To determine how many containers of size 3.7 tons are needed to hold all the gravel from one truck, we need to first calculate how many tons of gravel are in one truck.
How many containers of this size are needed to hold all the gravel from one truck?Since each truck holds 7.5 cubic yards of gravel, and the weight of one cubic yard of gravel is 1.48 tons, we can calculate the total weight of gravel in one truck as follows:
7.5 cubic yards x 1.48 tons per cubic yard = 11.1 tons
Therefore, each truck carries 11.1 tons of gravel.
To determine how many containers of size 3.7 tons are needed to hold all the gravel from one truck, we can divide the total weight of gravel in one truck by the capacity of each container:
11.1 tons ÷ 3.7 tons per container = 3 containers
Therefore, three containers of size 3.7 tons are needed to hold all the gravel from one truck.
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4. Select all the inequalities that have the same graph as x <4 a
(A.) x < 2
Bx+6 <10
C.) 5x < 20
Dx-2>2
x<8
7<4
Option (B) x + 6 < 10 and (C) 5x < 20 have same graph.
From the given set of inequalities;
(A) x < 2 represents x ∈ (-∞, 2)
(B) X + 6 < 10 ⇒ x < 4
represents x ∈ (-∞, 4)
(C) 5x < 20 ⇒ x < 4
represents x ∈ (-∞, 4)
(D) x - 2 > 2 ⇒ x > 4
represents x ∈ (4, ∞)
(E) x < 4 represents x ∈ (-∞, 8)
We can see that inequalities (B) and (C) both represents x ∈ (-∞, 4)
Thus, the graph of both inequalities are same.
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Do you best to explain how the following diagram demonstrates the Pythagorean theorem
Answer:
Step-by-step explanation:
The theorem states that the square on the hypotenuse (longest side) of a right triangle equal the sum of the squares on the other 2 sides.
Counting the small squares gives us these areas.
We see that
Sum of squares on hypotenuse = 25.
and sum of squares on the other 2 sides = 9 and 16 which equals 25.
Find the exact location of all the relative and absolute extrema of the function. (Order your answers from smallest to largest t.)
f(t) = 4t3 + 4t with domain [−2, 2]
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
f has (select)(a relative minimum, a relative maximum, an absolute minimum, an absolute maximum, no extremum,) at (x, y) = ____________
The derivative of the given function is:
f'(t) = 12t^2 + 4
Setting f'(t) = 0 to find critical points, we get:
12t^2 + 4 = 0
t^2 = -1/3
This equation has no real solutions, which means there are no critical points on the interval [-2, 2]. Since the interval is closed and bounded, the function attains its maximum and minimum values at the endpoints of the interval.
We can find the values of the function at the endpoints:
f(-2) = -24
f(2) = 24
Therefore, the function has an absolute maximum of 24 at t = 2 and an absolute minimum of -24 at t = -2. There are no relative extrema.
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The height h and the base area B of a cone are given. Find the volume of the cone. Write your answer in terms of pi.
H = 9 units
B = 5pi square units
The volume is ____ cubic units
The volume of the cone is (5/3)π(9²) cubic units ≈ 381.7 cubic units.
The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. However, we are given the base area B instead of the radius, so we need to find the radius first.
We know that the area of a circle is A = πr², so if the base area of the cone is B = 5π square units, then πr² = 5π, which means r² = 5. Solving for r, we get r = √5.
Now that we have the height h = 9 units and the radius r = √5 units,
we can use the formula for the volume of a cone:
V = (1/3)πr²h.
Substituting the values, we get
V = (1/3)π(√5)²(9) = (5/3)π(9²) cubic units, which simplifies to ≈ 381.7 cubic units.
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The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 per hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2. A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 15, and the box ranges from 8. 8 to 10. 2. A line divides the box at 9. 5. Plot 1 A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 11, and the box ranges from 8. 7 to 10. A line divides the box at 9. 6. Plot 2 How does the mean and median change from plot 1 to plot 2? The mean and median remain the same. The mean decreases, and the median remains the same. The mean remains the same, and the median decreases. The mean and median decrease.
The mean decreases, and the median remains the same from plot 1 to plot 2.
In the first box-and-whisker plot, the hourly wages earned by 20 employees are displayed, with a range from $8.70 per hour to $11.50 per hour. The median, which is the value that separates the higher half of the data from the lower half, is $10 per hour. The mean, which is the average of all the wages, is calculated by adding up all the wages and dividing the total by 20.
When one employee earning $15 per hour quits and is replaced by a new employee earning $8 per hour, the second box-and-whisker plot is created. The range of wages extends from $8 per hour to $15 per hour, with a median of $9.50 per hour. Since the new employee is earning a lower wage, the mean hourly wage decreases.
Therefore, the correct answer to the question is that the mean decreases, and the median remains the same. It is important to note that while the median does not change in this case, it is not always the case in other situations where data is added or removed from a set. It is also important to note that box-and-whisker plots are helpful in visualizing the spread of data and identifying any outliers.
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Name
Chapter
5
1.On a calendar, each day is represented by a rectangle. To keep track of the date, you cross off the
previous day by connecting one pair of opposite corners of the rectangle, as shown.
10
E 177
11
F18
12
b. List the five triangle congruence theorems.
G10
a. Classify AABE by its sides and by measuring its angles. Explain your reasoning.
D
Date
c.For each of the triangle congruence theorems you listed in part (b), prove that AFBC = ACGF
using that theorem. (You will need to write five different proofs.)
The triangle theorems will be:
Side-Side-Side (SSS) Congruence Theorem:Side-Angle-Side (SAS) Congruence Theorem:Angle-Side-Angle (ASA) Congruence Theorem:Hypotenuse-Leg (HL) Congruence Theorem:Angle-Angle-Side (AAS) Congruence TheoremHow to explain the theoremSide-Side-Side (SSS) Congruence Theorem: If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the two triangles are congruent.
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The number of girls to boys in the education program is 5 to 1. If there are 90 students in the education program, how many are girls?
HELP PLEASE 25 points!
This is for entrepreneurship
What can the bank do to comply with their general computer or Internet policy?
Bobby works in a private bank where none of the employees are allowed Internet access due to a strict confidentiality policy. Employees can only access the internal applications. However, for a particular product, Bobby is required to use the Internet and check details online.
The bank can (BLANK)
Bobby’s Internet usage for personal as well as official use
To comply with their general computer or Internet policy while allowing Bobby to access the internet for a specific task, the bank can implement several measures to monitor and restrict Bobby's Internet usage for personal and official use.
First, the bank can establish a separate, secured network for employees who need internet access for work purposes. This network should be isolated from the internal network to protect sensitive information.Second, the bank can implement strict access controls and authentication measures, such as providing a unique username and password for Bobby to access the internet. Third, the bank can install a firewall and web filtering system that blocks access to non-work-related websites and content. This will prevent personal use of the internet while still allowing access to the necessary websites for Bobby's work.
Fourth, the bank can regularly monitor and audit Bobby's internet usage, including the websites visited, the amount of time spent online, and any data transmitted or received. Finally, the bank should provide training and guidelines to Bobby regarding the acceptable use of the internet for work purposes, emphasizing the importance of confidentiality and adherence to the bank's security policies.
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rewrite each equation using the properties of exponents
1. ([tex](\frac{4}{64\frac{5}{6} })^{\frac{1}{2} }[/tex]
2. [tex]3m\frac{1}{4} (mn\frac{1}{3} ) ^{\frac{3}{2} }[/tex]
3.[tex]2a\frac{1}{2} (5a\frac{1}{2} b\frac{1}{4} )^{2}[/tex]
The properties of exponents
1. [tex](64)^{1/2}[/tex] = √(64) = 8
2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]
3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]
The properties of exponents can be used to simplify and rewrite expressions involving powers and roots. The most common properties are:
Product of powers: [tex]a^m[/tex] * aⁿ = [tex]a^{m+n}[/tex]
Quotient of powers: [tex]a^m[/tex]/ aⁿ = [tex]a^{m-n}[/tex]
Power of a power: [tex](a^m)^n[/tex] = [tex]a^{mn}[/tex]
Power of a product: [tex](ab)^m[/tex] = [tex]a^m[/tex] * [tex]b^m[/tex]
Power of a quotient: [tex](a/b)^m[/tex] = [tex]a^m[/tex]/ [tex]b^m[/tex]
Using these properties, we can rewrite the given equations as follows:
1. [tex](64)^{1/2}[/tex] = √(64) = 8
The square root of 64 is 8. The power of 1/2 represents the square root.
2. [tex]3m(mn)^(3/2)[/tex] = [tex]3m(m^{3/2}n^{3/2})[/tex]
The power of 3/2 represents the square root of the square. We can use the product of powers property to combine the m and n terms under the same square root.
3. 2a(5ab)² = [tex]2a(25a^2b^2) = 50a^3b^2[/tex]
We can use the power of a product property to square the 5ab term, and then simplify by combining the like terms.
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Michelle has four credit cards with the balances and interest rates listed below. She wants to pay off her credit
cards one at a time, based on the interest rate. In which order should Michelle pay off her credit cards?
>>>>>a. 3,2,1,4<<<<
b. 1,2,3,4
c. 2,4,3,1
d. 4,1,3,2
Answer:
a) 3, 2, 1, 4
Step-by-step explanation:
If you have multiple credit cards with different APRs, it is best to pay off the card with the highest APR first. This is because you will save the most money in interest by paying off the highest-rate debt first.
Therefore, as Michelle has four credit cards, each with different APRs, she should pay them off in order of the highest to lowest interest rate.
Since the highest APR is 23%, credit card #3 should be paid off first.
The next highest APR is 19%, so credit card #2 should be paid off second.
Credit card #1 should be paid off next as it has an APR of 17%.
Finally, credit card #4 should be paid off last, as it has the lowest APR of 15%.
So the order in which Michelle should pay off her credit cards is:
3, 2, 1, 4Find the volume of a pyramid with a square base, where the side length of the base is
11. 8 ft and the height of the pyramid is 5. 2 ft. Round your answer to the nearest
tenth of a cubic foot.
The volume of the pyramid with a square base of side length 11.8 ft and a height of 5.2 ft is 240.0 cubic feet.
To find the volume of a pyramid with a square base of side length 11.8 ft and a height of 5.2 ft, you can use the following formula:
Volume = (1/3) × Base Area × Height
1: Find the base area.
The base is a square with a side length of 11.8 ft, so the area of the base is:
Base Area = Side Length × Side Length
Base Area = 11.8 ft × 11.8 ft
Base Area ≈ 139.24 square ft
2: Find the volume.
Now, use the formula to find the volume:
Volume = (1/3) × Base Area × Height
Volume = (1/3) × 139.24 sq ft × 5.2 ft
Volume ≈ 240.0368 cubic ft
3: Round your answer to the nearest tenth.
Volume ≈ 240.0 cubic ft
So, the volume of the pyramid is approximately 240.0 cubic feet.
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First one gets brainlist
the average january surface water temperatures (°c) of lake michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34.
the mean value of these temperatures is 4.312.
what is the variance of this data set?
The variance of the data set is 0.318652.
To find the variance of this data set, we need to use the formula:
variance = Σ(x - μ)² / n
Where Σ represents the sum, x is the value of each data point, μ is the mean value, and n is the number of data points.
Using this formula, we can calculate the variance as follows:
Variance = [(5.07 - 4.312)² + (3.57 - 4.312)² + (5.32 - 4.312)² + (3.19 - 4.312)² + (3.49 - 4.312)² + (4.25 - 4.312)² + (4.76 - 4.312)² + (5.19 - 4.312)² + (3.94 - 4.312)² + (4.34 - 4.312)²] / 10
Variance = [0.225769 + 0.449769 + 0.370656 + 1.323856 + 0.716164 + 0.006544 + 0.175684 + 0.382884 + 0.135556 + 0.000484] / 10
Variance = 3.18652 / 10
Variance = 0.318652
Therefore, the variance of the data set is 0.318652.
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What is 2/3 ÷ 1/6?
A: 4/6
B: 1/6
C: 3/6
D: 5/6
Answer:
4
Step-by-step explanation:
2/3 / 1/6
= 2/3 * 6/1
= 12/3
= 4.
Please help it would be amazing if you knew this
The solution of the function (f - g)(x) is 17x + 7.
How to solve composite function?A function relates input and output. A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function as follows:
f(x) = 10x + 3
g(x) = -7x - 4
Therefore, let's find (f - g)(x)
Hence,
(f - g)(x) = f(x) - g(x)
Therefore,
f(x) - g(x) = 10x + 3 - (-7x - 4)
f(x) - g(x) = 10x + 3 + 7x + 4
f(x) - g(x) = 17x + 7
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A cup has a capacity of 320 ml. It takes 58 cups to fill a bucket and 298 buckets to fill a tank. By rounding to 1 significant figure, estimate the capacity of the tank in litres.
______________________________
Notes: 1L = 1,000ml BUCKET:= 320ml × 58= 18,560mlTANK:= 18,560ml × 298= 5,382,000ml= 5,382,000ml ÷ 1,000= 5,382= ~ 5.4LThe Capacity of The Tank Is Approx. 5.4L_______________________________
Probability of a pair of dice landing on a 4 and on a 6
Answer:
1/3
Step-by-step explanation:
It would be 2 options out of 6 total which means 2/6. 2/6 reduces down to 1/3
If the energy of an object goes down by 50j...
-physics
If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy.
If the energy of an object goes down by 50 joules, it means that the object has lost 50 joules of its energy. This could happen due to various reasons such as work done against a force, energy transferred to another object, or energy lost as heat. Here's a step-by-step explanation:
1. Identify the initial energy of the object.
2. Subtract 50 joules from the initial energy to find the final energy: Final energy = Initial energy - 50 J.
3. Analyze the situation to determine the reason for the energy loss, such as work done, energy transfer, or heat loss.
4. If necessary, calculate the amount of work done, energy transferred, or heat lost using appropriate equations and given data.
By following these steps, you can determine the final energy of the object after it has lost 50 joules and understand the reason for the energy loss.
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A circle is circumscribed around a regular octagon with side lemgths of 10 feet. Another circle is inscribed inside the octagon. Find the area. Of the ring created by the two circles. Round the respective radii of the circles to two decimals before calculating the area
The area of the ring created by the two circles is approximately 1374.63 square feet.
Let's first find the radius of the circumscribed circle. We can draw a diagonal of the regular octagon, which will be twice the length of one of its sides, forming an isosceles triangle with two radii of the circle.
The angle at the center of the circle between two adjacent sides of the octagon will be 360 degrees divided by 8, or 45 degrees.
The angle at the top of the isosceles triangle will be half of that, or 22.5 degrees. Using trigonometry, we can find the radius of the circumscribed circle:
[tex]$\sin(22.5^\circ) = \frac{opposite}{hypotenuse}$$\sin(22.5^\circ) = \frac{10}{2r}$$r = \frac{10}{2\sin(22.5^\circ)} \approx 21.21$[/tex]
Next, we can find the radius of the inscribed circle. Drawing radii from the center of the octagon to the points where it touches the circle, we can form 8 congruent isosceles triangles, each with a base of length 10 and two equal legs.
The angle at the top of each triangle will be half of the central angle between two adjacent sides of the octagon, or 22.5 degrees. Using trigonometry again, we can find the length of each leg of the triangle:
[tex]$\tan(22.5^\circ) = \frac{opposite}{adjacent}$$\tan(22.5^\circ) = \frac{r'}{5}$$r' = 5\tan(22.5^\circ) \approx 2.93$[/tex]
Now we can calculate the area of the ring created by the two circles:
[tex]$A = \pi R^2 - \pi r'^2$$A = \pi (21.21)^2 - \pi (2.93)^2 \approx 1374.63$ square feetTherefore, the area of the ring created by the two circles is approximately 1374.63 square feet.\\\\\\\\[/tex]
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If a spinner will land on red 45% of the time, yellow 15% of the time, and blue 40% of the time, what are the chances it wont land on red
Answer:
55%
Step-by-step explanation:
Chances it wont land on red = chances of blue + chances of yellow
= 55%
A bookstore is offering a 25% discount for a new book during a two-
week sale. After the sale, the book will sell for the regular price of
$32. 0. The store has a total of 200 copies of the book.
If all of the copies of this book are sold, what is the number of
discounted books that the store sells to make a total of $5440. 00?
Let x be the number of discounted books that the store sells during the sale. Then, the number of books sold at the regular price after the sale is 200 - x.
During the sale, the discounted price of the book is 0.75 * 32 = $24.
The revenue from selling x discounted books is:
R1 = 24x
The revenue from selling (200 - x) books at the regular price is:
R2 = 32(200 - x)
The total revenue from selling all the books is:
R = R1 + R2
We want to find the value of x such that the total revenue is $5440.00:
R = 5440
Substituting the expressions for R, R1, and R2, we get:
24x + 32(200 - x) = 5440
Simplifying and solving for x, we get:
24x + 6400 - 32x = 5440
-8x = -960
x = 120
Therefore, the store sells 120 discounted books during the sale to make a total of $5440.00.
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Mathematics help nedd
To solve the equation, we need to first simplify both sides:
(4x - 6)/5 + 1 = (x + 1)/5 - 2/5
Multiplying both sides by 5 to eliminate the denominator:
4x - 6 + 5 = x + 1 - 2
Simplifying further:
4x - 1 = x - 1
Subtracting x from both sides:
3x - 1 = -1
Adding 1 to both sides:
3x = 0
Dividing both sides by 3:
x = 0
Therefore, the solution to the equation is x = 0.
Answer: x=28
Step-by-step explanation:
Given: <A=68
Find: x
Reasoning:
<B = 2x+x
<B= 3x
<C=x they say the sides across from <C is same as other side so the
angles are the same
Solution:
All angles of a triangle =180
<A + <B + <C =180 >substitute
68 + 3x + x =180 > combine like terms
68 + 4x = 180 > subtract 68 from both sides
4x=112 >divide both sides by 4
x=28
Kevin and his family are going camping.the tent has a width of 20ft,and the sides are 12ft long.how high is the tent in the middle?round to nearest tenth
Therefore , the solution of the given problem of unitary method comes out to be length (12 ft) that is less than its width (20 ft), which is the case with the tent.
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The hypotenuses of two right triangles created by halving the triangle can be viewed as the two sides of the triangle. Next, we have
=> h² = (12/2)² - (20/2)²
=> h² = 36 - 100
=> h² = -64
The fact that the outcome is bad indicates that we made a mistake. In this instance, it is because a legitimate triangular prism cannot be formed using the specified dimensions.
A triangular prism cannot have a length (12 ft) that is less than its width (20 ft), which is the case with the tent.
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The given segment is the diameter of a circle bar cd the coordinates of c are (-3,5) and the coordinates of d are (6,-2) . find the center of the circle
To find the center of the circle, we need to find the midpoint of the diameter segment CD.
Using the midpoint formula, we can find the coordinates of the midpoint M:
Midpoint formula:
M = ( (x1 + x2)/2 , (y1 + y2)/2 )
Plugging in the coordinates of C (-3,5) and D (6,-2):
M = ( (-3 + 6)/2 , (5 - 2)/2 )
M = (1.5, 1.5)
Therefore, the center of the circle is at point M with coordinates (1.5, 1.5).
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13. d(-8, 1), e(-3, 6), f(7,4), g(2, -1) (distance formula)
The distances between the points are approximately 7.07, 10.20, and 7.07.
To find the distance between the points d(-8, 1) and e(-3, 6), we use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(-3 - (-8))^2 + (6 - 1)^2]
distance = √[5^2 + 5^2]
distance = √50
distance ≈ 7.07
To find the distance between the points e(-3, 6) and f(7, 4), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(7 - (-3))^2 + (4 - 6)^2]
distance = √[10^2 + (-2)^2]
distance = √104
distance ≈ 10.20
To find the distance between the points f(7, 4) and g(2, -1), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(2 - 7)^2 + (-1 - 4)^2]
distance = √[(-5)^2 + (-5)^2]
distance = √50
distance ≈ 7.07
So, the distances between the points are approximately 7.07, 10.20, and 7.07.
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complete question:
Determine the distance between DE, EF and FG.
D(-8, 1), E(-3, 6), F(7, 4), G(2, -1)
Una presa se construye en un rio. El nivel del agua del estanque esta dado por n = 4,5t + 28, dónde t es el tiempo en años. Traza la gráfica y determina el nivel del agua que tenía la presa al ser construida. (ayuda por favor)
The initial water level is given as follows:
28 units.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The function for this problem is defined as follows:
n = 4.5t + 28.
The intercept is of b = 28, representing the initial amount of water.
The graph is given by the image presented at the end of the answer.
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Evaluate h'(9) where h(x) = f(x) · g(x) given the following.• f(9) = 9• f '(9) = −1.5• g(9) = 3• g'(9) = 2h'(x) =
In order to evaluate h'(9), we need to use the product rule, which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function. Mathematically, this can be expressed as:
(h(x))' = f(x)g'(x) + g(x)f'(x)
Using the given values, we can substitute them into the formula and solve for h'(9):
h'(x) = f(x)g'(x) + g(x)f'(x)
h'(9) = f(9)g'(9) + g(9)f'(9)
h'(9) = 9(2) + 3(-1.5)
h'(9) = 18 - 4.5
h'(9) = 13.5
Therefore, the value of h'(9) is 13.5.
In simpler terms, the product rule tells us that when we have a function that is the product of two other functions, we can find the derivative of that function by multiplying one function by the derivative of the other and adding it to the other function multiplied by the derivative of the first. In this case, we have two functions f(x) and g(x), and we use their respective values and derivatives to find the derivative of their product h(x).
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You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find the probability of p(odd or multiple of 5)
The probability we want to get is:
p(odd or multiple of 5) = 7/12
How to find the probability?The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.
The numbers that are odd or multiples of 5 in the set of outcomes are:
{1, 3, 5, 7, 9, 10, 11}
So 7 outcomes out of 12, then the probability is:
P = 7/12
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A bank is offering 3. 5% simple interest on a savings account. If you earned $525 in interest in 2 years, how much did you deposit in the savings?
The amount deposited is 7500 in the bank with 3. 5% simple interest on a savings account.
To solve this problem, we need to use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (amount deposited)
r = Interest rate per year (as a decimal)
t = Time (in years)
In this case, we know that the interest rate is 3.5% or 0.035 as a decimal.
We also know that the interest earned is $525, and the time period is 2 years.
So, we can plug in these values and solve for the principal:
525 = P * 0.035 * 2
Simplifying the equation, we get:
525 = 0.07P
Dividing both sides by 0.07, we get:
P = 7500
Therefore, the amount deposited in the savings account was $7500.
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Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol
(,,)
(
μ
,
p
,
σ
)
for the indicated parameter.
An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.
Group of answer choices
0
H
0
:
<0. 0016
p
<
0. 0016
1
H
1
:
≥0. 0016
p
≥
0. 0016
0
H
0
:
>0. 0016
p
>
0. 0016
1
H
1
:
≤0. 0016
p
≤
0. 0016
0
H
0
:
=0. 0016
p
=
0. 0016
1
H
1
:
<0. 0016
p
<
0. 0016
0
H
0
:
=0. 0016
p
=
0. 0016
1
H
1
:
>0. 16
The null hypothesis (H₀) and the alternative hypothesis (H₁) in symbolic form for this scenario are:
H₀: p = 0.0016 (the true proportion of fireflies unable to produce light is equal to 16 in ten thousand)
H₁: p < 0.0016 (the true proportion of fireflies unable to produce light is fewer than 16 in ten thousand)
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Abd and dbc are linear pairs, and abd and evc are vertical angles. if mabd = 5(2x + 1), mdbc= 3x + 6, and mebc = y+135/2, select all statements that are true
The following statements are true:
mabd + mdbc = 180 degrees
mabd = mevc
What are the true statements given that abd and dbc are linear pairs, abd and evc are vertical angles, and the measures are given?According to the definition of linear pairs, the two angles add up to 180 degrees. Therefore, mabd + mdbc = 180 degrees.
According to the definition of vertical angles, they have the same measure. Therefore, mabd = mevc.
Since abd and evc are vertical angles, and mabd = mevc, then mabd = mebc. Therefore, we can substitute mabd in the equation mebc = y+135/2 to get 5(2x + 1) = y+135/2.
We can solve for y to get y = 10x + 260.
Now we can substitute this value of y into the equation mebc = y+135/2 to get mebc = 10x + 347.5.
Therefore, none of the statements in the question that mention mebc are necessarily true or false, since we don't have enough information about the value of x to determine its measure.
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