Answer:
A) AAA
Step-by-step explanation:
This proved similarity, but not necessarily congruency. If the angles are the same in a triangle, they could be smaller and larger versions of themselves. They will have the same shape, but not necessary the same size. The side lengths will be proportional. If the scale factor between the two triangles is 1 , then the triangles would be congruent, but they could have any scale factor greater or less than 1 too.
what is the term that describes measures that would be taken to decrease the size of a professional sports league or organization?
The term that describes measures that would be taken to decrease the size of a professional sports is contraction.
Contraction is the act of decreasing or drawing collectively to make smaller; the alternative of expansion. In this case, the proprietors need to lessen the wide variety of groups with the aid of using removing franchises which are dropping the maximum money. Players who're on Minor League or break up contracts aren't completely assured their salaries. A participant on a break up or Minor League settlement will earn the prorated part of his Major League earnings for time spent at the Major League roster.
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The length of a line is 12.3 cm, correct to 1 decimal place.
Write down the upper bound of the length of the line.
The upper bound of the length of the line is 12.34 cm
How to determine the upper bound of the length of the lineFrom the question, we have the following parameters that can be used in our computation:
Length of the line = 12.3 cm
From the question, we understand that
Time = rounded to the nearest one decimal place
The highest number that can be rounded to 12.3 to the nearest one decimal place is 12.34
This means that
Upper bound = 12.34
Hence, the upper bound is 12.34 cm
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Find the derivative please
Answer:
[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]
Step-by-step explanation:
Apply natural logarithm chain rule:
[tex] \displaystyle{y = \ln(u) \to y' = \dfrac{u'}{u}}[/tex]
Where u is a function. The ' symbol indicates that the function to be derived. From this formula, we will have:
[tex] \displaystyle{y' = \dfrac{ \left (\dfrac{1 + x}{1 - x} \right)'}{ \dfrac{1 + x}{1 - x}}}[/tex]
Now we have to derive quotient functions, we can use quotient rule for this:
[tex] \displaystyle{y = \dfrac{u}{v} \to y' = \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]
Where u and v are functions. Therefore, from numerator:
[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{(1 + x)'(1 - x) - (1 + x)(1 - x)'}{ {(1 - x)}^{2} }}[/tex]
Derive using power rule and constant rule where:
[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: \: ( c \in \mathbb{R})}[/tex]
Thus:
[tex] \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1(1 - x) - (1 + x)( - 1)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x- ( - 1 - x)}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{1 - x + 1 + x}{ {(1 - x)}^{2} }} \\ \\ \displaystyle{ \left( \dfrac{1 + x}{1 - x} \right)' = \dfrac{2}{ {(1 - x)}^{2} }}[/tex]
Therefore, we will now have:
[tex] \displaystyle{y' = \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}}}[/tex]
Simplify expressions:
[tex] \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ {(1 - x)}^{2}} \times \dfrac{1 - x}{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ 1 - x} \times \dfrac{1 }{1 + x} } \\ \\ \displaystyle{ \dfrac{ \dfrac{2}{ {(1 - x)}^{2} }}{ \dfrac{1 + x}{1 - x}} = \dfrac{2}{ (1 - x)(1 + x)}}[/tex]
Therefore, the derived function is:
[tex] \displaystyle{ y' = \dfrac{2}{1 - {x}^{2} }}[/tex]
In factoring the expression 12x²y³ + 20x³y, which of the following is the greatest
common factor?
(F) 8x³y³
(G) 8x²y
(H) 4x²y
(I) 4xy
Answer:
12 and 24 gcf = 4
so the only choice left is
(H) 4x²y
(I) 4xy
12x²y³ + 20x³y = lowest of x is x² and y is y
then its
(H) 4x²y
CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
Graph the function and identify the domain and range.
y=-0.25x^2
(-∞, ∞) is the domain of y=-0.25x² and (−∞,0] is range.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given function is y=-0.25x²
y equal to minus zero point two five times of x square.
We need to find the domain and range of the function.
Let us find few points of x and y.
x 0 1 2 3 4
y 0 -0.25 -1 -0.5625 -4
In the given attachment the graph is given.
The domain is:
{x∣x is R} or (-∞, ∞)
The range is {x∣x≤0} or (−∞,0]
Hence, the domain of y=-0.25x² is (-∞, ∞) and range is (−∞,0].
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A mixture of monatomic and diatomic gases has specific-heat ratio gamma = 1.52. What fraction of its molecules are monatomic?
Its molecules' monatomic fraction is 0.444.
Define fractionAn element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The fact that
The formula gamma monatomic
Determines the specific heat ratio of monoatomic gas.
5/3=1.67
Calculates the specific heat ratio of a diatomic gas.
Gamma monatomic =7/5=1.4
We have a monoatomic and diatomic gas mixer with a gamma mixer specific heat ratio of 1.52.
Calculating the monoatomic gas fraction is as follows:
Let's assume that "x" is the percentage of monoatomic
1.67* x+1.4* (1-x)=1.52
1.67* x+1.4-1.4* x=1.52
0.27* x=0.12
x = 0.12/0.27
x= 0.444
Its molecules' monatomic fraction is 0.444.
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how many groups of five can be chosen that contain at most three women? a group of five that contains at most three women can contain no women, one woman, two women, or three women. so, the number of groups of five that contain at most three women is
The no. of groups of five can be chosen that contain at most three women is 60.
The method we use to solve this is combination method.
What is combination in mathematics?Mathematical combinatorics is a division that deals with counting.
Combinatorics can assist us in counting the possible sequences in which something can occur.
Numerous applications of combinatorics can be found in other branches of mathematics, such as graph theory, coding and cryptography, and probability.
In mathematics, you can also have combinations, such as linear combinations or combinations of functions.
solutionTo solve this we use combination method of mathematics
The no. of groups of five can be chosen is
⁵C₃ * ⁴C₂
⇒ (5 * 4 * 3! / 3! * 2!) * (4 * 3 * 2! / 2! * 2!)
⇒ (5 * 4 / 2 * 1) * (4 * 3 / 2 * 1)
⇒ 5 * 2 * 2 * 3
⇒ 60
The no. of groups of five can be chosen that contain at most three women is 60.
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Select the correct answer.
Of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit to climb the mountain. What is
the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
the probability that a person picked at random from the group is a male or female is fit to climb Mount Shasta is 0.472 (or in percent near 47.2%).
How do you calculate probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
What are the 3 types of probability?Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).
Subjective Probability. Definition of Relative Frequency.
1. Determine the number of male climbers:
200 men - 100%
x men - 12 %
. Of the 60 people in California who are physically capable of climbing Mount Shasta, 24 are men, leaving 36 women.
The likelihood that a guy will be selected at random from the group is
The likelihood that a random member of the group is physically capable of climbing Mount Shasta is: 0.472
0.472 (or, in percentage terms, close to 47.2%).
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A weather forecaster says that the temperature is changing at a rate of -8° per hour. At this rate, how long will it take for the temperature change to be -24°? It will take _____ hours for the change in temperature to be -24
The transition to -24 degrees will take three hours .The balance between energy coming into and going out of the planet's system determines its temperature.
What influences how the temperature fluctuates?The balance between energy coming into and going out of the planet's system determines its temperature. The Earth warms up when incoming solar energy is absorbed by the Earth system. Earth does not warm as a result of solar energy being reflected back into space. Earth cools as energy that has been absorbed is ejected back into space.Since 1880, the Earth's average temperature has increased by 0.14° F (0.08° C) every decade; however, since 1981, the pace of warming has increased by 0.32° F (0.18° C) per decade, or more than twice as fast. Using NOAA's temperature data, 2021 ranked as the sixth-warmest year ever.Explanation:
-8% / -24 = 3.
The transition to -24 degrees will take three hours.
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6. The people at the party ate 16 hot chickin wings and 26 mild chickine wings. What percent of the chickin wings ere mild?
28.1%
O 22.5%
O 61.5%
O 61.9%
Answer: 61.9%
Step-by-step explanation:
First, add 16 and 26 together to get the total of chicken = 42
Then take 26 divided by 42, then times 100% = 61.9%
Is the product of √1024 and -3.4 rational or irrational? Explain your answer.
Answer:
The product is rational-------------------------------------------
The first number is:
[tex]\sqrt{1024} =\sqrt{32^2} =32[/tex]And the second number is -3.4.
Both numbers are rational, hence their product is rational.
Answer:
Rational as it is a terminating decimal.
Step-by-step explanation:
Given expression:
[tex]\sqrt{1024} \cdot -3.4[/tex]
Rewrite 1024 as 32²:
[tex]\implies \sqrt{32^2} \cdot -3.4[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies 32 \cdot -3.4[/tex]
Multiply the numbers:
[tex]\implies -108.8[/tex]
Therefore, the product is a terminating decimal.
A rational number is a number that can be expressed as the ratio of two integers (where the denominator does not equal zero).
A terminating decimal can be written as a rational number.
To convert a terminating decimal into a rational number, multiply the number by a multiple of 10 that eliminates the decimal, then divide by the same number:
[tex]\implies \dfrac{-108.8 \cdot 10}{10}[/tex]
[tex]\implies -\dfrac{1088}{10}[/tex]
Reduce the fraction to its simplest form by dividing the numerator and denominator by 2:
[tex]\implies -\dfrac{544}{5}[/tex]
Therefore, the product of √1024 and -3.4 is rational as it is a terminating decimal.
Erin makes the following statements. The scale factor from ∆ABC to ∆XYZ is 31. The area of ∆XYZ is 13 the area of ∆ABC.
The statement made by Erin about the triangles is false
How to determine the true statements?From the question, we have the following parameters that can be used in our computation:
The scale factor from ∆ABC to ∆XYZ is 31. The area of ∆XYZ is 13 the area of ∆ABC.As a general rule of dilation (i.e. scale factors),
The area of the image of the dilation is the square of the scale factor multiplied by the area of the pre-image shape
Mathematically, this is represented as
Area of the image of the dilation = scale factor² * Area of the pre-image shape
Using familiar terms, we have
Area of ∆XYZ = (31)² * the area of ∆ABC.
The above statement is true and it is not the same as Erin's statement
Hence, Erin is incorrect
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5 1/5 - 1 3/4 what’s the answer
Answer: 69/20
Step-by-step explanation:
5 1/5 = 26/5
1 3/4 = 7/4
26/5 - 7/4
= 104/20 - 35/20
= 69/20
Given g(x) = -2x + 1, solve for a when g(x) = 5.
If the short on a clock is in 9 and the long hand is on 10 what time is it?
Answer: 9:50 AM/PM
Step-by-step explanation: Since the shorthand (hour) is on the 9, the hour is 9:00. The long hand (minutes) is on the 10, so it is 50. So, therefore we have 9:50. We don't know if it's am or pm, so we don't know if it's in the morning or the afternoon.
describe the solution set for the system of equations that consists of the equation of the line shown and .y=1/2x-3
The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
What is the equation?
The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.
Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.
The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.
So, given equations:
y = 1/2 * x - 3
y = - 1/2 * x - 3
As we are aware, a line's slope-intercept form is:
y = m x + c
Therefore, it is clear from equations 1 and 2 that:
m1 = 1/2 and c1 = -3
m2 = -1/2 and c2 = -3
Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."
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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?
a. They have the same slope but different y-intercepts, so they have no solution.
b/. They have the same slope but different y-intercepts, so they have one solution.
c. They have different slopes but the same y-intercept, so they have no solution.
d. They have different slopes but the same y-intercept, so they have one solution.
which functions have a zero at x equals 4? check all that apply. and (x )equals negative 2 x squared minus 18 x minus 40 b. c (x )equals 2 x squared minus 11 x plus 12 c. e (x )equals 3 x cubed plus x squared minus 48 x minus 16 d. a (x )equals x squared minus 3 x minus 28 e. b (x )equals x cubed minus 4 x squared minus x plus 4
The function that have a zero at x = 4 are
f(x) = 2x^2 - 11x + 12 f(x) = 3x^3 + x^2 - 48x - 16 f(x) = x^3 - 4x^2 - x + 4The first function is
f(x) = -2x^2 - 18x - 40
Substitute the value of x = 4
f(4) = -2(4)^2 - 18(4) - 40
= -2(16) - 72 - 40
= -32 - 72 - 40
= -144
The result is not zero
The second function is
f(x) = 2x^2 - 11x + 12
f(4) = 2(4)^2 - 11(4) +12
= 32 - 44 + 12
= 0
The result is zero
The third function is
f(x) = 3x^3 + x^2 - 48x - 16
f(4) = 3(4)^3 + 4^2 - 48(4) - 16
= 192 + 16 - 192 - 16
= 0
The result is zero
The fourth function is
f(x) = x^2 - 3x - 28
f(4) = 4^2 - 3(4) - 28
= 16 - 12 - 28
= -24
The fifth function is
f(x) = x^3 - 4x^2 - x + 4
f(4) = 4^3 - 4(4)^2 - 4 + 4
= 64 - 64 - 4 + 4
= 0
Therefore, the function f(x) = 2x^2 - 11x + 12, f(x) = 3x^3 + x^2 - 48x - 16 and f(x) = x^3 - 4x^2 - x + 4 have zero at x equals 4
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X+y=0,5x+y=4 using substitution method
Answer:
(1, - 1 )
Step-by-step explanation:
x + y = 0 → (1)
5x + y = 4 ( subtract 5x from both sides )
y = 4 - 5x → (2)
substitute y = 4 - 5x into (1)
x + 4 - 5x = 0
4 - 4x = 0 ( subtract 4 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
substitute x = 1 into (1) and solve for y
1 + y = 0 ( subtract 1 from both sides )
y = - 1
solution is (1, - 1 )
hadlee spent 1/4 of her money on christmas presents she had 180 remaining . how much did hadlee soend on christmas present
The amount for handle soend on Christmas present will be 240.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.
Now,
Since, Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.
Let the amount for handle soend on Christmas present = x
Hence, The amount for handle soend on Christmas present will be;
⇒ x - 1/4x = 180
⇒ 3/4x = 180
⇒ 3x = 180 × 4
⇒ 3x = 720
⇒ x = 240
Thus, The amount for handle soend on Christmas present will be 240.
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2x34x56
im in -8ht garde and me no know multipcacion pls hulp
Answer:
Step-by-step explanation:
3,808
Answer: 3808
Step-by-step explanation:
2 times 34 = 68
68 times 56 = 3808
Answer is 3808
Solve the following compound inequality.
9x + 6 > 132 and -7x + 19 < -128
The solution of the inequality 9x + 6 ≥ 132 and -7x + 19 < -128 is x ≥ 14 and x > 21.
How to solve compound inequality?Compound inequalities are a type of inequality that has two or more parts.
In other words, a compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
9x + 6 ≥ 132 and -7x + 19 < -128
Let's solve them independently.
9x + 6 ≥ 132
subtract 6 from both sides of the inequality
9x + 6 ≥ 132
9x + 6 - 6 ≥ 132 - 6
9x ≥ 126
divide both sides by 9
x ≥ 126 / 9
x ≥ 14
-7x + 19 < -128
subtract 19 from both sides of the inequality
-7x + 19 - 19 < - 128 - 19
-7x < - 147
divide both sides by - 7
x > - 147 / -7
x > 21
Therefore, the solution is x > 21 and x ≥ 14
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bailey tried to prove that \triangle fgj\sim \triangle fhi△fgj∼△fhitriangle, f, g, j, \sim, triangle, f, h, i in the following figure, but her proof is wrong.
The first error Bailey made was in the justification for his initial statement. The correct term to use is reflexive property.
What is the Reflexive Property of Congruence?An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.
If A is an angle, then A is an angle.
Angle A intersects Angle A.
An angle will always be equal to or congruent to itself, according to the reflexive property of congruence.
So, for instance, given an angle, B, so:
∠B ≅ ∠B
Based on the reflexive property of congruence and the illustration provided:
∠F ≅ ∠F
Therefore, the first error Bailey made was in the justification for his initial statement. The correct term to use is reflexive property.
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Complete question;
Bailey tried to prove that FGJ~FHI in the following figure, but her proof is wrong. What is the first mistake Bailey made in the proof?
14% of americans like to only cook and 48% of americans like to only shop, while 85% enjoy either cooking or shopping. what is the probability that a randomly selected american enjoys both activities?
The probability that a randomly selected american enjoys both activities is 23 % .
Given :
14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .
14 % = 0.14
48 % = 0.48
overlapping is 85 % = 0.85
P ( A ) = 0.14
P ( B ) = 0.48
P ( A and B ) = 0.85
we know that,
P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )
= 0.14 + 0.48 - 0.85
= 0.62 - 0.85
= -0.23
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suppose a ladybug is walking randomly along the rim of a very large disc. every second, it either moves forward one unit along the rim with probability 12, moves backwards one unit with probability 16, or stays still with probability 13. suppose the ladybug is at position 0, 1, or 2 at time t with probabilities 14, 14, and 12. what is the probability that the ladybug will be at position 1 at time t 1?
The probability that the ladybug will be at position 1 at time t+1 is ((1/2)*(12/50) + (1/2)*(16/50)) = 14/50 = 0.28.
Why does probability matter?Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.
How do you determine probability?The probability is computed by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
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Two angles which each measure less than 90° are complementary.
If the statement is false give a counterexample.
Responses
A False; 40° and 50°.False; 40° and 50°.
B False; 110° and 20°.False; 110° and 20°.
C False; 30° and 80°.False; 30° and 80°.
D The statement is true.
The given statement is true. The example is 40° and 50°.
What is counterexample?
An example that satisfies the condition(s) of a mathematical statement but does not result in the conclusion of the statement is referred to as a counterexample.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
If the sum of two angles is 90°, then the angles are complementary angles each other.
40° and 50° both angles are less than 90°.
The sum 40° and 50° is 90°.
Thus, 40° and 50° are complementary to each other.
Therefore the given statement is true.
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a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees. in how many ways can this company buy them?
Number of ways can this company buy them is 1623160.
Given :
a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees.
Number of ways = [tex]35_C_6[/tex] or C ( 35 , 6 )
we know that ,
C ( n , r ) = n! / ( n - r ) ! r!
substitute
= 35 ! / ( 35 - 6 ) ! 6!
= 35 * 34 * 33 * 32 * 31 * 30 * 29! / 29! * 6!
= 35 * 34 * 33 * 32 * 31 * 5 / 5 * 4 * 3 * 2 * 1
= 35 * 17 * 33 * 32 * 31 / 4 * 3
= 35 * 17 * 11 * 8 * 31
= 1623160 ways
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At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half. write two different expressions that represent the new cost of the items, using s for the cost of each shirt & P for the cost of a pair of pants. Explain the different information each one shows.
The required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,
Given that,
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
let y be the total cost for each different item
cost of the shirt = s - 10 and pair of pants = 2p
According to the question,
y = s - 10 / 2 and y = 2p / 2
Thus, the required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,
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jim is considering pursuing an ms in business analytics degree. he has applied to two different universities. the acceptance rate for applicants with similar qualifications is 30% for university x and 45% for university y. what is the probability that jim will be accepted at both universities?
The probability of acceptance of Jim at both the University as per given acceptance rate is equal to 0.135.
As given in the question,
Acceptance rate of Jim application at University x is equal to 30%
Acceptance rate of Jim application at University y is equal to 45%
Probability of acceptance of application in University x is:
P(x) = 30 /100
= 0.30
Probability of acceptance of application in University y is:
P(y) = 45 /100
= 0.45
Probability of acceptance of application at both the University is:
P(x and y) = P(x) × P(y)
= 0.30 × 0.45
= 0.135
Therefore, the probability of acceptance application at both the University is equal to 0.135.
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how many cups is it?
The number of cups that will be in 3 gallons is 48 cups.
How to calculate the number of cups?It is important to note that ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Based on the information, the number of cups won a gallons will be:
= 64 / 4
= 16 cups.
Therefore, the cups that will be in 3 gallons will be:
= 3 × 16. cups
= 48 cups.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
m∠5 + m∠6 are linear pairs, so their sum has to be 180°.
m∠2 + m∠3 = m∠6 because of the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the two opposite interior angles. (using this logic, m∠1 equals the sum of m∠5 and m∠3, and m∠4 equals the sum of m∠2 and m∠2).
m∠2 + m∠3 + m∠5 = 180° because the triangle sum property says that the sum of a triangle's interior angles will equal 180°.
