There were 90 grapes in the container at first.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Let's assume that there were x grapes in the container at first.
Arianna ate 0.45 of the grapes, which means she ate 0.45x grapes.
Alex ate 35% of the grapes, which means he ate 0.35x grapes.
The total number of grapes eaten is the sum of what Arianna and Alex ate:
0.45x + 0.35x = 0.8x
This means that 0.8x grapes were eaten, and the number of grapes left is x - 0.8x = 0.2x.
We know that there were 18 grapes left, so we can set up an equation:
0.2x = 18
Solving for x, we get:
x = 90
Therefore, there were 90 grapes in the container at first.
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A bag contains 3 red marbles, 2 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that both marbles drawn will be red?
Answer:
1/9 ≅ 0.11
Step-by-step explanation:
suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will draw two cards without replacement from a standard deck. if both cards are hearts, your friend will pay you $16 . otherwise, you have to pay your friend $3 . step 2 of 2 : if this same bet is made 762 times, how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values.
It means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.
To calculate the expected value of this bet, we first need to determine the probability of drawing two hearts and the probability of not drawing two hearts.
There are 52 cards in a standard deck, with 13 cards of each suit (hearts, diamonds, clubs, and spades). To calculate the probability of drawing two hearts without replacement, we consider the following:
1st card: The probability of drawing a heart is 13/52, as there are 13 hearts in the deck and 52 cards total.
2nd card: After drawing one heart, there are 12 hearts left and 51 cards total. The probability of drawing another heart is 12/51.
Thus, the probability of drawing two hearts is (13/52) * (12/51).
Next, we need to find the probability of not drawing two hearts. This can be calculated by subtracting the probability of drawing two hearts from 1.
Probability of not drawing two hearts = 1 - [(13/52) * (12/51)]
Now, we can calculate the expected value of the bet:
Expected value = (probability of winning * winnings) + (probability of losing * losses)
In this case, the winnings are $16, and the losses are $3.
Expected value = [(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)
Now, let's calculate the expected value for 762 bets.
Expected value for 762 bets = 762 * {[(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)}
Round the final expected value to two decimal places. If it's a positive value, it means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.
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What is the axis of symmetry of the graph of the function f(x) = 2x^2 + 8x − 5?
Answer:
The axis of symmetry is at x = -2.
Step-by-step explanation:
To find the axis of symmetry of a quadratic function in the form of f(x) = ax^2 + bx + c, you can use the formula x = -b / (2a).
In the function f(x) = 2x^2 + 8x − 5, a = 2 and b = 8, so we can plug those values into the formula and get:
x = -b / (2a) = -8 / (2 * 2) = -2
Therefore, the axis of symmetry of the function f(x) = 2x^2 + 8x − 5 is located at x = -2.
This means that the graph of the function is symmetric with respect to the vertical line x = -2. Any point on the graph that is a distance of t from the line x = -2 will have a corresponding point on the graph that is also a distance of t from the line.
Please show working out.
A line has the equation y = 3x + k. What is the gradient of the line?
3
when the line is at the y=ax+b form the gradient is equal to a
professor kelp decides to write a procedure that produces at random any permutation except the identity permutation, in which every element ends up where it started. he proposes the procedure permute-without-identity. does this procedure do what professor kelp intends?
The procedure permute-without-identity does what Professor Kelp intends.
As per the given question,
Professor Kelp wants to write a procedure that produces any permutation randomly except the identity permutation in which every element ends up where it started.
He has proposed the procedure permute-without-identity. We need to check whether this procedure does what Professor Kelp intends or not.
Procedure permute-without-identity:
Generate a permutation π ∈ Sn−1 uniformly at random. (Note that the identity permutation is not in Sn−1.)
Return the permutation obtained by shuffling the elements of π using a uniformly random shuffle.
Randomly shuffle the list using the Fisher-Yates shuffle, which creates a uniformly random permutation of the list.
Professor Kelp's procedure permute-without-identity chooses a permutation at random from the set of all permutations except the identity permutation.
So, there are n! - 1 possible choices of π.
Then, the elements of π are shuffled randomly using a uniformly random shuffle.
The identity permutation is excluded from π as it is not included in Sn-1.
Since the identity permutation is not included in Sn-1, it cannot be chosen by the procedure permute-without-identity.
Hence, the procedure does what Professor Kelp intends.
This procedure achieves the desired outcome by avoiding the case where all elements end up where they started.
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How could you correctly rewrite the equation 4(5+3)=2(22-6) using distribution property
Answer: 4(5+3) = 4(5) + 4(3) = 20 + 12 = 32
Step-by-step explanation:
Answer:
32=32 ?
Step-by-step explanation:
events that occur in the extremes of the normal curve have a very small probability of occurring. group of answer choices true false
The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.
The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.
So, as one moves further from the mean, the probability of occurrence decreases exponentially.
So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.
Therefore, the statement is True.
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The possible range for the length of AC is greater than what but less than what .
Answer:10
Step-by-step explanation: one side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides
Answer: 5.83095
explanation:
miss america winners from the 1920's and 1930's had a average bmi of 19.2. a sample of recent winners had reported bmis of 18.3, 19.6, 19.9, 18.8, 18.2, 18.1, 18.1, 18.3, 18.3, 18, and 19.8 . do recent winners appear to be significantly different from those in the 1920s and 1930s? (assume normality)
A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.
To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.
The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.
Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.
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Scott filled his gas tank up with 19 5/9 gallons of gas. If he uses 1 5/6 gallons of gas each day, after how many days will he need to refill his tank?
Answer:
Using division the answer to the equation is 10 2/3 but the correct answer to the question would most likely be he needs to refill his tank after 10 days.
Step-by-step explanation:
19 5/9 ÷ 1 5/6 = 10 2/3
Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?
WRONG ANSWER = REPORTED
Answer:
47/60
Step-by-step explanation:
You want to know the probability of a randomly selected student is on the honor roll or varsity team when 176 of 240 students are on the honor roll, 48 are on the varsity team, and 36 are on both.
One or the otherThe probability of A or B is ...
P(A+B) = P(A) +P(B) - P(A·B)
The probability of interest is ...
P(honor roll + varsity) = P(honor roll) + P(varsity) - P(honor roll & varsity)
P(honor roll + varsity) = 176/240 +48/240 -36/240 = (176 +48 -36)/240
= 188/240 = 47/60
The probability of interest is 47/60.
[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
The probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex][tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]
We can use the inclusion-exclusion principle to find the number of students who are on the honor roll or are members of the varsity team.
This principle states that:
[tex]\sf |A\cup B| = |A| + |B| − |A\cap B|[/tex]where:
A and B are sets,|A| is the cardinality (number of elements) of set A, andA∩B is the intersection of sets A and B.Using this principle, we can find that:
[tex]\begin{aligned}\sf |Honors\cup Varsity|& =\sf |Honors| + |Varsity| − |Honors\cap Varsity|\\& =\sf 176 + 48 - 36\\& =\sf\red{188}\end{aligned}[/tex]
Therefore, there are 188 students who are on the honor roll or are members of the varsity team.
The probability that a randomly selected student is on the honor roll or is a member of the varsity team is then:
[tex]\begin{aligned}\sf P(Honors\cup Varsity)& =\sf \dfrac{|Honors\cup Varsity|}{|Total|} \\ &=\sf \dfrac{188}{240} \\&=\boxed{\bold{\: \dfrac{47}{60}\:}}\end{aligned}[/tex]
Therefore, the probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex]
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]
deena has pairs of white socks, pairs of black socks, pair of red socks, and pairs of navy socks in her sock drawer. each pair of socks is folded together. if she pulls a pair of socks out of her drawer in the morning without looking, what is the probability that she will choose a pair of navy socks?
The final answer is 1 / 11
Deena has a total of 11 pairs of socks in her sock drawer. One pair of those 11 pairs is navy socks. Therefore, the probability that she will choose a pair of navy socks is 1/11.What is probability? Probability is the numerical measure of the possibility of an event taking place. Probability is calculated by dividing the number of successful outcomes by the total number of possible outcomes.The probability of Deena picking navy socks is calculated as:Probability of selecting navy socks = Number of pairs of navy socks/ Total number of pairs of socks in the drawerNumber of pairs of navy socks = 1Total number of pairs of socks in the drawer = 1 /11Probability of selecting navy socks = 1/11Therefore, the probability that Deena will select a pair of navy socks is 1/11.
Therefore, the answer is 1 / 11.
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of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. how many of the students earned a c for the course?
Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.
To find the number of students who earned a C in the course, we'll follow these steps:
1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.
We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.
Now let's perform the calculations:
Step 1: We know that the total number of students is 180.
Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:
41 (A students) + 3 (B students) = 44 (A and B students)
Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):
180 (total students) - 44 (A and B students) = 136 (C students)
So, 136 students earned a C for the course.
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Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5.25 hours and charged him $116 for parts. The total was $719.75. Which equation could be used to determine cc, the cost of labor per hour?
One way to approach this problem is to use the formula:
total cost = cost of parts + cost of labor
We can plug in the given values:
719.75 = 116 + cost of labor x 5.25
Simplifying:
603.75 = cost of labor x 5.25
To solve for the cost of labor per hour (cc), we can divide both sides by 5.25:
cc = 603.75 / 5.25
Simplifying:
cc ≈ 114.76
Therefore, the equation that could be used to determine the cost of labor per hour is:
cc = (total cost - cost of parts) / hours of labor
or:
cc = (719.75 - 116) / 5.25
Find the inverse of the following function: f(x)=[tex]\sqrt[3]{4x+7}[/tex]
All functions have an inverse function, and for a function to have an inverse. The inverse of [tex]f(x) = 3\sqrt(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex]
What is the inverse function?The inverse function, often known as the "inverse mapping," is a function that "undoes" another function's operation. If a function f(x) translates an input x to an output y, the inverse function f(-1)(y) transfers the result y back to the input x.
To find the inverse of the function f(x) = 3√(4x + 7), we need to solve for x in terms of y.
Step 1: Replace f(x) with y
[tex]y = 3√(4x + 7)[/tex]
Step 2: Cube both sides to eliminate the cube root
[tex]y^3 = 27(4x + 7)[/tex]
Step 3: Simplify and solve for x
[tex]y^3 = 108x + 189[/tex]
[tex]x = (y^3 - 189)/108[/tex]
Step 4: Replace x with [tex]f^-1(x)[/tex]
[tex]f^-1(x) = (x^3 - 189)/108[/tex]
Therefore, the inverse of [tex]f(x) = 3√(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex] .
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The bishop family brought a case of water containing 24 bottles. During one week,Lydia drank 1/8 of the bottles,Mitchell drank 33 1/3% of the bottles,Alexa drank 0.25 of the bottles, and Todd drank the rest.What % did todd drink.
Todd drank 29.17% of the bottles. First, we need to calculate the total number of bottles drank by Lydia, Mitchell, and Alexa.
Lydia = (1/8) x 24 = 3 bottles
Mitchell = (33 1/3%) x 24 = (1/3) x 24 = 8 bottles
Alexa = 0.25 x 24 = 6 bottles
The total number of bottles drank by Lydia, Mitchell, and Alexa is 3 + 8 + 6 = 17 bottles.
Therefore, the number of bottles Todd drank is 24 - 17 = 7 bottles.
To find the percentage of bottles Todd drank, we can use the following formula:
Percentage = (Part/Whole) x 100%
Where the Part is 7 and the Whole is 24.
Percentage = (7/24) x 100% = 29.17%
Therefore, Todd drank 29.17% of the bottles.
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when estimating a task, what values are you likely to use? choose all that apply.group of answer choices2 days2 hours2 minutes2 sprints2 weeks
However, depending on the project, other units of time, such as minutes or sprints, may also be used.
When estimating a task, the values that are likely to be used include 2 hours, 2 days, and 2 weeks. These values are commonly used in project management for estimating the time required to complete a task.
An estimation is an approximate calculation of the time, effort, or resources required to complete a particular task or project.
It is a critical aspect of project planning, and a good estimate can help ensure that the project is completed on time and within budget. The most common time values used when estimating a task are hours, days, and weeks.
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After a blizzard the amount of snow on the ground melted by 3 inches one day and then another 8 inches the next day. write an expression that represents the total change in the amount of snow on the ground over the two days.
The expression that represents the total change in the amount of snow on the ground over the two days is -3 + (-8) = -11
The problem asks for the total change in the amount of snow on the ground over two days after a blizzard. The problem states that the snow melted by 3 inches one day and 8 inches the next day. The expression that represents the total change can be found by adding the two changes together. However, since the snow is melting, we need to use negative values to represent the change. Therefore, we can write the expression as:
-3 + (-8)
Simplifying this expression, we get:
-3 - 8 = -11
Therefore, the total change in the amount of snow on the ground over the two days is -11 inches.
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A Dress, is discounted at 75% off. The original price is $185.
What is the sales price?
O $46.25
O $42.50
O $36.25
$32.75
The discount is 75% off the original price of $185.
To find the amount of the discount, we can multiply the original price by 0.75:
$185 x 0.75 = $138.75
Therefore, the dress has been discounted by $138.75.
To find the sales price, we can subtract the discount from the original price:
$185 - $138.75 = $46.25
Therefore, the sale price of the dress is $46.25.
4. Use the spinner to decide where soch event would be located on the scale
below. Write the letter for each event in the appropriate place on the
probability scale.
The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or
4
1
2
0
Impossible
4
2
3
2
a. The spinner landing on 1
b. The spinner landing on an even number
c. The spinner landing on the number 8
3
d. The spinner landing on a number
e. The spinner landing on the left side of the circle
Unlikely
Probability Scale
125
1
2
Equally Likely to
Occur or Not Occur
1
Likety
1
Certain
The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or 4 and correct options are:
a. The spinner landing on 1 - 1 (Likely)
b. The spinner landing on an even number - 2 and 4 (Equally likely to occur or not occur)
c. The spinner landing on the number 8 - Impossible (0)
d. The spinner landing on a number - 1, 2, 3, and 4 (Equally likely to occur or not occur)
e. The spinner landing on the left side of the circle - Unlikely (2)
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
Here,
a. The spinner landing on 1 - There is only one section labeled 1 on the spinner, out of a total of 8 sections. Therefore, the probability of the spinner landing on 1 is 1/8. On the probability scale provided, this probability would be located closer to "Likely" than to "Equally Likely to Occur or Not Occur", but not as close to "Certain".
b. The spinner landing on an even number - There are 4 sections labeled with even numbers (2 and 4), out of a total of 8 sections. Therefore, the probability of the spinner landing on an even number is 4/8 or 1/2. On the probability scale provided, this probability would be located exactly halfway between "Equally Likely to Occur or Not Occur" and "Certain".
c. The spinner landing on the number 8 - There is no section labeled 8 on the spinner, so this event is impossible. On the probability scale provided, this probability would be located at the very bottom of the scale, labeled "Impossible".
d. The spinner landing on a number - Every section of the spinner is labeled with a number, so this event is certain to occur. On the probability scale provided, this probability would be located at the very top of the scale, labeled "Certain".
e. The spinner landing on the left side of the circle - There are 2 sections labeled with numbers that are on the left side of the circle (1 and 2), out of a total of 8 sections. Therefore, the probability of the spinner landing on the left side of the circle is 2/8 or 1/4. On the probability scale provided, this probability would be located closer to "Unlikely" than to "Equally Likely to Occur or Not Occur", but not as close to "Impossible".
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the surface area of a rectangular prism is 1300 square inches. find the surface area of a similar solid that is larger by a scale factor of 3.
The surface area after larger by scale factor is 11700 [tex]in^2[/tex].
What is surface area?The surface area οf an οbject refers tο the οverall space filled by its surfaces. Many 3D shapes in geοmetry have variοus surface areas, which may be quickly estimated using the fοrmulas we shall learn in this lessοn. Twο categοries are used tο classify the surface area:
Curved surface area οr Lateral surface areaSurface area in tοtalHere the given rectangular prism ,
Surface area = 1300 square inches
Here the given prism is larger by scale factor of 3 then,
=> surface area = 1300[tex]\times3^2[/tex] = 1300[tex]\times9[/tex] = 11700 [tex]in^2[/tex].
Hence the surface area after larger by scale factor is 11700 [tex]in^2[/tex].
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simplify the square root 0.2 squr 25y^2 if y<0
b) squr 1/16x^2 if x greater then or equal to 0
The simplified expression for expression √0.2 × √25y² will be √5|y| and for 1/16x² if x is greater than or equal to 0 simplified expressions will be (1/4)x.
a) Simplifying the expression √0.2 × √25y² using the properties of square roots, we get:
= √0.2 × √25y²
= √(0.2 × 25 × y²)
= √(5y²)
= √5 × √y²
= √5 × |y|
Since y<0, we need to take the absolute value of y to ensure that the result is positive. Therefore, the simplified expression is √5|y|.
b) Simplifying the expression √(1/16 x²), we get:
= √(1/16 x²)
= (1/4) √(x²)
= (1/4) |x|
Since x≥0, we do not need to take the absolute value of x. Therefore, the simplified expression is (1/4)x.
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Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answer:
13
Step-by-step explanation:
The volume of the pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
The base area of the pyramid is equal to the area of one of the square sides, which is:
Base area = 12 in * 12 in = 144 in^2
Therefore, the volume of the pyramid is:
Volume = (1/3) * 144 in^2 * 14 in = 2,688 in^3
Each wax cube has a volume of:
Volume of a wax cube = 6 in * 6 in * 6 in = 216 in^3
To find out how many wax cubes Josiah needs, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,688 in^3 / 216 in^3 = 12.4444...
Since we can't use a fraction of a wax cube, Josiah will need to use 13 wax cubes to make the candle.
Haroldo, Xerxes, Regina, Shaindel, Murray, and Georgia are invited to a dinner party. They arrive in a random order and all arrive at different times. What is the probability that Xeres arrives first AND Regina arrives last?
The probability that Xeres arrives first AND Regina arrives last is 3.33%.
What is probability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
Here The number of possible arrangements of n elements is given by:
[tex]A_n=n![/tex]
In this problem:
6 people are invited, so the number of ways they can arrive is T = [tex]6![/tex]
Xeres first and Regina last, for the middle 4 there are way D= 4! ways
Then the probability is P = [tex]\frac{D}{T}=\frac{4!}{6!}[/tex] = 0.0333 = 3.33%
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Help me solve e this question?
The correct statement regarding the transformations is given as follows:
g(x) is stretched vertically by a factor of 5 and translated 3 units to the right.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The transformations to the parent function in this problem are given as follows:
Multiplication by 5 -> vertical stretch by a factor of 5.x -> x - 3: translation right 3 units.More can be learned about translations at brainly.com/question/28174785
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Please help me, only 20 points if answered !!
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ s=\pi \end{cases}\implies \pi =\cfrac{\theta \pi (4)}{180}\implies \cfrac{180}{4\pi }\cdot \pi =\theta\implies 45=\theta[/tex]
Your station charges $6.50 for a lubrication job. As a promotion you sell six coupons for lubrication jobs for $32.50 What percentage discount are you offering for customers who purchase the 6-coupon lube booke (to the nearest tenth)
Answer:
16.7%
Step-by-step explanation:
The regular price for a lubrication job is $6.50. With the promotion, customers can purchase 6 coupons for $32.50.
To find the percentage discount offered, we need to compare the regular price with the discounted price.
The regular price for 6 lubrication jobs would be:
$6.50 x 6 = $39
With the coupon book, the customer pays $32.50 for 6 lubrication jobs.
The amount of discount is:
$39 - $32.50 = $6.50
Therefore, the percentage discount offered is:
($6.50 / $39) x 100% = 16.7%
So the station is offering a discount of 16.7% to customers who purchase the 6-coupon lube book.
]
D
5²
25
2) A two-dimensional preimage is dilated by a scale factor to result in a new image. Fill in the
blanks with the number needed to calculate the area of the new image compared to the area
of the preimage.
25
1
If the scale factor is , then the area of the preimage is multiplied by or to calcu-
late the area of the new image.
()'
Answer:
Let’s start by defining the variables:
Let A be the area of the preimage.
Let k be the scale factor.
If the scale factor is k, then the area of the preimage is multiplied by k² to calculate the area of the new image. Therefore, we have:
Area of new image = k²A
We are given that:
k = 1/5
Therefore, we have:
k² = (1/5)² = 1/25
The area of the preimage is not given. Therefore, we cannot calculate the area of the new image
solve for y
A)115º
B)108º
C)90º
D)130º
Answer:
[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the measure of} \ \tt \angle Y.[/tex]
[tex]\textsf{We are given a shape, but we aren't given what shape it is.}[/tex]
[tex]\large\underline{\textsf{What is a Shape?}}[/tex]
[tex]\textsf{A Shape is a specific outline sometimes dependent of how many sides it has.}[/tex]
[tex]\underline{\textsf{Shapes that depend on outlines;}}[/tex]
[tex]\textsf{Non-Polygons,}[/tex][tex]\textsf{Shapes that aren't quadrilaterals,}[/tex][tex]\textsf{Any shapes that are not classified under something.}[/tex][tex]\underline{\textsf{Shapes that depend on the number of sides;}}[/tex]
[tex]\textsf{Mainly the opposite.}[/tex]
[tex]\textsf{Polygons,}[/tex][tex]\textsf{Quadrilaterals,}[/tex][tex]\textsf{Any shapes that are classified under something.}[/tex][tex]\textsf{Because our shape has 5 sides, it's dependent on the amount of sides it has, which}[/tex]
[tex]\textsf{makes the shape a Polygon.}[/tex]
[tex]\large\underline{\textsf{What is a Polygon?}}[/tex]
[tex]\textsf{A Polygon is a closed shape that classifies as a;}[/tex]
[tex]\textsf{Triangle, or any shape with 3 sides,}[/tex][tex]\textsf{Square/Rectangle, or any shape with 4 sides,}[/tex][tex]\textsf{Pentagon, or any shape with 5 sides,}[/tex][tex]\textsf{Hexagon, or any shape with 6 sides,}[/tex][tex]\textsf{Heptagon, or any shape with 7 sides,}[/tex][tex]\textsf{Octagon, or any shape with 8 sides,}[/tex][tex]\textsf{Nonagon, or any shape with 9 sides,}[/tex][tex]\textsf{Decagon, or any shape with 10 sides.}[/tex][tex]\textsf{The list goes on forever.}[/tex]
[tex]\textsf{Our shape is a Pentagon, due to the shape having 5 sides.}[/tex]
[tex]\large\underline{\textsf{What is a Pentagon made up of?}}[/tex]
[tex]\textsf{A Pentagon is a polygon that has 5 sides, meaning that it has 5 angles.}[/tex]
[tex]\textsf{The total of the angles is what we should find out with a pattern.}[/tex]
[tex]\underline{\textsf{What is the total of all the angles' measures of a Pentagon?}}[/tex]
[tex]\textsf{A Triangle has 3 sides with 3 angles, which add up to 180}^{\circ}.[/tex]
[tex]\textsf{A Quadrilateral has 4 sides with 4 angles, which add up to 360}^{\circ}.[/tex]
[tex]\textsf{The Pattern is that when an extra side is added, the total measure of the angles}[/tex]
[tex]\textsf{increase by 180}^{\circ}.[/tex]
[tex]\textsf{A Pentagon has 5 sides with 5 angles, which add up to} \ \boxed{\tt 540^{\circ}.}[/tex]
[tex]\textsf{Now that we know the total, we can form an equation.}[/tex]
[tex]\tt 540^{\circ} = 135^{\circ} + 112^{\circ} + 88^{\circ} + y^{\circ} + 90^{\circ}[/tex]
[tex]\textsf{Remember that Right Angles are 90}^{\circ} \ \textsf{angles that are represented with a box}[/tex]
[tex]\textsf{symbol.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Now that we have our equation, we should \underline{combine like terms}, then use the}[/tex]
[tex]\textsf{\underline{subtraction rule of equality} to find the measure of y.}[/tex]
[tex]\underline{\textsf{Combine Like Terms;}}[/tex]
[tex]\tt 540^{\circ} = \boxed{135^{\circ}} + \boxed{112^{\circ}} + \boxed{88^{\circ}} + y^{\circ} + \boxed{90^{\circ}}[/tex]
[tex]\tt 540^{\circ} = 425^{\circ} + y^{\circ}[/tex]
[tex]\underline{\textsf{Use the Subtraction Rule of Equality;}}[/tex]
[tex]\tt 540^{\circ} - 425^{\circ} = 425^{\circ} - 425^{\circ}+ y^{\circ}[/tex]
[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]
Look at the pattern below.
step 1 with 1 square
step 2 with 3 squares
step 3 with 6 squares
step 4 with 10 squares
How does the pattern grow at each step?
Choose 1 answer:
Answer: The pattern grows by adding the consecutive counting numbers starting from 1.
For example:
Step 1: 1 square
Step 2: 1 + 2 = 3 squares
Step 3: 1 + 2 + 3 = 6 squares
Step 4: 1 + 2 + 3 + 4 = 10 squares
So at each step, the number of squares increases by adding the next consecutive counting number.
Step-by-step explanation: