The greatest integer that will divide both 4900 and 168 exactly is 28.
What is Least Common Multiple?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
For example, the LCM of 6 and 8 is 24. Hence 24 is divisible by both 6 and 8.
First, Prime Factorizing 4900
4900 = 7 x 7 x 2 x 2 x 5 x 5
and, Prime Factorizing 168
168 = 2 x 2 x 2 x 3 x 7
So, the Common multiple of 4900 and 168 is 2 x 2 x 7 = 28.
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Final answer:
The greatest integer that will divide both 4900 and 168 exactly is 4.
Explanation:
The greatest integer that will divide both 4900 and 168 exactly is 4.
To determine this, we can use the concept of greatest common divisor (GCD). The GCD is the largest positive integer that divides two given numbers without leaving a remainder. In this case, the GCD of 4900 and 168 is 4.
One way to find the GCD is to factorize both numbers and determine the common factors. In this case, the prime factorization of 4900 is 2^2 * 5^2 * 7^2, and the prime factorization of 168 is 2^3 * 3 * 7.
The common factors are 2^2 and 7^1, which multiplied together give us 4. Therefore, 4 is the greatest integer that will divide both 4900 and 168 exactly.
Solve the following system. Q
-8x - 8y = 0 and -8x + 2y = -20
Answer:
x=2 and y=−2
Step-by-step explanation:
I will solve your system by substitution.
−8x−8y=0;−8x+2y=−20
Step: Solve−8x−8y=0for x:
−8x−8y+8y=0+8y(Add 8y to both sides)
−8x=8y
−8x
−8
=
8y
−8
(Divide both sides by -8)
x=−y
Step: Substitute−yforxin−8x+2y=−20:
−8x+2y=−20
−8(−y)+2y=−20
10y=−20(Simplify both sides of the equation)
10y
10
=
−20
10
(Divide both sides by 10)
y=−2
Step: Substitute−2foryinx=−y:
x=−y
x=−(−2)
x=2(Simplify both sides of the equation)
Solve for x in the diagram below.
Answer:
8x+30°=110°
8x=80°
x=10°
Step-by-step explanation:
because the angles are vertical => they are equal
Luis is asked to construct a triangle with a 35° angle and a 45 angle How many different triangles could he draw with
these angle measures?
There is only one unique triangle that can be drawn with a 35° angle and a 45° angle, as the third angle is determined to be 100° to make the sum 180°.
To determine how many different triangles can be constructed with a 35° angle and a 45° angle, we can use the fact that the sum of angles in a triangle is always 180°. Adding the given angles, we get 35° + 45° = 80°. Subtracting this from 180° gives us the third angle, which is 180° - 80° = 100°. Since the sum of the angles is 180° and all angles are determined, there is only one unique triangle that can be drawn with these angle measures
Sofia places 26 tiles representing each letter of the alphabet into a bag. Five of the tiles represent the vowels A, E, I, O, and U. Sofia will randomly select 1 tile from the bag and without replacement select another tile from the bag. Sofia will draw two tiles from the bag 260 times. What is a reasonable prediction for the number of times Sofia will select a consonant tile and a vowel tile?
Answer:
42 times.
Step-by-step explanation:
The number of total alphabet = 26 tiles
The number of vowels = 5
The number of consonant = 26 - 5 = 21
Sofia will randomly select 1 tile from the bag and without replacement select another tile from the bag.
The probability to select consonant at first time = 21/26
Total tiles after the first selection = 26 - 1 = 25
The probability to select vowels at second time = 5/25
The probability to select consonant and vowels = [tex]\frac{21}{26} *\frac{5}{25} =\frac{21}{130}[/tex]
Sofia will draw two tiles from the bag 260 times.
The prediction for the number of times Sofia will select a consonant tile and a vowel tile = [tex]\frac{21}{130} *260=42 \ times[/tex]
Which inequality matches the graph?
A) x > 2
B) x < 2
C) x = 2
D) x ≥ 2
Answer:
D
Step-by-step explanation:
how do you write12 minutes to noon digital form
Answer:
11:48 AM
Step-by-step explanation:
Answer:
11:48 am
Step-by-step explanation:
not sure if I did this right but 60-12=48. before noon would be am so it would be 11:48 am
sorry if its wrong qwq
A business owner receives a 5000 loan with 13% interest, charged at the end of each year
Answer:
The answer is 5,650
Step-by-step explanation:
The loan is 5,000 and the interest is 13%
First you have to get the percent to a decimal and then multiply it by the loan which in this case is 5,000
13/100 = 0.13
0.13 x 5000 = 5650
Round 234,983.3 to the nearest hundred
Thanks ❤️
Attendance at a museum more than tripled this week.last week,186 people went to the museum. Write and inequality to show how many people
Answer:
Step-by-step explanation: your unknown would be BABY IAN GOT TIME TO ANSWER YO QUESTION?!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-6+7x=y, what is the y-intercept?
What’s the difference from a number chart and a hundred chart
The number chart is when the number line helps with the concept of sequencing, and base-10 blocks reinforce place value
In the hundred chart , it consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.
What is a Number chart and Hundred chart?
Hundred Chart : A hundreds chart is highly useful for children who are learning to count to 100 and strengthening their numerical fluency. With a hundreds chart, numbers read from left to right in rows of 10, starting from the top left corner with the number 1, all the way down to 100 in the bottom right corner
Number Chart : A table listing numbers in numerical order is known as a numbers chart. The numbers in this arrangement will be 1 through 10 in the first line, 11 through 20 in the second line, 21 through 30 in the third line, and so on. There are various types of specific number charts, such as charts for the hundreds that include the digits 1 through 100.
Given data ,
In the hundred chart , it consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows. The layout allows children to count left to right by ones, and down by tens.
And ,
The number chart is when the number line helps with the concept of sequencing, and base-10 blocks reinforce place value
Types of Number Chart
Even Numbers Chart. An even numbers chart represents all the numbers that are divisible by 2.
Odd Numbers Chart. An odd numbers chart represents all the numbers that are NOT divisible by 2
Prime Numbers Chart
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Which is the equation of the given line in slope-intercept form? y= -1/4 x +1 y= -4x+1 y=4x-1 y=4x=+1
Answer:
[tex]y=4x+1[/tex]
Step-by-step explanation:
The line is shown in the attachment.
The slope of this line is given by: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through (0,1) and (1,5)
Plug in the points to get:
[tex]m=\frac{5-1}{1-0}=4[/tex]
The equation of this line is given by [tex]y=mx +b[/tex], where b=1 is the y-intercept.
From the graph the y-intercept is 1, because the line intersects the y-axis at (0,1).
Therefore the equation is [tex]y=4x+1[/tex]
The icecream parlor has 30 flavors, but for the last week they have only had 25 flavors. Find the percent of change. Tell if it is an increase or decrease.
Answer:
The percent of change is 20%.
And it is increased by last month.
Step-by-step explanation:
Given:
The ice cream parlor has 30 flavors, but for the last week they have only had 25 flavors.
Now, to find the percent of change.
Flavors ice cream parlor has = 30.
Flavors last week they had = 25.
So, the flavors increased from last week by:
[tex]30-25=5\ flavors.[/tex]
Now, to get the percent of change:
[tex]\frac{5}{25} \times 100[/tex]
[tex]=\frac{500}{25}[/tex]
[tex]=20\%.[/tex]
Thus, the percent of change is 20%.
The flavor is increased by last month.
Therefore, the percent of change is 20%.
And it is increased by last month.
Final answer:
The percent of change is a decrease of 16.67%, calculated by subtracting the new amount of flavors from the original, dividing by the original amount, and multiplying by 100.
Explanation:
To find the percent of change in the number of flavors at the ice cream parlor, we will subtract the original amount of flavors from the new amount, divide that by the original amount, and then multiply by 100. The original amount of flavors was 30, and the new amount is 25. Here is the calculation:
Subtract the new amount from the original amount: 30 - 25 = 5
Divide the change by the original amount: 5 ÷ 30 = 0.1667
Multiply by 100 to get the percent: 0.1667 x 100 = 16.67%
The percent of change is a decrease of 16.67% since the number of flavors went down from 30 to 25.
a fireman leaned a 36 foot ladder against a building. if he placed the ladder 7 feet from the base of the building what angle is formed between the ladder and the ground
Answer:
78.79°
Step-by-step explanation:
A fireman placed a ladder of length 36 feet against a building.
Now, if he placed the ladder 7 feet from the base of the building, then the angle formed between the ladder and the ground will be [tex]\theta[/tex] (Say).
Now, the ladder, the base ground and the building forms a right triangle and the ladder is the hypotenuse of the triangle and [tex]\theta[/tex] is the base angle.
So, [tex]\cos\theta = \frac{\textrm {Base length}}{\textrm {Ladder length}} = \frac{7}{36}[/tex]
⇒ [tex]\theta = \cos^{-1}(\frac{7}{36}) = 78.79^{\circ}[/tex] (Answer)
Solve for x: 3x = 2/5
Answer:
x=2/15
Step-by-step explanation:
3x=2/5
/3 to both sides
3×/3=2/5/3
x=2/15
reduce the fraction 34/48 to its lowest term
Answer: 17/24
Step-by-step explanation: To write the fraction 34/48 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 34 and 48.
Since the factors of 34 are 1, 2, 17, 34 and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, the greatest common factor of 34 and 48 is 2.
So we divide the numerator and the denominator of 34/48 by 2.
34 divided by 2 is 17 and 48 divided by 2 is 24.
So 34/48 written in lowest terms is 17/24.
100 POINTS!!! will give BRAINLIEST to the person who does all 3 correctly! With explanation!
Answer:
Option A, %29.2
Step-by-step explanation:
Step 1: Find the total fixed expenses
150 + 30
180
Step 2: Find the percentage
180 / 617
0.2917... * 100
%29.17
%29.2
Answer: Option A, %29.2
Answer:
29.2%
Step-by-step explanation:
The fixed expenses are rent and the emergency fund
150+30 =180
The total income is 617
The percent is fixed expenses/income
180/617
.291734198
Multiply by 100% to change from decimal from to percent
29.1734198%
Rounding to the nearest tenth
29.2%
A car approaches a stop sign going 5 m/s before it comes to a stop. If it does this in 4 seconds, what was
its acceleration?
Answer:
Acceleration = -1.25 m/s²
Step-by-step explanation:
Given data:
initial velocity = 5 m/s
Final velocity = 0 m/s since the car stopped
change in time = 4 seconds
Acceleration = change in velocity/change in time
Acceleration = (Final velocity - Initial velocity)/time
Acceleration = (0-5)/4
Acceleration = -5/4
Acceleration = -1.25 m/s²
The acceleration in negative since the car was reducing speed to stop, it can also called deceleration.
It travels 10 m and then stops.
KinematicsIt refers to the study of motion.
Given
Initial speed (u) = 5m/s
Time (t) = 4 sec
How to find distance?We know the equation of motion
[tex]\rm v = u + at\\v^{2}- u^{2} = 2as[/tex]
As final velocity (v) = 0
Then
[tex]v = u +at \\\\0 = 5 + 4a\\\\a= \dfrac{5}{4}[/tex]
then
[tex]\begin{aligned} \rm v^{2}- u^{2} &= 2as \\0^{2} - 5^{2} &= 2*\dfrac{5}{4} *s\\25 &= \dfrac{5}{2}*s \\s &= 10 m\\\end{aligned}[/tex]
Thus, it travels 10 m and then stops.
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Write 5.5.5.5. in
exponential notation.
Answer:
5.5.5.5
= 5^4
=625
Explanation:
5 to the power of 4 is equal to 625
Redefined format 5.5.5.5 as 5 * 5 * 5 * 5, converted to exponential notation as 5^4. The base is 5, exponent is 4, showing multiplication of the base 4 times.
Explanation:The number 5.5.5.5 that you've provided seems to have a format error considering the extra dots you've used. If by any chance you meant 5 * 5 * 5 * 5, it in exponential notation is 54. '5' is the base and '4' is the exponent, the latter representing the number of times the base is multiplied by itself. In this case 5 is multiplied by itself 4 times.
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Wal-Mart sells a case of 24 cans of Diet Coke for $6.88 Kroger sells a 12 pack of Diet Coke for $3.99 which is Best Buy?
The cost per can of Diet Coke is cheaper at Wal-Mart than Kroger. Wal-Mart sells a can for approximately $0.287, while Kroger sells a can for approximately $0.3325. Therefore, Wal-Mart is the best buy.
Explanation:To determine the best buy between Wal-Mart and Kroger, we need to calculate the price per can of Diet Coke for each store.
For Wal-Mart, the case contains 24 cans for $6.88. So, we divide the total cost by the number of cans: $6.88 ÷ 24 = $0.287 per can
For Kroger, the pack contains 12 cans for $3.99. So, again we divide the total cost by the number of cans: $3.99 ÷ 12 = $0.3325 per can
Comparing the two prices, $0.287 per can from Wal-Mart is cheaper than $0.3325 per can from Kroger. Therefore, buying the case of Diet Coke from Wal-Mart is the best buy.
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Wal-Mart offers a better buy for Diet Coke compared to Kroger, with a price of $0.287 per can versus Kroger's $0.3325 per can.
First, calculate the price per can at Wal-Mart.Wal-Mart sells a case of 24 cans for $6.88.Price per can = $6.88 / 24 cans = $0.287 per can.Next, calculate the price per can at Kroger.Kroger sells a 12 pack for $3.99.Price per can = $3.99 / 12 cans = $0.3325 per can.Finally, compare the prices:Wal-Mart: $0.287 per canKroger: $0.3325 per canWal-Mart offers the better buy since the price per can of Diet Coke is cheaper at Wal-Mart ($0.287) compared to Kroger ($0.3325).
Complete the sentence to finish the explanation of how you could show that points A, B, and C on the coordinate plane are collinear.
Answer:
First blank: the equation of the line that passes through A and BSecond blank: is a solution of the equation
Explanation:
Three or more points are collinear if and only if they are on the same line, and, thus they are solutions, of the same equation of the line.
When you know two points through their coordinates you can always find the equation of the line:
Point A (x₁, y₁)Point B (x₂, y₂)You can find the slope, m, of that line by using the slope formula:
m = rise / run = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)And then, you apply the point-slope equation:
y - y₁ = m (x₂ - x₁)Since you know m, x₁, and y₁, your equation is determined.
Once you have your equation, substitute the x and y coordinates with the coordinates of the point C. If, and only if, the equation is satisfied, the point C is on the same line and the three points are collinear.
Write the numbers ten to fifteen in descending order and then circle the prime numbers
Answer:
10
11
12
13
14
15
prime numbers:11,13,15
Answer:
Step-by-step explanation:
15,14,13,12,11,10
If you had 26/12 dollars how much money would that be in dollars and cents
Answer:
$2.17
Step-by-step explanation:
12 goes into 26 2 times.
with 2 left over
2/12 = 1/6
1/6 of a dollar is
divide 100/6 = 16.67
Bill buys a stock that decreases by 20% on the first day, and then on the second day the stock increases by 30% of its value at the end of the first day. What was the overall percent increase in Bill's stock over the two days?
Please answer someone!
The over all percent increase in Bill's stock over the two days is 4%
Step-by-step explanation:
The given is:
Bill buys a stock that decreases by 20% on the first dayOn the second day the stock increases by 30% of its value at the end of the first dayWe need to find what was the overall percent increase in Bill's stock over the two days
Assume that Bill buys the stock by $x
∵ Bill buys the stock by $x
∵ The stock decreases by 20% on the first day
- Find the 20% of x
∵ 20% × x = [tex]\frac{20}{100}[/tex] × x = 0.2 x
∴ The cost at the end of the 1st day = x - 0.2 x = 0.8 x
∵ The stock increases by 30% of its value at the end of the 1st day
- Find the 30% of 0.8 x
∵ 30% × 0.8 x = [tex]\frac{30}{100}[/tex] × 0.8 x = 0.3 × 0.8 x = 0.24 x
∴ The cost at the end of the 2nd day = 0.8 x + 0.24 x = 1.04 x
To find the percentage of increased find the increasing amount and divide it by the original cost, then multiply the quotient by 100%
∵ The increasing amount = 1.04 x - x = 0.04 x
∵ The percentage of increase = [tex]\frac{0.04x}{x}[/tex] × 100%
∴ The percentage of increase = 0.04 × 100% = 4%
The over all percent increase in Bill's stock over the two days is 4%
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Evaluate the expression below when x=9.5 and y=3. 12x - 3y exponent 2
Explain what you would do first to simplify the
expression below. Justify why, and then state the
result of performing this step.
12r²4
41
DONE
First, distinguish the mathematical elements in the expression 12r²4. Multiply the numbers 12 and 4 to give 48, then substitute this value back in to obtain the simplified expression, 48r². The property of multiplication allows this reordering and regrouping without affecting the result.
Explanation:To simplify the given expression, 12r²4, the first step involves distinguishing the mathematical elements present. In this case, we have multiplication of numbers and a variable. Technically, the expression is equivalent to 12*r^2*4, since there is multiplication between each element.
We proceed with multiplication, starting with the numerical value. In this case, multiply 12 and 4 to get 48. Substitute this resulting value into the expression, yielding 48r². The justification for this operation is the property of multiplication, which is associative and commutative. It allows us to change the order of the numbers being multiplied or group them differently without changing the result.
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Toby wants to find the volume of a solid toy soldier.
He fills a rectangular container 8 cm long, 6 cm wide,
and 10 cm high with water to a depth of 4 cm. Toby
totally submerges the toy soldier in the water. The
height of the water with the submerged toy soldier is
6.6 cm. Which of the following is closest to the
volume, in cubic centimeters, of the toy soldier?
Answer:
Toby wants to find the volume of a solid toy soldier.He fills a rectangular container 8 cm long, 6 cm wide,and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?
A. 125 B. 156 C. 192 D. 208 E.317
The volume of the toy is 125 cubic cm ,option A is the closest answer.
Step-by-step explanation:
Given:
A rectangular container .
Length of the container =8 cm
Width of the container = 6 cm
Height of the container when water is filled = [tex](h_1)[/tex] = 4 cm
Height of the container when the toy is submerged = [tex](h_2)[/tex] =6.6 cm
Volume of the toy = Volume of the container with the toy - Volume of the container (with water)
Volume of the toy = [tex](l\times b\times h_2) - (l\times b\times h_1)[/tex]
= [tex](l\times b\times)(h_2-h1)[/tex]
= [tex](6\times 8)(6.6-4)[/tex]
= [tex]48\times 2.6[/tex]
= [tex]124.8[/tex] cubic centimeters.
So,the closest value to the volume of the toy is 125 cubic centimeters.
The closest volume, in cubic centimeters, of the toy soldier is 124.8 cm³.
To find the volume of the toy soldier submerged in water, we can use the following steps:
1. Calculate the initial volume of water in the container: 8 cm x 6 cm x 4 cm = 192 cubic cm.
2. Determine the final volume of water with the toy soldier submerged: 8 cm x 6 cm x 6.6 cm = 316.8 cubic cm.
3. Subtract the initial volume of water from the final volume with the toy soldier submerged: 316.8 cubic cm - 192 cubic cm = 124.8 cubic cm.
Therefore, the closest volume, in cubic centimeters, of the toy soldier is 124.8 cm³.
Which graph represents the solution to the given system?
Y=-x+5
y= 1/4 x+10
Answer:
See attachment
Step-by-step explanation:
The given system is :
[tex]y = - x + 5[/tex]
[tex]y = \frac{1}{4}x + 10[/tex]
Let us equate both equations and solve for x.
[tex] - x + 5 = \frac{1}{4}x + 10[/tex]
[tex] - 4x + 20 = x + 40[/tex]
[tex]20 - 40 =x + 4x[/tex]
[tex] - 20 = 5x[/tex]
[tex]x = - 4[/tex]
[tex]y = - - 4 + 5 = 9[/tex]
The the two lines of this system will meet at (-4,9)
The graph is shown in the attachment.
I don’t know Da answer
A cleaning solution contains 60% water. How much water is in a 32 oz container of cleaning solution?
Answer:
19.2 oz water
Step-by-step explanation:
32 oz times 60%
32
x .6
19.2