The Rate at which she practices piano per day will be 34 minutes.
We know that Proportional relationships are relationships between two variables like x and y when their ratios got equivalent.
For example, [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex]. This is the proportional relationship between the variables, a, b, c, and d. In this a is equal to c (a = c) and b is equal to d(b = d).
In our question, the proportional relationship between total minutes (m) and the number of days (d) is given by:
m = 34d.
We need to find the rate, which can be defined as the total minutes spent on practice piano per day.
Minutes spent = m
Days = d
Rate = [tex]\frac{m}{d}[/tex]
So, we know, m = 34d
[tex]\frac{m}{d}[/tex] = [tex]\frac{34}{1}[/tex] = 34
Hence, The rate is 34 minutes per day.
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Refer to Question 1. If a sample of 10 bottles were selected and the average number of ounces was 12.005, what is the value of the test statistic? The population standard deviation is 0.01. Round your answer to three decimal places.
The test statistic has a value of -633.6915 if a sample mean of 10 bottles was chosen, and the average number of ounces was 12.005.
As stated. Sample mean is 10.
12.005 people on average.
0.01 is the standard deviation.
The test statistic's value is -633.6915 when calculated using the formula:
T = mean - average population / s/root n
= 10-12.005 / 0.01/3.16
= -2.005 /0.0031
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both pays tribute to a person, a group, an institution, or an idea and is essentially the same as an informative speech.
The correct answer is (d) which is commemorative speech
Given that,
A speech that praises, honors, recognizes, or pays tribute to a person, an event, an idea, or an institution
Given choices : a. speech of award b. introductory speech c. speech of tribute d. commemorative speech
What is commemorative speech ?
An address of honor given to celebrate or extol the virtues of a person, organization, place, event, idea, or institute is known as a commemorative (or ceremonial, or epideictic) speech. This speech goes beyond simple praise or thanks. It is more of an appreciation and celebration.
So, The correct answer is (d) which is commemorative speech
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If the perimeter of this isosceles triangle is at most 45 centimeters, which inequality could be used to find the value of p?.
The inequality that can be used to find p is 7p -12 < 45.
What is a Triangle?
A triangle is a polygon with three sides, three angles, and three vertices.
The perimeter of the given triangle is at most 45 centimeters.
The perimeter of a triangle is equal to the sum of all sides.
The sides given is 3p-6 , 3p-6 ,p
So,
3p-6 +3p-6 +p < 45
7p -12 < 45
Hence the answer is, the inequality that can be used to find p is 7p -12 < 45.
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What’s more 90% or 29/30
Answer:
29/30
Step-by-step explanation:
29/30 as a percentage is %96.67 which is more than 90%
college students and stds: a recent report estimated that 25% of all college students in the united states have a sexually transmitted disease (std). due to the demographics of the community, the director of the campus health center believes that the proportion of students who have a std is lower at his college. he tests h0: p
Yes because (50)(0.25) and (50)(1 - 0.25) are both at least 10. This means we can use the normal distribution to model the distribution of sample portions.
What is a Normal distribution in statistics?
Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.
25% = 0.25
Then (50)(0.25) > 10 and also (50)(1 - 0.25) > 10.
Hence, we can use the normal distribution to model the distribution of sample portions.
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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
0 , x<0
f(x) = ((x^2)/4) , 0 <= x <= 2
1 , 2<= x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) P(X %u2264 1)
(b) P(0.5 %u2264 X %u2264 1)
(c) P(X > 1.5)
(d) The median checkout duration [solve 0.5 = F(mew)]
(e) Use F'(x) to obtain the density function f(x)
(f) Calculate E(X)
(g) Calculate V(X) and %u03C3x
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge
E[h(X)].
By using the concept of probability, it can be calculated that
a) P(X [tex]\leq[/tex] 1) = 0.25
b) P(0.5 [tex]\leq[/tex] X [tex]\leq[/tex] 1) = 0.1875
c) P(X > 1.5) = 0.4375
d) Median = 1.414
e) F'(X) = 0.5x , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2
0, otherwise
f) E(X) = 1.33
g) V(X) = 0.2311, SD(X) = 0.4807
h) E(h(X)) = 2
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
The cdf is
f(x) = [tex]\left \{ {\frac{x^2}{4}},{ 0 \leq x \leq 2} \atop {1, x=2}} \right.[/tex]
Now,
a) P(X [tex]\leq[/tex] 1) = [tex]\frac{1^2}{4} = 0.25[/tex]
b) P(0.5 [tex]\leq[/tex] X [tex]\leq[/tex] 1)
= [tex]\frac{1^2}{4} - \frac{0.5^2}{4}\\\\\frac{3}{16}\\\\0.1875[/tex]
c) P(X > 1.5) = 1 - P(X [tex]\leq[/tex] 1.5)
[tex]1 - \frac{1.5^2}{4}[/tex]
0.4375
d) Let [tex]\mu[/tex] be the median
P(x [tex]\leq \mu[/tex]) = 0.5
[tex]\frac{\mu^2}{4} = 0.5[/tex]
[tex]\mu^2 = 0.5 \times 4 =2\\\mu = \sqrt{2}\\\mu = 1.414[/tex]
e) F'(x) =
[tex]\frac{2x}{4}, 0 \leq x \leq 2\\0, otherwise[/tex]
F'(X) = 0.5x , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2
0, otherwise
f) E(x) =
[tex]\int_0^2 x \times 0.5 xdx\\=0.5 \times \frac{x^3}{3} |_0^2 \\=0.5 \times \frac{2^3}{3}\\=\frac{4}{3}\\=1.33[/tex]
g) V(X) = E([tex]X^2[/tex]) -[tex](E(X))^2[/tex]
E(X^2) =
[tex]\int_0^2x^2(0.5x)dx \\0.5 \times \frac{x^4}{4}|_0^2\\2[/tex]
[tex]V(X) = 2 - (1.33)^2[/tex]
V(X) = 0.2311
SD(X) = [tex]\sqrt{0.2311} = 0.4807[/tex]
h) h(X) = [tex]X^2[/tex]
E(h(X)) = [tex]\int_0^2X^2({0.5X)dx[/tex]
= [tex]0.5 \frac{x^4}{4}|_0^2[/tex]
= [tex]0.5 \times \frac{2^4}{4}[/tex]
= 2
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Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.
The process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition is shown below:
What is a polynomial?A polynomial is the quotient (with or without a remainder). multiplying this polynomial by the polynomial's divisor We get a polynomial with updated exponents and coefficients, so it's closed under multiplication.
A polynomial is defined as an equation composed of variables, constants, and exponents that are joined together using mathematical operations such as addition, subtraction, multiplication, and division.
If no remainder exists, the dividend is equal to the quotient multiplied by the divisor.
The quotient and divisor, as well as their product, the dividend, are both polynomials.
If there is a residual, it is added to the product of the quotient and divisor.
The polynomial dividend is the sum of the remainder and the product of the quotient and divisor.
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What is the SAS congruence theorem?.
The SAS Congruence Theorem means proving congruence by Side Angle Side Theorem .
The two figure which are "Congruent" means that the two figures are same in all aspects including shape and size .
The term SAS Congruence is also known as Side Angle Side congruence, which is used to describe relation of two figures that are congruent.
Under this criterion, if two sides of a triangle are equal to two sides of another triangle, and the angle formed by these sides in two triangles are equal, then these two triangles are congruent.
Therefore , The SAS Congruence Theorem means proving congruence by Side Angle Side Theorem .
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The cost of food at a wedding is $150 plus $17 per person attending. Write an equation
that gives the total cost of food as a function of the number of people attending. What is
the cost for 47 people?
a. y = 17x - 150; $649
the cost for 47 people?
A. y = 17 -150; $649
B. y = 150x +17; $7067
C. y = 17x + 150; $949
D. y = 150x - 17; $7033
Answer:
$949
Step-by-step explanation:
→ Write a function
y = 150 + 17x
→ Substitute in 47
949
Could the students use 24 paper squares to make quilts with 5 rows of
paper squares. Use the array I attached at the bottom to solve this pls.
From the given array and by division, we can say that; No, it would not be possible for the students to use 24 paper squares to make quilts with 5 rows of paper squares.
How to solve division word problems?We are told that the students want to use 24 paper squares to make quilts with 5 rows of paper squares.
To get the number of possible rows they can make from this, what we need to do is to divide the number of required rows by the number of paper squares to the maximum number of paper squares for each row. Thus;
24/5 = 4.8
Thus, since it is 4.8 , it means that they would not have enough for five rows.
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3. The math club and the science club had fundraisers to buy supplies for a hospice. The math
club spent $235 buying six cases of juice and one case of bottled water. The science.
club spent #110 buying four cases of juice and two cases of bottled water. How much
did a case of juice cost? How much did a case of bottled water cost?
Cost of Case of Juice:
Cost of Case of Water:
Cost of Case of Juice: 20
Cost of Case of Water: 15
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Here, we let
cost of a case of juice = x
cost of a case of water = y
6x + 1y = 135...(1)
4x + 2y = 110.....(2)
Now, we multiply equation (1) by 2 and equation (2) by 1 and we get
12x + 2y = 270
4x + 2y = 110
Now, we subtract equation (1) from equation (2) and we get
8x = 160
x = 20
and y = 15
Hence, the Cost of a Case of Juice: 20
Cost of Case of Water: 15
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As you finish listening to your favorite compact disc (CD), the CD in the player slows down to a stop. Assume that the CD spins down with a constant angular acceleration. If the CD rotates clockwise at 500 rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60 s with constant angular acceleration, what is ααalpha, the magnitude of the angular acceleration of the CD, as it spins to a stop? How many revolutions does the CD make as it spins to a stop?
20.1 rad/s^2
10.8 revolutions
CD makes approximate 10.9 resolutions to make as it spins to a stop.
Here we have to determine the number of rotations N ,the CD spun before it comes to a stop. We first need to express the initial angular velocity ω , in terms of rad/s by applying the conversion factor ω = 2πf × 1/60 min/s where f = 500 rpm.
Then we apply the equation for the angular displacement of the CD upon coming to a stop,
Ф= (ωi²-ωf²)/2α , We have the final angular velocity of ωf = 0 rad/s and an angular acceleration of α = 20.1 rad/s² Now we proceed with finding Φ.
Ф= (ωi²-ωf²)/2α
= {(2Πf×1/60min/s)² - ωf²}/2α
= {(2π(500 rpm) × 1/60 min/s) -0 rad/s}/2(20.1 rad/s²)
≈ 68.19792... rad
Now we divide the answer by 2π to find the answer ,N, or
N = Ф/2π
N = (68.19792... rad)/2ππ
N ≈ 10.9 revolutions
So, CD makes approximate 10.9 revolutions to make it stop.
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which two features of igneoous rocks are determined by their cooling rate
It is crystal size and rock texture.
Volcanic rocks are another name for extrusive rocks. According to their texture and mineral or chemical makeup, igneous rocks are categorized. The rate of cooling affects the texture of the rock. The crystals grow larger as the rock cools more slowly.
Thanks,
As the last answer for today.
Happy Thanksgiving
- Eddie E.
FIND THE ERROR A classmate is finding the slope of the line that passes through (-2, 8) and (4, 6). Describe the error. What feedback can you provide to help them correct the error?
The slope of the line passing through the points (-2, 8) and (4, 6) is -1/3 .
We know that the slope of a line passing through two given points is calculated by the formula:
[tex]{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}[/tex]
Now the given points are (-2, 8) and (4, 6)
Hence slope = (6-8) / (4-(-2)) = -2/6 = -1/3
The slope of a line indicates its slope and direction. Finding the slope of lines in a coordinate plane can help predict whether two lines are parallel, perpendicular, or have no relationship at all without actually using a compass.
The slope of a line can be determined using any two distinct locations on the line. The slope of a line formula is used to determine the ratio of "vertical change" to "horizontal change" between two different points on a line. In this essay, we will understand the slope-finding method and its uses.
Therefore the slope of the line is -1/3
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2. Find the sum, S, for the arithmetic series described? Remember to use the formula
Using the given formula, the sum of S(n) for the arithmetic series is 565.5.
In the given question we have to find the sum S(n) for the arithmetic series
The given formula is S(n)=n/2 {a(1)+a(n)}
The given values are a(1)=12, a(n)=75,n=13
We just have to put values in given formula
S(n)=n/2 {a(1)+a(n)}
S(n)=13/2 (12+75)
S(n)=6.5*87
S(n)=565.5
Hence, the sum of S(n) for the arithmetic series described is 565.5.
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A dot plot titled Number of books read this month going from 0 to 5. 0 has 4 dots, 1 has 8 dots, 2 has 5 dots, 3 has 0 dots, 4 has 3 dots, and 5 has 2 dots.
Use the dot plot to help you complete the statements.
A cluster is located at 4 and 5 and another is at
.
A gap is located at
.
A peak is located at
.
We can see two clusters (a group of values that stick together):
One cluster at 0, 1 and 2 and the second one at 4 and 5.A gap is at 3 (no dots, no books read)A peak is at 1 (greatest number of dots, 8 books read)Please attach the picture (dot plot or other graph or figure) next time.
What is the mean of first 10 whole numbers?.
The mean of the first 10 whole numbers is 4.5.
What is mean?
A amount that includes a price intermediate between those of the acute members of some set is known as mean.
Main body:
In this question we have to find the mean of the first 10 whole numbers. Whole numbers are all non-negative integers which start from 0. Now the mean of the first 10 whole numbers will be the mean of numbers from 0 to 9, as the count of numbers from 0-9 is 10. Use this concept to reach the answer.
Mean of numbers is equal to the sum of the numbers divided by the count of the numbers that is
Mean = sum of numbers/ total numbers …………………….. (1)
To find the mean of the first 10 whole numbers, we will find the sum of numbers from 0 to 9 as 0-9 are the first 10 whole numbers.
So, the sum of the first 10 whole numbers is 0+1+2+3+4+5+6+7+8+9=45.
Now putting the values in equation (1) we get, mean = 45/10 = 4.5
Hence, the mean of the first 10 whole numbers is 4.5.
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firm x can forward integrate into distribution distributors are highly dependent on the product necessary distribution networks are tightly held by a single distributor end-users have inelastic demand for the product
Firm X is least likely to capture gains from the innovation when end users have inelastic demand for the product.
When the demand is inelastic for the product, firm X will be least likely to capture the gains, because the firm will not able to adjust prices for any added production cost.
Production costs allude to the costs an organization causes by assembling an item or offering support that produces income for the organization. Production costs can incorporate various costs, for example, work, unrefined components, consumable assembling supplies, and generally above.
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Write an equation in point-lope form of the line that pae through the given point and with the given lope m. (-6,1); m = 6
The equation of line passes through (-6,1) and has slope 6 will be y=6x+37.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the line passes through (-6,1) and has a slope of 6,
The equation of line passes through (-6,1) and has slope 6 is found as,
y-y₁=m(x-x₁)
y-1=6(x-(-6)
y-1=6(x+6)
y-1=6x+36
y=6x+36+1
y=6x+37
Thus, the equation of line passes through (-6,1) and has slope 6 will be y=6x+37.
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Find the missing variables. Round to the nearest tenth if necessary.
The value of a and b are; 4.8 and 10.8 respectively.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We have been given a figure which shows that;
Let x, y z, and u lines are parallel.
Therefore, by using proportion we can say that
a/ 12 = 4/ 10
thus, a = 4/ 10 (12)
a =2(12)/ 5
a = 24/5
a = 4.8
Now, 12/b = 10/8
b = 12 (8/10)
b = 6(8)/ 5
b 54/5
b = 10.8
Hence, tha value of a and b are; 4.8 and 10.8 respectively.
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the principle that individuals will be given only the level of access that is appropriate for their specific job role or function is called .
The principle that individuals will be given only the level of access that is appropriate for their specific job role or function is called Principle of Least Privilege (PoLP)
What is Privilege Creep?The IT team will frequently need to re-grant credentials so that users may accomplish certain tasks when businesses choose to revoke all administrative capabilities from business users. For instance, many commercial off-the-shelf (COTS) apps and legacy programmes used in enterprise IT systems need privileges to function. The IT staff needs to restore local administrator access to business users so they can utilise these approved and necessary programmes.
As privileges are rarely removed once they have been granted again, organisations may find that many of their users eventually have local administrator rights once more.A user is only provided the minimal levels of access - or permissions - required to carry out his or her job functions under the principle of least privilege (PoLP), which is a notion in information security. It is widely regarded as a best practise in cybersecurity and is a crucial step in safeguarding privileged access to highly valuable data and assets. Beyond human access, least privilege applies.
Least privilege :Applications, systems, and linked devices that require rights or permissions to carry out a necessary operation can all use the paradigm. Least privilege enforcement makes sure the machine tool only has the minimal access required. A mechanism to centrally store and secure privileged credentials is necessary for least privilege enforcement, combined with adaptable policies that can balance cybersecurity and compliance needs with operational and end-user needs.
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Let random variable R represent the the number of visitors to a certain museum during a given day. The following table shows the probability distribution of the random variable.Which of the following claims about the distribution of random variable R is best supported by the histogram? A. The most likely number of visitors to the museum on a given day is between 450 and 500. B. The mean number of visitors to the museum is much less than the median number of visitors. C. The mean number of visitors to the museum is much greater than the median number of visitors. D. On a given day, the number of visitors from 100 through 500 will occur with equal probabilities. E. On a given day, it is equally likely for the museum to have less than 300 visitors as it is to have more than 300 visitors.
The mean number of visitors to the museum is much greater than the median number of visitors.
What is median?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simples to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.
Option (a) is unquestionably incorrect since the probability that there will be 450 to 500 investors is extremely low (0.05), and investors are not, in fact, the visitors with the highest possibility of visiting the museum.
We will take the midpoint value of the class intervals as the given distribution is expressed as class intervals in order to simplify the data in this distribution.
Mean = 306
Since the mean(306) is coming out to be greater than the median (300)
Therefore the correct option is,
(C) the mean number of visitors to the museum is much greater than the median number of visitors.
Hence the mean number of visitors to the museum is much greater than the median number of visitors.
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consider a wire of length . the wire is to be cut into two pieces of length and . suppose the length is used to form a circle of radius and the length is used to form a square with side of length . what value of will minimize the sum of their areas?
For the maximum area, the wire should be bent in the form of a circle and for the minimum area, the wire should bend into an equilateral triangle.
What is the area of any geometrical shape?
The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.
Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.
One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.
Perimeter = 3 m
3*side = 3 m
side = 1 m
Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4} $ $ \times $ (side)^2$[/tex]
A = 0.4330 m² -----(I)
Now the circumference of the circle = 5 m
2π×r = 5
r = 5/2π
r = 0.7957 m.
Now the area of the circle = π×r²
= 3.14 × (0.7957)²
= 1.988 m² --------(II)
From (I) and (II), we can say that
Area of the equilateral triangle < Area of the circle
Hence, for the maximum area, the wire should be bent in the form of a circle and for the minimum area, the wire should bend into an equilateral triangle.
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Which is a term in both the sequence f'n )= F n 1 )+ 4?.
The first term in both sequences f(n) = f(n - 1) + 4 and f(n)=3(5)^(n-1), is -1.
What is a geometric sequence?
The sequence where each word is varied by another by a common ratio is known as a geometric progression or geometric sequence. When we add a constant (which is not zero) to the term before it, the sequence's subsequent term is created. The following symbols stand in for it: a, ar, ar2, ar3, ar4, etc.
Geometric Progression (GP), a form of sequence in mathematics, is a series in which each subsequent term is created by multiplying each preceding term by a set integer, known as a common ratio. A geometric sequence of integers that follows a pattern is another name for this development.
We have,
f(n) = f(n - 1) + 4
And,
f(n) = 3(5)ⁿ⁻¹
f(1) = 3
Putting n=1
f(n) = f(n - 1) + 4
Now,
f(1) = f(1 - 1) + 4
3 = f(0) + 4
⇒ f(0) = 3 - 4 = -1
Here f(0)= -1
and f(n) = 3(5)ⁿ⁻¹
Now,
f(1) = 3 × (5)¹⁻¹ = 3 × (5)⁰ = 3 × 1 = 3
f(1) = 3
Hence, the first term in both sequences is -1.
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Find the absolute maximum and minimum of the function f(x,y)=x2+y2 subject to the constraint x4+y4=1296. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: attained at ( , ), ( , ), ( , ), ( , ). Absolute maximum value: attained at ( , ), ( , ), ( , ), ( , ).
Minimum value and maximum value attained at 36 and [tex]2\sqrt{648}[/tex] respectively.
What is maxima and minima ?Maxima and minima of a function are the largest and smallest value of the function respectively either within a given range or on the entire domain. Collectively they are also known as extrema of the function. The maxima and minima are the respective plurals of maximum and minimum of a function.
Given that f = [tex]x^{2}[/tex]+ [tex]y^{2}[/tex]
Let g = [tex]x^{4}[/tex] + [tex]y^{4}[/tex] = 1296
By Lagrange Multipliers: grad(f) = λ grad(g)
or <2x, 2y> = λ <4[tex]x^{3}[/tex], 4[tex]y^{3}[/tex]>
Equating like entries:
2x = 4λ[tex]x^{3}[/tex]=> x(2λ[tex]x^{2}[/tex] - 1) = 0
2y = 4λ[tex]y^{3}[/tex] => y(2λ[tex]y^{2}[/tex] - 1) = 0
Now there possible 3 cases :
(i) If x = 0, then [tex]x^{4}[/tex] + 0 = 1296 => x = ±6.
(ii) If y = 0, then 0 + [tex]y^{4}[/tex]= 1296 => y = ±6
(iii) Otherwise, we have 2λ[tex]x^{2}[/tex] - 1 = 0 = 2λ[tex]y^{2}[/tex] - 1 => λ([tex]x^{2}[/tex] - [tex]y^{2}[/tex]) = 0.
If λ = 0, then both x = 0 and y = 0 and this is not possible since [tex]x^{4}[/tex]+ [tex]y^{4}[/tex]= 1296.
Otherwise,[tex]x^{2}[/tex] = [tex]y^{2}[/tex] ⇒ [tex]x^{4}[/tex] + [tex]x^{4}[/tex] = 1296 => x = ± [tex]648^{1/4}[/tex]
(with x and y will have different signs)
Now we have following critical points (in lexicographic order):
(- [tex]648^{1/4}[/tex], - [tex]648^{1/4}[/tex])
(- [tex]648^{1/4}[/tex], 648^(1/4))
(-6, 0)
(0, -6)
(0, 6)
(6, 0)
( [tex]648^{1/4}[/tex], - [tex]648^{1/4}[/tex])
( [tex]648^{1/4}[/tex], [tex]648^{1/4}[/tex])
Minimum value attained at f(±6, 0) = f(0, ±6) = 36
Maximum value attained at f(± [tex]648^{1/4}[/tex], [tex]648^{1/4}[/tex]) = f(± [tex]648^{1/4}[/tex], - [tex]648^{1/4}[/tex]) = [tex]2\sqrt{648}[/tex]
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HELP
what is the output of the function when the input is 0?
Answer: The input is the x variable and the output is the y variable, so the equation is y=0 which is just a line on the x axis
**the thicker line in the picture is what the line should look like.
a culture of bacteria has an initial population of 8600 bacteria and doubles every 5 hours. using the formula p t
The exponential growth formula for bacteria growth is P(t) = 8600 [tex](2)^(t/5)[/tex].
What is exponential growth?
Exponential growth is a pattern of data that exhibits a greater increase over time, resulting in an exponential curve. Exponential is also a mathematical term meaning "with exponents". For example, if you raise a number to the 10th power, the number increases exponentially. Exponential growth is growth that increases at a constant rate.
Here given take Initial number of bacteria = 8600. rate of growth = 2.
It doubles every year. Then doubling time = 5 hours.
Now population growth after t years,
P(t) = Po [tex](2)^(t/5)[/tex]
=> P(t) = 8600 [tex](2)^(t/5)[/tex]
Therefore exponential growth formula is P(t) = 8600 [tex](2)^(t/5)[/tex].
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The length of a rectangle is 3 times the width. The difference between the length and the width is 8.
The length of the rectangle is 12 units long.
What is a Rectangle?A rectangle is a geometric figure with equal opposite sides.
The angle between two consecutive sides is 90 degrees.
Area of rectangle = length x width. Perimeter of rectangle = 2 (length + width).
let's assume,
length = l, width = w
Given the,
The length of the rectangle is 3 times the width
l = 3w
The difference in length and width is 8 feet
l-b = 8
According to equations 1 and 2
3w - w = 8
2w = 8
w = 4
Substitute into expression 1
l = 3(4)
l = 12 units.
So the rectangle is 12 units long.
your question is incomplete, but most probably the full question was
The length of a rectangle is 3 times the width. The difference between the length and the width is 8 feet. Determine the rectangle's length
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TRUE/FALSE. the altitude from the vertex angle to the base of an isoceles triangle is also a prependicular bisector
Its true that perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.
Given that,
We have to find perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.
We know that
Let us take a triangle ABC and draw an altitude CD
Being an isosceles triangle
In ΔACD and ΔCDB
CD=CD (common )
CA=CB ( equal opposite sides)
∠ A=∠ B (the angle between the opposing sides is also equal)
Triangle ACD and triangle CDB are congruent
So , AD=DB by CPCT
So, its true
Therefore, Its true that perpendicular bisectors also exist for the height from an isosceles triangle's vertex angle to its base.
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Which equation can replace 3x plus 5y equals 59 in the original system and still produce the same?.
13x = 39 can be used in place of the equation 3x + 5y = 59.
Which of the following ordered pairs represents a solution to the linear equation system 2x 3y equals 6?Only D(0,2) falls on the line, as can be seen. Another way to check is to plug the values of the points' x and y coordinates into the equation 2x3y=6, which, as can be seen, only has one solution (0, 2).
What is the name of the equation system that has a solution?An assignment of values to the variables x1, x2,..., xn such that each of the equations is satisfied is the definition of a solution of a linear system. The solution set is the collection of all conceivable solutions.
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