The Suarez family paid $15.75 for 3 movie tickets.how much would they have paid for 12tickets?
A hallway measuring 90 feet x 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot. How much cleaning solution is required to clean the hallway
315 fluid ounces of cleaning solution are required to clean the hallway.
Finding the corridor's entire area and multiplying it by the cleaning solution needed per square foot can help us determine how much cleaning solution will be needed to thoroughly clean the hallway.
In order to determine a rectangle's area, multiply its length by its width. The hallway in this instance is 90 feet long and 7 feet wide. Consequently, the hallway's overall size is:
Area = Length x Width
= 90 feet x 7 feet
= 630 square feet
The total area must now be multiplied by the amount of cleaning agent required per square foot, which is 0.5 fluid ounce:
Amount of cleaning solution = Area x Amount per square foot
= 630 square feet x (1/2 fluid ounce/square foot)
= 315 fluid ounces
Therefore, 315 fluid ounces of cleaning solution are required to clean the hallway.
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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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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.
What is 8.027 in 2different ways
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 perimeter of a rectangle is 40 cm. The length is 12cm longer than the width. Find the dimensions.
Tanx/cscx + sinx/tanx
the quotient of a number x and 4 is 13
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?
486 is 72% of what amount
the iv has 500mg of antibiotics in 250 ml bag. The patient receives this antibiotic three times a day. how many mg of medication has the patient received in 24 hours and how many ml have been infused in 24 hour
John works two jobs. As a security guard he earns $8.75 per hour. As a landscaper he earns $14.00 per hour. One week John worked a total of 30 hours and earned $283.50. How many hours did he work at each job?
Explanation of how to find the number of hours John worked at each job given his total hours and earnings.
Explanation:The given problem: John worked a total of 30 hours and earned $283.50. He earns $8.75 per hour as a security guard and $14.00 per hour as a landscaper. We need to find out how many hours he worked at each job.
Step-by-step solution:
Let x be the hours worked as a security guard and y be the hours worked as a landscaper. Set up the equations: x + y = 30 and 8.75x + 14y = 283.50. Solve the system of equations to find x and y.Answer: John worked 15 hours as a security guard and 15 hours as a landscaper.
Let f(x)=13x+7. Find f−1(x).
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
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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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?
The area of a rectangle is 336 square inches. If the width of a rectangle is 6 inches. What is the length of the rectangle?
Answer:
56
Step-by-step explanation:
how does Golden Ratio work?
The Golden Ratio, represented by phi (Φ) and approximately equal to 1.618, is a mathematical relationship where the ratio of the total length to the longer section of a line is the same as the ratio of the longer section to the shorter section. It is closely related to the Fibonacci sequence, and its aesthetically pleasing properties are evident in various aspects of nature and design.
The Golden Ratio, also known as the golden section or golden mean, is a unique mathematical relationship that has fascinated many for centuries. It occurs when a line is divided into two parts such that the whole length divided by the longer part is equal to the longer part divided by the shorter part. This ratio is often symbolized by the Greek letter phi (Φ) and is approximately equal to 1.61803.
The Golden Ratio is frequently found in the Fibonacci sequence, where each number is the sum of the two preceding ones. For example, starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. As the numbers get higher, the ratio of successive Fibonacci numbers approximates the Golden Ratio.
Frank can type a report in 4 hours and James takes 6 hours how long will it take the two of them typing together
Frank can type the report in 4 hours and James takes 6 hours. Together, it will take them 2.4 hours to type the report.
Explanation:To find out how long it will take for Frank and James to type a report together, we need to calculate their combined rate of typing. Frank can type the report in 4 hours, so his typing rate is 1/4 of the report per hour. James takes 6 hours to type the report, so his typing rate is 1/6 of the report per hour. To find their combined rate, we add their individual rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
Therefore, working together, Frank and James can type 5/12 of the report per hour. To find out how long it will take to type the entire report, we divide the total report (1 whole) by their combined rate (5/12 per hour): 1 / (5/12) = 1 * (12/5) = 12/5 = 2.4 hours. So, it will take them 2.4 hours to type the report together.
To determine how long it will take for Frank and James to type a report together, we add their individual typing rates and divide the total report by their combined rate.
Explanation:To determine how long it will take for Frank and James to type a report together, we need to calculate their combined typing rate. Frank can type the report in 4 hours, which means he types at a rate of 1/4 of the report per hour. Similarly, James can type the report in 6 hours, which means he types at a rate of 1/6 of the report per hour.
To find their combined rate, we add their individual rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12. This means that together, they can type 5/12 of the report per hour.
To find out how long it will take for them to complete the report, we can divide the total report by their combined rate: 1 / (5/12) = 12/5 = 2.4 hours. Therefore, it will take Frank and James approximately 2.4 hours to type the report together.
If f is a smooth function, then
curl(gradf) = 0 i + 0 j + 0 k
.
true or false
The statement is true. The curl of the gradient of a smooth function is always zero.
Explanation:The statement is true, **if f is a smooth function**, then curl(grad f) = 0 i + 0 j + 0 k.
The gradient of a scalar function f is given by grad f = ∇f. The curl of a gradient is always zero, which means that the curl of grad f is equal to zero.
This is because the curl measures the rotation or circulation of a vector field, and a gradient is a vector field that represents the rate of change of a scalar function in each direction. Since a scalar function does not have any rotation or circulation, the curl of grad f is zero.
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the perimeter of a rectangle is 32 centimeters. the width is 7 centimeters what is the area of the rectangle
The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed, with mean (in milligrams) μ and standard deviation σ = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses and you obtain a P-value of 0.052. Which of the following is true?
Answer:
some evidence against H0 can be seen, and a study using a larger sample size will be recommended
Step-by-step explanation:
The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed, with mean (in milligrams) μ and standard deviation σ = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses and you obtain a P-value of
going by the parameters
standard deviation is 3
mean of the sample=μ
There is some evidence against H0, and a study using a larger sample size will be essential
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
what is the value of 4x to the second power +5x when x =1
a quart of heavy cream cost 2.99 how much would 2 1/2 gallon cost
The cost for 2 1/2 gallons of heavy cream would be $11.96.
First, we need to understand the relationship between quarts and gallons. There are 4 quarts in a gallon. Given that 1 quart of heavy cream costs $2.99, we can calculate the cost per gallon by multiplying the cost of one quart by 4.
Cost per gallon = $2.99 × 4 = $11.96
Now, to find the cost for 2 1/2 gallons, we multiply the cost per gallon by 2.5.
Cost for 2 1/2 gallons = $11.96 × 2.5 = $29.90
However, since we are dealing with currency, it is more appropriate to express the final answer as a fraction to maintain the two decimal places of the dollar amount. Therefore, we can write $29.90 as $29 4/5, or $29.80, which is equivalent to $29 4/5 or $29.96 when rounded to the nearest cent.
To express $29.90 as a fraction, we convert the dollars to cents and then write it as a fraction.
$29.90 = 2990 cents
Now, we divide by 100 to convert back to dollars.
$29.90 = [tex]\frac{2990}{100} = \frac{299}{10}[/tex]
To express this as a mixed number, we divide 299 by 10.
$29.90 = [tex]29 \frac{9}{10}[/tex]
Since $29.90 is the same as $29 4/5 when rounded to the nearest cent, we have:
$29.90 = $29 4/5 = $29.80
Therefore, the cost for 2 1/2 gallons of heavy cream, when rounded to the nearest cent, is $29.80, which is equivalent to $29 4/5 or $29.96 when rounded to the nearest cent. However, the exact calculation without rounding would be $29.90, which is $11.96 per gallon times 2.5 gallons.
Vonda has 3 more quarters than dimes in her pocket. She has no other coins. The total value of her coins is $1.80. How many quarters and dimes does Vonda have?
Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $55. For one performance, 20 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $950. What was the price of each kind of ticket?
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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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.