the first cup, the total number of cups is

$N+1=25+1=26$

The equation that we have to solve is

$(5)/(2)x-1=-31$

We proceed as follows:

First of all, we add +1 on both sides of the equation,

$(5)/(2)x-1+1=-31+1\n(5)/(2)x=-30$

Now we multiply by 2 on both sides:

$(5)/(2)x\cdot 2=-30\cdot 2\n5x=-60$

And now we divide both sides by 5:

$(5x)/(5)=(-60)/(5)\nx=-12$

Let's call:

k = Karma's age

f = father's age

We are told that Karma is 13 years old, so

k = 13

Also, Karma's age is 2 years less than 3/8 of the father's age, so we can write

$k=(3)/(8)f-2$

By combining the two equations,

$13=(3)/(8)f-2$

And solving for f, we find:

$(3)/(8)f=13+2\n(3)/(8)f=15\n3f=15\cdot 8 =120\nf=(120)/(3)=40$

So, the father's age is 40.

Let's call:

T = 16 the total volume of the tank (16 gallons)

We also know that the car burns 0.03 gallons per mile, so the amount of fuel consumed after x miles is

$0.03 x$

This means that the amount of fuel left after x miles is

$16-0.03x$

We also know that the amount of fuel left is 4 gallons, therefore:

$16-0.03x=4\n0.03x=16-4\n0.03x=12\nx=(12)/(0.03)=400$

So, 400 miles.

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There were 1200 boys at a school assembly. The ratio of boys to girls at the assembly was 20:23. How many girls were at the assembly?

Answers

The required number of girls in the school assembly is 1380.

Given,
There were 1200 boys at a school assembly. The ratio of boys to girls at the assembly was 20:23. Number of girls in the assembly line is to be determined

What is the Ratio?

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Representation of ratio of two values a and b, ratio = a:b.

Let the number of girls in the school assembly be x.
There were 1200 boys at a school assembly. The ratio of boys to girls at the assembly was 20:23. So the ratio can be written as,
1200 : x = 20 : 23
1200 / x = 20 / 23
x = 1200 * 23 / 20
x = 60 * 23
x = 1380
Here, the number of girls in the school assembly is 1380.

Thus the required number of girls in the school assembly is 1380.

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I believe the answer is 1,600 girls

Answers

AAAA
BBAB
ABAB
ABBB
BABA
(I can choose multiple)

Answers

Answer:

BBAB, ABAB, and BABA

Step-by-step explanation:

Use the probability/combination theorem.

1. the athletes were either running or jumping. if the ratio of the number of runners to the number of jumpers was 9 to 5 and 2170 were observed, how many were jumpers?2. sam found that if the product of 5 and a number is increased by 8, the result is 10 more than the product of 3 and the number. what is the number?

3. if g(x) = -4 x^2 - 3, find g(-3)

4. solve for y: 3x + 4y = 8 -y

Answers

In number 1 ;

2170 = 14

5/14*2170 = 775

ans: 775 jumpers

Does every point lie in a quadrant

Answers

No because some points can lie in the y & x-axises

How much interest is earned on a principal of $671.37 invested at an interest rateof 4% for four years?

Answers

ANSWER:

The interest earned on a principle of $671.37 at an interest rate of 4% for four years is $ 107.42.

SOLUTION:

Given, p = $671.37, R = 4%, t = 4.

We need to find the simple interest for the above given values of amount, rate and years.

We know that

$Simple Interest $=\left((p * r * t)/(100)\right)$$

where, p = principal amount ; r = rate of interest ; t = number of years

By substituting the values we get,

$=\left((671.37 * 4 * 4)/(100)\right) \n\n$=\left((2685.48 * 4)/(100)\right) \n\n$=\left((2685.48)/(25)\right)$$=107.4192$$

Simple interest is $ 107.42 approximately.

Hence, the interest earned on a principle of $671.37 at an interest rate of 4% for four years is $ 107.42.

Answer:

$26.8548

Step-by-step explanation:

Round each addend to the nearest whole number and estimate the sum
19.43+11.5+3.08

Answers

19+12+3=34

because 11.5 is right between 11 and 12 you always round up

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