1 ACTIVITY: Estimating a Part
Work with a partner. Use a model to estimate the answer to each question.
e. What number is 65% of 30?

Answer:

true

Step-by-step explanation:

there is a nice rule for when a number is divisible by 13 :

starting with the lowest digit value (the last on the right) form blocks of 3 digits as numbers and give them alternating signs (starting with +).

if the last block (the last on the left) has less than 3 digits, just use the remaining ones as a number.

add all these numbers (with their associated signs).

if the number calculated by this (alternative) sum is divisible by 13 then the original number is divisible by 13.

if N = abcdefghi, then (ghi - def + abc) must be divisible by 13, so that N is also divisible by 13.

in our case, N = abcabc.

the block calculation is therefore abc - abc = 0, which is always divisible by 13.

so, any number formed like this must be divisible by 13.

FYI - a quick look at why that is :

N = abcabc =

= a×10⁵ + b×10⁴ + c×10³ + a×10² + b×10 + c =

= a×(10⁵ + 10²) + b×(10⁴ + 10) + c (10³ + 1) =

= a×100100 + b×10010 + c×1001

define d = 1001 = 77×13

and we get

a×d×100 + b×d×10 + c×d

a sum is divisible by a number, if every summed up term is divisible by that number.

since d is a factor in every term, and d is divisible by 13, so is every term and therefore the whole number.

so, every number in the form of abcabc is divisible by 13.

It is true that every number in the form N = ABCABC, where ABC represents a three-digit string, is divisible by 13.

Let's consider the number N = ABCABC, where ABC represents a three-digit string. We can express N as follows:

N = 1000 * ABC + ABC

= 1001 * ABC

Notice that 1001 is divisible by 13, as 1001 = 13 * 77. Therefore, if ABC is any three-digit string, 1001 * ABC is divisible by 13.

Since N = 1001 * ABC, and 1001 is divisible by 13, it follows that N is also divisible by 13. This holds true for every number in the form ABCABC, where ABC is a three-digit string.

This pattern holds for any three-digit string repeated twice, ensuring that every number in the form ABCABC is divisible by 13.

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Answer:

49

Step-by-step explanation:

step 1: Add the ratios 2:7 which is 2+7=9

step 2: divide the bigger ratio (7) by the total calculated in step 1 (9) and multiply by the total number given (63)....

step 3: we have 7/9×63 which is 49

therefore the bigger number is 49

Answer:

a+3b^2

Step-by-step explanation:

Answer:

124/67 and 1/3

Step-by-step explanation:

The second ratio is 1.5/4.5, which readily reduces to 1/3.

Dividing both numerator and denominator of 24.8 / 13.4 by 2 yields the simpler 12.4 / 6.7  or  124/67.  This latter result cannot be reduced.

Answer:

the answer is 1/2

Step-by-step explanation:

-(-D) = -(-1/2)

2 negatives make a positive so it would be 1/2 or in other cases, 0.5

Answer: 45%

Step-by-step explanation:

Converting the word problem into words, we have:

18= x/100*40

Solving for it, we get that x=45.

Answer:

$180 - (15% * $180) = $153

Step-by-step explanation:

Answer:

$153

Step-by-step explanation:

Hello!

Original Price: $180

Original Percentage: 100% (multiplier = 1)

Discount: 15% (multiplier = 0.15)

Given that the Original Percentage is 100% and the Discount is 15%, we are trying to find 85% of the Original Price.

Sale Price: 85% of Original Price (multiplier = 0.85)

The sale price is $153.

Answer:

rounds to 672

Step-by-step explanation:

This is a proportion question.

572     85

___ = ___

 x       100

Do 572 x 100 first to get 57,200.

Then divide 57,200 by 85 to get around 672 students.

However, I haven't done these kinds of questions in a long time, therefore I could be wrong.

On a snowy day 85% of the students of Wilson high school were present., There were 672 students enrolled at Wilson high school.

To find out how many students were enrolled at Wilson high school, we can use the information given in the question. We are told that 85% of the students were present on a snowy day, and that 572 students were present. To find the total number of students enrolled, we can set up a proportion: Present students / Total students = Percentage present / 100 Let's plug in the values we know: 572 / Total students = 85 / 100 To solve for the total number of students, we can cross-multiply and solve for Total students: 572 * 100 = Total students * 85 57200 = Total students * 85 Dividing both sides by 85: 57200 / 85 = Total students Total students = 672 Therefore, there were 672 students enrolled at Wilson high school.

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Answer:

i think it would be greatest common factor

Step-by-step explanation:

Answer:

0.2 centimeters

Step-by-step explanation:
Strategy 1:

Make the equation: 5=a•s, where s is the scale factor and "a" is the number of centimeters which 5 meters

First, we need to find the scale factor. 50 meters would be s times greater than 2 centimeters. Find s by first converting meters into centimeters
50m=5000cm. 5000cm=2cm*s, so s = 2500
5m=a*2500, a=0.002 meters, and 0.002 meters is equal to 0.2 centimeters.

Strategy 2:
the ratio of the scale drawing to real life will always stay the same, so
2 cm / 50 meters = x / 5 meters, and cross multiply to get
x cm* 50 m = 2 cm * 5 m, so
x cm * 10 = 2 cm
x cm = 2/10 cm
x cm = 0.2 cm

Strategy 3:
Notice that 5 meters is 10 times smaller than 50 meters, so on the scale drawing, we are looking for a number 10 times smaller than 2 centimeters, so  2/10=0.2 cm

Answer:

0.2

Step-by-step explanation:

2 = 50

x = 5

50/5 = 10

do the same on the other side

so 2/10 = 0.2

Answer:

3.14159

Step-by-step explanation:

Answer:

He can process 45 engines in 2 hours.

Step-by-step explanation:

2 hours = 120 minutes

You can multiply 3 to 40 because 40x 3 = 120, but you have to do the same to 15, so 15 x 3 = 45.

Or you can divide the engines (15) by minutes (40) to find out how many engines can be processed per minute.

15/40 = 0.375 an engine per minute.

Then multiply that by 120, which is two hours in minutes.

0.375 x 120 = 45

Answer:

a) 49 degrees     b) 56 degrees

Step-by-step explanation:

a) Vertical angles are lines that intersect each other that always form the same angles on "opposite" sides. Angle x and the 49 degrees are vertical angles, which means that x also has to be 49 degrees.

- - -

b) We know that any triangles' three internal angles combined equal 180 degrees.

Since we already know two out of three angles in the triangle (63 and 49) we can find the last unknown angle: 180 - (63 + 49) = 68. The unknown angle in the triangle is 68 degrees.

We also know that all straight lines are 180 degrees. The line that angle y rests on is 180 degrees. So we can subtract the 68 degrees from 180 degrees to find that y = (180 - 68) / 2, because angle y is the same on the other side of the 68 degrees.

So:
y = (180 - 68) / 2
y = 112 / 2
y = 56

Angle y is 56 degrees.

Apologies if my explanation is confusing.

Answer:

a) x = 49° C

b) y = 48° C

Step-by-step explanation:

a) x is 49° C because we know that opposite angles are the same which means that x is opposite to 49° C which makes it also 49° C.

b) y is 48° C because angles in a Triangle always add up to 180° C which means that 180 - 83 - 49 = 48 which makes the answer 48° C.

Answer:

For the first problem, it would be 2.25 grams.

For the second problem, it would be 10.45 pounds.

For the third problem, it would be 13.3735 more grams of flour

For the fourth problem it would be 6.25 inches long.

Step-by-step explanation:

1st problem:

3 - 0.75 = 2.25

2nd problem:

5.75 / .55 = 10.45454545 (so if we simplified it, then it would be 10.45)

3rd problem:

15.285 * 7/8 = 13.3735

4th problem:

31.25 / 5 = 6.25

I see that someone has already answered 1-4 so i will answer 5

so for 2 gallons it is 35.75 so to find out the amount for 4 gallons you would add 35.75+35.75 to get your answer of 71.5

hope this helped :>

Answer:

2/3 or 66%

Step-by-step explanation:

If you divide 12 into 3 groups you get 4. 4 + 4 = 8 therefore 8/12 = 66%

Answer:

2. It will be a 7 3/4in x 12 1/4in rectangle

4.  31,987 in^2

6. 30 547/640 in^3

Step-by-step explanation:

2. This is a cross-section. In order to get the cross-section, you take your shape. (a 7 3/4 x 12 1/4 x 3 3/4 rectangle) and essentially you remove the last dimension (Height).

4. Take your surface area value (319 35/64) and multiply it by 100 (10 per dimension length and width). This leaves you with 319.87x100 = 31,987 in^2

6. (308 35/64)/10. Pretty easy, take 308.546875, divide by 10, and you get 30.8546875, which is 30 547/640 in^3 in fractions.

Answer:

2. It will be a 7 3/4in x 12 1/4in rectangle

4.  31,987 in^2

6. 30 547/640 in^3

Step-by-step explanation:

2. This is a cross-section. In order to get the cross-section, you take your shape. (a 7 3/4 x 12 1/4 x 3 3/4 rectangle) and essentially you remove the last dimension (Height).

4. Take your surface area value (319 35/64) and multiply it by 100 (10 per dimension length and width). This leaves you with 319.87x100 = 31,987 in^2

6. (308 35/64)/10. Pretty easy, take 308.546875, divide by 10, and you get 30.8546875, which is 30 547/640 in^3 in fractions.

Answer:

1. 72.33.24. none5.none6.97. 08. 4

Step-by-step explanation:

Answer:

1 home + 1 triple + 5 double

1 +3+5×2

1+3+10=14

35-14 =21 singles

21/35×100=60%

Answer:

The total percent decrease is [tex]$a+b-\frac{a b}{100}$[/tex]

Step-by-step explanation:

         Step 1: Finding the two percentage decrease

         Step 2: Finding their difference

Step 1 of 2

Let the decrease by a% be 100-a

Then b% decrease is

[tex]$$\begin{aligned}\frac{b}{100} \times(100-a) &=\frac{100 b-a b}{100} \\\frac{100 b}{100}-\frac{a b}{100} &=b-\frac{a b}{100}\end{aligned}$$[/tex]

Step 2 of 2

The percentage difference between the two percentages is,

[tex]$$\begin{aligned}&(100-a)-\left(b-\frac{a b}{100}\right)=100-a-b+\frac{a b}{100} \\&100-a-b+\frac{a b}{100}=100-\left(a+b-\frac{a b}{100}\right)\end{aligned}$$[/tex]

Since 100 is the total percent [tex]$a+b-\frac{a b}{100}$[/tex] is the percentage decrease.

Answer: $21.45

Step-by-step explanation:

FACTS:

1 yard costs $5.72.

She bought 3.75 yards

Total cost= cost per yard x number of yards

Total: t

t= 5.72x3.75

t= $21.45

She spent $21.45 for 3.75 yards of material

Answer:

Given:

Jason can type at a rate of 40 words per minute.

Find:

The time taken for him to type a 2000 words essay

Step-by-step explanation:

Using the Conversion factor.

Jason's typing essentially converts "minutes" into "words" and vice versa, so we can use a conversion factor.

We need to arrange the data so that the "words" units cancel and we are left with "minutes" units:

time = 2000 words * 1 minutes/40 words

2000/40 minutes = 50 minutes

The time taken for him to type a 2000 words essay is 50 minutes.

Answer:

C. Increase

Step-by-step explanation:

Since the new value is larger than the original value, there was an increase in the number, so it is called percent of increase.

Answer:

Step-by-step explanation:

Let's say that 50% of people liked ice cream in 2020. In 2022, 65% of people liked ice cream. There is an increase of people liking ice cream. So, it is called a percent increase.

Remember...

A) A percent change can be either an increase OR a decrease.

B) A decrease can only LOWER the percentage

So, it has to be C.

Answer:

[tex]B=\sqrt{2}[/tex]

Step-by-step explanation:

Original equation:

[tex]B = \sqrt{2+\sqrt{3}} - \sqrt{2 - \sqrt{3}}\\[/tex]

Square both sides:

[tex]B^2=(\sqrt{2+\sqrt{3}})^2 + 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}}) + (-\sqrt{2-\sqrt{3}})^2[/tex]

Cancel out the square roots and squares:

[tex]B^2=2+\sqrt{3}}+ 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}}) + 2-\sqrt{3}[/tex]

Add the sqrt(3) and -sqrt(3) as well as 2 and 2

[tex]B^2=4 + 2(\sqrt{2+\sqrt{3}} * (-\sqrt{2 - \sqrt{3}})[/tex]

Use the identity: [tex]\sqrt{a} * \sqrt{b} = \sqrt{a * b}[/tex] to rewrite the two square roots being multiplied:

[tex]B^2=4 + 2(-\sqrt{(2+\sqrt{3}) * (2 - \sqrt{3}}))[/tex]

Use difference of squares: [tex](a-b)(a+b) = a^2-b^2[/tex]

[tex]B^2=4 + 2(-\sqrt{2^2-\sqrt{3}^2})[/tex]

Square both sides

[tex]B^2=4 + 2(-\sqrt{4-3})[/tex]

Subtract:

[tex]B^2=4 + 2(-\sqrt{1})[/tex]

Evaluate square root of 1:

[tex]B^2=4 + 2(-1)[/tex]

Multiply

[tex]B^2=4 -2[/tex]

Subtract

[tex]B^2=2[/tex]

Take square root of both sides:

[tex]B=\sqrt{2}[/tex]

Answer:

84 ounces

Step-by-step explanation:

Total pounds of popcorn bought = 64 pounds

1/4th kept for family ==> 1/4 * 64 = 16 lbs

Remainder = 64-16 = 48 lbs

1/8th of remainder to club ==> 1/8 * 48 = 6 lbs to club

Remainder left over = 48-6 = 42 lbs

Distributed 42 lbs between each of 8 friends equally
Each friend gets 42/8 lbs = (42/8) * 16 = 84 ounces

Since there are 16 ounces in a pound

From the given information each friend receives 84 ounces of popcorn.

Let's solve the problem using thee concept of Fractions

1. Miriam bought 64 pounds of popcorn.

2. She kept 1/4 of the popcorn for her family. So, the amount of popcorn left after this step is [tex]\(64 \times \frac{3}{4}\)[/tex].

Now, let's calculate the popcorn remaining after Miriam keeps some for her family:

[tex]\(64 \times \frac{3}{4} = 48\)[/tex] pounds.

Next, Miriam gave 1/8 of the remaining popcorn to her club, leaving her with [tex]\(48 \times \frac{7}{8}\)[/tex] pounds.

Now, let's calculate the popcorn remaining after Miriam gives some to her club:

[tex]\(48 \times \frac{7}{8} = 42\)[/tex] pounds.

Finally, she distributed the rest equally among 8 friends. To find out how much each friend gets, we'll divide the total popcorn left by the number of friends:

Amount each friend gets =[tex]\(\frac{42}{8}\)[/tex] pounds.

The problem asks for the answer in ounces, not pounds.

To convert pounds to ounces, we know that 1 pound is equal to 16 ounces. So, to get the amount of popcorn each friend gets in ounces, we'll multiply the previous answer by 16:

Amount each friend gets = [tex]\(\frac{42}{8} \times 16\)[/tex] ounces.

Amount each friend gets = [tex]\(84\)[/tex] ounces.

So, each friend will get 84 ounces of popcorn.

In summary, Miriam's 64 pounds of popcorn were reduced to 42 pounds after sharing with her family and club. Finally, the remaining popcorn was divided equally among her 8 friends, with each friend receiving 84 ounces.

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Answer:

1/4

Step-by-step explanation:

V = LWH

V = (1/2 ft)(1/2 ft)(1 ft)

V = 1/4 ft³

Answer:

432 in³

Explanation:

Given measurements:

To convert feet to inches, multiply by 12

Volume of rectangular prism:

⇒ L × W × H

⇒ 6 × 6 × 12

⇒ 432 in³

Answer:

4

Step-by-step explanation:

3+(-2) is the same as 3-2 which is 1. and since with multiple exponents you work from the top you have 4 to the power of 1^4. 1^4 is 1, so it's 4^1, which is 4.

Answer: A

Step-by-step explanation:

A. yes because -52 and -32 are separated by a distance of 20 units

B. no because -3.4 and 2.2 are not separated by more than 5 units

C. no because -4.2 and 1.3 are not separated by more than 5 units

D. no becasue 5 and 1 are not separated by more than 5 units

Answer:

A, B, C

Step-by-step explanation:

A coordinate is written as (x, y) where:

For a pair of coordinates to be separated by a vertical distance of greater than 5 units, the difference in their y-values should be greater than 5.  To find the difference between two values, subtract the smaller value from the larger value.

A.  (-1, -52) and (-1, -32)

Difference in y-values:  (-32) - (-52) = 20

B.  (1.8, -3.4) and (1.8, 2.2)

Difference in y-values:  (2.2) - (-3.4) = 5.6

C.  (-3.5, -4.2) and (-3.5, 1.3)

Difference in y-values:  (1.3) - (-4.2) = 5.5

D.  (4, 5) and (4, 1)

Difference in y-values: 5 - 1 = 4

Therefore, coordinate pairs A, B and C are all separated by a vertical distance of greater than 5 units.

Answer:

$66

Step-by-step explanation:

25% of 80 = 20

80 - 20 = 60

10% of 60 = 6

60 + 6 = 66