The triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
What is congruent?In mathematics, congruent means that two shapes or objects have the same size and shape. They match exactly when superimposed on each other. Congruence also applies to angles, where two angles are said to be congruent if they are equal in measure. Congruence can also refer to the equality of two expressions, where two expressions are congruent when they have the same value. In other words, congruence is a term used to describe a relationship between two objects or shapes that are exactly the same size and shape.
In order to prove that two triangles are similar, we need to show that their corresponding angles are congruent. Given that angles T, X, and U are all equal, and angles X, U, and Y are all equal, we can therefore conclude that angles T and Y are also equal. This means that triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
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The corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write : TUV ~ XYZ
What is congruent?
Congruent is a term used in geometry to describe two figures or objects that have the same shape and size. In other words, if two figures are congruent, they are identical in every way, except that they may be oriented differently or located in different positions in space.
To prove that TUV ~ XYZ, we need to show that the two triangles are similar, which means that their corresponding angles are congruent and their corresponding sides are in proportion.
Given that T=X=U=Y, we can conclude that angle TUV and angle XYZ are congruent, and angle TVU and angle YXZ are also congruent. These two angles are the corresponding angles that are congruent in the two triangles.
To show that the corresponding sides are in proportion, we need to compare the ratios of the corresponding side lengths. We can start by comparing the ratio of the lengths of TU and XY:
TU / XY = (TU / TX) * (TX / XY) (by the transitive property of equality)
TU / TX = 1 (because T = X)
TX / XY = 1 (because U = Y)
Therefore, TU / XY = 1 * 1 = 1.
Similarly, we can compare the ratio of UV and YZ:
UV / YZ = (UV / UY) * (UY / YZ) (by the transitive property of equality)
UV / UY = 1 (because U = Y)
UY / YZ = 1 (because T = X)
Therefore, UV / YZ = 1 * 1 = 1.
Therefore, the corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write:
TUV ~ XYZ
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Expand and give answer for 4(1+5x)
Answer:
4+20x
Step-by-step explanation:
Use distributive property:
4*1 + 4*5x =
4+20x
Now that you have mastered multiplying fractions by whole numbers, let's solve the
problem in the Real-World Connection.
Uma made sand art using green, red, blue, pink, and white sand. She used of 2/3
a cup of each color. How much sand did she use in all?
Answer:
10/3
Step-by-step explanation:
2/3+2/3+2/3+2/3+2/3=10/3
Find the area of a circle with diameter = 16 units.
Answer: ;)
The area of a circle is 64 square units
Step-by-step explanation:
Area of a circle a=64 square units in terms of
Step-by-step explanation:
Given that the diameter of a circle is 16
That is d=16
Therefore radius r=8
Now to find the area of a circle :Area of a circle square units
Substitute r=8 we get
Area of a circle
Therefore the area of a cicle is 64 square units
Area of a circle a=64 square units in terms of
Which economic system has no government involvement in the market? a. capitalism b. communism c. socialism d. No economic system is free from government involvement. Please select the best answer from the choices provided A B C D Mark this and return
Answer: D is correct.
Step-by-step explanation:
The economic system that has no government involvement in the market is d. No economic system is free from government involvement.
In reality, there is no government intervention because at some point the government will comes in , this could actually be minimal, only in the free market is where there is no government intervention.
It should be noted that in this free market, there is an unregulated system of economic exchange, where the act of taxes collection as well as quality controls, has no economic interventions which can be attributed to the government. Because of this, option D is correct.
I hope this helped! Brainilist is highly appreciated! <333
Please help me solve this differential equation problem. Please show as many steps as you can.
(b) u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠λ₁ orλ₂ as the coefficients can only be determined when the value of p is not equal to either of the eigenvalues λ₁ or λ₂.
What is eigen values?Eigenvalues are scalars associated with a linear transformation or a matrix. They can be used to determine the stability of the system and describe the behavior of the transformation.
In this case, the eigen values λ₁ and λ₂ are constants, and the solution to the differential equation y' + Ay = f₀e^pt can be solved by using the method of undetermined coefficients.
This method involves using a linear combination of the eigenvectors, which are associated with the eigenvalues λ₁ and λ₂.
The solution for this differential equation is then given by u₁e^λ₁t +u₂e^λ₂t (pI-A)⁻¹ f₀e^pt f for p ≠ λ₁ or λ₂.
This is because the coefficients can only be determined when the value of p is not equal to either of the eigenvalues λ₁ or λ₂. If p is equal to one of these eigenvalues, then the solution cannot be determined as the coefficients become indeterminate.
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How do I show a parallelogram that is not a rectangle with an area of 18 square units( the smallest square on the grid has an area of 1 square unit)
Tests show that the lives of light bulbs are
normally distributed with a mean of 750 hours
and a standard deviation of 75 hours. Find
the probability that a randomly selected light
bulb will last between 675 and 900 hours.
525 600 675 750 825 900 975
P = [?]%
Hint: use the 68 - 95 - 99.7 rule.
Enter
Answer: like three out of a thousand, would be likely to last less than 525 hours or more than 975 hours.
Step-by-step explanation:
normal distribution is shaped like a bell curve with the average (mean) at the center.
A light bulb in your problem is most likely to last about 750 hours. One standard deviation up from that would be 750 + 75, which is 825 hours, and one standard deviation down is 750 - 75, which is 675 hours.
According to the empirical rule, the interval from the average to +1 standard deviation (750 to 825) and the interval from the average to -1 standard deviation (675 to 725) each have a 34.1% probability.
From +1 to +2 standard deviations and -1 to -2 standard deviations (825 to 900 and 600 to 675) the probability is 13.5% for each interval.
From +2 to +3 standard deviations and -2 to -3 standard deviations (900 to 975 and 525 to 600) the probability is 2.1% for each interval.
These percentages are the same for any normal distribution problem. If you add up the chances you can find the probability a light bulb will last an increasing range of times centered around the average:
Within one standard deviation of the average: 68.3% (chance it will last 675 to 825 hours)
Within two standard deviations of the average: 95.4% (chance it will last 600 to 900 hours)
Within three standard deviations of the average: 99.7% (chance it will last 525 to 975 hours)
And only a very few, like three out of a thousand, would be likely to last less than 525 hours or more than 975 hours.
Jenny made $144 for 9 hours of work.
At the same rate, how much would she make for 12 hours of work?
Answer:
Step-by-step explanation:
the answer is 192
9hrs=$144
12hrs=X
you cross multiple
12x144/9
which give you $192
Answer:
Jenny made $144 for 9 hours of work so you divide 144 by 9 and you get 16.
$16 is the amount of money that Jenny makes in an hour. To check if it's correct you multiply 16 by 9 and you should get 144.
So, since the question wants you to find how much she makes for 12 hours of work, you multiply 16 times 12 and you should get 192.
In conclusion, Jenny makes $192 for 12 hours of work.
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Solve the problems below as a group.
Suppose Jemma wanted to divide cup of pancake batter to make 4 mini pancakes.
What fraction of a cup of batter will each pancake get?
9 The rectangle to the right shows 1 cup divided
into 3 equal sections. How much does each
section represent?
10 Shade of the rectangle to show cup.
1/3
11 You need to divide cup equally to make 4 pancakes.
Divide each third of the rectangle vertically into 4 equal parts.
Then shade of the rectangle to show 1 of the 4 pancakes.
4
12 The overlapping section shows the fraction of a cup of batter that each pancake
will get. What is this fraction?
1
3
13
÷4=
14 What multiplication equation also solves of ?
4
15 How is 4 related to
÷ X
x ¹?
1
3
4
hood
Jemna has to devide [tex]1[/tex] cup pancake in [tex]4[/tex] mini pan cakes so that the batter be distributed in a fraction of [tex]\frac{1}{4}[/tex] th form
[tex]9[/tex]. The rectangle will be [tex]\frac{1}{3}[/tex] in fraction.
[tex]10[/tex]. Out of [tex]3 boxes[/tex] [tex]1[/tex] should be shaded.
[tex]11[/tex]. [tex]\frac{1}{3}[/tex] of [tex]4[/tex]
[tex]13[/tex]. [tex]\frac{1}{12}[/tex]
[tex]14[/tex]. [tex]\frac{1}{12}[/tex]
[tex]15[/tex] In division the value gets reciprocate ÷[tex]\frac{1}{3}[/tex][tex]\frac{4}{1}[/tex] = [tex]\frac{1}{3}[/tex]* [tex]\frac{1}{4}[/tex] by changing into multiplication.
What do you mean by fraction?Fractions are referred to as the components of a whole in mathematics. A single item or a collection of objects can be the whole. When we cut a slice of cake in real life from the entire cake, the portion represents the fraction of the cake.
[tex]9[/tex]. To calculate how much of a cup of dough will go into each pancake, divide [tex]1[/tex]÷[tex]4[/tex] to get [tex]\frac{1}{4}[/tex]
Let's now examine the rectangle that depicts a cup divided into three equally sized parts. Divide 1 by 3 to determine how much each portion represents as [tex]\frac{1}{3}[/tex]
[tex]10[/tex]. Out of [tex]3 boxes[/tex] [tex]1[/tex] should be shaded
[tex]11[/tex]. [tex]\frac{1}{3}[/tex] of [tex]4[/tex]
[tex]13.\frac{1}{12}= \frac{1}{3}[/tex]÷[tex]4[/tex][tex]=\frac{1}{3} *\frac{1}{4}[/tex]
[tex]14[/tex] Same as previous one
[tex]15[/tex] In division the value gets reciprocate ÷[tex]\frac{1}{3}[/tex][tex]\frac{4}{1}[/tex] = [tex]\frac{1}{3}[/tex]* [tex]\frac{1}{4}[/tex] by changing into multiplication.
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Can someone please help me
A graph of A(x) and B(x) in the interval 0 ≤ x 100 on a cartesian coordinate is shown below.
The solution of A(x) = B(x) to the nearest integer is (35, 8).
What is an exponential function?In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the two plans for speeding up its technical support time, we can logically deduce the following exponential functions;
[tex]A(x) = 15.7(0.98)^x \\\\B(x) = 11(0.99)^{x}[/tex]
By critically observing the graph of the two exponential functions, we can logically deduce that the point of intersection (solution) is in quadrant I, which is given by the ordered pair (35, 8).
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pls help fast!!! Find the equation of a line parallel to y=−3x−5that passes through the point (2,−1).
Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.
Explain about the parallel lines?Two or more lines that have been spaced the same apart, never merging but never diverging, are said to be parallel. Parallel lines run indefinitely in both directions because, as we mentioned earlier, lines are non-stop.
As long as they are consistently spaced at the same distance apart, they don't necessarily need to be straight lines.
equation of a line : y = −3x−5
Comparing with slope-intercept form of line.
y = mx + c
m is the slope and c is the y intercept.
m = -3
Parallel lines have the same slopes:
m = -3 and passing points (2,−1).
Using the point -slope equation:
y - y 1 = m(x - x1)
y + 1 = -3(x - 2)
y = -3x + 6 - 1
y = -3x + 5
Thus, the equation of a parallel line with the slope -3 and passing point (2,−1) is found as : y = -3x + 5.
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Complete question:
Find the equation of a line parallel to y=−3x−5that passes through the point (2,−1).
Which of the following expressions is equal to 9?
4 x (one-half x 6) ÷ 3
6 ÷ (one-fourth x 3 x one and one-fourth)
8 + (one-third x 6) ÷ 5
10 − (one-fifth x 10) + 1
Kyra and some friends go to a climbing gym. She records how high each person climbed.
Answer:
what type of a question is this man can send me the full question so i can answer to you??
Answer: 12 1/2
Step-by-step explanation:
thats the answer
When John waters, his plants each day he keeps track of how many liters he uses. He measures in 1/8 liter amounts, and never uses more than 1 L the amount he uses each day varies, but he figures that if all the amounts work evened out he uses 1/2 L a day how did John decide this?
Find X and if it's a decimal round to the nearest tenth. 50 points
Answer:
x = 40
Step-by-step explanation:
given a line DE parallel to a side AC of the triangle and intersecting the other two sides, it intersects those sides proportionally , that is
[tex]\frac{CE}{BE}[/tex] = [tex]\frac{AD}{BD}[/tex] ( substitute values )
[tex]\frac{25}{x-25}[/tex] = [tex]\frac{15}{24-15}[/tex]
[tex]\frac{25}{x-25}[/tex] = [tex]\frac{15}{9}[/tex] ( cross- multiply )
15(x - 25) = 9 × 25 = 225 ( divide both sides by 15 )
x - 25 = 15 ( add 25 to both sides )
x = 40
Write an equation for the translation of y=4/x
that has the given asymptotes.
X=-2
Y=7
Answer:y=4/x−4−3
Step-by-step explanation:Explanation:
translation of 4 units right
translation of 3 units down
y=f(x)→y=f(x−4)−3
Use the following financial information to find the entry you would make on an income statement for INCOME BEFORE TAXES for the year ended December 31, 2011: Gross Sales, $223,000; Sales Returns and Allowances, $11,200; Sales Discounts, $1,800; Merchandise Inventory, January 1, 2011, $67,600; Merchandise Inventory, December 31, 2011, $78,300; Net Purchases, $84,000; Freight In, $950; Salaries, $107,200; Rent, $19,500; Utilities, $1,450; Insurance, $2,150; and Income Tax, $14,900.
INCOME BEFORE TAXES for the year ended December 31, 2011 is $669.
how to find gross profit ?Gross Profit = Gross Sales - Sales Returns and Allowances - Sales Discounts - Cost of Goods Sold
Cost of Goods Sold = Beginning Inventory + Net Purchases + Freight In - Ending Inventory
Cost of Goods Sold = $67,600 + $84,000 + $950 - $78,300 = $74,250
Gross Profit = $223,000 - $11,200 - $1,800 - $74,250 = $135,750
Operating Expenses = Salaries + Rent + Utilities + Insurance = $107,200 + $19,500 + $1,450 + $2,150 = $130,300
Income Before Taxes = Gross Profit - Operating Expenses - Income Tax
Income Before Taxes = $135,750 - $130,300 - $14,900 = $669
Therefore, the entry for INCOME BEFORE TAXES for the year ended December 31, 2011 is $669.
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Find the surface area of each of the following right prisms using the formula SA=LA+2B
5 by 5 grid y=3-1/2x
Answer:
46_ parce que c'est comme ça
Just 11 and 13 it’s simplifying linear Expressions
Based on the given task content; the solution to the linear expressions 4(2b + 2) - 3 and -4 + 8p - 6p - 5 + 20p is 8b + 5 and -9 + 22p respectively.
How to simplify linear expressions?11. 4(2b + 2) - 3
open parenthesis
= 8b + 8 - 3
= 8b + 5
12. -4 + 8p - 6p - 5 + 20p
combine like terms
-4 - 5 + 8p - 6p + 20p
= -9 + 22p
In conclusion, 8b + 5 and -9 + 22p is the solution to the linear expressions 4(2b + 2) - 3 and -4 + 8p - 6p - 5 + 20p respectively.
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What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108[/tex]
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3 ft long with a diameter of 1.8 ft. Suppose oil is drained at a rate of 1.7 ft³ per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Answer:
4 minutes
Step-by-step explanation:
You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)
VolumeThe volume of a cylinder can be found using the formula ...
V = (π/4)d²h . . . . . . . diameter d, height h
Then the volume of the oil tank is ...
V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³
TimeThe time it takes to empty the tank is found by dividing the volume by the rate:
(7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min
It will take about 4 minutes to empty the tank.
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Please help with this answer, I will give brainliest to whoever answers correctly.
Answer:
2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))
Step-by-step explanation:
We can use the identity for the sum of two sines to rewrite the expression as follows
sin 4ẞ + sin 10ẞ = 2sin(7ẞ/2)cos(3ẞ/2)
Similarly, we can use the identity for the sum of two cosines to rewrite the expression as follows
22ẞ + sin 16ẞ = 2cos(19ẞ/2)cos(3ẞ/2)
Therefore, we have
sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2sin(7ẞ/2)cos(3ẞ/2) + 2cos(19ẞ/2)cos(3ẞ/2)
Factoring out the common factor of cos(3ẞ/2), we get
sin 4ẞ + sin 10ẞ + 22ẞ + sin 16ẞ = 2cos(3ẞ/2)(sin(7ẞ/2) + cos(19ẞ/2))
Therefore, the expression can be expressed as a product of 2cos(3ẞ/2) and the sum of sin(7ẞ/2) and cos(19ẞ/2).
I need help with this please
From the calculation that we have in the question, the volume of the rectangular prism is 30 cm^3.
How do you find the volume of a rectangular prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional shape that has six rectangular faces, where each pair of opposite faces are congruent and parallel. It can be thought of as a stretched cube, where the length, width, and height are all different.
We have that the volume of the rectangular prism is
V = lbh
V = 2 * 3 * 5
V = 30 cm^3
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the companies bounce zone and jump world run many trampoline parks around the country. the box plots show the number of trampolines at their park. which conclusion is best supported by the box plots?
The conclusion that is best supported by the box plots on the trampoline parts owned by Bounce Zone and Jump World is B. For both companies, about 25% of the parks have 21 or fewer trampolines.
What does the box plot show ?The box plot shows that both Bounce Zone and Jump World have 21 or fewer trampolines in about 25 % of their parks.
We know this because both Bounce Zone and Jump World have box plots where the box starts from 21 trampolines. The beginning of a box in a box plot represents the 25% mark or the first quartile so everything that falls below it is less than 25%. Bounce Zone and Jump World therefore have 21 or less trampolines in 25% of their parks.
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The options for the question is:
Bounce Zone has more parks than Jump World.For both companies, about 25% of the parks have 21 or fewer trampolines.Jump World has a park with 25trampolines, but Bounce Zone does not.For both companies, about half the parks have more than 26 trampolines.A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
Answer:
[tex]\boxed{\frac{8}{13} }[/tex]
Step-by-step explanation:
Probability is found by dividing the number of favorable outcomes by the total number of outcomes.
[tex]\text{P}=\dfrac{\text{favorable outcomes}}{\text{total outcomes}}[/tex]
For this problem, the favorable outcome is selecting a blue or green marble. There are 8 outcomes for this because there are 6 outcomes for blue and 2 fr green.
The total outcomes are all the marbles. Each marble could be an outcome, so there are 13 outcomes (1 for each marble).
[tex]\text{P}=(\text{blue or green})=\dfrac{8}{13}[/tex]
This fraction cannot be reduced, so the probability of selecting a blue or green marble is 8/13.
Complete Question:
A bag holds 13 marbles, 6 are blue, 2 are green, and 5 are red. You select a marble from the bag. What is the probability that the marble you select is either blue or green?
A. 5/26
B. 8/13
C. 5/13
D. 8/26
The table shows the number of people who rode two different carnival rides during the first hour of the fair on opening day:
Swing Ride
Total
96
144
240
Children
Adults
Total
Based on the data in the table, which statement is true?
Ferris Wheel
72
108
180
OA. P(adult|rode the swing ride) = P(adult)
OB.
OC. P(adult[rode the Ferris wheel) + P(adult)
OD. P(rode the swing ridelchild) *P(rode the swing ride)
P(child|rode the Ferris wheel) = P(rode the Ferris wheel)
24
36
60
Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:
A. P(aduIt|rοde the swing ride) = P(aduIt)
What dο the different fοrms οf data mean?A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.
This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00
A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)
This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.
B. This assertiοn is nοt true οr accurate.
P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)
This assertiοn Iacks bοth cIarity and vaIidity.
We can caIcuIate the prοbabiIities using the given data as fοIIοws:
P(aduIt|rοde the swing ride) = 96/240 = 0.4
P(aduIt) = (144+108)/360 = 0.8
P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6
P(rοde the swing ride|chiId) = 96/240 = 0.4
P(rοde the swing ride) = 240/360 = 2/3
P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133
Therefοre, the statement that is true based οn the given data is:
OA. P(aduIt|rοde the swing ride) = P(aduIt)
because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).
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Answer:
Step-by-step explanation:
Based οn the infοrmatiοn in the tabIe, the statement that is true based οn the given data is:
A. P(aduIt|rοde the swing ride) = P(aduIt)
What dο the different fοrms οf data mean?
A systematic cοIIectiοn οf a specific quantity might be referred tο as data. It cοnsists οf the variοus ways that amοunt can be expressed tοgether in a set. It is a set οf data intended tο be utiIized fοr a certain οbjective, Iike an anaIysis οr survey. It is pοssibIe tο refer tο anything as infοrmatiοn when it is οrganized.
This assertiοn may οr may nοt be accurate. WhiIe we are aware that 96/240 = 0.4 οf the fair's tοtaI 240 rides were taken by chiIdren, we cannοt be pοsitive that this figure accurateIy refIects the fair's tοtaI number οf chiIdren. $450.00 + $200.00 + $175.00
A. AduIt|tοοk the swing ride: P(aduIt|P) (aduIt)
This cIaim may nοt aIways be accurate. AIthοugh 0.6 οf the fair's tοtaI aduIt attendees rοde the swing ride, it is uncIear whether this percentage accurateIy refIects the fair's tοtaI aduIt attendance.
B. This assertiοn is nοt true οr accurate.
P(aduIt [had a ride οn the Ferris wheeI]) + C (aduIt)
This assertiοn Iacks bοth cIarity and vaIidity.
We can caIcuIate the prοbabiIities using the given data as fοIIοws:
P(aduIt|rοde the swing ride) = 96/240 = 0.4
P(aduIt) = (144+108)/360 = 0.8
P(aduIt[rοde the Ferris wheeI) + P(aduIt) = (72/180) + (144+108)/360 = 0.6
P(rοde the swing ride|chiId) = 96/240 = 0.4
P(rοde the swing ride) = 240/360 = 2/3
P(chiId|rοde the Ferris wheeI) = 24/180 = 0.133
Therefοre, the statement that is true based οn the given data is:
OA. P(aduIt|rοde the swing ride) = P(aduIt)
because the prοbabiIity οf an aduIt riding the swing ride (0.4) is the same as the οveraII prοbabiIity οf being an aduIt (0.8).
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Ronaldo has three and three-sevenths sandwiches. He shares three-fourths of them with his family. How many sandwiches did Ronaldo share?
Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .
what is unitary method ?A mathematical strategy for resolving proportionality issues is the unitary method. Finding the value of one unit of a quantity and utilising that value to determine the value of a different number of units of the same quantity is what this process entails. The unitary technique can be used, for instance, to determine the cost of any quantity of apples if you know that 5 apples cost $10. $10/5 = $2 would be the price of one apple. By multiplying the quantity of apples by the price of one apple, you could then calculate the price of any other number of apples. For instance, 8 apples would cost 8 x $2, or $16, to purchase.
given
Ronaldo eats sandwiches that are three and three-sevenths of a sandwich, which is an incorrect fraction:
3 3/7 = (7*3 + 3)/7 = 24/7
He divides these sandwiches into thirds and fourths among his family, making a total of:
(3/4) * (24/7) = (324)/(47) = 18/7
We can change this incorrect fraction into a mixed number because:
18/7 = 2 and 4/7
Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .
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A javelin is being launched into the air 31 feet away from the launch site is a lamp. If the javelin is travelling vertically at 3 feet per second, what is the rate of change of the angle of elevation (θ) from the lamp to the javelin when the javelin is 37 feet off the ground?
The rate of change of the angle of elevation from the lamp to the javelin when the javelin is 37 feet off the ground is zero.
Rate of changeLet's denote the distance from the lamp to the point directly below the javelin by x, and the height of the javelin above the ground by y. Then we have two right triangles: one with legs x and y, and hypotenuse 31, and another with legs x and 37-y, and hypotenuse 37. Using the Pythagorean theorem, we can write:
x^2 + y^2 = 31^2
x^2 + (37-y)^2 = 37^2
Taking the derivative with respect to time t of both sides of each equation, we get:
2x(dx/dt) + 2y(dy/dt) = 0
2x(dx/dt) - 2(37-y)(dy/dt) = 0
Solving for (dy/dt) in terms of (dx/dt), we get:
(dy/dt) = x(dy/dx)/(-y+37)
At the given moment when the javelin is 37 feet off the ground, we have y = 37, and so:
(dy/dt) = x(dy/dx)/(-y+37) = x(dy/dx)/(-37+37) = 0
This means that the rate of change of the angle of elevation is zero at this moment. In other words, the angle of elevation is not changing at the moment when the javelin is 37 feet off the ground.
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matt mopped 1/40 of the floor every 1/4 hour.The area of the floor was 3,000 square feet.what is the unit rate in square feet per hour.which represents matt mopping the floor
Answer:
75 square feet
Step-by-step explanation:
you will just multiply by 1 over 40 as it is the ratio that he works in one hour