Yes, a unit rate is a rate at which the the comparison is one unit.
A unit rate is a ratio between two separate units with one as the denominator.
Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc. The most fundamental and historically significant field of mathematics is arithmetic, which is also the one we use the most frequently in daily life. This subject is all about mathematical procedures and problems centered on numbers.
We actually solve mathematical puzzles during our daily activities, whether we mean to or not. For instance, whether buying fruits or vegetables, engaging in other transactions, or determining how quickly something will happen, etc.
When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the denominator of a rate is 1, we refer to it as a unit rate.
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A builder is framing windows of a new with lumber each side of the window must be one piece of lumber. The windows should be three feet high and three feet wide. How many windows can be framed with three 10-foot long pieces of lumber
The number of windows which can be framed with three 10-foot long pieces of lumber given the dimensions of the windows is; two and a half.
What is the number of windows that can be made using the lumbers given the dimensions of the windows?It follows from the task content that the number of windows that can be made given the dimensions of the windows be determined.
On this note, it follows that since the windows are 3 feet high and 3 feet width, the perimeter of each window(square shaped) covered by lumber is;
P = 4s
P = 4 × 3
P = 12 feet.
Hence, each window requires 12 feet of lumber.
However, since the builder has only three 10-foot long pieces of lumber which is equivalent to; 3 × 10 = 30 feet worth.
The number of windows that can be made is;
= 30/12
= 2.5.
Ultimately, only 2 and a half windows can be framed from the three 10-foot long pieces of lumber.
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which term is larger log_25(1/625) or log_16(1/64)
Write an absolute value inequality and a compound inequality for a length of 8.9mm with a tolerance of 0.15mm
The absolute inequality will be x ≥ | 8.9 ± 0.15 |mm and the compound inequality will be x > 8.75, x< 9.05.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Given that the length is 8.9 mm with a tolerance of 0.15mm.
The absolute inequality will be written as below:-
x ≥ | 8.9 ± 0.15 |mm
The compound inequality will be written as:-
x > 8.75,
x < 9.05.
Therefore, the absolute inequality will be x ≥ | 8.9 ± 0.15 |mm and the compound inequality will be x > 8.75, x< 9.05.
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If a kid has to read 11 chapters of a book in eight days how many chapters sould the read each day?
Answer:
About 1 and 1/4 chapters per day.
Step-by-step explanation:
There are 11 chapters, and eight days to read them. So we divide 11 by 8. 11/8 = 1.375, which is approximately 1 and 1/4.
Find the missing terms in each geometric sequence.
1. 256, ___, ___, -32, -64
2. 27, 9, ___, ___, 1/3
3. 5x^2, ___, 5x^6, 5x^8, ___, ...
Answer:
1) 256, -128, 64, -32
2) 27, 9, 3, 1, 1/3
3) 5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰,
Step-by-step explanation:
1. In this geometric series each term is obtained by multiplying the previous term by (-1/2) or dividing by (-2).
256 ÷ (-2) = - 128
-128 ÷ (-2) = 64
64 ÷ (-2) = (-32)
The geometric series is:
256, -128, 64, -32...
We can find the common ratio by dividing the second term by first term.
2) 27, 9, ___, _________, 1/3
[tex]\sf \boxed{\bf common \ ratio= \dfrac{second \ term}{first \ term}}[/tex]
[tex]\sf = \dfrac{9}{27}\\\\ = \dfrac{1}{3}[/tex]
[tex]\sf 9*\dfrac{1}{3}=3\\\\3*\dfrac{1}{3}=1[/tex]
The geometric series is:
27, 9, 3, 1, 1/3....
3) 5x², _____, 5x⁶, 5x⁸, _____, ....
Here, we can take 3rd term and 4th term to find the common ratio.
[tex]\sf common \ ratio = \dfrac{5x^8}{5x^6}\\\\[/tex]
[tex]\s = x^{8-6}\\\\=x^2[/tex]
5x² * x² = 5x⁴
8x⁸ * x² = 8x¹⁰
The geometric serious is:
5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰, ...
[tex]\sf 1.) \ 256, -128, 64, -32,..\\ \\ 2.) \ 27, 9, 3, 1, 1/3,... \\ \\3.) \ 5x^2, 5x^4, 5x^6, 5x^8,5x^{10} , ...[/tex]
[tex]\sf Geometric \ formula: ar^{n-1}[/tex]
where 'a' is first term, 'r' is common ratio.1)Find the common ratio:
next term ÷ previous term32 ÷ -64 = -1/2Equation: [tex]256(-\frac{1}{2} )^{n-1}[/tex]
2nd term: [tex]256(-\frac{1}{2} )^{2-1}=-128[/tex]
3rd term: [tex]256(-\frac{1}{2} )^{3-1}=64[/tex]
2)Find common ratio:
next term ÷ previous term9 ÷ 27 = 1/3Equation: [tex]27(\frac{1}{3} )^{n-1}[/tex]
3rd term: [tex]27(\frac{1}{3} )^{3-1}=3[/tex]
4th term: [tex]27(\frac{1}{3} )^{4-1}=1[/tex]
3)Find the common ratio:
next term ÷ previous term5x^8 ÷ 5x^6 = x^2Equation: [tex]5x^2 (x^2)^{n-1}[/tex]
2nd term: [tex]5x^2 (x^2)^{2-1} = 5x^2 (x^2) = 5x^{4}[/tex]
5ht term: [tex]5x^2 (x^2)^{5-1} = 5x^2 (x^8) = 5x^{10}[/tex]
whats is 0.5x+2=6 answer
Answer:
x=8
Step-by-step explanation:
starts with 0.5x+2=6, so move the constant to the right, 0.5x=6-2, then calculate the right side, 0.5x=4, then divide both sides, and x=8
Answer:
x = 8
Step-by-step explanation:
Get variable on left and constants on right
0.5x = 6 - 2
0.5x = 4
Divide both sides by 0.5
x = 8
Write an equation of the line through each pair of points in slope-intercept form.
(-1,-4) and (3,-4)
The equation of line is y = -4
Given the points:
(x₁, y₁) = (-1, -4)
(x₂, y₂) = ( 3, -4)
The slope-intercept form:
y = mx + b
Where, m is the slope and b is the y-intercept, that is (0, b)
The formula for slope:
m = (y₂ – y₁) / (x₂ – x₁)
We have given
x₁ = -1
x₂ = 3
y₁ = -4
y₂ = -4
So,
m = (-4 – (-4)) / (3 – (-1)) = (-4 + 4) / (3 + 1) = 0/4 = 0
Therefore we have the equation of the line as:
y = mx + b
-4 = 0(x) + b
-4 = 0 + b
b = -4
Therefore, the equation of line y = -4
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Put these numbers in order from least to greatest.
13/16
79/80
-10/32
-9
-9, -10/32, 13/16, 79/8]
Step-by-step explanation:
use ur brain
The man in a video spent 9 minutes and 2 seconds filling his bathtub before taking a bath. After taking the bath, his partner told him that taking a bath was wasting water and that he should shower instead.
Question: How long would he need to run the shower to use the same amount of water as the bath that he took?
Hints:
On the bathtub faucet, it takes 00:00:26:82 seconds to fill a gallon
For the shower head, it takes 00:00:10:84 seconds to fill a gallon
According to the Centers for Disease Control and Prevention (CDC), the average shower lasts 8 minutes. If you like to linger in the shower for longer than 15 minutes, you might want to rethink your hygiene routine.
According to board-certified dermatologist Dr. Edidiong Kaminska, MD, the recommended maximum shower time is about 5 to 10 minutes. This is enough time to cleanse and hydrate the skin without overdoing it. “Our skin needs water, just like our bodies, but if we over- or under-do it, then it may have consequences,” she adds.
And if you have dry skin or eczema, Dr. Anna Guanche, MD, FAAD, says shorter, lukewarm showers are recommended. Moreover, the Baylor College of Medicine says it’s especially important to avoid hot showers in the wintery months since the heat can damage the surface of the skin, which can lead to inflammation and increase symptoms of eczema.
Side effects of long showers
While a long, hot shower might seem like the best way to pamper your body, over-showering may dehydrate the skin. “The purpose of showering is to hydrate and cleanse the skin, but warm or hot showering for prolonged periods strips away natural oils of the skin and opens up our pores and allows moisture to escape,” Kaminska says.
To keep moisture in, she usually recommends applying a body moisturizer after showering to the skin since it allows the water (hydration) to stay in the skin and not escape.
i know its easy but my brain isn't working and my friends aren't answeringngngng
The number of apples in the 12th bag is 9.
How to find the number of apples in the 12th bag using mean number?There are 12 bags of apples on the market stalls.
The mean number of apples in each bag is 8.
Therefore, the number of apples in the 12th bag can be calculated as follows:
mean = ∑fx / ∑f
Hence,
let the number of apples in the 12th bag = a
mean = 6 × 1 + 7 × 4 + 8 × 2 + 9 × 3 + 10 × 1 + x × 1/ 1 + 4 + 2 + 3 + 1 + 1
mean = 6 + 28 + 16 + 27 + 10 + x / 12
mean = 87 + x / 12
8 = 87 + x / 12
cross multiply
96 = 87 + x
x = 96 - 87
x = 9
Hence, the number of apples in the 12th bag is 9.
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Using the scale factor you just found, what is the length of the unknown side on the smaller rectangle?
what scale factor did you find and is there a photo of the rectangle?
Yesterday Philip ate three meals totaling 1600 calories. He ate a total of 750 calories for breakfast and lunch. How many calories did he eat at dinner?
Find the coordinate of point C on AB such that the ratio of AC to CB is 3:6
B= (5,6)
A= (-4,-6)
Answer:
Step-by-step explanation:
Solution for Point C is located on AB such that the ratio of AC : CB is 3:2. ... A: Here point B lies on the line AC with coordinates A(-3,4) and C(2,-6), ...
The area of a square is calculated
by squaring the length of one side
of the square.
Simplify
(7-5) x (2 + 4) =
Answer:
7-5=2
2+4=6
2×6=12
you always work the Parenthesis 1st
What's equivalent to -8
Answer: try 1 or 0
Step-by-step explanation:
Answer: 8
Step-by-step explanation:
(-8)= 8
use the properties of exponents to write an equivalent expression that is a product of distinct primes, each raised to an integer power.
10 to the 5th power times 9 to the 2nd power over 6 to the 4th power
Answer:
10 to the 5th power times 9 to the 2nd power over 6 to the 4th power
write an equation for the difference of 7 and a number is 18
In a circle of music lovers, 14 people play the piano or violin, 8 people are piano players, and
5 people play both instruments. Find the number of violin players.
Answer:
11 people
Step-by-step explanation:
14-8+5
6+5
11
b. Find the sum of the first ten terms of the Fibonacci sequence. Divide the sum by 11 . What do you notice?
According to the question, the Fibonacci series is a series of sequence of numbers. It follows one standard property which states that every third term in the series is the addition of first term and second term.
Now, the first ten terms of the Fibonacci sequence is as follows:
Fibonacci Series = [tex]{1,1,2,3,5,8,13,21,34,55}[/tex]
The sum of the first ten number of the Fibonacci series is as follows:
Sum = [tex]1+1+2+3+5+8+13+21+34+55 = 143[/tex]
As per question, divide the calculated sum by eleven. Therefore, it can be written as:
Required Division = [tex]\frac{143}{11} = 13[/tex]
Hence, the solution for the given series is [tex]13[/tex].
What is a Fibonacci series?
Fibonacci series is an infinite series of sequences of numbers. The important property of this series is, every third term is the addition of the first and second term. In this, the first term either starts with zero or one.
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5. The coordinates of X are (a - 5, -2a) . The coordinates of Y are (a + 1, 2a) . If the distance between X and Y is 10, find the value of a.
Applying the distance formula, the value of a is 2 or -2.
What is the Distance Formula?The distance formula is:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following:
d = XY = 10 units
X(a - 5, -2a) = (x1, y1)
Y(a + 1, 2a) = (x2, y2)
Plug in the values into the distance formula
10 = √[((a + 1) - (a - 5))² + (2a - (-2a))²]
10 = √[(a + 1 - a + 5)² + (2a + 2a)²]
10 = √(6² + (4a)²)
10 = √(36 + 16a²)
10² = 36 + 16a²
100 = 36 + 16a²
0 = -100 + 36 + 16a²
0 = 16a² - 64
16a² - 64 = 0
Factorize
16(a² - 4) = 0
16(a - 2)(a + 2) = 0
a = 2 or a = -2
Therefore, applying the distance formula, the value of a is 2 or -2.
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State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The vertex angles of an isosceles triangle are congruent.
Two vertex angles of an isosceles triangle are equal but not necessarily all three so the given statement is not always true.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
An isosceles triangle is a triangle whose two sides will be the same, but the third side may or may not be equal.
So, the angle associated with the same side will same but the remaining angle will or will not be the same.
Hence "Two vertex angles of an isosceles triangle are equal but not necessarily all three so the given statement is not always true".
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You and a friend are hiking in the Swiss Alps. You want to climb to a ledge that is 6 meters above you. The height of the grappling hook you throw is given by the function h(t)=-4.9t² +10t+1.5 Can you throw it high enough to reach the ledge? Why or why not? (Support your answer mathematically.)
According to the given function, we can throw it to the height of 6.6 m. So, yes we can throw it high enough to reach the ledge.
What is a Quadratic equation?The given equation is quadratic. A quadratic equation is defined as an equation of a single variable with the highest power of 2. In general, the quadratic equation can be expressed as h(x)= [tex]ax^2- bx + c[/tex], where a, b and c are arbitrary constants. The solution for a quadratic equation is given by:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
The maximum of a quadratic equation is given by:
= [tex]c-\frac{b^2}{4a}[/tex]
The length to be covered by throwing=6 meters
It is given that the height of the grappling hook you throw is a function h(t) = -4.9t² + 10t + 1.5
Here a =4.9, b = 10 and c = 1.5
The maximum of a quadratic equation is given by:
[tex]c-\frac{b^2}{4a}[/tex]
[tex]1.5-\frac{10^2}{4*(-4.9)}[/tex]
6.6
A throw can be made to reach the wall since the height of wall is less than the maximum value that is 6.6 m.
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Can someone explain to me how to solve 5-(3-2)+2
I've looked it up and the answer is 6 but I don't understand how to get there. Plus we need to show our work so please help! I will give 22 points
Answer:
Step-by-step explanation:
brackets first
5 - (3-2) + 2
5 - (1) + 2
5 - 1 + 2
4 + 2
6
Answer:
5-(3-2)+2
5-1+2
4+2
6
Step-by-step explanation:
Follow PEMDAS
P ()
E: Exponent
M: Multiplication
D: Division
A: Addition
S: Subtraction
And you answer each equation going from Left to Right
c and d are inversely proportional and are
both positive.
The equation of proportionality is c
a) Does c increase or decrease if d
increases?
b) Does d increase or decrease if c
increases?
2/07
5
d'
if d increases c will decrease AND if c increases d will decrease.
WHAT IS RATIO AND PROPORTION ?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalizes two ratios. For illustration, the ratio may be expressed as follows: 1: 3 (If there are 1 boy and 3 girls, then there are 3 girls for every 1 boy.)
CALCULATIONsince c and d are inversely proportional
a) if d increases c will decrease
because it is the property of the ratio and proportion
and same will be applied in b
b) if c increases d will decrease
that is obvious....
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What is the value of 6x2 + x if x = 5?
65
35
905
155
Answer:
If it is [tex]6(5)^2[/tex] then the answer is 150
Step-by-step explanation:
So, follow PEMDAS
Parenthesis
Exponent
Multiplication
Division
Addition
Subtraction
First square 5 because there is an exponent [tex]6(5)^2 = 6(25)[/tex]
Next multiply 6 times 25 and you get 150!
Answer:
d) 155
Step-by-step explanation:
The value of x is,
→ x = 5
Now the expression is,
→ 6x² + x
Let's solve the expression,
→ 6x² + x
→ 6(5)² + 5
→ 6(25) + 5
→ 150 + 5
→ 155
Hence, the answer is 155.
please helpppp :3
URGENT
I need this answered please
Given that R = 4x − 9y Find x when y = 1 and R=1 ?
Answer:
x=2.5
Step-by-step explanation:
R = 4x − 9y
We know that R=1 and y=1 so we can substitute that in
1=4x-9
Then solve as a normal algebraic equation
add 9 to both sides
10=4x
divide both sides by 4
2.5=x
a number y multiplied by 5 is no less than 5/6 An inequality is
Answer:y/5=5/6
Step-by-step explanation:based on given conditons
