The dimensions of the rectangle are either 10cm x 24cm or
24cm x 10cm having perimeter 68 cm.
What is Pythagorean theorem?
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
A rectangle has 4 angles measure of each is 90°.
A diagonal of rectangle divides it into two right angled triangles.
Pythagorean theorem can be applied on these triangles to get the desired values.
According to the given question:
Let the length and breadth of rectangle be x and y .
Perimeter: 2x + 2y = 68 (Given)
Using Pythagorean theorem diagonal: [tex]x^2+y^2=26^2[/tex]
Using perimeter, x + y = 34
∴ x = 34 - y
Substituting this is the equation for diagonal
[tex](34-y)^2 +y^2=26^2\\1156 - 68y + 2y^2 = 676\\2y^2 - 68y + 480 = 0\\y^2 - 34y + 240 = 0\\(y - 10)(y - 24) = 0[/tex]
Therefore dimensions of rectangle are either 10cm x 24cm or
24cm x 10cm.
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For a certain population of penguins, the distribution of weight is approximately normal with mean 15. 1 kilograms (kg ) and standard deviation 2. 2 kg. Approximately what percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg ?.
56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.
Given,
The mean of the population, μ = 15.1 kg
Standard deviation, σ = 2.2 kg
We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;
Here,
z score = x - μ / σ
The z-score calculates how far the measure deviates from the mean by standard deviation.The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.
x = 16.5
z score = x - μ / σ
z = (16.5 - 15.1) / 2.2 = 0.64
Z = 0.64 has a p-value of 0.7389.
x = 13
z score = x - μ / σ
z = (13 - 15.1) / 2.2 = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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HELP WHATS 565 divid by 000000.666 x X -k
Answer:
565/0.666=848.348
Step-by-step explanation:
if you needed variables added to the equation then show a picture and I can answer it.
State the coordinates of the point.
Answer:
Step-by-step explanation:
B
Answer 0,4
Answer:
(-5,-1)
Step-by-step explanation:
Start at the orginal. This is (0,0), the middle of the graph. From that point you move 5 spaces left. That is the -5 in the answer. Then from that point, you move one space down. That is the -1 in the answer.
The sum of two numbers is 2. The difference between 8 and twice the smaller number is two less than four times the large number. Find the numbers.
Answer:
larger number = 3
smaller number = -1
Step-by-step explanation:
x = larger number
y = smaller number
x+y=2
8-2y=4x-2 ---> 10 = 4x+2y
10 = 4x+2y
5=2x+y
y = 5-2x
2x=5-y
x+5-2x = 2
-x+5=2
-x=-3
x=3
3+y=2
y=-1
1.7 × 4= with a rounded answer
Consider the line y = 5/7x+1.
Find the equation of the line that is parallel to this line and passes through the point (-5, 6).
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 6).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of parallel line:
Equation of perpendicular line:
П
X√√
0=0
$
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]
now, keeping in mind that perpendicular lines have negative reciprocal slopes
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]
so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]
16 = -7v - 8 + 3v Solve for v.
Simplify your answer as much as possible.
To solve for v, isolate the variable by dividing each side by factors that don't contain the variable.
Solve for v.
[tex]16=-7v-8+3v[/tex][tex]v = -6[/tex] ← Our SolutionHope this helps!
A robot can complete 4 tasks in hour. Each task takes the same amount of time.
5/6
a. It takes the robot
(Simplify your answer.)
-
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
hour(s) to complete one task.
1 task will complete in 12.5 minutes
The robot can complete 9.6 task in 1 hour
Given,
Number of task a robot can complete = 4
Time taken by robot = 5/6 of 1 hour
5/6 of 1 hour = 5/6 × 60 minutes
= 300/6
= 50 minutes
Then,
4 task takes 50 minutes
1 task = 50 minutes / 4 task
= 12.5 minutes
So,
1 task = 12.5 minutes
x task = 60 minutes
1 : 12.5 = x : 60
1/12.5 = x / 60
1*60 = 12.5*x
60 = 12.5x
x = 60/12.5 = 4.8
x= 4.8
Therefore,
The robot can complete 4.8 task in 1 hour
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PLEASE HELP ME AND TELL ME HOW YOU DID IT AND THANKS 25 POINTS HELP
square root of 81 divided by 3
Answer: Yes
Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications
The scatterplot shows the relationship between the length of a pendulum and the time it takes to complete one full swing.
Which transformations would linearize these data using a power model? Check all that apply.
ln(Length), ln(Time)
ln(Length), Time
log(Length), log(Time)
Length, log(Time)
Length, Time2
Answer:
a) ln(Length), ln(Time)
c)log(Length), log(Time)
e)Length, Time²
Step-by-step explanation:
Answer:
the person above me is correct!
Step-by-step explanation:
P(AIB) can be read as "the probability that A occurs given that B has
occurred."
OA. True
OB. False
SUBMIT
P(AIB) can be read as "the probability that A occurs given that B has occured. This is true.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred in probability theory.
Conditional probability: p(A|B) is the likelihood of event A occurring if event B occurs. For example, if you drew a red card, what is the likelihood that it is a four (p(four|red))=2/26=1/13? So there are two fours out of the 26 red cards (given a red card), so 2/26=1/13.
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A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If ( x , y ) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.
Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:
(x, y) → (SFx, SFy) = (0.4x, 0.4y)
Where:
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Complete Question:
A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.
If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?
answer choices
(0.4x, 0.4y)
(x + 20, y + 20)
(x + 0.4, y + 0.4)
(20x, 20y)
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
7, 7/1
Step-by-step explanation:
The ratio 7:49 can be simplified to 1:7.
Wich rule best represents the dilation applied to circle I to create circle II?
Answer:
Step-by-step explanation:
F 3/8x 3/8y
what is (2 x 10 to the power of 5) divided by (4 x 10 to the power of 2)
Match each number with its estimated power of 10
The matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
What are Exponents?
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
We have to match the following terms :
1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵
2) 219,000 = 2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵
3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶
4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵
5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶
Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶
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The bookstore sold 40 biographies and
100 mysteries. Find the ratio of biographies
to mysteries sold
Answer:
2 : 5 or 2/5
Step-by-step explanation:
The ratio is 40 : 100, which can simplify into 2 : 5.
solve the equation by elimination method 4x-2y=8,5x+3y=6
Answer:
Point form:
(18/11 , -8/11)
Equation form:
x=18/11 , y=-18/11
the power of a test is measured by its capability of a) rejecting a null hypothesis that is true. b) not rejecting a null hypothesis that is true. c) rejecting a null hypothesis that is false. d) not rejecting a null hypothesis that is false.
The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer
what is power with respect to probability?
Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.
Power = P[ rejecting a null hypothesis that is false.]
So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false
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an individual was making blankets for a few friends. the individual used 6.3 feet of fabric for one blanket. if the individual makes 4 blankets, how many feet of fabric will the individual have used to make 4 blankets (round to the nearest whole number)?
Answer:
25
Step-by-step explanation:
6.3= 1 blanket
to find 4 blankets you multiply 6.3 by 4
6.3x4=25.2
to the nearest whole number
25
Ann and Ben tranlate document from German into Englih. A et of document that would take Ann 10 day would take Ben 12 day. Ann tart to tranlate the document. After 2 day Ann and Ben both work on tranlating the document. How many more day will it take to complete the work?
You mut how your working
After Ann start to translate the document in 2 days, they need more 4.4 days to complete the work.
A unit work would take Ann 10 days to complete, means each day Ann completes 1/10 work
She works for 2 days, hence the work done = 2 x 1/20 = 2/10
The remaining work = 1 - 2/10 = 8/10
Then Ben joins.
A unit work would take Ben 12 days to complete, means each day Ben completes 1/12 work.
Each day, both Ann and Ben will complete:
1/10 + 1/12 = 11/60 unit work
The remaining work = 8/10
Hence, if each day 11/60 work can be completed, to complete 8/10 work, they need:
8/10 : 11/60 = 48/11 = 4.4 days
Therefore we can conclude, after Ann works for 2 days, they need more 4.4 days to complete the work.
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In the following figure, AD is the bisector of ZBAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that AAEG = AAFG by the AAS congruence postulate. Do you agree or disagree? Explain.
I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HLThe problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent
The AAS have it that the two triangles being compared should have their two angles and the side not included being equal
The Angle - Angle - Side = AAS, here include
< FA,G - < AFG - AG
< EAG - < AEG - AG
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Which description matches the graph of the inequality y <|x-2| + 1
A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
What is inequality?
Inequality is a relationship between two expressions or values that is not equal to each other.
This inequality may be written in two ways:
(a) y < x - 2 + 1
or
y < x - 1
(b) y < -x +2 + 1
or
y < -x + 3
A graph of the inequality is shown below. The shaded region satisfies the inequality.
Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.
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Complete the sentence…?
is 10 times as much as 0.11
Answer: 1.1
Step-by-step explanation:
10 * .11 is 1.1
When multiplying decimals by ten you move the decimal place once to the right.
Answer:
1.1
Step-by-step explanation:
0.11 x 10 = 1.1
You are moving the decimal point over once (x 10).
11) -8x + 2x-16 <-5x+7x
Which set of ordered pairs shows the result of a dilation by a factor of 2 around the origin?
The set of ordered pairs that represent dilation factor of 2 is
a. A' (2, 12) B' (12, 12) C' (2, 4)
How to find the coordinates of the imageDilation is a method of transformation which uses a scale factor. The scale factor determines if the dilation is magnification or shrinking
|0 < r < 1| is shrinking
|r > 1| is magnification
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
From the graph the coordinates are read and following the given transformation rule we have
preimage image
A (1, 6) → (1 * 2, 6 * 2) → A' (2, 12)
B (6, 6) → (6 * 2, 6 * 2) → B' (12, 12)
C (1, 2) → (1 * 2, 2 * 2) → C' (2, 4)
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An x-ray machine for animal cot 125,000. If the loan i for 10 year, and the interet paid i $65,625, what i the interet rate on the loan?
The interest rate on loan is 5.25%.
What is principal amount?
The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is I=P.r.t
Given, Principal amount=$125,000, time=10years, Interest=$65,625.
Let r be the rate of interest, on applying simplest interest formula
I=P.r.t
Where P=principal amount, r=rate, t=time.
I=125,000 x r x10
65,625=125,000 x r x10
r=[tex]\frac{65,625}{125,000(10)}[/tex]
r=0.0525
r=5.25%
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Each month, kaisorn deposits $50. 00 onto her public transportation card. It costs her $2. 50 per trip to ride the subway. Thom deposits $40. 00 on his public transportation card. It costs him $2. 00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2. 5x = y 40 − 2x = y 50 + 2. 5x = y 40 + 2x = y 50 − 2. 5y = x 40 − 2y = x 50 + 2. 5y = x 40 + 2y = x.
The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
The correct option is (A)
Given,
In the question:
Kaisorn deposits $50. 00 onto her public transportation card.
It costs her $2. 50 per trip to ride the subway.
Thom deposits $40. 00 on his public transportation card.
It costs him $2. 00 per trip to ride the subway.
Now, According to the question:
x → represents the number of trips
y → represents the amount remaining in each account
According to the given condition:
The system of equations represents their transportation costs is :
50 − 2. 5x = y
40 − 2x = y
Hence, The system of equations represents their transportation costs is:
50 − 2. 5x = y
40 − 2x = y
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I need help with this
The value of the function (f + g)(x) = [tex]x^{2}[/tex] -5x + 9
What is a Function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
f(x) = - 2x + 4, g(x) = [tex]x^{2}[/tex] -3x + 5
(f+g)(x) = f(x) + g(x)
So by adding the two functions
(f + g)(x) = -2x + 4 + [tex]x^{2}[/tex] -3x + 5
(f + g)(x) = [tex]x^{2}[/tex] -5x + 9
In conclusion, the value of [tex]x^{2}[/tex] -5x + 9
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