Null hypothesis: H₀ : μ = 55
Alternative hypothesis: H₁: μ [tex]\neq[/tex] 55
Given,
Rating = 55 mpg
For a two-tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis. In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.
the claim is the jeep has a 55 mpg rating and we want to test whether the rating is correct or incorrect. So, it is a two-tailed hypothesis because the rating can be less than or more than 55 mpg.
Therefore, H₀ : μ = 55
H₁: μ [tex]\neq[/tex] 55
These are the required null and alternative hypotheses.
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a local ice cream store is analyzing the day's sales. each serving came in either a cup or a cone, but not both, and the ratio of servings to cups was 7:47:47, colon, 4. what was the ratio of servings to cones?
The ratio of servings to cones is 47:4.
In mathematics, a ratio is a way of comparing two or more values. It is usually represented as a fraction, with the values being separated by a colon (:). For example, if you have 7 apples and 4 oranges, the ratio of apples to oranges would be 7:4. This can also be written as 7/4 or 1.75. Ratios can also be written as a decimal or a percentage. Ratios can be used to compare quantities, sizes, or measurements in different units.
If the ratio of servings to cups is 7:47:47:4, that means for every 7 servings, there are 47 cups.
Since the servings came in either a cup or a cone, but not both, the ratio of servings to cones is the remaining portion of servings that are not accounted for in the ratio of servings to cups.
So, it's 7 servings + 47 cups = 47 servings + 4 cups.
Therefore, the ratio of servings to cones is 47:4.
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coach mac finds a new practice court for the basketball team. if the width of the rectangular lot is 16 feet less than the length, and the perimeter is 160 feet, what are the dimensions of the new practice court?
perimeter of rectangle = 2W + 2L
first complete these equations: 160 = ?W + ? L ; W = L - ?
The dimensions of the new practice court is 45.5 feet by 29.5 feet.
The equations should be completed as 160 = 2W + 2L; W = L - 16
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W) or P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Since the width of the rectangular lot is 16 feet less than the length, we have:
W = L - 16
Substituting the given parameters into the perimeter formula, we have;
160 = 2L + 2W
160 = 2(L - 16) + 2L
160 = 2L - 32 + 2L
160 = 4L - 32
4L = 182
L = 45.5 feet.
For the width, we have:
W = L - 16
W = 45.5 - 16
W = 29.5 feet.
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a passenger jet took 3 hours to fly 1800 miles in the direction of the jet stream. The return trip against the jet stream took 4 hours. What was the jets speed in still air and the jet streams speed?
The speed of the jet in still air is 525miles per hour and the speed of the jet stream is 75miles per hour
What is speed ?speed is defined as the rate of change of distance with time. It is measured in meter per second and it is a scalar quantity. It has other units like miles per hour, kilometers per hour e.t.c
The speed of the jet with jet stream = displacement /time = 1800/3 = 600 miles/hour
The speed of the jet against = distance /time = 1800 / 4 = 450 miles per hour
The speed of the jet in still air will be the average speed of the jet to and fro. = (600+450)/2
= 1050/2
= 525 miles per hour
Therefore the speed of the jet in still air = 525 miles per hour
Also, the the jet stream speed = 525- 450 = 75 miles per hour.
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For every pound a company spends on advertising, it spends 49 pence on its website. Express the amount spent on advertising to its website as a ratio in its simplest form.
NEED ANSWER ASAP
The ratio of the the total amount spent on advertising to the amount spent on its website is 100: 49.
Now, According to the question:
There are 100 pence in one pound. Money can be written as, for example, £5.50, which means five pounds and fifty pence. The decimal point separates the pounds from the pence.
"Information available from the question"
For every pound a company spends on advertising, it spends £0.49 pence on its website.
Ratio of the the total amount spent on advertising to the amount spent on its website is,
= 1/0.49
[tex]= \frac{1*100}{0.49*100}[/tex]
= 100/49
= 100 : 49
Therefore, the ratio of the the total amount spent on advertising to the amount spent on its website is 100: 49.
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in a room of 60 people. whts the probability that there exist people that share the same birthday? assuming no one was born on feb 29?
The probability that there exists people who share the same birthday is 0.995.
Considering that all the 365 days are equally likely to be the birthday of a person and all the events that a person has birthday on 'y' are independent of others.
Under the said assumptions, let's say that there are n number of people in the room. If we number the people from 1 to n, then the total number of possibilities of birthdays are (365)^n.
Therefore, the possible combinations that all birthdays are different:
365 * 364 * 363 * .... * (365- n+1)
Thus, the probability that all birthdays are different is:
[tex]\frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
To get the probability of at least two people sharing the same birthday is,
[tex]1- \frac{365* 364 * 363* .... (365- n+1)}{365^n}[/tex]
= 1 - 0.0058
= 0.9942
=0.995
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what is an appropriate way to visualize a list of the eye colors of 120 people? select all that apply.
The appropriate way to visualize a list of the eye colors of 120 people is pie chart and dot plot.
A pie chart is a circular statistical graphic in which the slices represent numerical proportions. In a pie chart, the arc length of each slice reflects the amount it stands for.
Pie charts can be used to show percentages of a whole group and show percentages at a particular moment. In contrast to bar graphs and line graphs, pie charts do not show changes over time.
A dot plot, also known as a strip plot or dot chart, is a simple style of data visualization in which data points are shown as dots on a graph with an x- and y-axis.
The things you and your partner choose to eat are a wonderful example.
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The following question may be like this:
What is an appropriate way to visualize a list of the eye colors of 120 people? select all that apply.
pie chart box plotscatter plotdot plot.A number tripled and tripled again is 819. What is the number? Show your work.
3(_____ x)= 819
_____x= 819
The number is ______.
tell what you put in the empty spots pls!!
The number representing the property of tripled a number two times and getting result 819 is equal to 91.
Let us consider a required number be 'x'.
Triple a given number is represented by 3x.
Tripled a tripled number again is expressed as 3 × ( 3x )
Result of a tripled a tripled number is equal to 819
⇒ 3 × ( 3x ) = 819
⇒ 9x = 819
Divide both the side by 9 we get,
⇒9x /9 = 819 /9
⇒ x = 91
Therefore, the required number having property of tripled and tripled a number again with result 819 is equal to 91.
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The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May he swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine
The balance of Jamie's checking account in the month of May is given as follows:
$20.
How to obtain the balance?The balance in the month of May is obtained applying the proportions in the context of this problem.
He swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine, hence the June balance is of:
-9 + 69 = $60.
The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May, hence the May's balance is given as follows:
3x = 60
x = $20.
Missing InformationThe problem asks for the balance of the checking account in the month of May.
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emmanuel weighs 150 pounds. about how many hours will it take him to metabolize one standard drink?
Emmanuel weighs 150 pounds. about 2 hours will it take him to metabolize one standard drink
Every hour, the body processes one normal drink. If you have 5 standard drinks, your body will take 5 hours to absorb the alcohol.
In general, the liver can digest one ounce of liquor (or one standard drink) in one hour. If you consume more than this amount of alcohol, your system will get saturated, and the excess alcohol will accumulate in your blood and physiological tissues until it can be metabolized.
It takes your liver around an hour to break down the amount of alcohol in a standard alcoholic drink (one beer, one glass of wine, or one shot).
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what are the dimensions of a rectangular tract of land when it’s perimeter is 44 kilometers and it’s area is 120 square kilometers
Answer:
The dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:
Length = 10 kilometers
Width = 12 kilometers
Explanation: To find the dimensions of a rectangular tract of land when its perimeter and area are known, you can use the formulas:
Perimeter = 2(length + width)
Area = length * width
We know that:
Perimeter = 44 kilometers
Area = 120 square kilometers
So, we can use these values to set up the following equation:
44 = 2(length + width)
And we can solve for length and width.
44 = 2(length + width)
22 = length + width
And now we know that the sum of the length and width of the rectangular tract is 22 kilometers.
Now we have to use the area formula:
Area = length * width
120 = length * width
We can use the value we have for the sum of the length and width to find either the length or the width of the rectangular tract.
For example, we can use the equation:
length = 22 - width
And substitute it into the area equation:
120 = (22 - width) * width
And then we can solve for width:
120 = 22 * width - width^2
width^2 - 22 * width + 120 = 0
We can use the quadratic formula to solve for width.
width = (22 +/- sqrt(22^2 - 4 * 1 * 120))/ 2
So,
width = (22 +/- sqrt(484 - 480))/ 2
width = (22 +/- sqrt(4))/ 2
width = (22 +/- 2)/ 2
width = (24)/ 2
width = 12
So, the width of the rectangular tract is 12 kilometers.
And we can use the equation:
length = 22 - width
to find the length
length = 22 - 12 = 10
So, the dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:
Length = 10 kilometers
Width = 12 kilometers
a marble is selected at random 3 times from a bag of 2 green marbles, 2 blue marbles, and 2 red marbles. the selected marble is replaced each time. what is the probability that at least 1 of the selections is blue?
The odds of choosing a red and a blue are 6/20 (4/20), or 3/5.
What is meant by probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true.A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. The likelihood that something will happen is known as probability. The number of possible outcomes is divided by the total number of possible outcomes to determine probability.The balls in the bag are unaware of what was drawn the first time because the two choices are separate.
Six of the 20 pebbles in the bag are red. The odds of selecting a red are 6/20.
Four of the 20 pebbles in the bag are blue. Picking a blue one has a 4/20 chance.
Multiplying the odds of each event will yield the likelihood of two independent events.
The likelihood of selecting a red followed by a blue is 6/20 (4/20), or 3/5.
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Lewis needed to find the difference in lengths between the hypotenuse and the longest leg of this triangle. His work is shown below.
Triangle A B C. Side B C is 16 and side A C is 12. Hypotenuse A B is labeled c.
The difference in lengths between the hypotenuse and the longest leg of the triangle is 4.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
By Pythagoras Theorem,
Hypotenuse² = (Leg 1)² + (Leg 2)²
(AB)² = (BC)² + (AC)²
c² = 16² + 12²
c² = 256 + 144
c² = 400
c = √400
c = 20
Length of longest leg = 16
Difference = 20 - 16 = 4
Hence 4 is the difference between the length of the hypotenuse and the longest leg.
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(01.03 MC)
What is the domain of the rational function f(x)=
x²+x-20 -?
X-4x²-9x+36
The domain of the rational function in this problem is given as follows:
All real values except x = -3, x = 3, x = 4.
How to obtain the domain of the function?The domain of a function is the set composed by all the input values that the function accepts.
The function in this problem is a fraction, meaning that the denominator cannot be zero.
The denominator is given as follows:
x³ - 4x² - 9x + 36.
The roots of the denominator are given as follows:
x = -3, x = 3, x = 4.
Hence the domain is all real values except those, meaning that the second option is the correct option.
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8×1+3×
1
10
+8×
1
100
+9×
1
1000
=
Answer:
108,138
Step-by-step explanation:
Hope this helps :)
A bakery offers 10 kinds of cookies, 5 of which are frosted. The baker wants to put 3 different cookies in bags to sell.
From the 10 types of cookies, what is the probability that the baker places 3 frosted cookies into a bag?
A: 4/5
B: 5/126
C: 1/12
D: 3/20
Answer:
I think 3/20 of a chance of putting 3 frosted cookies in bags to sell.
Step-by-step explanation:
Hope it helps! =D
Rank the four math operations (+, -, x, LaTeX: \div÷) in order of importance. Defend your ranking with real world examples using math vocabulary and skills we have learned this year
We can see here that ranking the four math operations in order of importance, we have:
AdditionMultiplicationSubtractionDivisionWhat is a math operation?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.
Addition (+) is the most important of the four operations because it is the foundation of all arithmetic. It is used in everyday life for basic calculations such as adding up a grocery bill or calculating the total cost of a purchase with tax. It is also used in more advanced mathematical concepts such as algebra and calculus.
Multiplication (x) is the second most important operation because it is used to find the total number of items in a group or the total area of a shape. It is also used in more advanced mathematical concepts such as solving equations and finding derivatives.
Subtraction (-) is the third most important operation because it is used to find the difference between two numbers. It is also used in more advanced mathematical concepts such as algebra and calculus.
Division (÷) is the least important of the four operations because it is a reverse operation of multiplication, which is more important and more frequently used. It is used to find the number of times one number is contained within another or the size of a group when the total size and number of groups is known.
All four math operations are important and useful in different ways, but the order of importance is based on how frequently they are used and how foundational they are to other mathematical concepts.
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what is 5g=20 step by step
Answer:
4
Step-by-step explanation:
It says 5g is 20. To figure out the value of g, you need to divide 5g by 5, and 20 by 5, which gives the answer of g=4
Jorge’s family has visited 38 of the 50 states in America. What fraction of the states
have they visited?
To find the fraction of the states that Jorge's family has visited, we can use the formula:
visited states / total states
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
So, Jorge's family has visited 19/25 of the states in America.
Jorge's family has visited 19/25 of the states in America.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
19 out of the 25 American states have been visited by the Jorge family.
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If the price of gas increases by 5% again next week, will the price be 10% higher than it was
originally? Explain your reasoning.
If the price of gas increases by 5% again next week, then the price be approx 10% higher than it was originally because again shows that their is two times increment of 5%.
Let the price of gas is x.
The price of gas is increased by 5% in a week. So after increment the price of gas = x + x × 5%
After increment the price of gas = x + 5x/100
After increment the price of gas = (100x + 5x)/100
After increment the price of gas = 105x/100
After increment the price of gas = 1.05x
The gas price again increase by 5%.
Now the price of gas after again increment = 105x/100 × 105%
The price of gas after again increment = 105x/100 × 105/100
The price of gas after again increment = 11025x/10000
The price of gas after again increment = 1.1025x
Now we find the total increment in two weeks
Percent Increment = (1.1025x - x)/x × 100
Percent Increment = 0.1025x/x × 100
Percent Increment = 0.1025 × 100
Percent Increment = 10.25%
Then we can say that approx 10% the cost of oil increased then originally.
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PLEASE SOMEONE HELP ME!!
I need this turned in by 10:00
The slope-intercept form of the linear function is given as follows:
y = 0.8x + 8.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The graph crosses the y-axis at y = 8, hence the intercept b is given as follows:
b = 8.
When x increases by 10, y increases by 8, hence the slope m is given as follows:
m = 8/10
m = 0.8.
Then the function is defined as follows:
y = 0.8x + 8.
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at the time of this writing 1 u.s. dollar is worth 1.28 canadian dollars. an automobile in toronto sells for 25,500 canadian dollars. the same car sells in detroit for 21,000 u.s. dollars. what is 25,500 canadian dollars equivalent to in u.s. dollars?
1.21 Canadian dollars is equivalent to 1 US dollar
What is 25,500 Canadian dollars equivalent to in US dollars?A monetary exchange rate, also known as a foreign exchange rate, is the rate at which one currency can be exchanged for another. Exchange rates are determined by the foreign exchange market and can fluctuate based on supply and demand.
Since an automobile in Toronto sells for 25,500 Canadian dollars and the same car sells in Detroit for 21,000 US dollars.
Thus, 25,500 Canadian dollars equivalent in US dollars will be:
25,500 Canadian dollar /21,000 US dollars = 1.21
Thus, 1.21 Canadian dollar is equivalent to 1 US dollar dollars
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need the answer asap ! thank you to anyone who helps <3 !
Answer:
B
Step-by-step explanation:
What you're seeing is a (x,y,z) plane.
At this point, it's just plug and play.
Looking at choice B....
(1) + (2) + (2)(3) = 1 + 2 + 6 which is indeed 9
(2)(1) + (2)(2) + 3(3) = 2 + 4 + 9 which is indeed 15
(1) + (-3) = 1 - 3 which is indeed -2
A 4-kilogram bag of apples costs $8.80. What is the unit price?
Answer: 0.455
Step-by-step explanation:
I figured how to get $1? (The unit price?) so I did 4 divided by 8.8
Answer: The unit price is $2.20 per kilogram of apples
Step-by-step explanation:
Divide $8.80 with 4
8.80/4 = 2.20 per kilogram
Solve m=n^2 for n
Pls I need it asap
Answer:
n = √m
Step-by-step explanation:
Now we have to,
→ find the required value of n.
The equation is,
→ m = n²
Then the value of n will be,
→ m = n²
→ n² = m
→ [ n = √m ]
Hence, the value of n is √m.
What are the coordinates of the point on the directed line segment from (-9, 9) to (7, -7) that partitions the segment into a ratio of 3 to 5?
The coordinates of the point that partitions the segment is given as : (-3, 21)
How to solve for the segmentTo find the coordinates of the point on the directed line segment from (-9, 9) to (7, -7) that partitions the segment into a ratio of 3 to 5, we can use the concept of vector addition.
First, we can represent the directed line segment as a vector, with the initial point (-9, 9) being the tail, and the terminal point (7, -7) being the head. The vector representing the directed line segment is:
V = <7 - (-9), -7 - 9> = <16, -16>
To partition the segment into a ratio of 3 to 5, we can represent the partition point as a scalar multiple of the vector V:
P = (-9, 9) + (3/8)V = (-9, 9) + (3/8)(16, -16)
The scalar multiple 3/8 is used to get the partition point, it's calculated by dividing the desired ratio (3) by the sum of the ratio (3+5)
Then, we can find the x and y coordinates of the point P by applying the scalar multiple to the components of the vector:
P(x, y) = (-9, 9) + (3/8)(16, -16) = (-9, 9) + (3/8)(16, -16) = (-9 + 316/8, 9 - 3-16/8) = (-9 + 6, 9 + 12) = (-3, 21)
So the coordinates of the point on the directed line segment that partitions the segment into a ratio of 3 to 5 are (-3, 21).
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Answer:(−3,3)
Step-by-step explanation:
If Ronald and his family drive 72 miles per hour (mph), how far do they travel in 1 hour
Answer:
72 miles
Step-by-step explanation:
its obvious
5^2-log(5)5
pls help
Answer:
5
Step-by-step explanation:
log(5)5=1
5^2-1 = 5^1 = 5
Your cousin is building a new house. The layout of the first floor is shown in the diagram above. Using the
diagram and knowledge of polynomials find the following:
1. Write a polynomial that represents the length of the north side of the house. Then simplify the
expression.
2. Write a polynomial expression that represents the area of the kitchen. Then multiply to put the
polynomial in standard form.
3. Write a polynomial expression that represents the area of the bedroom. Then multiply to put the
polynomial in standard form.
4. Find the dimensions of the bathroom in terms of x. (Hint the west and east side of the house
should be equal.)
The length of the north side of the house is 2x^2 + 9x - 32
The length of the north side of the house.From the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have
North side = 5x - 4 + x^2 - 23 + x^2 + 4x - 5
Evaluate
North side = 2x^2 + 9x - 32
The area of the kitchenHere, we have
Length = 2x + 1
Width = x^2 + 4x - 5
So, we have
Area = (2x + 1) * (x^2 + 4x - 5)
Area = 2x^3 + 8x^2 -10x + x^2 + 4x - 5
Area = 2x^3 + 9x^2 - 6x - 5
The area of the bedroomHere, we have
Length = 5x - 4
Width = 5x + 4
So, we have
Area = (5x - 4) * (5x + 4)
Area = 25x^2 - 16
Dimension of the bathroomFrom the figure, we have
Dimensjon = 5x - 4 by (2x + 1 + x + 6 - 5x - 4)
Dimensjon = 5x - 4 by - 2x + 3
Hence, the dimension of the bathroom is 5x - 4 by - 2x + 3
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what language used orthogonality as a primary design criterion and more orthogonal than other languages?
ALGOL 68 is a language that prioritized orthogonality as a key design requirement. ALGOL 68's primary objectives and design tenets are as follows:
1. a thorough and clear design;
2. an orthogonal design
3. Safety
4. Efficiency: Mode-independent parsing, independent compilation, loop optimization, representations in small and big character sets, static mode verification, etc.
As a programming language, Algol 68 offers certain unique and practical concepts that were ground-breaking at the time and have appeared, in varying degrees, in various languages afterwards.
Orthogonal design, which means that core concepts stated in the language can be used anyplace that usage can be said to "make sense." Completeness and clarity of explanation (as facilitated by the adoption of two-level grammar, which sparked many critical reactions).
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It would help me soooo much if you could solve these two
Answer:
8) 27.75
10) See down below. May be 1.83 OR 123.75, depending on what your problem says
Step-by-step explanation:
Problem 8)
Let's first take apart [tex]2^{3}[/tex], which will be 8. Now, let's plug that back into the equation real quick:
12 + (8 ÷ [tex]\frac{2}{3}[/tex]) + 3.75
Since dividing a fraction can also be equal to multiplying the reciprocal of that same fraction, ÷ [tex]\frac{2}{3}[/tex] can be re-written as: * [tex]\frac{3}{2}[/tex]
Let's put that into the equation now and solve:
12 + (8 * [tex]\frac{3}{2}[/tex]) + 3.75
= 12 + 12 + 3.75
= 27.75
Problem 10) (I'm unsure if the sign after 80 is ÷ or +, but I'll do equations for both)
(If the sign after 80 is ÷, check these steps on how to solve):
Same methods as problem 8. Let's first break down [tex]4^{2}[/tex], which will be 16. Then, let's set the ÷ [tex]\frac{2}{5}[/tex] to * [tex]\frac{5}{2}[/tex] and solve:
80 ÷ (16 * [tex]\frac{5}{2}[/tex]) + 3.75
= 80 ÷ (40) + 3.75
= [tex]\frac{80}{40+3.75}[/tex]
= 1.82857
(If the sign after 80 is +, check these steps):
80 + (16 * [tex]\frac{5}{2}[/tex]) + 3.75
= 123.75