The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.
What is the length and the width of the rectangle?The formula used in calculating the perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width of the rectangle w = xLength of the rectangle l = 8xPerimeter P = 378ftPlug the given values into perimeter formula and solve for x .
P = 2( l + w )
378 = 2( 8x + x )
378 = 2( 9x )
378 = 18x
18x = 378
x = 378/18
x = 21
Now, we find the length and width of the rectangle.
Width of the rectangle w = x = 21ft
Length of the rectangle l = 8x = 8( 21 ) = 168ft
Therefore, the width of the rectangle is 21ft while its length is 168ft.
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How do I determaine the best answer for this?
The function 1 is,
[tex]y=\frac{1}{3}x[/tex]So rate of function is 1/3.
From the table function 2 it can be observed that the value of y is one third of x. The mathematical expression of function 2 is,
[tex]y=\frac{1}{3}x[/tex]So rate of function 2 is also 1/3.
Thus function 1 and function 2 have the same rate, 1/3.
In the figure below, line LN is tangent to circle O.
Which of the following can be concluded from the information?
A) ON is a radius of the circle.
B) angle MNO is a right triangle.
C) angle ONM is an obtuse angle.
D) angle OMN is a central angle of circle O.
The right information of the circle is as follows:
Triangle MNO is a right triangle.How to find the correct information of the circle?The line LN is the tangent to the circle O.
Tangent to a circle is a line that touches the circle at one point.
The point where tangent meets the circle is called point of tangency.
The tangent is perpendicular to the radius of the circle, with which it intersects.
Tangent to a circle is always perpendicular to the radius.
Therefore, the correct information from the circle can be found as follows:
Line ON is not the radius of the circle. The radius of a circle is a straight line from the centre of a circle to the circumference of a circle.The triangle MNO is a right triangle is the right information of the circle.Angle ONM is not an obtuse angle because it's less than 90 degrees. The angle OMN is 90 degrees. Therefore, the sum of the angles ONM and MON is equals to 90 degrees.OMN is not the central angle of the circle. The central angle of the circle is angle MON.learn more on tangent to circle here:https://brainly.com/question/4331689
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Answer: A) ON is a radius of the circle
Step-by-step explanation:
The line ON starts from the midpoint of the circle showing that it is half of the distance(radius)
About 13,800 adult Pacific newts made their annual migration between November 2020 and March 2021. Roughly 2/5 didn't survive the trip. About how many newts survived crossing the road?
If 13800 adult Pacific newts made their annual migration between November 2020 and March 2021, Roughly 2/5 didn't survive the trip, then the number of newts survived crossing the road is 8280 newts
The number of adult Pacific newts made their annual migration = 13800
Roughly 2/5 didn't survive the trip
Then the number of newts didn't survive = 13800×(2/5)
= 13800×0.4
= 5520 newts
To find the number of newts survived, we have to use subtraction
The number of newts survived crossing the road = 13800-5520
= 8280 newts
Hence, If 13800 adult Pacific newts made their annual migration between November 2020 and March 2021, Roughly 2/5 didn't survive the trip, then the number of newts survived crossing the road is 8280 newts
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A player tosses a fair coin n times. Each time, if the coin lands on Head, the player
win a dollar, otherwise, the player loses a dollar. What is the expected earning of the
player? What is the variance of the earning of the player? Now the player apply a
new strategy: the player will play the game until he gets a head. What is the expected
earning of the new strategy? Does the result depend on n?
the ______ is a point at which three or more lines intersect OPTIONS;A.median B.angleC.point of concurrencyD.perpendicular bisector
ANSWER:
C. point of concurrency
STEP-BY-STEP EXPLANATION:
The only point where these lines cross each other is called the point of concurrency.
Therefore:
The point of concurrency is a point at which three or more lines intersect.
The correct answer then is C. point of concurrency
what's the result of adding these two polynomials: (2x+y+1) + (2x⁶-y+1)? I'm doing a test and the correct answer says is 4x⁶-2y+1 but I'm not very sure it is the correct one. Can someone help me? :3
Answer
[tex]\begin{equation*} 2x^6+2x+2 \end{equation*}[/tex]Step-by-step explanation
Given the polynomials:
[tex]\begin{gathered} 2x+y+1 \\ \text{ and} \\ 2x^6-y+1 \end{gathered}[/tex]To add them we need to add the similar terms (terms with the same variable and degree), as follows:
[tex]\begin{gathered} (2x+y+1)+(2x^6-y+1)= \\ =2x^6+2x+(y-y)+(1+1)= \\ =2x^6+2x+2 \end{gathered}[/tex]Turtoneom Has a half-life of four years. Suppose a company has 400 mg of tortoni him. How much will be left after 20 years?
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &400\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &4 \end{cases} \\\\\\ A=400\left( \frac{1}{2} \right)^{\frac{20}{4}}\implies A=400\left( \frac{1}{2} \right)^5\implies A=12.5[/tex]
The function f(x) = 1(3)x models the number of virus cells present in a sample after x minutes. About how many cells will be present after 1 1/2 minutes? (round to the nearest whole number)
Answer:
The number of cells that will be present is;
[tex]5\text{ cells}[/tex]Explanation:
Given that the function f(x) models the number of virus cells present in a sample after x minutes.
[tex]f(x)=1(3)^x[/tex]Aftere 1 1/2 minutes, the number of cells present can be calculated by substituting;
[tex]x=1\frac{1}{2}[/tex]In the model.
Substituting, we have;
[tex]\begin{gathered} f(x)=1(3)^x \\ f(1\frac{1}{2})=1(3)^{1\frac{1}{2}} \\ f(1\frac{1}{2})=1(3)^{1.5} \\ f(1\frac{1}{2})=5.196 \\ f(1\frac{1}{2})\approx5 \end{gathered}[/tex]Therefore, the number of cells that will be present is;
[tex]5\text{ cells}[/tex]Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the time it takes to run a mile. Is the random variable x discrete or continuous?
The variable represents time. The time in which a person runs a mile will depend on the speed of that person, and that can take almost any value, thus, here the variable is continuous.
Is the variable discrete or continuous?First, when a variable is discrete and when it is continuous?
A variable is discrete if it only can take some selected values on a given interval, while a variable is continuous if it can take any value (or at least a dense set) of values in that interval.
For example, the numbers that one can roll on a dice form a discrete set, because the values can only be {1, 2, 3, 4, 5, 6}, just to given an example.
Now, in this case, the variable represents time. Time almost always is a continuous variable, in this case, the time is the time in which a person runs a mile. So that variable can take almost any value (depends on the speed of the person).
So we conclude that this is a continuous variable.
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Micaela is working two summer jobs, making $13 per hour tutoring and making $10
per hour landscaping. In a given week, she can work at most 13 total hours and must
earn a minimum of $140. If a represents the number of hours tutoring and y
represents the number of hours landscaping, write and solve a system of inequalities
graphically and determine one possible solution.
The equations will be a+ y ≤ 13, since Micaela can't work more than 13 hours and also she needs to earn at least $140 each week, so other equation will be 13a + 10y ≥ 140.
What is inequalities?Inequality, a declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
a = number of hours spent tutoring
y = number of hours spent landscaping
Micaela can't work more than 13 hours, so a + y ≤ 13.
Also, she needs to earn at least $140 each week, so 13a + 10y ≥ 140.
Using intercepts, you may graph things in this format on paper. They must be transformed into slope-intercept form in order to be graphed on a standard graphing calculator.
For instance, if a = 12 and y = 2, then a + y = 13 hours, and 12(13) + 2(10) = $176. Micaela puts in her maximum number of hours and earns more than she should.
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Using the side lengths
Given
The three sides are given 24, 30 and 18.
Explanation
To find the triangle is acute, obtuse or right triangle.
To determine whether the triangle is acute, right, or obtuse.add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute.
A
If the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.
Now c.
[tex]\begin{gathered} 30^2=24^2+18^2 \\ 900=576+324 \\ 900=900 \end{gathered}[/tex]Answer
Hence the sum of the squares of the two smaller sides is equal to the square of the largest side , then it is right triangle.
The correct option is A.
A square has an area of 25cm squared. What is the length of each side?
(b) A square has a perimeter of 28cm. What is the length of each side?
Step-by-step explanation:
the length of each side will be 5 because the area of a square is L×Lwhich can also be said as 5×5=25
2. perimeter is addition of all sides which is solved as L+L+L+L= 28cm
also: 7+7+7+7= 28cm
Before art class starts, Gordon makes sure that each table has a full bowl of paint. He has 1/2 of gallon of paint and it able to fill the bowls for all 7 tables. How many gallons of paint does each table have?
Based on the fact that Gordon has 1/2 gallons of paint and is able to fill up bowls in 7 tables, the number of gallons of paint each table has is 1/14 gallons of paint
How to find the number of gallons?Gordon has 1/2 gallons of paint and knows that this amount of paint can given each bowl in all 7 tables, a full bowl of paint.
The amount of paint that each bowl gets can therefore be calculated by the formula:
= Gallons of paint Gordon has / Number of tables
Solving for the paint each bowl has gives:
= 1/2 ÷ 7
= 1/2 x 1/7
= 1/14 gallons of paint
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what is the equation for finding the volume of a rectangular solid ?
Answer: Width x length x height = volume
i think
Step-by-step explanation:
What is f(g(13))?
A mapping diagram is shown.
Answer:
(c) 32
Step-by-step explanation:
Given a map between x, g(x), and f(g(x)), you want to find f(g(13)).
Using a mapYou want the function value that results when 13 is the argument of g(x), and g(x) is the argument of f(x).
Locate the input (13) in the left column of the diagram. Follow the arrow to find g(13) = 16. Follow the arrow again to find f(16) = 32.
f(g(13)) = 32
Noah invested $2500 in an account paying 3% simple interest. What was the total
amount in his account after 5 years?
Answer:
$2,875
Step-by-step explanation:
Interest = Principal x rate x time
Interest = $2500 x 0.03 x 5
Interest = $375
Original value + interest = Total amount
$2,500 + $375 = $2,875
Find the value of x.
Answer:
64 = x
Step-by-step explanation:
The angles are alternate interior angles and alternate interior angles are equal when the lines are parallel
128 = 2x
Divide each side by 2
128/2 = 2x/2
64 = x
Answer:
x = 64
Step-by-step explanation:
We know that,
If lines are parallel, the alternate angles are also equal.
Therefore,
[tex] \sf2x = 128[/tex]
Now, let us solve for x.
For that, divide both sides by 2.
[tex]x = 64[/tex]
what does 2056x18394= / anyone up to ta lk
The product of the multiplication of (2056 * 18394) is 37818064.
As per the question statement, we are provided with the multiplicative statement of two numbers, 2056 and 18394.
We are required to perform the above mentioned multiplication and determine the product in the simplified form a number.
To solve this question, we simply need to multiply 2056 and 18394, and mention the upcoming product as our required answer, i.e.,
(2056 * 18394) = 37818064.
Hence, The product of the multiplication of (2056 * 18394) is 37818064.
Multiplication: In Mathematics, Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division which means the repeated addition of groups of equal sizes. Product: In mathematics, a product is the result of a multiplication, or an expression that identifies two or more factors or numbers of decimals to be multiplied.To learn more about Multiplication & Products, click on the link below.
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Please help me with this, I am not sure what to do.
Since [tex]x[/tex] is approaching 1 from the left/below, we take the part of [tex]f(x)[/tex] that is defined over [tex]x<1[/tex], for which we have
[tex]f(x) = \dfrac{x-1}{\sqrt{x-1}}[/tex]
Since [tex]x\neq1[/tex], we can simplify this to
[tex]f(x) = \dfrac{x-1}{(x-1)^{1/2}} = (x-1)^{1/2} = \sqrt{x-1}[/tex]
and this is continuous at [tex]x=1[/tex], so we can evaluate the limit by directly substituting [tex]x[/tex].
To summarize:
[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} \frac{x-1}{\sqrt{x-1}} = \lim_{x\to1} \sqrt{x-1} = \sqrt{1-1} = \boxed{0}[/tex]
Solve the equation. e – 36 = 133 A. e=97 B. e=107 C. e= 169 D. e=179
Answer:
d
Step-by-step explanation:
Darla wants to buy 3 identical gift cards. She wants to make sure her total
cost is no more than $3 above or below $75. Which of the following
inequalities represents this situation?
A. 13c-75 ≤3
B. 175+3c| ≤ 3
C. 13c-21 ≤60
D. 13c+21 ≤60
The inequality that represents this situation is Option(A.) 3c - 75 ≤ 3.
What are Inequalities?Inequality is created when two or more algebraic expressions are compared using the symbols >, <, ≥, or ≤. They represent mathematical expressions when neither side is equal. The majority of the time, size comparisons between two numbers on the number line are made using inequalities.Given:
Darla wants to buy 3 identical gift cards.
The total cost is no more than $3 above or below $75.
Let's assume that the cost of one gift card is $c.
Total Cost of 3 gift cards = $3c
Also, the total cost is no more than $3 above or below $75.
Hence, it would be -75 and less than 3.
Therefore, the inequality is 3c - 75 ≤ 3.
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If I round 7/15 it will be 1. O True O False
2.сBOP-6-5-4-3-2-10В'Por boloAlA. (x.A. (x,y)+(-x,y+6)B. (x,y) → (x + 6,-y)(x,y) - (x - 12. y+6)D. (x,y)-(-x+6,-y)B.
SOLUTION
For the image point A has the coordinates (-3, 6) and A' is (3, -6) so with a translation of
[tex](x,\text{ y )}\rightarrow\text{ (}x+6,\text{ -y )}[/tex]We see A(-3, 6) as
[tex]A(-3,6)\rightarrow(-3+6,-6)\rightarrow A^{\prime}(3,-6)[/tex]And B(-2, 2) as
[tex]B(-2,2)\rightarrow(-2+6,-2)\rightarrow B^{\prime}(4,-2)[/tex]Therefore the correct translation is
[tex](x,\text{ y )}\rightarrow\text{ (}x+6,\text{ -y )}[/tex]Option B is the correct answer.
A construction crew needs to pave a road that is 202 miles long. The crew paves 9 miles of the road each day. The length, L. (in miles), that is left to be paved
after d days is given by the following function.
L(d)=202-9d
Answer the following questions.
(a) How many miles of the road does the crew have left to pave after 12 days?
94 miles
(b) If 139 miles of the road is left to be paved, how many days has the crew been.
paving the road?
days
Answer:
7 days.
Step-by-step explanation:
139 = 202 - 9d subtract 2002 from both sides of the equation
-63 = -9d Divide both sides of the equation by -9
7 = d
Written as a simplified polynomial in standard form, what is the result when (x+7)^2 is subtracted from7
7-(x^2+14x+49)
7-x^2-14x-49
-x^2-14x-42
In this project, you are asked to use data from a Survey that Sr. Barbara conducted in her MT 120 classes to determine whether the students in the class were randomly guessing the identities of the two men in the photos. This part of the project will be a lot like several of the explorations of Chapter 1, where you are using a statistic (, and using an applet to calculate a p-value. Does the p-value support the idea that the students were guessing, or does the p-value suggest that students were doing something other than guessing?
If the students were doing something other than guessing, use the statistic ( from the data to estimate a reasonable value for the parameter (π). This part of investigation goes beyond what have been learned already in this class, and challenges to experiment a bit to find a better estimate for the true population parameter for this scenario.
Background: A study in Psychonomic Bulletin and Review (Lea, Thomas, Lamkin, and Bell, 2007) presented evidence that "people use facial prototypes when they encounter different names." Participants in that study were given photos of two faces and asked to identify which face is "Tim" and which is "Bob." Sr. Barbara is replicating this study with students in her MT 120 Applied Statistics classes. On September 26 - 27, she asked students in all three sections of MT 120 to identify from two photos, which face belongs to "Bob" and which to "Tim." Were her students simply guessing, or were they doing something other than guessing?
On September 26 and 27, Sr. Barbara gave her students an opportunity to participate in a quick survey about Tim and Bob. She asked the students to quickly identify whether the face on the left belongs to a man named Tim or to a man named Bob. Forty-two students completed this survey. The results of this survey is that 9 students said that Bob was on the left while 33 students said Tim was on the left.
1. Data Collection Methods:
To replicate the study that appeared in Psychonomic Bulletin and Review, Sister Barbara did not ask "all people" to identify the men in the photos, but rather just a sample from a larger population. You may recall that she asked you to look at photos of two men, and to identify whether the face on the left was Bob or Tim.
· How, where, and when was this data collected? Who did Sister Barbara survey?
· Who or what are the observational units, and what is the variable for each observational unit? What is the statistic?
· What does this sample (students in Sr. Barbara's MT 120 classes) suggest to us about the larger population? Did Sister Barbara take a simple random sample to collect this data? Do you think it is reasonable for her to assume that this sample is representative of some larger population?
· What is the population to which it would be reasonable to extend these results? Does it seem reasonable to extend the results of this study to all undergraduate students at Cardinal Stritch University? To the population of all students (both grads and undergrads) at Stritch? To people beyond Stritch? All people in the United States? Beyond the United States? Why?
2. Summary and Conclusions:
White a paragraph summarizing this study.
· What did you learn about students in Sr. Barbara's classes, Stritch students, or people in general? Do these results surprise you? Why?
· If the p-value suggests that Sr. Barbara's students were doing something other than simply guessing, suggest a better value for the parameter (or an interval of plausible values for the parameter). Explain how you determined a plausible value (or interval of plausible values) for the parameter. This question asks you to go beyond what you've learned (so far) in this course. Use critical thinking to identify a reasonable value (or interval of possible values) for the parameter. Explain how your are doing this.
· What do you think is going on here? Do you think the students were guessing, or is something else going on?
Answer: So the subject’s answer is Chapter 5.
Step-by-step explanation: Because there is no evidence that Armenians are smart, and in Chapter 5 people are more frustrated than kind.
what transformations take f(x) = 3x+1 to g(x) = −3x−5 ?
The transformation that took f(x) = 3x+1 to g(x) = −3x−5 is reflection and translation 4 units downwards
How to find the transformationsgiven data
f(x) = 3x+1
g(x) = −3x−5
Reflection
Reflections changes the sign of the both coordinates
from to
f(x) = 3x + 1 f'(x) = -3x - 1
Translation
Translation downwards leads to subtraction with the required units in the y coordinates. In this case 4 units
from to
f'(x) = -3x - 1 f''(x) = -3x - 5
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Answer:
Either of ...
reflection across the y-axis, and translation down 6reflection across the x-axis and translation down 4Step-by-step explanation:
You want the transformations that take f(x) = 3x+1 to g(x) = -3x-5.
TransformationThe x-term of the transformed function has a sign opposite that of the original function. That can be accomplished by either of (a) reflection across the y-axis (replaces x by -x), or by (b) reflection across the x-axis (replaces f(x) by -f(x)).
Either way, an additional translation is required. That translation can be either vertical or horizontal, and may be done either before or after the reflection.
Horizontal reflectionReflecting f(x) across the y-axis means it becomes ...
f(-x) = 3(-x) +1 = -3x +1
In order to make that into -3x-5, we must add -6 to the function value:
g(x) = f(-x) -6 = (3(-x)+1) -6 = -3x -5
F(x) will be taken to g(x) = -3x-5 by reflection across the y-axis and translation down 6 units.
Vertical reflectionReflecting f(x) across the x-axis means it becomes ...
-f(x) = -(3x +1) = -3x -1
In order to make that into -3x-5, we must add -4 to the function value:
g(x) = -f(x) -4 = -(3x +1) -4 = -3x -5
F(x) will be taken to g(x) = -3x-5 by reflection across the x-axis and translation down 4 units.
__
Additional comment
As noted above, the translation can be either horizontal or vertical. For example, translating the function 2 units to the right makes it f(x-2). Then reflection across the y-axis replaces x by -x, so we have ...
g(x) = f(-x-2) = 3(-x-2)+1 = -3x -6 +1 = -3x -5
To get g(x), we could translate right 2 units, then reflect across the y-axis.
We also note that point (-1, -2) is shared by f(x) and g(x), so reflection horizontally across the line x=-1, or vertically across the line y=-2 would also give the required transformation.
Determine whether the function is bounded above, bounded below, or bounded on its domain.
y = 2
D. The function is neither above nor below its bounds.
What do "bounded" and "unbounded" functions mean?An unbounded function is one that is not bounded. The function is referred to as being bounded (from) above by A if it has real values and f(x) A for all x in X. The function is referred to as being bounded by B (from below) if f(x) B for all x in X
How do you know whether a sequence is bounded or not?A sequence is considered to be constrained if it has bounds above and below. Unbounded sequences exist when a sequence is not bounded. Because 1/n1 for all positive integers n, for instance, the sequence 1/n is confined above. Further, it
If there is an integer 2 such that for all x from the domain D(f), one has f (x) 2, we say that a real function f is bounded from below. If there is a number K such that for every x from the domain D(f), one has f (x) 2, then we say that a real function f is bounded from above.
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Please pls pls j beg
Answer:
Y/n had nothing in his hand. His friend gave him 8 oranges for him to eat. But on his way home he saw a hungry child and decided to give away 4 oranges to the child. How many oranges does he have now?
The table shows claims and their probabilities for an insurance company. On any given claim, how much money can this company expect to pay?
The most appropriate choice for expectation will be given by-
Amount of money the company expected to pay = $10400
What is expectation?
At first it is important to know about probability of an event.
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.
Suppose x is a random variable with the probability function f(x). suppose [tex]x_1[/tex], [tex]x_2[/tex],....., [tex]x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1,[/tex] [tex]p_2,[/tex]....,[tex]p_n[/tex] be the corrosponding probabilities.
Expectation is given by the formula
[tex]p_1x_1 + p_2x_2....+p_nx_n[/tex]
Here,
Amount of money the company expected to pay =
$[tex](0 \times 0.70 +20000 \times 0.16+ 40000 \times 0.09 + 60000 \times 0.03 + 80000 \times 0.01 + 100000 \times 0.01)[/tex]
= $10400
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