[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 159°y = 140°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:y + a = 180[/tex]
( linear pair )
[tex]\qquad❖ \: \sf \:y + 40 = 180[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - 40[/tex]
[tex]\qquad❖ \: \sf \:y = 140 \degree[/tex]
And
[tex]\qquad❖ \: \sf \:x = a +( 180 - b)[/tex]
( Exterior angle = sum of opposite interior angles )
[tex]\qquad❖ \: \sf \:x = 40 + (180 - 61)[/tex]
[tex]\qquad❖ \: \sf \:x = 40 + 119[/tex]
[tex]\qquad❖ \: \sf \:159 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 159°y = 140°flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet-stream, the same jet travels 5360 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the jet stream?
Based on the time taken by the jet when flying with the wind versus against it, the rate of the jet and jet streams are:
In still air = 1,170 mphRate of wind = 170 mphWhat is the speed of the jet?The speed of the jet flying against the wind is:
= 3,000 / 3
= 1,000 mph
The speed with the jet stream is:
= 5,360 / 4
= 1,340 mph
Assuming the speed of the jet is x and the rate of wind is y, the formulas are:
x - y = 1,000
x + y = 1,340
Solving gives:
2x = 2,340
x = 1,170 mph
The rate of jet stream is:
x - y = 1,000
1,170 - y = 1,000
y = 170 mph
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2. Hospital records show that of patients suffering from a certain disease, 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover
The probability that of 6 randomly selected patients, 4 will recover is 0.03295
The chance of an event occurring is defined by probability.
Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.
The ratio of good outcomes to all possible outcomes of an event is known as the probability.
Let X represent the binomial random variable that represents the patient count. Let p represent the likelihood that the patient will survive, and q represent the probability that they will pass away. The solution to the problem is q = 75% = 0.75, p = 25% = 0.25, and n = 6.
Required probability = 6C4[tex](0.25)^{4} (0.75)^{2}[/tex]
= 0.03295
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need heeeelp please
Answer:
7.61577310586
Step-by-step explanation:
Pythagoras Theorem 7 squared + 3 squared= 49+9=58
[tex]\sqrt{58}[/tex]
Neil emptied his change jar and noticed he only had pennies, nickels, and quarters. He had coins for a total of . He had fewer quarters than nickels. How many pennies did Neil have? The solution is
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.
Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)
Hence:
0.1x + 0.05y + 0.25z = 4.6 (1)
Also:
x = 3y (2)
And:
z = y + 4 (3)
From the equations:
x = 18, y = 6, z = 10
Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies
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Can u guys please give me the correct answe
Answer:
90°(the figure is poorly drawn)
Step-by-step explanation:
the sum of the interior angles in a triangle is 180°120 ° and y are in a straight line, so 120° + y = 180 °
find y
180 - 120 = 60°
find x
180 - 60 - 30 = 90°
What number should come next in the sequence? 0.8, 0.35, -0.1, -0.55, ... FASTTTTT
Answer:
-1
Step-by-step explanation:
0.35 - 0.8 = -0.45
-0.1 - 0.35 = -0.45
-0.55 - 0.45 = -1
Find the mean for the scores 3,820, 5,500, 8,560, 4,400, 5,350
Answer:
5,526
Step-by-step explanation:
Mean of scores = Total Value of Scores / Number of Values
= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]
= 5,526
Answer:5526
Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers
According to indical equation solve 3×=1\81
Answer:
x = - 4
Step-by-step explanation:
using the rule of indices
[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then
[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is
[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus
x = - 4
Please help me l don’t understand
a. Let [tex]d[/tex] be the number of daytime calls Eshwa makes, and [tex]e[/tex] the number of evening calls. Then the cost [tex]C[/tex] (in pence) of making [tex]d+e[/tex] calls is
[tex]C = \boxed{50d + 40e}[/tex]
b. £1 = 100p, so the cost [tex]C'[/tex] (in £) is 1/100 of the cost found in part (a),
[tex]C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}[/tex]
c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is
[tex]C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}[/tex]
c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is
[tex]C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}[/tex]
d. Let [tex]e=40[/tex] and [tex]C'=42[/tex]. Solve for [tex]d[/tex].
[tex]42 = \dfrac d2 + \dfrac{2\cdot40}5[/tex]
[tex]42 = \dfrac d2 + 16[/tex]
[tex]\dfrac d2 = 26[/tex]
[tex]d = \boxed{52}[/tex]
at a particular high school, 42% of the students participate in sports and 25% of the students participate in drama. if 53% of the students participate in either sports or drama, what is the probability that a student participates in both sports and drama?
P( A Student participates in Both sports and Drama) =0.07
What is the probability?The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
To find the probability that a student participates in both sports and drama:
Let
A =Student participate in Sport
B = Student participate in Drama
Thus we have:
P(A) = 0.42
P(B) = 0.25
and
P(Ac and B or A and Bc) =0.53
P(Ac and B ) + P( A and Bc) =0.53
P(B) - P(A and B) + P(A) - P(A and B) = 0.53
0.25 - P(A and B ) + 0.42 - P(A and B) = 0.53
0.25+0.42 - 2 * P( A and B) = 0.53
0.67 - 2 * P(A and B) = 0.53
0.67 - 0.53 = 2* P(A and B)
0.14 = 2 * P(A and B)
0.14 / 2 = P( A and B)
0.07 = P( A and B)
that is:
P( A and B) = 0.07
P( A Student participate in Both sports and Drama) =0.07.
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The probability that a student participates in both sports and drama is [tex]0.14[/tex].
What is the formula for P(AUB), where A and B are any two events?If [tex]A[/tex] and [tex]B[/tex] are any two events, then the probability of the joint event [tex](A\cup B)[/tex] is given by the following formula: [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.
Suppose [tex]S[/tex] denotes that "a student participates in sports" and [tex]D[/tex] denotes that "a student participates in drama".
So, we have [tex]P(S)=\frac{42}{100}=0.42[/tex], [tex]P(D)=\frac{25}{100}=0.25[/tex], [tex]P(S\cup D)=\frac{53}{100}=0.53[/tex].
We want to find the probability that a student participates in both sports and drama i.e., we want to find [tex]P(S\cap D)[/tex].
By the above formula, we obtain:
[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}[/tex]
Therefore, the probability that a student participates in both sports and drama is [tex]0.14[/tex].
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b) The diameter of a circular coin is 1.14 cm. How many coins of the same size are required to place in a straight row to cover 2.85 m length (without leaving any gap between each coin)
Answer:
250.
Step-by-step explanation:
if one coin covers 1.14 cm, then the required number can be calculated according the equality:
required_number=(given_length/given_diameter);
Then:
[tex]number=\frac{2.85*100}{1.14} =\frac{285}{1.14} =250[coins].[/tex]
P.S. note, the given length is in [meter], the diameter is in [cm].
ill give you brainliest :)
Following the instructions for the inequalities gives the following results:
1. 4<7, both sides multiplied by 7
= 28<49, both sides multiplied by 6
= 168<294, both sides multiplied by 3
= 504<882, both sides multiplied by 10
= 5,040<8,820
2. 11>2, add 5 to both sides
= 16>3, add 3 to both sides
= 19>9, add -4
= 15>5
3. -4<-2, subtract 6
= -10<-8, subtract 8
= -18<-16, subtract 2
= -20<-18
4. -8<8, divide by -4
= 2>-2, divide by -2
= -1<1
5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.
What are inequalities?Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.
Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.
Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.
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Write 80.54 as a mixed number.
Answer:
Step-by-step explanation:
[tex]80.54=80+0.54=80+\frac{54}{100} =80+\frac{27}{50} =80\frac{27}{50}[/tex]
4. Simple Interest: An investment earned 4% simple interest for 8 years. At its maturity, it was worth $5000. What amount was invested? (3
Answer:
To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.
Which of the following are polynomials?
A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2
Answer: C, E
Step-by-step explanation:
These are polynomials by the definition of a polynomial.
imageGiven: a = 2, b = 3, and c = 4. What is m measured angle C degree to the nearest tenth?
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
What is the measured angle C?From the law of cosines;
cosC = ( a² + b² - c² ) / 2ab
Where C is the angle C and a, b, and c are the three sides of the triangle.
Given the data in the question;
Side a = 2Side b = 3Side c = 4Angle C = ?Using law of cosine;
cosC = ( a² + b² - c² ) / 2ab
We substitute the values into the equation.
cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )
cosC = ( 4 + 9 - 16 ) / ( 12 )
cosC = -3 / 12
cosC = -0.25
We find the inverse of cosine.
C = cos⁻¹( -0.25 )
C = 104.477°
C = 104.5°
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
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Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is the following. 8
Answer: 5/36
Step-by-step explanation:
if x is normally distributed with U = 283 and o = 21 find p(x) is greater than 315
The probability that the value of p(x) is greater than 315 is 0.063754
How to determine the probability that the value of p(x) is greater than 315?From the question, the given parameters about the distribution are
Mean value of the set of data = 283Standard deviation value of the set of data = 21The actual data value = 315The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (315 - 283)/21
Evaluate the difference of 315 and 283
z = 32/21
Evaluate the quotient of 32 and 21
z = 1.524
The probability that the value of p(x) is greater than 315 is then calculated as:
P(x > 315) = P(z > 1.524)
From the z table of probabilities, we have;
P(x > 315) = 0.063754
Hence, the probability that the value of p(x) is greater than 315 is 0.063754
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distribution has a mean if 18 standard deviation of 4 a value of 24 is how many standard deviations away from the mean
A value of 24 is 2.5 standard deviations away from the mean
'How to determine the number of standard deviations away from the mean?The given parameters about the distribution are:
Mean = 18
Standard deviation = 4
Value = 24
Let the number of standard deviations away from the mean be x.
The value of x is calculated using
Mean + Standard deviation * x = Value
Substitute the known values in the above equation
18 + 4 * x = 24
Subtract 18 from both sides of the equation
4 * x = 6
Divide both sides of the equation by 4
x = 1.5
Hence, a value of 24 is 2.5 standard deviations away from the mean
So, the complete parameters about the distribution are:
Mean = 18
Standard deviation = 4
Value = 24
24 is 2.5 standard deviations away from the mean
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Any helppppppp??????
First find volume of both the cylinders:
Cylinder Volume Formula: πr²h
(r => radius, h => height)
*Container A:
r = 8
h = 15
πr²h = π(8)²(15) = 960π³
*Container B:
r = 11
h = 13
πr²h = π(11)²(13) = 1573π³
What % of container B is empty after the pumping is complete?
The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:
[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)
Hope it helps!
Select the correct answer.
Which statement is true about function f, which is shown in the graph?
ƒ(x) = -8x5 + 4x³ + 5x
Answer:
I think its A
Step-by-step explanation:
ALOT KF POINTS PLEASE HELP The measures of two exterior angles are given in the figure below.
Choose an equation that could be used to represent one of the exterior
angles and a logical conjecture about the exterior angles of a triangle.
An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B
What is a triangle?The term triangle refers to a figure that has three sides. There are several types of triangles such as the;
Isosceles triangleScalene triangleRight angled triangleDespite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.
Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B
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One circle has a circumference of 12x cm. Another circle has a circumference of 32x cm. What is the ratio of the
radius of the smaller circle to the radius of the larger circle?
O 3:8
O 8:3
O 1:3
O 3:1
Answer:
3 :8
Step-by-step explanation:
12 : 32 = 3:8
I believe that is right.
URGENT!!!!!!
Use arrow notation to describe the translation of point P(–5, –4) to point P′(–8, –7).
The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:
(x,y) -> (x - 3, y - 3).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:
(x,y) -> (x - 3, y - 3).
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The function y = x2 + 3 is a transformation of the function y = x2. How is the y-intercept of the function affected by the transformation?
The y-intercept of the graph of y = x2 is shifted down 3 units.
The y-intercept of the graph of y = x2 is shifted to the left 3 units.
The y-intercept of the graph of y = x2 is shifted to the right 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
-----------------------------------------------------------------------------------------------
Answer on Edmentum is:
The y-intercept of the graph of y = x2 is shifted up 3 units.
Explanation:
The graph of a function in the form y = f(x) + k is the graph of f shifted up k units. The graph of y = x2 + 3 is the graph of y = x2 shifted 3 units up, so the y-intercept of the graph of y = x2 is shifted up 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the parent function f(x) = x^2
If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;
g(x) = f(x) + 3
g(x) = x^2 + 3
Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3
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Consider the given statement.
If it is not Monday, then there are students in the gym.
For each statement below, determine whether it is equivalent to the given statement, the negation of the given statement, or neither of these.
Statement Equivalent Negation Neither
It is not Monday and there are not students in the gym.
It is Monday or there are students in the gym.
If there are not students in the gym, then it is Monday.
There are not students in the gym or it is not Monday.
Answer:
NegationStatementEquivalentNeitherStep-by-step explanation:
If it is not Monday, then there are students in the gym.
Negation: It is not Monday and there are not students in the gym.
Statement: It is Monday or there are students in the gym.
Equivalent: If there are not students in the gym, then it is Monday.
Neither: There are not students in the gym or it is not Monday.
500 portions of strawberries have been ordered for the tournament, but because of bad weather only
5
6
of the order has been delivered.
10% of those delivered are given to the players and staff.
How many portions of strawberries can be sold?
We conclude that 375 portions can be sold.
How many portions can be sold?
We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:
p = (5/6)*500 = 416.6
Which we can round to the next whole number, 417.
Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:
N = 417*(90%/100%) = 417*0.9 = 375
We conclude that 375 portions can be sold.
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If 5 bags weigh the same as 3 blocks, how many blocks will 9 bags weigh?
OA) 3 blocks
OB) 4.4 blocks
OC) 5.4 blocks
OD) 15 blocks
Answer: C. 5.4 Blocks
Step-by-step explanation:
Given information
5 bags = 3 blocks
Set variable
Let x be the number of blocks
Constructure proportional equation
[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]
Cross multiply the fraction
[tex](3)~*~(9)~=~(5)~*~(x)[/tex]
[tex]27~=~5x[/tex]
Divide 5 on both sides
[tex]27~/~5~=~5x~/~5[/tex]
[tex]\Large\boxed{x=5.4~blocks}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
oc
Step-by-step explanation:
5 times .6 equals 3
9 times .6 equals 5.4
What is the missing factor in the equation? Assume x * 0 and y* 0.
(5x²)(7) = 3xV²
5y
10
O
O
3x
लौजे अने
5y
4x
O 2xy²
5
O 9x³y
25
Answer:
[tex]\sf b) \quad \dfrac{y^3}{4x}[/tex]
Explanation:
[tex]\sf \left(\dfrac{6x^2}{5y}\right) \left(?}\right) = \left(\dfrac{3xy^2}{10}\right)[/tex]
cross multiply variables
[tex]\sf ? = \left(\dfrac{3xy^2 (5y)}{10(6x^2)}\right)[/tex]
distribute inside parenthesis
[tex]\sf ? = \left(\dfrac{15xy^3}{60x^2}\right)[/tex]
remove parenthesis and simplify
[tex]\sf ? = \dfrac{y^3}{4x}[/tex]
express 350 as a product of prime factors
Answer:
2^1 × 5^2 × 7^1 = 350
Step-by-step explanation:
2, 5, 7 are prime
first step is to divide the number 350 with the prime factor 2
continue dividing the number 175 by the next smallest prime factor
stop until you can't divide anymore
https://www.cuemath.com/numbers/factors-of-350/