There were no more books checked out in March than in April.
What is the pictograph about?The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.
The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.
To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:
5 books (March) - 5 books (April) = 0 books
Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.
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Carson is organizing textbooks on his bookshelf. He has a Spanish textbook, a math textbook, a history textbook, and a health textbook. How many different ways can he line the textbooks up on his bookshelf?
Carson can line up his textbooks on his bookshelf in 24 different ways
What is Permutation?
Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.
What is Combination?
The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.
According to the given information:
Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:
n! / (n - r)!
where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).
On substituting the values in the formula,
4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24
Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.
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Find a pair of integers whose difference gives zero.
A)8 and 1
B)8 and 2
C)8 and 3
D)-8 and -8
Answer:
Answer is D.
Please mark my answer as Brainliest if you found this one helpful.
(x^2-1)^3=64(X^2-1)^2
Answer:
x = ±1, ±√65
Step-by-step explanation:
You want the solution to (x² -1)³ = 64(x² -1)².
SolutionSubtracting the right side, we have ...
(x² -1)³ -64(x² -1) = 0
(x² -1)²(x² -1 -64) = 0
Zero product ruleThe solutions make the factors zero:
x² -1 = 0 ⇒ x = ±1
x² -65 = 0 ⇒ x = ±√65
Solutions are x = ±1 and x = ±√65.
__
Additional comment
The solutions ±1 are each multiplicity 2.
Imagine that two friends, Lola and Joni, each buy an iPod touch for $400, and pay with a credit card. When this happens, the credit card company pays Apple, and the friends become indebted to the credit card company. For every year they don't pay back the debt, the company charges them interest: a percentage of what they owe. The interest rate is called an annual percentage rate (APR), while the amount owed is called a balance.
Calculate how much each person would owe over time if neither made any payments to the credit card company, assuming interest is calculated once per year.
Balance after...
Person: APR 0 years 1 years 2 years 3 years 6 years
Lola 6%:
Joni 36%
In reality, credit card companies don't charge interest every year, they charge interest every month. To determine the monthly interest rate, divide the APR by 12.
Lola has an annual rate of 6%. So Lola has a monthly rate of
0.5%
Joni has an annual rate of 36%. So Joni B has a monthly rate of:
3%
Given that both Lola and Joni charge $400 initially calculate how much each person would owe over time if neither made any payments to the credit card company, assuming interest is compounded monthly.
Balance after...
Person: APR 0 years 1 years 2 years 3 years 6 years
Lola 6%
Joni 36%
Do you think it matters how often credit card companies charge interest? Explain.
Yes it matters because the more often they calculate the interest the higher the amount goes.
If neither friend made any payments for 10 years, how much would the $400 iPod end up costing in total (with monthly compounding)?
Lola's total cost (balance after 10 years): $
Joni's total cost (balance after 10 years): $
Amy's total cost: $697.26
Mackenzie's total cost: $11904.62
How to solveAmount = P = 340
Amy's interest rate = ra = 6% = 0.06
Mackenzie's interest rate = rm = 30% = 0.3
Amount is compounded yearly.
Amount at the end of the year is calulated as
Pn= P(1+r)
We will use Excel to fill given table
Person APR 0 1 2 3 6
Amy 6% 340.00 360.40 382.02 404.95 482.30
Mackenzie 30% 340.00 442.00 574.60 746.98 1641.12
Amy has an annual rate of 6%. So Amy has a monthly rate of 6 /12 = 0.5% = 0.005
Mackenzie has an annual rate of 30%. So Mackenzie has a monthly rate of 30/12 = 2.5% = 0.025
Pn= P(1+r)
Here will be replaced by a number of months and r is relaced by monthly interest rate
We can modified this formula as
12n
Pn= P(1+)
Where n and r is same as in first part of question.
We will use excel to fill given table
Person APR 0 1 2 3 6
Amy 6% 340.00 360.97 383.23 406.87 486.90
Mackenzie 30% 340.00 457.26 614.97 827.06 2011.86
From the above two tables, it is clear that it does matter how the company charges interest. When compounded monthly, the amount will more as compared to when compounded yearly. So,
Yes it matters because the more often they calculate the interest the higher the amount goes.
If neither friend made any payments for 12 years, we can add one more column to calculate for n = 12.
Amy's total cost: $697.26
Mackenzie's total cost: $11904.62
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a baseball stadium keeps track of how many hot dogs each customer orders. the data is organized into the frequency table below. what os the relative frequency of customers ordering five hot dogs?
a.) about 5%
b.) about 7%
c.) about 8%
d.) about 14%
The relative frequency of customers ordering five hot dogs is 7%, option B is correct.
To find the relative frequency of customers ordering five hot dogs, we need to divide the frequency of customers who ordered five hot dogs by the total number of customers.
The total number of customers is the sum of the frequencies in the table:
Total frequency = 90 + 45 + 18 + 18 + 14 + 13 = 198
The frequency of customers ordering five hot dogs is 14, so the relative frequency is:
Relative frequency of customers ordering five hot dogs = (frequency of customers ordering five hot dogs) / (total frequency) = 14 / 198 = 0.0707
To express this as a percentage, we can multiply by 100:
Relative frequency of customers ordering five hot dogs = 0.0707 * 100% = 7.07%
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3. Rochelle helped in the garden 7 days during the last 4 weeks. Use the
numbers in the box to complete the sentences comparing her time in
the garden.
Numbers can be used more than once. Write each number in the
appropriate box.
For every day(s) Rochelle helped, she did not help
For every
day(s).
1 3 4 7 28
day(s).
day(s) Rochelle did not help, she helped
For every 3 days Rochelle helped, she did not help for 1 day.
For every 4 days Rochelle helped, she did not help for 1 day.
For every 7 days Rochelle helped, she did not help for 6 days.
For every 28 days Rochelle helped, she did not help for 21 days.
Let's use the terms provided to complete the sentences comparing Rochelle's time in the garden.
Since Rochelle helped in the garden for 7 days during the last 4 weeks, we can calculate the total number of days in 4 weeks and then find the number of days she did not help.
There are 7 days in a week, so in 4 weeks, there are 4 x 7 = 28 days.
Rochelle helped for 7 days, so she did not help for 28 - 7 = 21 days.
Now, let's complete the sentences:
For every 1 day(s) Rochelle helped, she did not help for 3 day(s).
For every 3 day(s) Rochelle did not help, she helped 1 day(s).
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The distance between Town P and Town Q is 237.5 Km. At 11.30 a.m a van travels from
Town P to Town Q at an average speed of 35 km/h. At the same time, a car travels from
Town Q to Town P along the same route at an average speed of 60 km/h.
a)At what time will the vehicles meet on the way?
b) How far will each vehicle have travelled when they meet?
Answer:
So when the two vehicles meet, the van has travelled 87.5 km and the car has travelled 150 km.
Step-by-step explanation:
(a) Let's call the time it takes for the two vehicles to meet "t". We know that the distance between the two towns is 237.5 km, and the combined speed of the two vehicles is 35 km/h + 60 km/h = 95 km/h. Using the formula distance = speed × time:
237.5 = 95t
Solving for t:
t = 237.5/95
t ≈ 2.5 hours
So the two vehicles will meet on the way 2.5 hours after 11.30 a.m., which is at 2.00 p.m.
(b) To find how far each vehicle has traveled when they meet, we can use the formula distance = speed × time again. The van travels at 35 km/h for 2.5 hours, so it travels:
distance = speed × time = 35 km/h × 2.5 hours = 87.5 km
The car travels at 60 km/h for 2.5 hours, so it travels:
distance = speed × time = 60 km/h × 2.5 hours = 150 km
So when the two vehicles meet, the van has traveled 87.5 km and the car has traveled 150 km.
What is the midpoint of the line segment with the given endpoints (4,6) (3,-3)
Help it’s urgent
The coordinates of the midpoints of the given line segment is:
(3.5, 1.5)
How to find the midpoints of a line segment?The midpoint of a line segment is simply referred to as the center of that specific line segment.
Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.
The coordinates of the endpoints of the line are:
(4,6) and (3,-3)
The formula to find the coordinates of the midpoint of the line is:
(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Thus, we have:
(x, y) = (4 + 3)/2, (6 - 3)/2
= (3.5, 1.5)
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From the observation deck of a skyscraper, Brandon
The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
How to solveGiven that:-
The angle is = 45
The height of the skyscraper is 1140 feet.
The horizontal distance will be calculated by applying the angle property in the right angle triangle.
tan45 = ( P / B )
B = P / tan45
B = P Since ( tan45 =1 )
B = 1140 feet.
Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
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From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Two cars are traveling in the same direction. The first car is going 45 mi/h and the second car is going 60 mi/h. The first car left 2 hours before the second car. How many hours will it take for the second car to travel the same distance as the first car
The time taken for the second car to travel the same distance as the first car is 6 hours.
What is the time of motion of the second car?
The time taken for the second car to travel the same distance as the first car is calculated as follows;
let the time taken for the second car to travel the same distance = t
distance traveled by second car = 60t
the time taken for the first car = t + 2
distance traveled by the first car = 45(t + 2)
Since both distance are equal, we will have the following equations;
60t = 45 (t + 2)
60t = 45t + 90
15t = 90
t = 90/15
t = 6
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to manufacturing floor
T
30 in.
72 in.
to loading dock
D
48 in.
36 in.
g) What is the longest rod that can be carried to the loading dock? Round to
the nearest tenth of an inch.
Answer:
To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.
First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:
m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4
where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).
Using point-slope form, we get the equation of the line CD as:
y - 48 = (-1/4)(x - 0)
y = (-1/4)x + 48
Now, we can find the perpendicular distance from point T to the line CD as follows:
d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)
d = 42 / sqrt(17) ≈ 10.21
Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).
PLS HELP ASAP PLSSSSSS
Answer:
a) |x -8| = 6
b) |x -15| = 0
Step-by-step explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
2 and 1415SolutionsThe solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
ParametersGiven the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0
You deposit $300 each month into an account earning 2% interest compounded
monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
a) The future value of the account after 30 years can be calculated using the formula:
FV = P * ((1 + r/n)^(n*t))
where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:
FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60
So you will have $150,505.60 in the account after 30 years.
b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:
$300 * 360 = $108,000
c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:
$150,505.60 - $108,000 = $42,505.60
Answer:
a) you will have approximately $133,381.85 in the account in 30 years.
b) a total of $108,000 into the account over 30 years.
c) a total of $25,381.85 in interest over 30 years.
Step-by-step explanation:
NASA launches a rocket at
t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t^2+43t+339
.
(A) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round answer to 2 decimal places)
The rocket splashes down after
seconds._______
(B) How high above sea-level does the rocket get at its peak? (Round answer to 2 decimal places)
The rocket peaks at _____
meters above sea-level._____
Answer:
(A)
[tex] - 4.9 {t}^{2} + 43t + 339 = 0[/tex]
[tex]49 {t}^{2} - 430t - 3390 = 0[/tex]
[tex]t = \frac{ - ( - 430) + \sqrt{ {( - 430)}^{2} - 4(49)( - 3390)} }{2(49)} = \frac{430 + \sqrt{849340} }{98} = 13.79[/tex]
The rocket splashes down after 13.79 seconds.
(B) h'(t) = -9.8t + 43 = 0
t = 43/9.8 = 215/49 = 4.39 seconds
h(4.39) = 433.34 meters
At t = 4.39 seconds, the rocket peaks at
433.34 meters above sea level.
35. The equation v=20Vt + 273 relates the speed v, in m/s, to the air
temperature t in Celsius degrees.
a. Find the temperature when the speed of sound is 340 m/s.
b. Find the temperature when the speed of sound is 320 m/s.
a. The temperature is about 3.35 degrees Celsius at 340 m/s, the speed of sound.
b. The temperature is about 2.35 degrees Celsius at 320 m/s, or the speed of sound.
Describe Speed?Speed is a scalar physical quantity that quantifies the rate of motion of an object. It is described as the distance that an object covers in a specific period of time. Meters per second (m/s) is the SI unit for measuring speed.
The speed formula is as follows:
Speed = distance / time
Depending on the purpose, speed can also be stated in different units, such as kilometres per hour (km/h), miles per hour (mph), or feet per second (ft/s).
The concept of speed, which is used to describe how objects move, is important to physics. It plays a significant role in a variety of fields of science, engineering, and technology, including sports, aircraft, and transportation. For the purpose of analysing and forecasting the behaviour of physical systems, it is essential to comprehend the idea of speed.
a. We can change v = 340 into the equation and solve for t to determine the temperature when the speed of sound is 340 m/s:
v = 20Vt + 273
340 = 20Vt + 273
67 = 20Vt
t = 67/20
Therefore, the temperature is about 3.35 degrees Celsius when the sound travels at 340 m/s.
b. We may once more enter v = 320 into the equation and solve for t to determine the temperature when the speed of sound is 320 m/s:
v = 20Vt + 273
320 = 20Vt + 273
47 = 20Vt
t = 47/20
As a result, the temperature is roughly 2.35 degrees Celsius at 320 m/s, the speed of sound.
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Several trusses are needed to build the frame of the shed roof. Each roof truss is 16 inches apart, as measured from the centers of the beam widths.
The roof could be constructed so that the ridgeline of the roof is parallel to the longest dimension of the shed (first picture below) or it could be constructed so that the ridgeline of the roof is parallel to the shortest dimension of the shed (second picture below).
The number of roof trusses that would be needed for the longest length is 2
Calculating the number of roof trusses that would be neededThe longest lengths from the question are given
Longest lengths = 28 and 22
Next, we expand the lengths of the roof trusses
This is to calculate the greatest common factor (GCF) of the lengths
So, we have
28 = 2 * 2 * 7
22 = 2 * 11
Multiplying the common factors gives the GCF
So, we have
GCF = 2
This means that the number of roof trusses that would be needed for the longest length is 2
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Given that X is a normal random variable with a mean of 40 and a standard deviation of 8 what is P (34
The probability is given as follows:
P(34 < X < 46) = 0.5468 = 54.68%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 40, \sigma = 8[/tex]
The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:
Z = (46 - 40)/8
Z = 0.75
Z = 0.75 has a p-value of 0.7734.
Z = (34 - 40)/8
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
Hence:
0.7734 - 0.2266 = 0.5468 = 54.68%.
Missing InformationThe probability is:
P(34 < X < 46).
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Explain how you know what a fraction was multiplied by when the product is greater than a factor.
When the product of a fraction and a factor is greater than the factor, it means that the fraction is greater than 1.
Why is this true of fractions ?Due to the principles of multiplication, when multiplying a value greater than 1 with a given amount, the product will be larger than the original number. To provide an example, if we multiply 5 by 2, the result will be 10, which is greater than 5.
By extension, if we multiply a fraction with a factor that's greater than 1, the resulting product will be greater in size as compared to the initial quantity. For instance, when we calculate 1/2 multiplied by 3, the outcome is 3/2, which surpasses the worth of 1/2. Hence, it can be deduced that any result which exceeds its own source was obtained through multiplication by value greater than 1.
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sin negative-1 (-3sqrt/2) in radians
The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.
We have:
cos²θ + sin²θ = 1
Since sine is negative and cosine is positive, we know that:
sinθ = -sqrt(1 - cos²θ)
Substituting cosθ = 3√(2)/2, we get:
sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2
Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.
Since cosine is positive in the fourth quadrant, we have:
cos⁻¹(3√(2)/2) = π/4
Substituting this value, we get:
sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4
Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
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Help pleaseeeee I would appreciate it
(1) The result of the row operation R₂ ↔ R₃ is [ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
(2) The result of the row operation 3R₁ ↔ R₁ is [24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
What is the result of the row operation?
The result of the row operation in the matrix is calculated as follows;
R₂ ↔ R₃, implies changing row 2 and row, and the result would be;
[ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
The result of obtained from 3R₁;
3R₁ = [24 - 27 -21 - 18]
3R₁ ↔ R₁ is determined as; (the row interchange)
[24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
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The formula for the volume of a prism is V = area of base x height. What is the volume and surface area of each of these prisms? Show your thinking
The volume of the prism is V = 4000 cm³
Given data ,
Let the volume of the prism be represented as V
Now , the value of V is
Let the height of the prism be h = 10 cm
Let the width of the prism be w = 20 cm
Let the length of the prism be l = 20 cm
So , the base area of prism = l x w
Base area = 400 cm²
Now , the volume of the prism is V = 400 x 10
V = 4000 cm³
Hence , the volume of prism is V = 4000 cm³
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What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
The equation of a parabola with a vertical axis and vertex (h, k) is given by:
(x - h)² = 4p(y - k)
How to explain the equationIn the equation, where p is the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
If the vertex is at the origin (h=0, k=0), then the equation simplifies to:
x² = 4py
where p is still the distance from the vertex to the focus (and also the distance from the vertex to the directrix).
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Jade is constructing wooden figures for a park.
She is making six of them and fitting them
together to form part of a stage. What is the total
volume of all of the parts? Show your work.
10 ft
3 ft
4 ft
It is to be noted that the volume of all the wooden figures will come to.
Why is this so?Each wooden figure as shown in the image is
L = 4ft
W = 4ft
H = 10ft
Where L = Length, w= Width and H = height.
The volume of a cuboid is L x W x H
So we have
4 x 4 x 10
Since there are six of the figures, we restate the expression as:
6 x 4 x 4 x 10
= 960 Ft³
Thus, volume of all of the parts is 960 Ft³
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
What linear function equation is represented by this graph?
ANSWER: 1
3
x−4 just took the test
Answer:
The linear function is y = (1/3)x - 4.
Step-by-step explanation:
The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is
y = (1/3)x - 4.
if a clock shows it is 3 o'clock, how could you describe the smaller angle made my the two hands of the clock? solve this problem any way you choose
The smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
What is an angle?A figure known as an angle is created by two rays or line segments that meet at a place known as the vertex of the angle. The sides or legs of the angle are other names for the rays or line segments.
According to question:To determine the smaller angle made by the two hands of a clock when it is 3 o'clock, we can use the following formula:
angle = |(11/2) * m - 30h|
where:
m is the number of minutes past the hour (in this case, since it is 3 o'clock, m = 0)
h is the hour (in this case, h = 3)
By using this formula, we get:
angle = |(11/2) * 0 - 30(3)| = |0 - 90| = 90
Therefore, the smaller angle made by the two hands of the clock at 3 o'clock is 90 degrees.
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The cubic polynomial shown below has zeroes at x=-1and x= only and has a relative maximum at (3,8). Which of the following is its y-value when x=5?
The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.
Therefore the option C is correct.
What is polynomial?A polynomial expression is described as an algebraic expression with variables and coefficients.
If the zeroes of the polynomial are negative 4, 2, and 2.
Then the factors will be (x + 4), (x - 2), and (x - 2).
Then the cubic polynomial will be
→ (x + 4) (x - 2) (x - 2)→ (x + 4) (x² - 4x + 4)→ (x³ - 12x + 16)we can write the polynomial equation as:
y = C(x³ - 12x + 16)
Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.
y = 0.25 (x³ - 12x + 16)
y = 0.25 (6³ - 12 × 6 + 16)
y = 0.25 (216 - 72 + 16)
y = 0.25 (160)
y = 40
Note that there was no diagram provides, i solved a similar question
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reasoning.
19. Challenge: Find the lengths of BC, DE, and FG in the diagram
below.
A
1
30°
B
0.5
C
D
E
-1.5√3
F
G
The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively. This can be solved by using trigonometric functions.
What are trigonometric functions?Trigonometric functions are used to describe relationships involving angles and sides of triangles. They are used to calculate the sizes of angles and distances between points. These include sine, cosine, tangent, secant, cosecant and cotangent.
This can be solved by using trigonometric functions.
First we need to find the length of FA to solve the question further.
FA = 1.5+ FD
AG = FA cos 30
AG = 1.5 √3
AG = 1.5 FD √3/2 = 1.5√3 (as cos 30 = √3/2)
DF = 1.5
Thus, FA = AB+BD+FD
FA = 1 + 0.5 + 1.5
So, the length of FA is 3.
Now, for the triangle, ΔABC
as ∠BAC= 30
BC = AB/2
= 0.5
This is because the angle of the right triangle is 30°and we know that when the angle of a right triangle is 30° the length of opposite side is exactly equal to half of the length of the hypotenuse.
For ΔADE,
as ∠DAE= 30, and AD= 1.5
DE= AD/2
= 0.75
For ΔGAF,
as ∠GAF= 30, and FA= 3
FG = FA/2
= 1.5
The length of BC, DE and FG are 0.5, 0.75 and 1.5 respectively.
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Electronics store reduced price of tv From $900 to $837
The percentage decrease of the TV from $900 to $837 is 7%
Percentage decreaseOriginal price of TV = $900New price of TV = $837Percentage decrease = Difference in price / original price × 100
[tex]=\dfrac{(900-837)}{900} \times 100[/tex]
[tex]=\dfrac{63}{900} \times 100[/tex]
[tex]= 0.07 \times 100[/tex]
[tex]= 7\%[/tex]
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Complete question-
An electronics store reduced the price of a TV from $900 to $837. What was the percent of decrease?
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
C(t)=18(0.91)t
The initial temperature of the soda is 18 degrees Celsius.
Its temperature after 20 minutes is 2.73 degrees Celsius.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = a(b)^x
Where:
a represents the base value, initial value, or y-intercept.x represents time.b represents the rate of change.When time, t = 0, the initial value can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(0)=18(0.91)^{0}[/tex]
C(0) = 18(1)
C(0) = 18 degrees Celsius.
When time, t = 0 = 20, the temperature can be calculated as follows;
[tex]C(t)=18(0.91)^{t}\\\\C(20)=18(0.91)^{20}[/tex]
C(20) = 2.73 degrees Celsius.
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Complete Question:
A can of soda is placed inside a cooler. As the soda cools its temperature C (t) in degrees Celsius after t minutes is given by the following exponential function.
[tex]C(t)=18(0.91)^{t}[/tex]
Find the initial temperature of the soda and its temperature after 20 minutes?
The sides of a square are increased
by a scale factor of 3. The area of
the larger square is what percent of
the area of the smaller square?
So the area of the larger square is 900% of the area of the smaller square.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is typically expressed in square units, such as square meters (m²) or square feet (ft²). To find the area of a shape, you need to measure the length and width of the surface or region and then multiply those measurements together.
Here,
If the sides of a square are increased by a scale factor of 3, then the new square will have sides that are 3 times as long as the original square. The area of a square is proportional to the square of its sides, so the area of the new square will be 3² = 9 times as large as the area of the original square. Therefore, the area of the larger square is 900% of the area of the smaller square.
Alternatively, we can use the formula for the area of a square, A = s², where A is the area and s is the side length. If the side length is increased by a scale factor of 3, then the new side length is 3s. Therefore, the area of the new square is:
A' = (3s)²
= 9s²
The ratio of the area of the new square to the area of the original square is:
A' / A = (9s²) / (s²)
= 9
Multiplying by 100% to convert to a percentage, we get:
A' / A = 900%
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