Answer: y = 15
Step-by-step explanation:
Subtract both sides by 3
3 + y = 18
y = 15
Is 17/4 an mixed number an improper fraction
Answer:
improper fraction
Step-by-step explanation:
A mixed number has a whole number and a fraction.
An improper fraction is a fraction with a numerator bigger than the denominator.
Since 17 > 4 and there is no whole number, this is an improper fraction.
It can be changed to a mixed number by dividing the numerator by the denominator
17 ÷4 = 4 and there is a remainder of 1. The remainder goes over the denominator
4 1/4
Answer: It's an improper fraction
Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:
[tex]5\frac{1}{7}[/tex]
Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the whole number (4 in this case) would be the whole number, and the faction would be 1/4
So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]
To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.
Function A a line which passes through the points (2 , 3) and (-1 , -3) Function B Y= 1/2X +2 The rate of change of function A is the rate of change of function B.
The rate of change of function A is not same with the rate of change of function B.
What is rate of change of linear function?The slope of a linear function is another name for its rate of change.
The slope and the function's starting value are both included in the slope-intercept form equation of a line. When the input of a linear function is 0, the output is the initial value, or y-intercept.
Function b is in slope intercept form as Y= 1/2X + 2 and here the slope is 1/2
calculation of slope pf function A
The slope, m of the linear function is calculated using the points (2 , 3) and (-1 , -3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (3 + 3) / (2 + 1)
m = (6) / (3)
m = 2
The slopes are not the same
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The slope of a line can be used when building a ramp. Gordon is helping to build a wheelchair ramp for a neighbor's house. For every 12 inches of horizontal distance, the height of the ramp increases 1 inch.
Question 1
Part A
The height of the ramp when it connects to the house is 9 inches. What is the length of the ramp in yards?
Part B
Explain how you determined the length.
Enter the correct answers in the boxes.
The ramp is 9 inches tall, so the length of the ramp is 9×
=
inches, which is equal to
feet, and that is equal to
yards.
Answer:
Part A:
To find the length of the ramp in yards, we need to first determine the horizontal distance covered by the ramp. The slope of the ramp is 1/12, meaning that for every 12 inches of horizontal distance, the height of the ramp increases by 1 inch. Since the height of the ramp when it connects to the house is 9 inches, we can use this information to determine the horizontal distance covered by the ramp.
9 inches / (1/12) = 108 inches
To convert inches to yards, we divide by 36, so
108 inches / 36 inches/yard = 3 yards
Part B:
To determine the length of the ramp, I used the information provided about the slope of the ramp and the height of the ramp when it connects to the house. I used the slope of the ramp (1/12) to calculate the horizontal distance covered by the ramp. Then I converted the horizontal distance from inches to yards by dividing by 36. Finally, I obtained 3 yards as the length of the ramp.
Answer:
Part A = 3 yards
Part B = 9 x 12 = 108 inches = 9 feet = 3 yards
Step-by-step explanation:
Part A
1 inch height - 12 inches length
9 inches height - 9 x 12 = 108 inches length
36 inches = 1 yard
108 inches = 108/36 = 3 yards
Part B
Shown above
The ramp is 9 inches tall, so the length of the ramp is 9 x 12 = 108 inches.
1 feet = 12 inches
108 inches = 108/12 feet = 9 feet
1 yard = 3 feet
9 feet = 3 yards.
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Keisha reads a label on a measuring cup that shows 16 fluid ounces is the same as 2 cups. Using this information, how many fluid ounces are in 4.5 cups?
There are 36 fluid ounces in 4.5 cups
How to calculate the number of fluid ounces in 4.5 cups?
Keisha reads a label on a measuring cup
The reading shows that 16 fluid ounces is the same as two cups
Therefore the number of fluid ounces in 4.5 cups can be calculated as follows
16/2
= 8
8 × 4.5
= 36
Hence there are 36 fluid ounces in 4.5 cups
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Leah walks to soccer practice on Saturday. She leaves her home and walks 6 blocks north. Leah then turns east and walks 4 more blocks to the soccer field. How far is the soccer field from leah’s home ? Round your answer to the nearest tenth.
Answer: The soccer field is about 8.6 blocks away from Leah's home.
Step-by-step explanation:
The soccer field is about 8.6 blocks away from Leah's home.
Leah walks 6 blocks north and 4 blocks east. To find the total distance she walked, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The distance is the square root of (6 blocks)^2 + (4 blocks)^2 = 36 + 16 = 52 then square root of 52 = 7.21
The distance of the soccer field from Leah’s home is 7.21 blocks, but it can be rounded to nearest tenth which is 8.6
the average of the first two multiples is 28 and the average of the last two is 44 what is the greater multiples on abby's list
Answer:
108
Step-by-step explanation:
average of first two multiples = 28
sum of first two multiples = 28 * 2 = 56
average of last two multiples = 44
sum of last two multiples = 44 * 2 = 88
average of all four multiples = ( 56 + 88 ) / 4 = 36
value of greater multiple = (88 + 56) - 36 = 108
Problem No. 5 A 55-seater bus was 40% full of its capacity on leaving the depot. At the first stop only my friend and I boarded the bus. At the second stop one third of the passengers alighted and 9 passengers boarded. At the third stop I, together with 10 other passengers, got off the bus and 5 boarded. How many passengers were on the bus as it pulled away from the stop?
Answer: 12 passengers.
Step-by-step explanation:
55 x 0.40 = 22
22 + 2 = 24
24 ÷ 3 = 8
8 + 9 = 17
17 - 12 = 5
5 + 5 = 10
Abe’s apple orchard plants both green apple trees and red apple trees. This years planting will include 21 red apple trees and 18 green apple trees. What is the ratio of green apple trees to red apple trees.
Find the average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2]
The average rate of change of g(x) =5x^3+4/x^2 on the interval [-1,2] is -2
What is a function?A function can be defined as a law, rule or expression explaining the relationship between two variables.
These variables are called;
The independent variableThe dependent variableFrom the information given, we have the function;
g(x) =5x^3+4/x^2
For the interval, {1, -2}
Let's substitute the value of x as 1
g(1) = 5(1)³ + 4/(1)²
find the values
g(1) = 5 + 4/1
g(1) = 9/1 = 9
For x = -2
g(-2) = 5(-2)³ + 4/(-2)²
find the values and substitute
g(-2) =5(-8) + 4/ -8
g(-2) = -40 + 4/-8
add the numerators
g(-2) = -36/8
divide the values
g(-2) = -9/2
The average change = 9 ÷ -9/2 = 9 × 2/-9 = -2
Hence, the value is -2
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A fair coin is tossed 12 times. How many different sequences of tosses could there have been, if the number of tosses was even.
The number of different sequences of tosses could there have been, if the number of tosses was even 1/2
How to determine the number of tosses?You should understand that the tosses involves a sequence which is an array of numbers in a particular order
The question reads thus How many different sequences of tosses could there have been, if the number of tosses was even.
Number of tosses = 12
The tosses are 1,2,3,4,5,6,7,8,9,10,11,12 = 12 Times
The even numbers are
2,4,6,8,10,12 = 6 times
The Probability of the toss is 6/12
Therefore the number of tosses equals 1/2
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how to solve this long division
Answer:
Step-by-step explanation:
Answer:
0.5 is the answer
Step-by-step explanation:
2 clearly cannot be divided by 4
So what we have to do is put a 0 over the 2 and a decimal in the place after the 2 and bring down a 0 making it 20÷4=5
Don't forget the decimal point that was necessary to create the 20
That makes the answer 0.5
The brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1386.4 cm³ be significantly high?
If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.
How to find the lower and upper limits?Mean = 1085.2 cm³
Standard deviation = 125.6 cm³
Hence,
Lower limit = Mean - 2 x Standard deviation
Lower limit =1085.2 - 2 x 125.6
Lower limit =1161.2 - 251.2
Lower limit =910
Upper Limit = Mean + 2 x Standard deviation
Upper Limit = 1161.2 + 2 x 125.6
Upper Limit =1161.2 +251.2
Upper Limit =1412.4
The limit of values is from 910 to 1412.4.
A value below 910 will be is considered low and a value above 1412.4 will be considered high
Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.
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A population of pea aphids doubles every week. The population begins with 300 individual pea aphids. In how many weeks will the population reach 9,600 individuals?
Answer:
To find out how many weeks it will take for the pea aphid population to reach 9,600 individuals, we need to determine how many times the population needs to double to reach that number.
We can use logarithms to find this out. Using the rule log(A) / log(B) = log(A) to base B, we can calculate the number of times the population needs to double.
log(9600) / log(2) = log(9600) to base 2 = 9.98
So the population needs to double 9.98 times.
Since the population doubles every week, it will take 9.98 weeks for the population to reach 9,600 individuals.
Vote Branliest!
Answer: 5 weeks
Step-by-step explanation: Based on the information given, let's conduct an equation. It'd look something like this:
300 * [tex]2^{x}[/tex] = 9600
Now, we need to "reduce" the greatest common factors on both sides of the equation. This is so we can find the value of "x" It should look like this:
[tex]2^{x}[/tex] = 32
Now, we need to covert both sides to have the same base, which should look like this:
[tex]2^{x} = 2^{5}[/tex]
Based on the information given, we now know that x = 5, making it have a constant rate of 5 weeks to reach 9,600 individuals. I hope this helped!
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 16 gallons of fuel, the
airplane weighs 1988 pounds. When carrying 50 gallons of fuel, it weighs 2175 pounds. How much does the airplane weigh if it is carrying 64 gallons of fuel?
The plane weights 1988 pounds when it has 16 gallons of fuel on board. It is 2175 pounds heavier when carrying 50 gallons of fuel. w= 2500 .
How much does the airplane weigh if it is carrying ?The following correlation is true if the relationship between weight and fuel consumption is linear:
[tex]$\frac{2175 \text { pounds }-1988 \text { pounds }}{50 \text { gallons-16gallons }}=\frac{W-1988 \text { pounds }}{64 \text { gallons-16galons }}$[/tex]
We resolve this equation:
w = 2500.
Assume that the weight of an airplane, measured in pounds, is a linear function of the fuel tank's capacity, measured in gallons. The aircraft weighs 2030 pounds while carrying 20 gallons of fuel. It weighs 2225 pounds while carrying 50 gallons of fuel. It weighs 2338 pounds while carrying 52 gallons of fuel. Weight (in pounds) of an airplane fuel consumption (in gallons) Per gallon, Jet-A Prist is 6.75 pounds. A 100LL gallon weighs 6.0 pounds. 6.0 pounds per gallon for extras.
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Winston leaned a 32-foot ladder against the side of a building. The
base of the ladder is 3 feet from the base of the building. The top of
the ladder is 15 feet from the top of the building. How tall is the
building? Provide an answer accurate to the nearest tenth of a foot.
Answer:
the building is approximately 28.3 feet tall, accurate to the nearest tenth of a foot.
Step-by-step explanation:
The height of the building can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the building is the hypotenuse, and the base of the ladder and the top of the ladder form the other two sides.
The height of the building can be found using the following formula:
h = √(32^2 - 15^2)
h = √(1024 - 225)
h = √(799)
h ≈ 28.3 ft
16 People fit comfortably in a 8 feet by 9 feet area. Use this value to estimate the size of a crowd that is
5 feet deep on both sides of the street along a 2-mile section of a parade route.
Answer:
Step-by-step explanation:
It is impossible to accurately estimate the size of the crowd without knowing how many people are standing in each foot of space. However, if we assume that 16 people fit in a 9 ft x 8 ft area, then we can estimate the size of the crowd in a 2-mile section of the parade route that is 5 feet deep on both sides of the street.
Assuming a 5-foot deep crowd on both sides of the parade route, we can estimate that there would be 40 feet of crowd on one side of the parade route and 40 feet of crowd on the other side of the parade route. This means that there would be a total of 80 feet of crowd across the 2-mile parade route.
Using the assumption that 16 people fit in a 9 ft x 8 ft area, we can estimate that there would be 1280 people across the 2-mile parade route (80 feet x 16 people). This is a rough estimate, as it does not account for the gaps between people, which would likely reduce the total number of people in the parade route.
Hey guys does anyone have any idea how to solve for the smiley face? I am really struggling and could use some help.
The smiley face is solved to get a value of 72
How to solve to get the value of the smiley faceThe solution to the value of the smiley face is solved by forming some equations
Using the third row that have only squares
8 square - 6 square + 3 square = 60
2 square + 3 square = 60
5 square = 60
dividing through by 5
square = 60 / 5 = 12
hence a square is 12
Using the second row
12 square + 5 star = 234
substituting a square = 12
12 * 12 + 5 star = 234
144 + 5 star = 234
5 star = 234 - 144
5 star = 90
dividing through by 5
star = 90 / 5 = 18
hence a star is 18
using the first row
square + 3 triangle + star = 57
substituting square = 12 and star = 18
12 + 3 triangle + 18 = 57
3 triangle + 30 = 57
3 triangle = 57 - 30
3 triangle = 27
dividing through by 3
triangle = 27 / 3 = 9
hence triangle = 9
solving for the smiley face
substituting the values of the figures
18 (9 + 18 - 12) + 12 (18 + 9 + 9) = smiley face
solving the parenthesis
smiley face = 18 (15) + 12 (36)
smiley face = 18 * 15 + 12 * 36
smiley face = 702
hence the smiley face is 702
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Change the fraction 7/12 to a decimal. Round to the nearest thousandth.
The answer to this question is 0.583
Which of the following is the correct solution set?
{ } or empty set
{infinite set of points on the line}
{point in Quadrant 1}
The solution set for the given graph is a null set or empty set.
What is set?Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form.
Given is a graph of parallel lines, as we know in the system of linear equations, equations having parallel lines yields no solutions, therefore, for this also, there is no solution,
Therefore, the set will be null set or empty set.
Hence, the solution set for the given graph is a null set or empty set.
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Select the correct answer.
Which type of investment offers both capital gains and interest income?
Α. property
B. CDs
C. stocks
D. bonds
Answer:
D
Step-by-step explanation:
Please help me find answer
Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is qual to the number of gift bags. Raoul needs to make. Then find how many wristbands and how many movie passes raoul can put in each gift bag if he evenly distributes the items.
Please help I am stuck I am doing work nonstop on all weekends if I don’t get this right and done please help and will give brainlesst for the correct answer
Answer:
Step-by-step explanation:
I do know give me brainliest first
Answer:
24 gift bags
Step-by-step explanation:
Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!
May I have heart, 5 star, and brainliest please?
Solve for x 2/5=6/21-x
The value of x is 6
How to calculate the value of x ?2/5 = 6/21-x
Cross multiply both sides
2(21-x)= 30
42-2x= 30
collect the like terms
-2x= 30-42
-2x= -12
Divide both sides by the coefficient of x which is 2
2x/2 = 12/2
x= 6
Hence the value of x is 6
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Jemma has a colletion of 240 coins. Of these coins, 20% are dated before 1910, 15% are dated between 1910 and 1950 and the remainder are dated after 1950. How many coins are dated after 1950?
So on solving provided question we can say that the probability 20% of these coins are pre-1910, 15% are between 1910 and 1950, and the remaining 75% are post-1950.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Emma has a collation of 240 coins.
Of these coins, 20% are dated before 1910, 15% are dated between 1910 and 1950 and the remainder are dated after 1950.
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find the value of x
transversals
Answer:
x = 9
Step-by-step explanation:
[tex] - 1 + 14x = 12x + 17 \\ 2x = 18 \\ x = 9[/tex]
I WILL MARK BRAINLIEST INSTANTLY.
Answer:
2nd option
Step-by-step explanation:
[4 -7] * [a b] * = [1 0]
[-1 2] [c d] [0 1]
4 * a + (-7) * c = 1
4 * b + (-7) * d = 0
-1 * a + 2 * c = 0
-1 * b + 2 * d = 1
4a - 7c = 1 ==> equation 1
4b - 7d = 0 ==> equation 2
-a + 2c = 0 ==> equation 3
-b + 2d = 1 ==> equation 4
(-b + 2d = 1) * 4 ==> make -b into -4b
-4b + 8d = 4
+ (4b - 7d = 0)
-4b+4b + 8d-7d = 4+0 ==> add equations 2 and 4 to cancel the variable b
8d-7d = 4 ==> -4b+4b=0 and adding anything by 0 will result in itself: 0+3=3
d = 4
-b + 2d = 1
-b + 2(4) = 1 ==> substitute 4 for d
-b + 8 = 1 ==> simplify
-b = -7 ==> subtract 8 on both sides
b = 7 ==> simplify
Since we got the values of b and d, the matrix now looks like this:
[4 -7] * [a 7] * = [1 0]
[-1 2] [c 4] [0 1]
Now solve for a and c using equations 1 and 3:
4a - 7c = 1 ==> equation 1
-a + 2c = 0 ==> equation 3
(-a + 2c = 0) * 4 ==> make -a into -4a
-4a + 8c = 0
+ (4a - 7c = 1)
-4a+4a + 8c-7c = 0+1 ==> add equations 1 and 3 to cancel the variable b
8c-7c = 1 ==> -4a+4a=0 and adding anything by 0 will result in itself: 0+3=3
c = 1
-a + 2c = 0
-a + 2(1) = 0 ==> substitute 1 for c
-a + 2 = 0 ==> simplify
-a = -2 ==> subtract 2 on both sides
a = 2 ==> simplify
Since we got the values of a and c, the matrix now looks like this:
[4 -7] * [2 7] * = [1 0]
[-1 2] [1 4] [0 1]
Hence, the answer is the 2nd option.
O
During a gift exchange, ten different gifts
are labeled 1-10 and placed in a pile.
Each person takes a turn selecting a gift
without replacing it. What is the
probability that the first gift chosen is gift
#3 and the second is gift #9?
Using the given conditions in the question,the probability that the first gift chosen is gift #3 and the second is gift #9 is (1/10) * (1/9) = 1/90.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Events with a probability of 0.5 or greater are considered likely, while those with a probability less than 0.5 are considered unlikely. The probability of all possible events in a given situation must add up to 1. In mathematical terms, probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
How can you measure the chance of something happening?The chance of something happening can be measured by probability. It's a number between 0 and 1, where 0 means it's impossible for the event to happen and 1 means it's certain to happen. The closer the number is to 1, the more likely the event is to happen.
The probability that the first gift chosen is gift #3 and the second is gift #9 is (1/10) * (1/9) = 1/90. This is because the probability of choosing any specific gift on the first turn is 1/10, and the probability of choosing any specific gift on the second turn, given that there are now 9 gifts left in the pile, is 1/9. Multiplying these probabilities together gives the overall probability of the first gift being #3 and the second gift being #9.
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Mean, Median and Mode of the following set of numbers.
13, 11, 17, 14, 20, 6, 15, 15, 12, 6, 13, 24, 22, 19
Answer:
Mean: [tex]14 \frac{11}{207}[/tex]
Median: 14.5
Mode: 6, 13, and 15
Step-by-step explanation:
We will start by arranging these numbers from smallest to greatest to get the median and mode:
6, 6, 11, 12, 13, 13, 14, 15, 15, 17, 19, 20, 22, 24
To get the mode, we will look. There are two 6, 13, and 15. So those three are our modes. Then, since there are 14 numbers, we will split the list in half and find the average of the two most inward numbers. We get:
6, 6, 11, 12, 13, 13, 14 15, 15, 17, 19, 20, 22, 24
Our two most inward numbers are 14 and 15, so we add the two together and then divide by 2, giving us:
14 + 15 = 29/2 = 14.5
So our median is 14.5.
Finally, we will add up all the numbers together, then divide by 14 to get our mean. We get:
6 + 6 + 11 + 12 + 13 + 13 + 14 + 15 + 15 + 17 + 19 + 20 + 22 + 24 = 207
Then we divide by 14:
[tex]\frac{207}{14} = 14 \frac{11}{207}[/tex]
So, our median is [tex]14 \frac{11}{207}[/tex].
Hope this helped!
The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 180 calories, and 108 calories are from fat. What percent of the total calories is from fat?
Answer:
60% of the total calories is from fat
Step-by-step explanation:
We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 1Y =
108
180
By multiplying both numerator and denominator by 100 we will get:
STEP 2Y =
108
180
×
100
100
=
60
100
STEP 3Y = 60
A manufacturer has an order from flower shop to make gift boxes. A gift box is to be constructed from a piece of cardboard 60x60 cm by cutting out squares from the corners and folding up the sides. What is the size of cut out that will provide a gift box of maximum volume?
To maximize the volume we need to cut squares with a side length of 20cm.
How to maximize the volume?
Suppose that the length of the sides of the squares that we cut is X, that will be the height of the box, then its volume will be:
V = (60 - X)*(60 - X)*X
Now we just need to maximize that cubic equation.
V = X*( X^2 - 120*X + 3600)
V = X^3 - 120X^2 + 3600X
To maximize this we need to differentiate it and find the value of X that makes it equal to zero, we will get:
V' = 3*X^2 - 2*120*X + 3600
V' = 3*X^2 - 240*X + 3600
Now we make this equal to zero:
3*X^2 - 240*X + 3600 = 0
The solutions are given by the quadratic formula:
[tex]X = \frac{240 \pm \sqrt{240^2 - 4*3600*3} }{2*3} \\\\\\X = \frac{240 \pm 120 }{6}[/tex]
We will take the smaller solution:
X = (240 - 120)/6 = 20
Because the other solution makes the volume equal to zero.
This means that we need to cut squares with a side length of 20 cm.
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