Final answer:
Sarah's original investment was calculated by dividing the final amount of $448 by 1 plus the percentage increase in decimal form, which gives us $350 as the original investment before a 28% growth.
Explanation:
The student is asking to calculate the original investment amount before a 28% increase resulted in a final amount of $448. To find the original investment, we divide the final amount by 1 plus the percentage increase in decimal form. In this case, the percentage increase is 28%, which is 0.28 in decimal form.
The formula to find the original investment (O) is:
O = Final Amount / (1 + Percentage Increase)
So, the original investment would be calculated as follows:
O = $448 / (1 + 0.28) = $448 / 1.28
After performing the division, we find the original investment is:
O = $350
Therefore, Sarah originally invested $350 in JetBlue stock.
Certain gases in the atmosphere trap heat on Earth.
What is the name of this phenomenon?
A.
the greenhouse effect
B.
global warming
C.
glacial melting
D.
cooling period
this is science not mathematics
Answer:
the answer is a
Step-by-step explanation:
A rectangular lawn measures 7m by 5m. A uniform border of flowers is to be planted along two adjacent sides of the lawn, as shown in the diagram. If the flowers that have been purchased will cover an area of 6.25 m^2, how wide is the border?
The width of the border is required.
The width of the border is 0.5 m.
Areal = Length of lawn = 7 m
w = Width of lawn = 5 m
x = Width of border
The figure of the lawn has been attached.
The area of the border will be [tex]6.25\ \text{m}^2[/tex] so,
[tex]x(x+7)+5x=6.25\\\Rightarrow x^2+7x+5x=6.25\\\Rightarrow x^2+12x-6.25=0\\\Rightarrow 100x^2+1200x-625=0\\\Rightarrow x=\dfrac{-1200\pm \sqrt{1200^2-4\times100\left(-625\right)}}{2\times100}\\\Rightarrow x=0.5,-12.5[/tex]
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the perimeter of a rectangle is 40 cm. The length is 12cm longer than the width. Find the dimensions.
A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. Determine the person's expectation if three envelopes contain a $533 check and three envelopes contain a $1039 check.
Answer with explanation:
Number of Envelopes possessed by the person = 6
Probability of selecting an Envelope is equal to [tex]/frac{1}{6}[/tex].
It is given that,three envelopes contains $ 533 check and another 3 Envelope contain $ 1039 check.We can consider that any of three checks contain $ 533 and another three $ 1089.
Expectation
[tex]E(x)=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}+x_{4}p_{4}+x_{5}p_{5}+x_{6}p_{6}\\\\\frac{1}{6} \times [533+533+533+1039+1039+1039]\\\\=\frac{1}{6} \times [4716]\\\\=786[\tex]
E(x)=786
49 percent of all people who buy running shoes don't run at all. Assuming 340,000 people buy running shoes, how many will use them to run in?
Suppose a culture of bacteria starts with 8000 bacteria. After one hour, the count is 9000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling time of the bacteria. Round the doubling time to the nearest 0.01 hours.
The exponential equation that models the number of bacteria in hours is N = 8000 * (1 + 0.125)^t. The doubling time of the bacteria is 5.55 hours.
Explanation:To find an exponential equation that models the number of bacteria in hours, we can use the formula: N = N0 * (1 + r)^t.
Where:
N is the final count of bacteria (9000)N0 is the initial count of bacteria (8000)r is the growth rate (unknown)t is the time in hours (1)Plugging in the values, we have:
9000 = 8000 * (1 + r)^1
Dividing both sides by 8000, we get:
1.125 = 1 + r
Subtracting 1 from both sides, we find:
0.125 = r
Therefore, the exponential equation that models the number of bacteria in hours is: N = 8000 * (1 + 0.125)^t.
To find the doubling time of the bacteria, we can use the formula: t = log(2)/log(1 + r).
Plugging in the value of r (0.125), we have:
t = log(2)/log(1 + 0.125)
Using a calculator, we find that t is approximately 5.5452 hours. Rounded to the nearest 0.01 hours, the doubling time of the bacteria is 5.55 hours.
the kilo-prefix in the metric system means __________________ units
insted of telling carmen her age ,sora gave this clue:my age is one-tenth of one-tenth of one-tenth of 3,000.
A church has 8 bells in its bell tower. Before each church service 5 bells are rung in sequence. No bell is rung more than once. How many sequences are there?
Using permutations, there are 6720 sequences of ringing the church bell before the church service.
What is permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
[tex]_{n} P_{r}=\frac{n !}{(n-r) !}\\\\_{8} P_{5} = \frac{8 !}{(8-5) !}\\\\_{8} P_{5} = 6720[/tex]
Number of permutations of bells = 6720
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A cupcake recipe asks for 3/4 of a cup of butter. Rob wants to make 1/3 of the original recipe. How many cups of butter will Rob need?
Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible
Suppose you earn 3% on a $1200 deposit for 5 years. Explain how the simple interest is affected if the rate is increased by 1% What happens if the time is increased by 1 year?
a) When the interest rate is increased by 1%, the simple interest increases from $180 to $240, a difference of $60.
b) When the time (period) is increased by 1 year, the simple interest increases from $180 to $216, a difference of $36.
What is the simple interest?Simple interest is the interest system that does not compute interest on the accumulated interest.
Unlike the compound interest system, simple interest calculates interest on the principal for each period.
Interest rate = 3%
Principal deposit = $1,200
Investment period = 5 years
Simple interest at 3% = Principal x Rate x Time
= $180 ($1,200 x 3% x 5)
Simple interest at 4% = Principal x Rate x Time
= $240 ($1,200 x 4% x 5)
Simple interest at 3% = Principal x Rate x Time
= $216 ($1,200 x 3% x 6)
Simple interest at 4% = Principal x Rate x Time
= $288 ($1,200 x 4% x 6)
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Increasing the interest rate from 3% to 4% on a $1200 deposit for 5 years raises the simple interest from $180 to $240, while extending the time from 5 to 6 years at the initial rate results in a raise from $180 to $216 in simple interest.
Understanding Simple Interest with Changes in Rate and Time
Simple interest is calculated by multiplying the principal amount, the interest rate, and the time the money is borrowed or invested. Using the provided example, if you deposit $1200 at a simple interest rate of 3% for 5 years, the interest is calculated as follows:
$1200 times 0.03 times 5 = $180
If the interest rate increases by 1%, the new interest rate becomes 4%. Thus, the simple interest for the increased rate is:
$1200 times 0.04 times 5 = $240
Therefore, an increase of 1% in the interest rate raises the simple interest earned from $180 to $240, an increase of $60.
If the time is increased by 1 year while keeping the original interest rate of 3%, the new time period is 6 years. The simple interest for the increased time is:
$1200 times 0.03 times 6 = $216
Extending the time by 1 year increases the total simple interest from $180 to $216, which is an extra $36 earned.
The number of students that hear a rumor on a small college campus t days after the rumor starts is modeled by the logistic function R(t)= 3,000 1+Bekt. If 5 students initially heard the rumor and 149 students heard the rumor after 1 day, then how long will it take 2,700 students to hear the rumor?
The logistic function is [tex]S[/tex] shaped curve which use to determine the statistical distribution over the energy states of a system.
The time will take for 2,700 student to hear the rumor is 2.495 days.
Given:
The given logistic function is,
[tex]R(t)=\frac{3000}{1+Be^{kt}}[/tex]
As per the question, at initial stage 5 students heard the rumor. At initial stage [tex]t=0[/tex].
Calculate the constant [tex]B[/tex] at initial stage.
[tex]R(t)=\frac{3000}{1+Be^{kt}}\\R(0)=\frac{3000}{1+Be^{k\times 0}}\\R(0)=\frac{3000}{1+B}[/tex]
Substitute [tex]R(0)=5[/tex].
[tex]\begin{aligned}5=\frac{3000}{1+B}\\1+B= \frac{3000}{5}\\B=599\\\end[/tex]
As per the question, after 1 day 149 students heard the rumor. After 1 day stage [tex]t=1[/tex].
[tex]R(t)=\frac{3000}{1+Be^{kt}}\\R(1)=\frac{3000}{1+Be^{k\times 1}}\\R(1)=\frac{3000}{1+B^k}[/tex]
Substitute [tex]R(1)=149[/tex] and [tex]B=599[/tex].
[tex]\begin{aligned}149=\frac{3000}{1+599e^k}\\e^k=\frac{(3000-1149)}{(599)(149)} \\\end{aligned}[/tex]
Calculate the time take to hear rumor by 2,7000 students.
[tex]\begin {aligned}2700=\frac{3000}{1+599(\frac{3000-149}{599\times 149})^t }\\\frac{3000}{2700}-1 =599(\frac{3000-149}{599\times 149})^t }\\t=\frac{ln(\frac{1}{(599)(9)})}{ln(\frac{3000-149}{599\times 149}) }\\t=2.495\:\rm days\\\end{aligned}[/tex]
Thus, the time will take for 2,700 student to hear the rumor is 2.495 days.
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You 495 miles from home and you are driving toward home at an average of 45mph. How long will it take to drive home if you maintain the same speed? (Hint: When you reach home, the x-value is zero.)
Answer:
f(x)=45x
Step-by-step explanation:
if the home is 495 miles away, 11 hours would take to drive home.
f(11)=45X11=495
Suppose that the mean GRE score for the USA is 500 and the standard deviation is 75. Use the Empirical Rule (also called the 68-95-99.7 Rule) to determine the percentage of students likely to get a score between 350 and 650? What percentage of students will get a score above 500?
Using the Empirical Rule, it is determined that 95% of students are likely to get a GRE score between 350 and 650, and 50% of students will get a score above 500.
According to the Empirical Rule (also known as the 68-95-99.7 Rule), about 95% of the values in a data set with a normal distribution will fall within two standard deviations of the mean. In this case, the mean GRE score is 500 and the standard deviation is 75. Using this rule, we can determine that 95% of the students would likely score between 500 - (2 imes 75) and 500 + (2 imes 75), equating to scores between 350 and 650.
Regarding the percentage of students that will get a score above 500, the distribution is symmetric around the mean in a normal distribution. Since the mean is 500, 50% of the values will lie above the mean and 50% will lie below. Therefore, 50% of students are expected to score above 500.
Eli is making guacamole he uses 2 tablespoons of cilantro for every 3 avocados at this rate how many table spoons of cilantro will he need for 9 avocados
The heights of women aged 20 to 29 is approximately Normal with mean 64 inches and standard deviation 2.7 inches. What proportion of these women are less than 58.6 inches tall?
Tanx/cscx + sinx/tanx
three men and four women stand in line at a checkout counter at a store. in how many ways can they stand in the line if we consider only their gender
there are 5040 ways for the three men and four women to stand in line at the checkout counter if we only consider their gender.
To determine the number of ways the three men and four women can stand in line at the checkout counter if we only consider their gender, we can use the concept of permutations.
There are 3 men and 4 women, so there are a total of (3 + 4 = 7) people in line.
We need to arrange these 7 people in a line. Since the order matters, we use permutations.
The number of ways to arrange (n) objects is given by (n) (n factorial).
So, the number of ways the 7 people can stand in line is [tex]\(7\).[/tex]
[tex]\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \][/tex]
Therefore, there are 5040 ways for the three men and four women to stand in line at the checkout counter if we only consider their gender.
Let f(x)=13x+7. Find f−1(x).
if juanita and her friends made nine friendship bracelets in three hours how many could they make in 15 hours? which proportion would be used to solve this problem
The Suarez family paid $15.75 for 3 movie tickets.how much would they have paid for 12tickets?
the quotient of a number x and 4 is 13
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets _____ interest rates to find willing buyers.
Final answer:
At an interest rate of 2%, below the equilibrium rate of 5%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers and reach the equilibrium.
Explanation:
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers. This situation outlines how the market responds when the interest rate is below the equilibrium level. If the interest rate is below equilibrium, there is an excess demand for financial capital; too many borrowers and not enough lenders at this low rate. To attract more lenders (sellers of financial assets), the interest rate would need to be increased. Conversely, when the interest rate is above the equilibrium, there is an excess supply, meaning there are more suppliers of loans than there are borrowers. Sellers in this scenario lower interest rates to attract more borrowers, bringing the market back to equilibrium.
This concept is parallel to the example where, at an interest rate of 21%, the supplied funds increase greatly while the demand falls sharply, leading to excess supply. Suppliers of financial capital, such as credit card companies, will then reduce their rates to encourage more borrowing, pushing the interest rate back toward the equilibrium. In the case of a government borrowing increase, if it leads to a higher demand for financial capital, this would cause the demand curve to shift to the right and result in a higher interest rate, potentially crowding out private investment.
Jamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?
Jamal use 1/2 yards of ribbon
Further explanationJamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?
Jamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. Therefore the total of ribbon Jamal used is:
[tex]\frac{1}{3} + \frac{1}{6} = \frac{2}{6} +\frac{1}{6}= \frac{3}{6} or \frac{1}{2}[/tex] yards of ribbon
How many yards of ribbon did Jamal use? Jamal use 1/2 yards of ribbon
The yard (yd) is English unit of length comprises 3 feet or 36 inches. It is by international agreement standardized as exactly 0.9144 meters. Yard is defined as a measurement of length that equals 3 feet or 36 inches. An example of a yard is the length measurement that is used to sell fabric.
A ribbois a thin band of material, typically cloth but also plastic or sometimes metal, used as decorative binding and tying.
We also can draw 1/3 yard of ribbon as 33.333% of all yards, and 1/6 as 16.6666% of all yards as shown in the picture below.
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Grade: 5
Subject: math
Chapter: yards
Keywords: ribbon, yard, package, bow, tie
A 200 centimeter-long wire is cut into three pieces. The second piece is 3 times as long as the first. The third piece is 2 times as long as the second. How long is each piece?
The lengths of the three wire pieces are 20 cm for the first piece, 60 cm for the second piece, and 120 cm for the third piece.
Explanation:A wire that is 200 cm long is cut into three pieces.
We are told that the second piece is 3 times as long as the first piece and the third piece is 2 times as long as the second piece.
Let's denote the first piece's length as x centimeters.
According to the problem, the second piece will then be 3x centimeters long, and the third piece will be 2 * 3x = 6x centimeters long.
To find the length of each piece, we need to set up the following equation based on the total length of the wire:
x + 3x + 6x = 200
Combining terms, we have:
10x = 200
Dividing both sides by 10, we find:
x = 20
Therefore, the first piece is 20 cm long, the second piece is 3 * 20 cm = 60 cm long, and the third piece is 6 * 20 cm = 120 cm long.
A tortoise is walking in the desert. It walks for
87.5
meters at a speed of
7
meters per minute. For how many minutes does it walk?
Which of the following is equivalent to the expression (3ab)(-5ab)?
The expression (3ab)(-5ab) is equivalent to [tex]-15a^2b^2[/tex], calculated by multiplying the coefficients (3 and -5) to get -15 and squaring the variables ab to get [tex]a^2b^2[/tex].
The expression in question, (3ab)(-5ab), involves the multiplication of two terms. To find an expression equivalent to (3ab)(-5ab), we simply need to multiply the coefficients and then multiply the variables. The coefficients here are 3 and -5, and when we multiply them, we get -15. Since the variable part is 'ab' for both terms, we multiply 'a' by 'a' to get a2 and 'b' by 'b' to get b2. Combining these, we get the final equivalent expression:
(3ab)(-5ab) = [tex]-15a^2b^2[/tex].
This is an example of reversing the distributive law and turning it into the factors or multiples. We see that expressions that, when evaluated, produce the same value are considered equivalent.
dora reaches her goal of $ 400 in savings.she decide to set a new goal of $900.how many $100 bills will she need to reach $900 in savings? explain your answer using words pictures or numbers
How to change 2/3 to eighteenths
The eighteenths of 2/3 is 12/18.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
let,
2/3 = n/18
What is the GCF of 3 and 18
3: 1,3
18: 1,2,3,6,9,18
GCF-3
Therefore, 2/3 = 12/18
because 3 × 6= 18
what you do to the denominator you have to do the numerator
so 2 × 6= 12.
hence, eighteenths of 2/3 is 12/18.
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