If wasps had eaten 20 apples then, 50 rotten apples were there and the rest of the apples were quality apples in the ratio of 4: 10: 20 respectively.
This is a problem from simple mathematical equations. We can solve this problem by following a few steps.
Let's consider x as the highest common factor of apples eaten by wasps, rotten and quality apples.
So, the number of apples eaten by wasps is, 4 × x = 4x
The number of rotten apples is, 10 × x = 10x
The number of quality apples is, 20 × x = 20x
As, we all know HCF of the numbers × ratio of numbers = The numbers
So, 4x = 20 as per the question.
Therefore, x = 5.
Now, we can write that the HCF is 5.
So, the number of rotten apples ≡ HCF × 10 = 5× 10 = 50.
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Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
27
Select all that apply.
A. natural numbers
B. whole numbers
C. rational numbers
D. real numbers
E. integers
. F. irrational numbers
The number 27 is a natural number, whole number, rational, real and an integer .
The number 27
And this number is a natural number and thus it is a natural number and a rational number too.
This is also an integer .
Reason: Natural number : A natural number is one that naturally and frequently appears. It is a whole, non-negative number as a result. N, the collection of natural numbers, can be defined in one of two ways: N = {0, 1, 2, 3, ...}
whole number: the sum of all natural numbers plus zero. neither a decimal nor a fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. 0, the negative, or a counting number.
Rational number: A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.
Real number: Rational, irrational, entire, and natural numbers are all examples of real numbers. Negative, positive, and zero numbers are all examples of integers.
Integer : An integer, pronounced is a whole number that can be positive, negative, or zero and is not a fraction.
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Step 1: Add 7 to
x
.
Step 2: Multiply by 6
The final term after following the steps is ( 42 + 6x ).
We are provided with some steps that we have to follow to reach the final answer or expression. The steps we have to follow to reach the final answer or expression are mentioned below;
Step 1: Add 7 to x
In the first steps we need to add 7 to the x. Mathematically this can be written as,
7 + x
Step 2: Multiply by 6
In the second step we need to multiply the entire term obtained in step 1 by 6 . Mathematically this can be written as,
( 7 + x ) × 6
= 42 + 6x
Thus, the final term is ( 42 + 6x ).
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1. Explain why the slope of line a is 2/6
A piece of rope 60 meters long is cut into two
pieces so that the longer piece is twice the
length of the shorter. How long are the two
pieces?
Answer:
short piece = 20
Longer piece = 40
Step-by-step explanation:
Comment
Let the shorter piece be x
Then the longer piece is 2x
Givens
The rope is 60 meters long
Equation
x + 2x = 60 meters Combine like terms
Solution
3x = 60 Divide by 3
3x/3=60/3
x = 20
When you looked at the thermometer last night, the temperature was 5° C. By morning, the temperature had risen 13°. By afternoon, the temperature had risen another 5°. Afterwards, the temperature dropped 10°. What is the temperature now?
Answer:
Step-by-step explanation:
13
Rotate ∆ABC by 90° clockwise, about the origin, and then reflect in the x-axis.
What are the coordinates of the new triangle?
Answer:
A = (1, 1)
B = (3, 2)
C = (2, 4)
Step-by-step explanation:
Vertices of the triangle:
A = (1, 1)B = (2, 3)C = (4, 2)Mapping rule for a 90° clockwise rotation about the origin:
(x, y) → (y, -x)
Therefore:
A' = (1, -1)B' = (3, -2)C' = (2, -4)Mapping rule for a reflection in the x-axis:
(x, y) → (x, -y)
Therefore:
A'' = (1, 1)B'' = (3, 2)C'' = (2, 4)Therefore, the coordinates of the new triangle are:
A = (1, 1)B = (3, 2)C = (2, 4)What is the slope of a line perpendicular to the line whose equation is x - y = 6. Fully reduce your answer. Answer: Submit Answer
Answer:
Explanation:
The standard form of an equation is expressed as y = mx+b
m is the slope
Given the equation x - y = 6
Rewrite in standard form;
-y = -x + 6
Multiply through by -1
-(-y) = -(-x) - 6
y = x - 6
Compare with the standard equation
mx = 1x
mx+b
m is the slope
Given
Approximate −12 + the square root of thirty-two to the nearest tenth
The approximate value of the expression given will be equal to -6.3.
An approximation may be defined bringing the value of a certain entity which is almost similar, but not exactly equal to the correct value. The expression can be written as −12 + √32. The value of √32 can be written as 5.656. Since, after decimal 6 to the right of 5 is greater than 5 so to the nearest tenth, we can write as 5.66. Therefore, √32 = 5.66
For the required value of the expression we can write,
−12 + √32
Putting the value of √32 = 5.66 in the expression we get
-12 + √32 = -12 + 5.66
After solving we get
⇒ -12 + √32 = -6.34
To the nearest tenth it will be -6.3.
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Help me with this ,8th grade math look at attachment
100 points
Answer:7
Step-by-step explanation:
Answer:
its 7!!!!
Step-by-step explanation: i just got it right im in 8th grade also!
10b4 +3b²-11 can you help
Answer: your answer in in the screenshot
Step-by-step explanation:
A rectangular prism has a length that is 3 inches shorter than the height and a width that is 5 inches longer than the height. Fill in the blanks to create an equation for the volume of the prism as a function of the height.
An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.
We are given a rectangular prism.A rectangular prism is no different than a cuboid.Let the height of the rectangular prism be "h".The length of the rectangular prism is "h-3".The width of the rectangular prism is "h+5".The volume of the rectangular prism is the same as that of the cuboid.The volume of the rectangular prism is the product of its length, its width, and its height.The volume of the rectangular prism is (h - 3)*(h + 5)*h.An equation for the volume of the prism as a function of the height is :Volume = (h - 3)*(h + 5)*hVolume = (h² + 2h - 15)*hVolume = h³ + 2h² - 15hTo learn more about prism, visit :
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On “2 fer Tuesday” 2 bagels with cream cheese cost $2.50. Jimmy wants to buy 2 dozen bagels (24 bagels). How much will this cost?
Let f (x) = px 2 + qx - 4 p, where p 0. Find the number of roots for the equation f (x) = 0 . Justify your answer.
Answer:
f(x) = 0
px^2 + qx - 4p = 0
abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)
x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)
x = (-q ± √(q^2 + 4^2·p^2))/(2·p)
Because q^2 + 4^2·p^2 > 0 there are two roots.
Which postulate could we use to prove that the angles
The Supplement postulate can be used to prove that the angles ∠CAB and ∠CAD are supplementary.
According to the Supplement Postulate, two angles are supplementary if they create a linear pair.
What are Supplementary angles?The pair of angles known as supplementary angles always add up to 180 degrees. These two perspectives are known as each other's supplements.If two angles sum up to 180 degrees, they are referred to as supplementary angles. When combined, supplementary angles make a straight angle (180 degrees). In other words, if angle 1 plus angle 2 equals 180 degrees, angle 1 and angle 2 are supplementary. In this instance, Angles 1 and 2 are referred to as "supplements" of one another.There are two types of supplementary angles: neighboring and non-adjacent.
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Johnny bought a candy bar for $0.89 and a soda for $1.50. How much did Johnny spend in all?
Answer:
$2.39, hope this helps,
Step-by-step explanation:
1.50+0.89=2.39
Answer: $2.39
Step-by-step explanation: 0.89 + 1.50
0.8 + 1.5 = 2.3
89 + 50 = 139
2.39
-4.2 + 3.3 in simplest form
use your equation from part b to predict the highway MPG for a car that gets 68 MPG in the city.part b equation:[tex]y = \frac{7x}{9} + \frac{125}{9} [/tex]
ok
[tex]\begin{gathered} \text{ y = }\frac{7(68)}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{476}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{601}{9} \\ \\ \text{ y = 66.8 } \end{gathered}[/tex]MPG = 66.8
In November, the price of a cell phone was double the price in March. In December, the price was $53, which was $25 less than the price in November.
What was the price of the cell phone in March?
The price of the cell phone in March was
Based on the price of the cell phone in November and December, the price of the cell phone in March was $39
How to find the price of the cell phone?To find the price of the cell phone in March, you need to first find the price of the cell phone in November.
The price of the cell phone in November was $25 more than the price in December:
= 25 + 53
= $78
The price in November was double the price in March so the price in March was:
= 78 / 2
= $39
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Megan is in charge of housekeeping at the Seaside Hotel. She makes sure there are enough clean towels for each room that has been booked for the night.
There is a proportional relationship between the number of rooms booked, x, and the number of towels Megan needs to supply, y.
By the analysis of the graph, the constant of proportionality is 2.
By analyzing the graph given we can infer that If five rooms are reserved, he must provide ten towels.
So x is the number booked and y is the number of towels, Then
x is directly proportional to y,
The given graph is linear in nature, as we increase x, there will be a significant increase increase in y, The constant of proportionality(k) tells us how much y will change when x changes.
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
Now, 10= k *5
[tex]k =\frac{10}{5} \\k =2[/tex]
Hence, the constant of proportionality k is 2.
and the equation of the given graph is y = 2x
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Grayson has $1.20 worth of nickels and dimes. He has twice as many nickels as dimes. Determine the number of nickels and the number of dimes that Grayson has.
The determined value of the number of nickels and the number of dimes that Grayson has is
x=6y=2This is further explained below.
What is the determined value of the number of nickels and the number of dimes that Grayson?Generally, The following phrase represents Jayden's complete financial worth:
Nickels are worth $0.05 each.
The dime value is equal to $0.10
The total value is equal to the sum of the values of the nickels and dimes.
where;
[tex]1.20= (0.05*2 x) +(0.1*x)[/tex]
0.1 x+0.1 x=1.2
0.2 x=1.2
[tex]x=\frac{1.2}{0.2}[/tex]
x=6
y=2
In conclusion, the Total number of dimes=6
Total number of nickels=12
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Four friends on a ski trip pay $210 each to share the rent of a cabin. The cost per person varies inversely
the number of persons. How many people sharing the rent would make the cost $120 per person?
Seven people sharing the rent would make the cost $120 per person.
What is Inversely Proportional?When two quantities are inversely proportional, that is, when an increase in one causes a decrease in the other and vice versa, they are said to be inversely proportional.
The general equation for inverse variation is y = k/x, where k is the proportionality constant and x and y are two variables.
Given:
The price paid by Four friends on a ski trip to share the rent of a cabin = $210
The cost per person varies inversely with the number of persons.
Let the cost be C and the number of persons be n,
C ∝ 1/n
So, the equation becomes, k = Cn.
Putting the values in the equation we obtain the value of k,
k = 210×4 = 840
We have to find the number of people sharing the rent that would make the cost $120 per person.
Using the equation,
k = Cn
840 = 120 × n
n = 840/120 = 7
Therefore, seven people sharing the rent would make the cost $120 per person.
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4. What is the equation of the line that represents your initial climb?
1 2/3 divided by 4/5
1 2/3 divided by 4/5
= 5/3 ÷ 4/5
make common denominators:
[tex]\frac{25}{15} /\frac{12}{15}[/tex]
invert one and multiply across:
[tex]\frac{25}{15} * \frac{15}{12}[/tex]
= 375/180
reduce:
25/12 or 2 1/12
The figures below are congruent. Name the corresponding angles.
Answer:
A goes to K. C goes to M. B goes to L.
Step-by-step explanation:
:)
Please help me this is due in an hour
Answer:
Your missing number is -87.5.
Step-by-step explanation:
You want to follow reverse order of operations to isolate your variable x
First, you plug in y= 700 to get::
700 = (24x)/7 +1000
Then subtract 1000 from both sides to get:
-300 = (24x)/7
Then multiply both sides by 7 to get:
-2100 = 24x
Then, divide by 24 to get:
-87.5 = x
Thus, your answer x= -87.5
evaluate T^T -[tex]x^{2}[/tex]+3x for x=-3
Answer:
The answer is -18
Step-by-step explanation:
- [tex](-3)^{2}[/tex] + 3(-3)
-9 + -9 = -18
when 64 is increased in the ratio 9 : 8, it becomes?
Recall that the ratio 9:8 can be written as follows:
[tex]\frac{9}{8},[/tex]therefore, when 64 is increased in the ratio 9:8 we get:
[tex]64\times\frac{9}{8}=72.[/tex]Answer: 72.
Answer:
72
Step-by-step explanation:
Since X : 64 = 9 : 8
Then we know X/64 = 9/8
Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64
X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72
Therefore 72 : 64 = 9 : 8
help me with this please
Answer:
-21/2
Step-by-step explanation:
-5-2= - 7
7-4=3(+, - = -)
-7×3/2= - 21/2
The table shown below gives the approximate distance from the sun for a few different planets. How much further (in km) from the sun is Saturn than Venus? Express your answer in scientific notation. Planet Approximate distance from the Sun (in km) Mercury 5.8 \cdot 10^75.8⋅10 7 5, point, 8, dot, 10, start superscript, 7, end superscript Venus 1.1 \cdot 10^81.1⋅10 8 1, point, 1, dot, 10, start superscript, 8, end superscript Earth 1.5 \cdot 10^81.5⋅10 8 1, point, 5, dot, 10, start superscript, 8, end superscript Saturn 1.4 \cdot 10^91.4⋅10 9 1, point, 4, dot, 10, start superscript, 9, end superscript Uranus 3\cdot10^93⋅10 9 3, dot, 10, start superscript, 9, end superscript
It is to be noted that Saturn is 1.29 *x 10⁹ km further from the sun than Venus.
What is the computation justifying the above results?Recall that we are given:
approximate distance from the sun for a few different planets.
Hence, to detect how much farther (in km) from the sun Saturn is than Venus we initiate a series of subtractions.
Recall that
Planet approximate distance from the sun ( km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
The distance of Saturn form the sun and Venus is given as
= Distance of Saturn from Sun - Distance of Venus from Sun
= 1.4 x 10⁹ - 1.1 * 10⁸ [Multiply 1.4 x 10 and we've got]
= 14 x 10⁸ - 1.1 * 10⁸
= (14 - 1.1) * 10⁸ [ Collect like terms and consolidate]
= 12.9 x 10⁸ [Revert back to the power of 9 and we have]
= 1.29 x 10⁹ km
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Full Question:
The table shown below gives the approximate distance from the sun for a few different planets. How much farther (in km) from the sun is Saturn than Venus? Express your answer in scientific notation.
Planet Approximate distance from the Sun (in km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
It is found that Saturn is 1.29 x 10⁹ km further from the sun than Venus.
How do scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
We have been given that the approximate distance from the sun for a few different planets.
Hence, to determine the farthest distance (in km) from the sun Saturn is than Venus, we get;
Planet the approximate distance from the sun ( km)
Mercury 5.8 x 10⁷
Venus 1.1 x 10⁸
Earth 1.5 x 10⁸
Saturn 1.4 x 10⁹
The distance between Saturn from the sun and Venus can be calculated as;
= Distance of Saturn from Sun - Distance of Venus from Sun
= 1.4 x 10⁹ - 1.1 x 10⁸
= 14 x 10⁸ - 1.1 x 10⁸
= (14 - 1.1) x 10⁸
= 12.9 x 10⁸
= 1.29 x 10⁹ km
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Question 19
There are 118 different elements in the periodic table. While giving a presentation, Clark says that there are 128 different
elements. Select each true statement.
A) There are actually 118 elements
B) The amount of error in Clark's estimate is 10.
C) The amount of error in Clark's estimate is 118.
D) To the nearest tenth percent, the percent error in Clark's estimate is 8.5%.
E) To the nearest tenth percent, the percent error in Clark's estimate is 10%.
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