The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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q1 suppose you take a sample of 16 people and ask them how fast they drive on interstate 94. after collecting your sample, you calculate that the mean is 75mph with a variance of 9mph. calculate a 90% confidence interval for the average speed of all drivers on i94.
A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)
Given that,
Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.
Solution is as given below :
90% Confidence Interval for μ is
μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]
μ = 75 ± (1.75) * 3/[tex]\sqrt{16}[/tex]
μ = (73.69, 76.31)
Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)
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how many real fourth roots does -1 have?
There are zero or null real fourth roots of -1.
What are real fourth roots?This means that the square root of the square root of a number is equal to the number's fourth root. Symbolically, the fourth root is also represented by multiplying the radical by 4, creating the number 4. The fourth root of 16, for instance, is 2, which means that 2 2 2 2 = 16. n, also known as the degree of the root, is a positive integer in this situation. The terms "square root" and "cube root" are used to describe roots of degree 2 and 3, respectively. The ordinal numbers fourth root, twentieth root, etc. are used to refer to roots of higher degree. It is a root extraction to calculate the nth root. A integer y such that y2 = x is referred to as the square root of an x in mathematics.
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Solve:-
[tex]\bf 7(5a - 4) - 1 = 14 - 8[/tex]
Answer:
a = 1
Step-by-step explanation:
Given equation,
→ 7(5a - 4) - 1 = 14 - 8
Now the value of a will be,
→ 7(5a - 4) - 1 = 14 - 8
→ 35a - 28 - 1 = 6
→ 35a - 29 = 6
→ 35a = 6 + 29
→ a = 35/35
→ [ a = 1 ]
Hence, the value of a is 1.
A 132 -inch is cut into two pieces. One piece is times the length of the other. Find the length of the shorter piece.
The length of the shorter piece is 33 inches.
According to the question,
We have the following information:
A 132 -inch is cut into two pieces. One piece is three times the length of the other.
Now, let's take the length of the shorter piece to be x inches and the length of another piece will be 3x inches.
Now, we have the following expression:
x+3x = 132
4x = 132
4 is in multiplication on the left hand side. So, it will be in the division on the right hand side.
x = 132/4
x = 33 inches
Hence, the length of the shorter piece is 33 inches.
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-3x -18 = -6
SO MUCH MATH I CANT DO
Answer:
x=-4
Step-by-step explanation:
-3x-18=-6
-3x=12
x=-4
Answer: x=-4
Step-by-step explanation:
Start off with the equation: -3x-18=-6
Add 18 to both sides: -3x=12
Divide by -3: x=-4
Hope this helped!
The temperature on a summer afternoon is 85°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees Fahrenheit.
The expression that can be used to find the temperature after it changes is 85°F + C
How to find a change in temperature?Temperature refers to the degree of hotness or coldness of a body at a particular time. It is measured in degree Celsius, degree Fahrenheit an Kelvin.
The instrument used to measure temperature is a thermometer.
Temperature on a summer afternoon = 85°FDecrease in temperature = -11°Flet
C = change in temperatureThe change in temperature = 85°F + C
= 85°F + (-11°F)
= 85 - 11
= 74°F
Therefore, the new temperature after a decrease in 11°F is 74°F
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I need help like asap !!!
only numbers and decimal points
1) In a group of 80 children, 35% of the
children are girls. 9 of the girls chose
volleyball as their favourite sport.
What percentage of the girls chose
volleyball?
11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.
Given that,
35 percent of the 80 kids in the group are girls. 9 of the female students selected volleyball as their preferred sport.
We have to find what percentage of the female students chose volleyball.
The total children's are 80.
The 35% are girls.
9 have selected the volleyball
So,
9/80
0.1125
The percent is
11.25%
Therefore, 11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.
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Tanisha and her children went into a restaurant that sells hamburgers for
$7.50 each and drinks for $1.75 each. Tanisha has $70 to spend and must buy
no less than 18 hamburgers and drinks altogether. If a represents the number
of hamburgers purchased and y represents the number of drinks purchased,
write and solve a system of inequalities graphically and determine one
possible solution.
HELP PLEASE QUICKLY THANKS
Graph will shift in both horizontal and vertical direction by 4 units.
What is straight line?
An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.
What is general equation of a Straight Line?
The general equation of a straight line can be given as ax + by + c = 0, where
a, b, c are constants, andx, y are variables.The slope is -a/bWhat do you mean by function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.
We have function,
fn(x) = x + 5
when the graph is translated by 4 units, we can write it as;
g(x) = fn(x) + 4
the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.
Therefore, graph will shift in both horizontal and vertical direction by 4 units.
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how to write as one fraction 7/2a+4/a*a
The fraction 7/2a+4/a*a can be written as (7 + 8a) / 2a
What is a fraction?
In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are in spoken common English. In other words, a fraction indicates the components of a whole or group of items.
Solution Explained:
First, we simplify the equation
= [tex]\frac{7}{2a} + \frac{4}{a} X a[/tex]
= [tex]\frac{7}{2a} + 4[/tex]
= [tex]\frac{7 + 8a}{2a}[/tex]
Therefore, the equation can be written as (7 + 8a) / 2a
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Three consecutive even integers have the property that when the product of the first two is taken, the result is four less than the square of the third one. What are the integers?
The three consecutive even integers are -2, 0 and 2.
How to calculate the value?Let the three consecutive even integers be x, x+2 and x+4.
Since the product of the first two is taken, the result is four less than the square of the third one. This will be:
x(x + 2) = (x + 4)² - 4
x² + 2x = x² + 8x + 16 - 4
x² + 2x = x² + 8x + 12
Collect like terms
x² - x² + 2x - 8x - 12
-6x - 12 = 0
-6x = 12.
Divide
x = -12/6
x = -2
x + 2 = -2 + 2 = 0
x + 4 = -2 + 4 = 2
They're -2, 0, and 2.
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The amount of seed in a bird feeder decreased 11 1/4 ounces in 5 days. The amount of seed decreased the same amount each day. What was the change in the amount of seed in the bird feeder after 7 days?
The change in the amount of seed in the feeder after 7 days is 78.75 ounces.
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.
For example, if you ran 80 meters in 10 seconds, you ran on average 8 meters in 1 second
To find the rate at which the amount of seed decreases.
11 1/4 ounces = 5 days
Dividing both sides of the equation by 5.
11 1/4 ounces = 1 day
Multiplying 7 on both sides to get the number for 7 days
7 x 11.25 ounces = 7 days
78.75 ounces = 7 days
If the amount of seed in a bird feeder decreases by 11 1/4 ounces in 5 days, the amount of seed decreases by 78.75 ounces.
The change in the amount of seed in the feeder in 7 days is 78.75 ounces.
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I NEED HELP PLS I GIVE YOU POINTS
Answer:
Option D: 160 square feet
Step-by-step explanation:
Area of the lawn
= (7 feet × 8 feet) + (13 feet × 8 feet)
= 56 square feet + 104 square feet
= 160 square feet
Jade ha 28 triangle card. He ha 4 time a many trading card a jordan. How many trading card do they have altogether
Jade and Jordan both have a total of 35 trading cards altogether.
Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.
As, Jade has 28 trading cards
Let Jordan has 'x' trading cards.
Now, as Jade has 4 times as many trading cards as Jordan.
So, 28 = 4x
4x = 28
x = 7
So, Jordan has 7 trading cards.
Now, they both have a total of 35 trading cards altogether.
Hence, Jade and Jordan both have a total of 35 trading cards altogether.
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For a science project each student needs 5 paper plates. If there are
15 students working on the project, how many paper plates are needed?
Answer:75
Step-by-step explanation:
since there are 15 students and they each need 5 plates you just do 15x5 and get 75
Identify x-intercepts, the vertex, and axis of symmetry of the graph f(x)= 1/4x (x-1)(x+7)
x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
What is, axis of symmetry, vertex and x - intercept?
A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.
A line's x-intercept is the location at which the x-axis is crossed.
Consider, the given equation,
[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]
Let,
[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex] ..(1)
To find x - intercept, plug y = 0 in above equation,
[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]
Therefore, x = 1 and x = -7 are the x - intercepts.
Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.
So,
[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]
Plug x = -3 in equation (1)
[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]
Therefore, the vertex is, (-3, -4).
The x - coordinate of the vertex is the axis of symmetry.
Therefore, axis of symmetry is x = -3.
Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
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A Pre-K teacher has a total of 4/5 ounces of paint. Th teacher puts 1/30 ounces of paint at each table. If the teacher sets up an equal number of tables in the 2 Pre-K classrooms, how many tables does he set up in each classroom?
Answer:
12 tables per classroom.
Step-by-step explanation:
We will assume that the teacher uses all of the 4/5 oz of paint. We can find how many samples of 1/30 oz are contained in the 4/5 oz by dividing:
(4/5)÷(1/30) = (4/5)*(30/1)
(4/5)*(30/1) = (120/5)
(120/5) = 24 samples of 1/30 oz paint in (4/5) oz total paint.
Each of the 2 Pre-K classrooms have the same number of tables, so we can divide 24 samples by 2 to find the number of tables in each classroom,
*24 samples/2 classrooms) = 12 tables/classroom
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
The formula for nth term in the given arithmetic sequence is 10 - 3n
For an nth term in an arithmetic sequence
U(n) = a + (n - 1)d
Where n is the number of terms
a is the first term
d is the common difference
From the sequence above
a = 7
d = 4 - 7 = - 3
The formula for an nth term is
U(n) = 7 + (n - 1)-3
= 7 - 3n + 3
Hence, the formula for nth term is 10-3n
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Divide and answer in simplest form: 45 ÷ 2
Answer:22.5
Step-by-step explanation:
lins bike travels 100 meters when her wheels rotate 55 times . whats the circumferences of her wheels
Answer:
Using formula to calculate the circumference of wheel: c=d/n
where
D is the distance bike travel
n is the number of times rotation
C is the circumference of the wheel
As per the statement:
Lin’s bike travels 100 meters when her wheels rotate 55 times.
here, n = 55 rotation and D = 100 meter.
then by definition:
meter c=100/55=20/11
Therefore, the circumference of her wheel is 1 9/11
the cat and rabbit's weight is 10 kg and so the dog and rabbit is 20 kg and the dog and cats weight isn24 kg so the question is what their weight togetheer> cat,dog,rabbit??
Answer:
27
Step-by-step explanation:
The cat weighs 7 kg.
The rabbit weighs 3 kg.
The dog weighs 17 kg.
You can check these answers by adding them together.
A cat plus the rabbit is 10 kg.
The rabbit and the dog is 20 kg.
The dog and cat is 24 kg.
The age distribution of a population is shown. a. The probability that a person chosen at random is at least 15 years old is %. b. The probability that a person chosen at random is 25−44 years old is %.
Answer is :
The chosen at random is 25 - 44 years old is = 26 %.
Probability determines how likely it is that a stated event would
occur. This event would occur. This probability lies between 0 and 1.
The probability that a person chosen at random is at least
15 years = sum of percentages of people at least 15 years old :
14 + 13 + 13 + 15 + 12 + 13 = 80%
the probability that a person chosen at random is 25 - 44 years old :
13% + 13% = 26%
Therefore The probability is 26%.
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Lolly wrote a total of 10 pages over 5 hours. How many hours will Lolly have to spend writing this week in order to have written a total of 20 pages?
Answer:
10 hours
Step-by-step explanation:
since she spent 5 hours writing 10 pages. you just have to multiple by 2 to know how long it will take to write 20 pages
how do i make v the subject of the formula, W=5+v/v-3
The expression that makes v the subject of the formula, W=5+v/v-3 is v= (5 + 3W)/ (W-1).
How can the subject of the formula be made?The concept is the concept of finding the subject of the formula in an expression.
To know the subject of the formula, we will need to perform some simplification:
W=5+v/v-3
then this can be expressed as:
W(v-3) = 5+v
Wv - 3W = 5+v
then we can rearrange the expression as:
Wv - v = 5 + 3W
then we can factorize the expression as :
v(W-1) = (5 + 3W)
v= (5 + 3W)/ (W-1)
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3. The mean of five positive numbers is 4. When another number is added, the mean becomes 8. Find the number added.
the answer
Answer:
28
Step-by-step explanation:
mean is when you add all the numbers divide it by the amount of terms
So to find the sum of the terms we just multiply 5 by 4
20 is the sum and since the mean is 8 with 6 terms we multiply those also
8x6
48 and to find the number we subtract 48 by 20
48-20
28
Hopes this helps please mark brainliest
7. The total cost of Mrs. Goodwin's donut purchase varies directly with the amount of donuts purchased. If
the total cost was $7.50 for 15 donuts, how many donuts can she purchase for $10.00?
The number of donuts that can be purchased for $10 is 20.
The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.
Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.
The price is directly proportional to the number of donuts purchased.
p ∝ n
We will remove the proportionality sign.
p = k*n
7.5 = k*15
k = 1/2
The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.
p = (1/2)n
10 = (1/2)n
n = 10*2
n = 20
Hence, the number of donuts that can be purchased for $10 is 20.
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twelve fair dice are rolled. what is the probability that the product of the numbers on the top faces is prime?
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
Define probability.In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.
Given,
12 fair dice rolled,
Probability that the product of the numbers on the top faces is prime:
⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁
6 × (1/6)⁵ × 3/6
1/2(1/6)⁴
Probability that the product of the numbers on the top faces is prime is 1/2(1/6)⁴.
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which is the name for the level of the independent variable intended to represent a neutral condition?
The level of a independent variable known to as the "Control group" is designed to portray a neutral state.
Define the term independent variable?The cause is the independent variable. Its value is unaffected by the other study variables.
You plan a study out whether variations in the room's temperature have an impact on students' math test results.
The interior temperature of the space is your independent variable. By making the room cooler for 1⁄2 the participants and warmer for other half, you can change the temperature.Experimental findings in mathematics are your dependent variable. Using a standardized test, you measure each participant's math prowess to see if there are significant temperature-related differences.Consequently, "control group" refers to a level of such an independent variable that is meant to stand in for "no treatment" or a neutral circumstance.
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What’s the value of x?
By using the property of similar triangles, it can be obtained that
Value of x is 7.2
What are similar triangles?
Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.
The different axioms of similarity are-
SAS axiom, AA axiom, SSS axiom
By the property of similar triangles,
[tex]\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2[/tex]
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