The initial length of the scarf is 50 centimeters.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.
Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:
L + 25h = length of scarf after h hours
Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:
L + 25(3) = 125
L + 75 = 125
L = 50
Therefore, the initial length of the scarf is 50 centimeters.
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Cassandra is knitting a scarf. She increases the length of
the scarf by 25 centimeters each hour she knits. After 3
hours, the scarf is 125 centimeters long what is initial length of scarf.
PLEASE HELP DUE TOMORROW:
Instructions: Fill in each matching colored box with same solution that makes each equation true. For example, if one red box was 3 then all the other red boxes must be 3. (JUST AN EXAMPLE)
Answer:
red=7
pink=4
purple=15
dark pink=22
gray=18
Find the measure of
The measure of exterior angle ACD is 132°
Exterior angle theorem of a triangleThe exterior angle theorem states that whenever a triangle's side is extended such that it creates another exterior(outside angle), the resultant exterior angle created is equal to the sum(addition) of the other two opposite (inner) interior angles of the triangle.
From the information given:
Angle A = 50; Angle B = 4x + 2, Angle ACD = 6x + 12
Therefore;
50 + 4x + 2 = 6x + 12
52 + 4x = 6x + 12
4x - 6x = 12 - 52
-2x = - 40
x = 20
Since x = 20, angle ACD = 6x + 12
The measure of angle ACD = 6(20) + 12 =132°
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Write the quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102).
The quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102) is f(x) = x²-3x-54
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given that, the quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102).
We know that, the standard form of the quadratic equation is given by,
x²-(α+β)x+αβ=0, where α and β are roots of the equation,
Therefore,
x²-(9-6)x+9(-6) = 0
x²-3x-54 = 0
Hence, the quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102) is f(x) = x²-3x-54
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a bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. if you pick six letters one at a time, what is the chance that you spell c-h-a-n-c-e?
A bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. The chance of spelling "chance" is approximately 0.0108 or about 1.08%.
First, we need to count the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n" from the 15 tiles in the bag. To do this, we use the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items and r is the number of items we want to choose. For example, to choose two "c"s from three, we can calculate:
C(3, 2) = 3! / (2! * (3 - 2)!) = 3
We can use this formula to calculate the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n":
C(3, 2) * C(3, 2) * C(3, 1) * C(3, 1) = 54
Therefore, there are 54 ways to choose the required letters out of the 15 tiles in the bag.
Next, we need to count the total number of ways to choose 6 tiles from the 15 in the bag. We can again use the combination formula:
C(15, 6) = 15! / (6! * (15 - 6)!) = 5005
Therefore, there are 5005 ways to choose any 6 tiles from the bag.
Finally, we can calculate the probability of spelling "chance" by dividing the number of ways to choose the required letters by the total number of ways to choose 6 tiles:
54 / 5005 ≈ 0.0108 or about 1.08%
So the probability of spelling "chance" when picking six tiles one at a time from the bag is approximately 0.0108 or about 1.08%.
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5. Solve for x.
S
(14x-15)
139⁰
V
U
T
The graph below is a discrete function:
8
246
0 2
A True
B) False
f(x)
6
8 10
12
14
Answer: A.
Step-by-step explanation:
5. A bag holds 4 white, 6 red, and 2 blue marbles. You choose a marble without looking, put it aside, and choose
another marble without looking. Find the probability of removing a white marble followed by a blue marble.
The required probability of removing a white marble followed by a blue marble is 2/33.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
There are 12 marbles in the bag in total, so the probability of selecting a white marble on the first draw is 4/12 or 1/3.
After the first marble is put aside, there are now 11 marbles in the bag, with 2 of them being blue. Therefore, the probability of selecting a blue marble on the second draw is 2/11.
To find the probability of selecting a white marble followed by a blue marble, we need to multiply the probability of the first event (selecting a white marble) by the probability of the second event (selecting a blue marble):
P(white, then blue) = P(white) x P(blue|white)
P(white, then blue) = (1/3) x (2/11)
Simplifying:
P(white, then blue) = 2/33
Therefore, the probability of removing a white marble followed by a blue marble is 2/33.
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Which property of real numbers is shown below?
3 + ((-5) + 6) = (3 + (-5)) + 6
O commutative property of addition
O identity property of multiplication
associative property of addition
commutative property of multiplication
given that x=a,y=b is the solution to the system of equations 2x+y=4, x-y=5 then what is the value of b to the power of a
Answer:
The answer is -8
Step-by-step explanation:
[tex]2x+y=4\\x-y=5\\\\[/tex]
after combining these into a singular equation, we get:
[tex]3x=9\\x=3[/tex]
substitute the value of [tex]x[/tex] into one of the equations:
[tex]x-y=5\\3-y=5\\y=-2[/tex]
now that we found the [tex]x[/tex] and [tex]y[/tex] value, we can substitute it into the term [tex]b^a[/tex] since we know that [tex]x=a[/tex] and [tex]y=b[/tex].
[tex]a^b\\a=x, b=y\\x=3, a=3\\y=-2, b=-2\\-2^3\\-8[/tex]
The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. How many gears does the bike have
The bike has 21 gears, 3 on the front and 7 on the rear cogset, giving a total of 21 average possible gear combinations.
The bike has 3 sprockets on the front and 7 sprockets on the cogset at the rear of the bike. This combination of 3 sprockets on the front and 7 on the rear creates a total of 21 possible gear combinations. This is calculated by multiplying the number of sprockets on the front by the number of sprockets on the rear. When you change the gear on the bike, you are changing the combination of the front and rear sprockets. By doing this, you can adjust the gearing of the bike to make it easier or harder to pedal depending on the terrain. Having a wide range of gears helps you to climb hills, accelerate and maintain speed on flat roads, as well as descend hills. Having 21 gears gives you a lot of options to make your ride as comfortable and efficient as possible.
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A point at (-4, 7) is rotated -90° about the origin. What are the new coordinates for the point?
Answers:
(4, -7)
(-7, 4)
(7, 4)
(-4, -7)
Which expression is NOT equal to 125?
5(5^3/2/5)^2
(5^3/5^4)^-3
5^-2/5^-5
5(5^5/5^3)
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
11, 20, 29, ...
Find the 43rd term.
The given sequence appears to be an arithmetic sequence, as the difference between consecutive terms is 9. To find the 43rd term, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term (11 in this case), n is the term number (43 in this case), and d is the common difference (9 in this case).
Plugging in the values, we get:
a_43 = 11 + (43 - 1) * 9
a_43 = 11 + 42 * 9
a_43 = 11 + 378
a_43 = 389
So the 43rd term of the sequence is 389.
I need help with number 8
[tex](3x^2+5x+4)+(6x+1)~~ = ~~3x^2+11x+5 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ (3x^5+15x^3+4)+(-3x^5+2x^2-8)\stackrel{ \textit{not on all cases} }{~~ = ~~15x^3+2x^2-4} ~~ \bigotimes[/tex]
During its first month of business, Dig the Dogs, Inc. purchased $900 of hotdogs of which it paid $300 and owes the rest. During the month, it sold 3/4 of its inventory for $1,000 on account. What is the amount of Cost of Goods Sold for the month ended?
Cost of goods sold (COGS) is an important accounting calculation that measures the costs associated with selling a company’s goods or services. Therefore, the cost of goods sold for the month ended is $600.
Cost of Goods Sold (COGS) is a measure of the cost of goods sold during the accounting period. It is calculated by subtracting the beginning inventory from the cost of goods purchased during the accounting period and then adding the ending inventory. For Dig the Dogs, Inc., the cost of goods sold for the month ended is calculated as follows: Beginning Inventory = 0 Cost of Goods Purchased = $900 Ending Inventory = $300 .COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory = 0 + 900 - 300 = $600 Therefore, the cost of goods sold for the month ended is $600.
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Add: 410 + 210 Write your answer in simplest terms
The addition of two numbers is 410+210 is 620.
From the given numbers,
First number is 410
Second number is 210.
One of the arithmetic operations is addition. The total of the numbers is provided. In other words, addition refers to the operation of adding the numbers together. "+" is the symbol used to denote addition. The outcome of the adding procedure is referred to as the sum. Addends are the numbers that are added together.
One of the four fundamental mathematical operations, addition indicates the sum of two or more numbers added together.The following are the rules of addition operation:
Positive Number + Positive Number = (Add) Positive NumberNegative Number + Negative Number = (Add) Negative NumberNegative Number + Positive Number = (Subtract) Take the sign of the number with the largest absolute valueNow,
⇒410+210=620
Therefore, the value is 620.
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in a normal distribution with a mean of 90 and a standard deviation of 5, which of the following scores lie within one standard deviation of the mean? select one: a. 5-90 b. 80-100. c. 85-95. d. 90-95.
The range of 85-95 is within one standard deviation of the mean in a normal distribution with a mean of 90 and a standard deviation of 5,the correct answer is c. 85-95.
The normal distribution is a bell-shaped curve that is centered around the mean and symmetrical about the mean. In a normal distribution with a mean of 90 and a standard deviation of 5, one standard deviation of the mean would be 85-95. This means that any score within this range is within one standard deviation of the mean.
To calculate this, we first look at the mean, which is 90. To find the value of one standard deviation from the mean, we need to subtract 5 from 90 to get 85. To find the upper limit of one standard deviation, we add 5 to 90 to get 95. Therefore, any score between 85 and 95 is within one standard deviation of the mean.
To summarize, any score within the range of 85-95 is within one standard deviation of the mean in a normal distribution with a mean of 90 and a standard deviation of 5. Therefore, the correct answer is c. 85-95.
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an advertising company designs a campaign to introduce a new product to a metropolitan area of population 5 million people. let p(t) denote the number of people (in millions) who become aware of the product by time t. suppose that p increases at a rate proportional to the number of people still unaware of the product. the company determines that no one was aware of the product at the beginning of the campaign, and that 10% of the people were aware of the product after 10 days of advertising. the number of people who become aware of the product at time t is:
The number of people who become aware of the product at time t is [tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
The advertising company wants to introduce a new product to a population of 5 million people. They assume that no one was aware of the product at the beginning of the campaign. They also know that after 10 days of advertising, 10% of the people became aware of the product. To find out how many people become aware of the product at time t, they use a function called p(t).
The function p(t) represents the number of people (in millions) who become aware of the product by time t. The company assumes that the rate at which p increases is proportional to the number of people still unaware of the product. This means that the more people who are unaware of the product, the faster the number of people who become aware of it will increase.
To express the proportionality mathematically, we can use the equation:
p'(t) = k [5 - p(t)]
Where p'(t) is the rate of change of p with respect to time t, and k is the proportionality constant that determines the speed of the increase. The quantity (5 - p(t)) represents the number of people who are still unaware of the product at time t. This means that as p(t) gets closer to 5 million, the rate of increase of p(t) will slow down.
To solve this equation, we need to use calculus. Integrating both sides of the equation, we get:
ln|5 - p(t)| = kt + C
Where C is the constant of integration. To determine the value of C, we use the initial condition that p(0) = 0. This means that at the beginning of the campaign, no one was aware of the product. Substituting this into the equation, we get:
ln|5 - 0| = k(0) + C
Simplifying, we get:
C = ln(5)
Substituting this value into the equation, we get:
ln|5 - p(t)| = kt + ln(5)
To find the value of p(t) at a specific time t, we can solve for p(t) by taking the exponential of both sides of the equation:
[tex]|5 - p(t)| = e^{kt+ln(5)}[/tex]
Simplifying, we get:
[tex]5 - p(t) = 5e^{kt}[/tex]
Or:
[tex]p(t) = 5(1 - e^{kt})[/tex]
To find the value of k, we can use the fact that 10% of the people were aware of the product after 10 days of advertising. This means that:
p(10) = 0.1(5) = 0.5
Substituting this into the equation, we get:
[tex]0.5 = 5(1 - e^{10k})[/tex]
Solving for k, we get:
k = -0.1 ln(0.9)
Substituting this value into the equation for p(t), we get:
[tex]p(t) = 5(1 - e^{-0.1ln(0.9)t})[/tex]
Simplifying, we get:
[tex]p(t) = 5(1 - 0.9^{\frac{t}{10} })[/tex]
This is the formula that tells us how many people will become aware of the product at time t.
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What is 136-117? Please help me.
Answer:
the answer is 19!
To make it easier you can also use an online calculator or if you have one in real life you can use it! You can also do it on paper!
Have a great day! :) <3
) This afternoon Beth left school, rode the bus 1/2 of a mile, and then walked 1/12 of a mile to get home. How much farther did Beth ride than walk?
Using this formula, we find that d = 2/3, meaning Beth rode 2/3 of a mile farther than she walked. The formula to solve this problem is d = 1/2 - 1/12, where d is the difference in distance between the bus ride and the walk.
Beth rode the bus 1/2 of a mile and then walked 1/12 of a mile to get home. To calculate how much farther she rode than walked, we need to subtract the distance walked from the distance ridden. The formula to solve this problem is d = 1/2 - 1/12, where d is the difference in distance between the bus ride and the walk. Using this formula, we find that d = 2/3, meaning Beth rode 2/3 of a mile farther than she walked.
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Factor 64+56. Write your answer in the form a(b+c) where a is the GCF of 64 and 56.
Answer:
8(8+7)
Step-by-step explanation:
64+56
8 is the GCF
8(8+7)
On a hot summer day, Brad and his friends decided to have a water fight. They threw water balloons for 33 minutes. When all the water balloons were gone, they sprayed water with hoses for 32 minutes. The water fight ended at 4:28 P.M. when Brad's dad showed up with ice cream. What time did the water fight start?
Answer:
3:23
Step-by-step explanation:
The water fight ended at 4:28 and lasted for 32 minutes so
4:28 - 32 minutes = 3:56
3:56 - 33 minutes = 3:23
The data in the table was produced by a researcher studying the
number of vegetables people ate for one week. Group A and Group B,
each with 20 people, recorded the vegetables that they ate. If a person
is chosen at random from those who ate at least 7 vegetables, what is
the probability that the person belonged to Group A?
The probability that the person belonged to Group A is given as follows:
Probability = number of people in Group A that ate at least 7 vegetables / total number of people that ate at least 7 vegetables.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The outcomes for this problem are given as follows:
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a plane ticket to beacelona is £175 the price decreased by 6%
how much is the plane ticket now?
A local gym offers its members the opportunity to choose between two fitness classes: yoga and dance. Of the
400
400400 gym members,
300
300300 regularly attend yoga,
80
8080 regularly attend dance, and
50
5050 regularly attend yoga and dance. Using this information, answer each of the following questions. Let
Y
YY be the event that a randomly selected gym member regularly attends yoga and
D
DD be the event that a randomly selected gym member regularly attends dance
The probability of a gym member attending yoga is 0.625 or 62.5%.
Probability is the likelihood or chance of an event happening. In this scenario, we have information about the number of gym members attending yoga and dance, which can be used to calculate the probability of a gym member attending yoga.
Out of the 400 gym members, 300 regularly attend yoga, and 50 attend both yoga and dance. This means that the number of gym members attending only yoga is 300-50=250. The probability of a gym member attending yoga can be calculated by dividing the number of gym members attending yoga by the total number of gym members.
Probability of a gym member attending yoga= Number of gym members attending yoga/Total number of gym members
Probability of a gym member attending yoga= 250/400
Probability of a gym member attending yoga= 0.625 or 62.5%
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Complete Question:
400 gym members, 300 regularly attend yoga, 80 regularly attend dance, and 50 regularly attend yoga and dance. Using this information, answer each of the following questions.
What is the probability that a gym member attends yoga?
The United States Postal Service has an online guide to make life easy for people using their
postal service. This is an extract.
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates - single piece rates
$0.44
First ounce (oz.) Letter size mail
Each additional oz. or fraction
First ounce Flat size mail **
Each additional oz. or fraction
First ounce Parcel ***
Each additional oz. or fraction
Standard Postcard ****
$0.17 per oz. up to 3.5 oz.
$0.88
$0.17 per oz. up to 13 oz.
$1.22
$0.17 per oz. up to 13 oz.
$0.28
* Letters: (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W,
max. weight 3.5 oz). Letter size mai over 3.5 ounces, see Flat size prices.
**Flats: (min. dimension: 11.5 L, 6.125" H, 0.25"W; max. dimension: 15 L, 12 H, 0.75 W).
*** Parcels: Anything larger.
**** Postcards: (min. dimension: 5L, 3.5" H, 0.007"W; max. dimension: 61, 4.25 H, 0.016 W).
I want to send two items through the post using first class mail.
One fts into an envelope 20 L, 10°H and 4"W and weighs 10oz.
The other fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz.
How much are the items going to cost me to send?
Answer:
The first item that fits into an envelope 20 L, 10°H and 4"W and weighs 10oz is a "Flat size mail." According to the rate chart, the first ounce of Flat size mail costs $0.88 and each additional ounce costs $0.17. The cost for the 10 ounces of this item will be $0.88 + 9 x $0.17 = $1.83.
The second item that fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz is a "Letter size mail." According to the rate chart, the first ounce of Letter size mail costs $0.44 and each additional ounce costs $0.17. The cost for the 2.5 ounces of this item will be $0.44 + 1.5 x $0.17 = $0.75.
So, the total cost for both items will be $1.83 + $0.75 = $2.58.
HELP..
Which of the following tables represents a linear function?
Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
Given are three tables in x and y and we have to find which table shows a linear relation.
We know in a linear relation between x and y the graph would be a straight line and also the slope would be constant
i.e. change of y/change of x for any pair in the table would be a constant.
Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.
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The monster under your bed loves fruit. To appease him you buy 4 pounds of grapes. You also buy some strawberries. Both fruits cost $1.20 per pound. You spend $6. How many pounds of strawberries did you buy?
Answer:
1 pound of strawberries
Step-by-step explanation:
4 x $1.20 = $4.80
$6 - $4.80 = $1.20
one pound is $1.20
Reflect (-3, -2) over the y-axis.
Then translate the result to the left 1 unit.
Answer:
-2, 2
Step-by-step explanation:
trust me
Given f(x)=4x^2+9x+9, find f(−1)
The value of the function f(-1) is -4
What is a function?A function is simply described as an equation that explains the relationship between the independent variable and the dependent variable.
From the information given, we have the function;
f(x)=4x^2+9x+9
To determine the value of f(-1)
substitute the value of x as- 1, we get;
f(-1) = 4(-1)² + 9(-1) + 9
expand the bracket, we get;
f(-1) = -4 -9 + 9
Add or subtract the values, we have;
f(-1) = -4
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