According to the question the volume formula to find the height of the pyramid is 9 units.
What is formula?Formula is a mathematical rule or equation expressed symbolically, that describes the relationship between different variables. It is a set of symbols or terms that expresses a relationship between different entities, such as numbers, objects, ideas, or concepts. Formulas are used to calculate, analyze, and predict data, and are essential in many scientific and mathematical fields.
The volume of a pyramid is given by the formula V = (1/3) × b × h, where b is the area of the base and h is the height of the pyramid.
Since the base of the pyramid is a right triangle, we can use the formula to find the area of a right triangle, A = (1/2) × b × h, to find the base of the pyramid.
A = (1/2) × 8 × 9 = 36
Now we can use the volume formula to find the height of the pyramid:
V = (1/3) × 36 × h
108 = (1/3) × 36 × h
108 = 12 × h
h = 9 units
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Three glasses of milk and 2 snack bars have a total of 67 carbohydrates (carbs), and 2 glasses of milk and 3 snack bars have a total of 63 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
The amount of carbs that is found in one glass of milk and one snack bar respectively would be = 40.2 and 25.2.
How to calculate the quantity of carb per items?The quantity of total milk = 3+2 = 5 glasses of milk
The quantity of total snack bar = 2+3 = 5
The total amount of carbs = 67+63 = 130
To calculate for the quantity of carb in a bottle;
= 3/5×67/1
= 201/5
= 40.2 carbs per bottle of milk.
To calculate for the quantity of carb per bar of snack:
= 2/5× 63/1
= 126/5
= 25.2 carbs per bar of snack.
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Please help please and thank u :)
Answer:
23 is the mode
Step-by-step explanation:
mode means the most common number
11. Triangles can be classified by their side lengths or by their angle measures. Sometimes triangles are classified using both classifications (side length and angle measure) but these can be redundant and unnecessary. Give an example of a classification based on both side length and angle measure that is unnecessary and explain why.
By answering the presented question, we may conclude that As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.
An isosceles triangle has two sides of equal length, but a right triangle has one angle that measures 90 degrees. As a result, an isosceles right triangle is one with two equal-length sides and one 90-degree angle.
The Pythagorean theorem states that in any right triangle, the two legs (the sides next to the right angle) are always of equal length. Hence, if we know that a triangle has one 90-degree angle and two equal-length sides, we already know that it is a right triangle and that the two legs are equal. As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.
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If I had 60 units needed and units per case was 14 how many full cases and additional items are needed to fufill the order
HELP! I ONLY HAVE 5 MINS LEFT! You and 15 other people are at a party. The host tells you that they have placed one special item in a bag with 16 items total. The host says that there is an 80% chance that the special item is still in the bag, and a 20% chance that it was taken out.
The host passes the bag around and each person selects an item at random. You decide to keep your item hidden while everyone else shows theirs, and no one finds the special item. What are the odds that the special item is in your item?
Answer:
67.5%
Step-by-step explanation:
There is a 67.5% chance that the special item is in your bag.
The initial probability that the special item is in the bag is 80%.
The probability that the special item is not in the bag is 20%.
The probability that the special item is not in any of the other 15 bags is 15/16 * 14/15 * 13/14 * ... * 3/4 * 2/3 = 1/2.
The probability that the special item is in at least one of the other 15 bags is 1 - 1/2 = 1/2.
The probability that the special item is in your bag is 80% * 1/2 = 67.5%.
Here is a breakdown of the probabilities:
* The special item is in the bag: 80%
* The special item is not in the bag: 20%
* The special item is in one of the other 15 bags: 1/2
* The special item is in your bag: 67.5%
12. The length of a rectangle is 6 meters longer than the width. If the total area of the rectangle is 16m², find the dimensions of the rectangle.
Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.
The formula for the area of a rectangle is:
Area = Length x Width
We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:
(x + 6) x = 16
Expanding the product and rearranging, we get a quadratic equation:
x² + 6x - 16 = 0
We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:
(x + 8) (x - 2) = 0
This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.
Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.
Therefore, the dimensions of the rectangle are 2 meters by 8 meters.
Step-by-step explanation:
can anyone help? :/ A dog is leashed to the corner of a house. How much running area does the dog have? Round your answer to the nearest square foot, if necessary.
Answer:
943 square ft.
Step-by-step explanation:
If the dog is leashed to the corner of a house with a rope or leash of a radius of 20 feet, then the dog can run in a 3/4 part of a circular area around the corner of the house.
The running area of the dog is given by the formula of the area of a 3/4 part of a circle:
A = 3/4* πr^2
where r is the radius of the circle.
Substituting the given value of r = 20 feet, we get:
A =3/4 *π(20)^2
A =3/4*22/7*400 square ft.
A=942.85 in nearest square ft it is 943 square ft.
A family has a gross income of $95,000.00 a year and pays a federal tax rate of 18%.
What is their net income after taxes?
Answer and Step-by-step explanation: To calculate the net income of the family after taxes, we need to first determine the amount of taxes they will pay.
The federal tax rate of 18% means that the family will pay 18 cents in taxes for every dollar of gross income they earn.
So, the amount of federal taxes the family will pay can be calculated as:
Federal taxes = Gross income x Tax rate
Federal taxes = $95,000.00 x 0.18
Federal taxes = $17,100.00
Now that we know the amount of federal taxes the family will pay, we can calculate their net income by subtracting the federal taxes from their gross income:
Net income = Gross income - Federal taxes
Net income = $95,000.00 - $17,100.00
Net income = $77,900.00
Therefore, the family's net income after paying federal taxes is $77,900.00.
Workout 461÷4 give your answer as a whole number and a reminder
Step-by-step explanation:
the answer is 115 remainder 1
Find the area and perimeter of the parallelogram. (Hint: Don't forget your units!)
7 cm
8 cm
4 cm
The area of the parallelogram is 28 square centimeters and the perimeter of the parallelogram is 30 centimeters.
Finding the area and perimeter of the parallelogram.Given that
Length = 7 cm
Width = 8 cm
Height = 4 cm
The area of a parallelogram can be found by multiplying the base by the height. In this case, the base is the length of the parallelogram, which is 7 cm, and the height is the height of the parallelogram, which is 4 cm.
Therefore, the area of the parallelogram is:
Area = base x height = 7 cm x 4 cm = 28 cm^2
The perimeter of a parallelogram is the sum of the lengths of all four sides.
So, we have
Perimeter = 2 x (length + width) = 2 x (7 cm + 8 cm) = 2 x 15 cm = 30 cm
Therefore, the area of the parallelogram is 28 square centimeters and the perimeter of the parallelogram is 30 centimeters.
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Ricky would like to retire with an amount of 200,000 she found a bank that offers 9% interest compounded yearly and has an initial investment of 20,000.how much time will Ricky have to wait until she attains the 200,000 in this situation?
Ricky will have to wait for 26.78 years to have 200,000 in her account with this investment.
How do you calculate how long Ricky will wait for her investment to reach 200,000?In order to determine the time it takes for Ricky's initial investment to grow to the desired amount, we can use the compound interest formula: A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account (in this case, 200,000)
P is the initial investment (in this case, 20,000)
r is the annual interest rate (in this case, 0.09 for 9%)
n is the number of times interest is compounded per year (in this case, 1 for yearly compounding)
t is the number of years
We are trying to solve for t, so we can rearrange the formula to:
t = ln(A/P) / (n * ln(1 + r/n))
Plugging in the values:
t = ln(200,000/20,000) / (1 * ln(1 + 0.09/1))
t = ln(10) / ln(1.09)
t ≈ 2.303 / 0.086
t ≈ 26.78
Ricky will have to wait approximately 26.78 years to have 200,000 in her account with this investment.
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In a survey of 180 people, it was found that 95 people liked tea 80 people liked milk and 35 did not like both tea and milk. 1)Find how many people like both tea and milk. 2)Represent the above information in a Venn-diagram.
In this Venn diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.
Venn diagram explained.
Let's use T to represent the set of people who like tea, M to represent the set of people who like milk, and U to represent the universal set of all 180 people. We know that:
|T| = 95 (the number of people who like tea)
|M| = 80 (the number of people who like milk)
|T ∪ M| = 180 - |T ∩ M| = 180 - 35 = 145 (the number of people who like either tea or milk)
To find the number of people who like both tea and milk, we can use the formula:
|T ∩ M| = |T| + |M| - |T ∪ M|
Substituting in the values we know, we get:
|T ∩ M| = 95 + 80 - 145 = 30
Therefore, 30 people like both tea and milk.
To represent this information in a Venn diagram, we can draw two overlapping circles to represent the sets T and M. The circle for T should contain 95 elements, and the circle for M should contain 80 elements. The overlap region between the circles should contain 30 elements. The region outside of both circles should contain 35 elements, since 35 people do not like either tea or milk. The Venn diagram would look like this:
_______________
/ \
/ \
/ T \
\ /
\_________________/
|
| 30
|
______/ \______
/ \
/ \
/ M \
\ /
\_________________/
In this diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.
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List the sample space for rolling a fair 12-sided die.
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = {1}
S = {12}
The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
What is sample space?Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.
In the given question,
The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.
Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.
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Graph X-3<8 and 6x<72
Answer:
x < 11 & x < 12
Step-by-step explanation:
x - 3 < 8 and 6x < 72
x < 11 & x < 12
1:20 - salesman allows a 5% discount for cash payment. What will be the discount allowed for a ash payment of GH¢5,600.00? A. GH 250.00
The discount allowed for a cash payment of GH 5,600.00 is given as follows:
GHC 280.00.
How to obtain the discount?The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.
There is a 5% discount, hence the value of the discount is obtained as follows:
0.05 x 5600 = GHC 280.00.
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Bokamoso rides a bicycle to school every day (taking the same route). If she rides at 16 km/h, it takes her 45 minutes to get to school. 1. How far does Bokamoso ride on the way to school?
5.40 km is the distance Bokamoso ride on the way to school
What is speed, distance and time?
Speed is determined by dividing the distance travelled by the time taken to travel it. It gives the amount of time it took to travel a certain distance divided by the distance travelled.
Speed is inversely correlated with time and directly correlated with distance. As a result, distance equals speed times time, and time equals distance divided by speed; as speed rises, distance travelled will shorten, and vice versa.
Bokamosa rides at 16 km / hr
To get to school = 45 min
= 45 * 0.75 hour
= 0.3375 hr
Distance = Speed * Time
d = 16 * 0.3375
= 5.40 km
Hence, 5.40 km is the distance Bokamoso ride on the way to school.
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Solve for x.
A. 7
B. 4
C. 3
D. 5
The correct option -D. 5; Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
Explain about the secant of circle:A line that precisely intersects a circle at two points is said to be a secant.
The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.
Using the Theorem:
The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:
4(4 + x) = 6²
16 + 4x = 36
4x = 36 - 16
4x = 20
x = 20/4
x = 5
Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
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The following data values represent a population. What is the variance of the population? u = 12. Use the information in the table to help you.
A. 18 B. 41 O C. 12 OD. 80
x 3 11 13 21
(x-μ)² 81 1 1 81
The variance of the population according to the given table is option B 41.
What is variance?The spread or dispersion of a set of data around its mean is measured by variance. It has the same units as the original data and is calculated as the average of the squared deviations from the mean. Variance is a frequently used statistical term to describe the diversity or variability of a population or sample. When the variance is modest, the data points are closely grouped around the mean, whereas when the variance is great, the data points are widely dispersed.
The variance is given by the formula:
variance = (sum of squared deviations from the mean) / (number of observations)
Using the table we have sum of squared deviations from the mean:
81 + 1 + 1 + 81 = 164
variance = 164 / 4 = 41
Hence, the variance of the population according to the given table is option B 41.
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PLEASE HELP!!! The height of a snowball thrown off a 192-foot cliff is modeled by the function h(t) = −16t^2 + 64t + 192, where h is height in feet and t is time in seconds. Find the time the snowball takes to reach the ground.
5 seconds
3 seconds
6 seconds
4 seconds
The snowball takes **6 seconds** to reach the ground according to the quadratic formula.
What is a quadratic equation?A quadratic equation of the form ax² + bx + c = 0 has one or more solutions provided by the quadratic formula. The equation is:
Where a, b, and c are the coefficients of the quadratic equation, x = (-b √(b2 - 4ac)) / 2a.
.We must determine when h(t) = 0 in order to determine how long it takes the snowball to reach the ground.
h(t) = −16t²+ 64t + 192
0 = −16t² + 64t + 192
By -16, divide both sides:
0 = t² - 4t - 12
Making use of the quadratic formula:
(-b √(b² - 4ac)) / 2a
a = 1, b = 4, and c = 12 are the values.
t = (-(-4) ± √((-4)² - 4(1)(-12))) / 2(1)
t = (4 ± √(16 + 48)) / 2
t = (4 ± √(64)) / 2
t = (4 ± 8) / 2
Hence, t = -2 or t = 6. The snowball takes **6 seconds** to reach the ground since time cannot be negative.
As a result, the response is **6 seconds**.
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.6 1 and 2, write the expression using words. In 1. (23,000-789) x 19 In 3-4, read the expressio Donald's score is less. 2.6+(88×3³)
If you purchase a plan from the Marketplace, all of these factors affect the cost of your monthly health insurance premium EXCEPT…
a. gender
b. age
c. location
d. type of plan (Platinum, gold, etc.)
The correct answer is (d) type of plan (Platinum, gold, etc.) does not affect the cost of your monthly health insurance premium, as this is the exception to the list provided.
The cost of your monthly health insurance premium is affected by various factors, including your age, gender, location, and the type of plan you choose. Let's briefly discuss each of these factors:
What is fraction?
A fraction is a numerical quantity that represents a part of a whole or a ratio between two numbers. It is represented by two numbers separated by a horizontal line, with the number above the line called the numerator and the number below the line called the denominator
a. Gender: Insurance companies may charge different premiums based on gender because certain health conditions or treatments may be more common in one gender than the other. However, it's important to note that some states have banned gender-based premium differences.
b. Age: Older individuals may be charged higher premiums than younger individuals because they are more likely to need medical care. However, the Affordable Care Act (ACA) limits the premium difference between older and younger individuals to a ratio of 3:1.
c. Location: Insurance companies may charge different premiums based on where you live because healthcare costs can vary by region. For example, healthcare costs in urban areas may be higher than in rural areas.
d. Type of Plan: The type of plan you choose, such as a Platinum, Gold, Silver, or Bronze plan, can affect the cost of your monthly health insurance premium. Platinum plans typically have the highest premiums but the lowest out-of-pocket costs, while Bronze plans have the lowest premiums but the highest out-of-pocket costs.
In summary, all of the factors listed except the type of plan (d) can affect the cost of your monthly health insurance premium.
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In 1870, the French writer Jules Verne
In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.
Who is the French writer?The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.
Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.
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Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36
stores this year shows mean sales of 78
units of a small appliance with a standard deviation of 13
units. During the same point in time last year, a random sample of 49
stores had mean sales of 90
units with standard deviation 16
units.
It is of interest to construct a 95 percent confidence interval for the difference in population means 1−2
, where 1
is the mean of this year's sales and 2
is the mean of last year's sales.
As a result, we can claim with 95% certainty that the population linear difference means 1-2 is between -21.48 and -2.52 units of small appliances.
What is a linear equation?In algebra, a linear equation has the form y=mx+b. The slope is denoted by B, while the y-intercept is denoted by m. Because y and x are variables, the preceding sentence is sometimes referred to as a "linear equation with two variables." Bivariate linear equations are two-variable linear equations. Linear equations may be found in various places: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the form y=mx+b, where m represents the slope and b represents the y-intercept, it is said to be linear. A linear equation is one that contains the formula y=mx+b, with m signifying the slope and b denoting the y-intercept.
We may use the following calculation to get a 95% confidence range for the difference in population means 1-2:
[tex](x1 - x2) t(\alpha/2, df) * \sqrt(s12/n1 + s22/n2)[/tex]
where:
Initially, we must compute the degrees of freedom:
[tex]df = ((s12/n1) + s22/n2)2/((s12/n1) + (s22/n2)2/(n2-1))\\df = ((13^2/36 + 16^2/49)^2) / ((13^2/36)^2/35 + (16^2/49)^2/48) = 67.94\\(78 - 90) 2.00 * \sqrt(132/36 + 162/49)\\CI = -12 +2.00 * 4.742\\CI = -12+ 9.484\\CI = (-21.48, -2.52) (-21.48, -2.52)[/tex]
As a result, we can claim with 95% certainty that the population difference means 1-2 is between -21.48 and -2.52 units of small appliances.
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Write 80cm to 2km as rate
One per 2,500 can be used to represent the rate of 80cm to 2km.
Writing measures as a rate.To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):
80 cm/100,000 = 0.0008 km
Now we can express the rate as:
0.0008 km per 2 km
Or we can simplify it by dividing both the numerator and denominator by 0.0008:
1 per 2,500
Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.
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!!ILL GIVE BRAINLIST!!
Find the unknown side length. Simplify radicals to simplest radical form.
Answer: q1. 12 i think q2. 39 i think
Step-by-step explanation
The perimeter of the given triangle is 3x² + 2 units
and its two sides are given in the figure. Find its
third side.
Step-by-step explanation:
Perimeter is the total of all three sides added together:
2x^2 + x + 3x^2 -3 + ? = 3x^2 + 2 Simplify a bit on the L
5x^2 + x -3 + ? = 3x^2 + 2 subtract 5x^2 from both sides
x-3 + ? = - 2x^2 + 2 subtract x from both sides
-3 + ? = - 2x^2 - x + 2 finally, add 3 to both sides
? = - 2x^2 -x + 5
i need help pleaseeee!!!
a. The number of red roses left t hours after the store opens [tex]R(t) = 400/2^{t/2}[/tex]
b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t
c. One possible solution is t ≈ 7.546 hours after the store opens.
d. there are 194 boxes of chocolates left.
e. you need to arrive at the store no later than 7.504 hours after it opens.
How to find the number of red roses left ?a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:
[tex]R(t) = 400/2^{t/2}[/tex]
b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:
C(t) = 200 - 0.15t
c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:
[tex]400/2^{t/2} = 200 - 0.15t[/tex]
Simplifying this equation, we get:
[tex]2^{t/2 + 1} + 0.15t - 400 = 0[/tex]
We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.
d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:
C(3.5) = 200 - 0.15(3.5) = 194.25
We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.
e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:
[tex]400/2^{t/2}= 36[/tex]
Simplifying this equation, we get:
2^(t/2) ≈ 11.111
Taking the logarithm of both sides, we get:
t/2 ≈ log2(11.111)
t ≈ 2 log2(11.111)
Using a calculator, we get:
t ≈ 7.504 hours after the store opens.
Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.
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Lucy invested her savings in two investment funds. The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B. Fund A returned a profit and Fund B returned a 6% profit. How much did she invest in Fund B, if the total profit from the two funds together was 2760?
Answer: 2,594.4 is your answer for fund A and 165.6 is your answer for Fund B
Step-by-step explanation:
9 x 3^15 can be written as 3^n.
What is the value of n?
Answer: n = 17
Step-by-step explanation: We can simplify 9 x 3^15 by first writing 9 as 3^2. Then we can use the rule that says when you multiply two numbers with the same base, you can add their exponents. So:
9 x 3^15 = 3^2 x 3^15 = 3^(2+15) = 3^17
Therefore, n = 17.
