Answer:
D
Step-by-step explanation:
3x - 2y = 10 → (1)
2y = 3x - 16 → (2)
substitute 2y = 3x - 16 into (1)
3x - (3x - 16) = 10
3x - 3x + 16 = 10
16 = 10 ← not possible
this indicates the system has no solution.
There is no solution to this system. Therefore, option D is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given that the system of linear equations are
3x - 2y = 10 -------(i)
2y = 3x - 16
3x-2y=16 -------(ii)
Subtract equation (ii) from equation (i), we get
3x-2y-(3x-2y)=10-16
0≠4
Therefore, option D is the correct answer.
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Question 60
Find the probabilities below using a standard 52 card deck.
By using the concept of probability, it can be calculated that-
1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]
5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur.
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
1) Number of ace card = 4
Number of '5' card = 4
P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]
= [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)
Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]
P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) Number of black coloured even numbered card = 10
Number of even numbered card = 20
Number of card of black colour = 26
P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]
= [tex]\frac{36}{52}[/tex]
5) Number of face cards of diamond = 3
P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
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Prove that the roots of the equation mx² + (m − 2)x − (m + 1) = 0 are real for all values of m
Answer:
Below
Step-by-step explanation:
For REAL numbers, the discriminant of the Quadratic Formula has to be a positive value (or zero)
b^2 - 4ac >= 0 where a = m b = m-2 c = -m-1
(m-2)^2 - 4(m)(-m-1) >=0
5m^2 +4 >= 0
5 m^2 +4 <===== will always be >= 0 for any value of 'm'
so all roots will be real
If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
The probability that the small bowl contains more cereal than the large one is 0.0228.
Given :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
we know that,
z = x - μ / σ
here
x = 0
μ = 1
σ = 0.5
= 0 - 1 / 0.5
= -1/0.5
= -1 / 05 / 10
= -1 * 10 / 5
= -10 / 5
= -2
if z = -2 then p value = 0.0228
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Full question :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
Express with an exponent.
125 =
A
5/3
с 3/5
B 5/5
Answer:A
Step-by-step explanation: 5 to the power of 3 is 5x5x5 which is 25x5 which then equals 125
1. Todd purchased a jumper for his infant son. The jumper clamps to the top of a door frame and has a spring from which the body of the jumper hangs to allow the infant to jump up and down. Included with the jumper are small weights, each identical in weight and size. The weights allow the user to adjust the initial height of the jumper by stretching the spring a certain distance. Todd adds 8 of the weights and notes the spring stretches 2 centimeters.
(a) According to Hook's Law, the amount that a spring is stretched, s, varies directly with the force applied to the spring by the weights, $F$. Write an equation that relates F and s for the spring on the jumper. (3 points)
F=ks 8=k 2
k=8/2 F=4 x
The equation that relates F and s for the spring on the jumper will be F=4x.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, Todd increases the weights by 8 and observes a 2 cm spring extension. According to Hook's Law, the force exerted on a spring by the weights directly affects how much it is stretched, or s.
The equation that relates F and s for the spring on the jumper is obtained as,
F=ks
8=k×2
k=8/2
F=4 x
Thus, the equation that relates F and s for the spring on the jumper will be F=4x.
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Ramesh took a loan of Rs 50,000 from Urmila at the rate of 10% p.a. If he paid a
half of the principal and all the interest at the end of 3 years, in how many years
should he pay the remaining amount with total interest of Rs 20,000 from the
beginning?
Answer:
Below
Step-by-step explanation:
In three years the interest will be
50 000 * .1 * 3 = 15 000
He pays this and 25 000 so his remaining loan is 25 000
we want to know how long will it be before this remaining loan
incurs 5 000 interest ( for a total of 20 000)
25000 * . 1 * n = 5000 shows n = 2 years more
( 5 years from original loan date)
In a Science class, there are thirty students. Ten are males and twenty are females. On the last quiz, three males and six females earned an A. What is the approximate probability of selecting a male or a student that earned an A on the quiz?
0.53
0.10
0.43
0.63
The nth term of a sequence is n²+20
a) Work out the first three terms of the sequence.?
b) How many terms in the sequence are less than 50 ?
8) Tom climbs 25 feet into the pear tree and pulls a pear from the tree. He throws it with an upward
velocity of 30 feet/second. How long will the pear be in the air if his Dad sees him and catches it at 6 feet above the ground?
The distance the pear will be in the air if his Dad sees him and catches if at 6 feet above the ground is 19/30 meters.
How to calculate distance?The term distance can be defined as a numerical qualitative measurement of how far apart points are from each other.
Distance is defined by the formula
d=v*t
The given parameters are:
v=30
s=6
height=25
Applying these parameters into the formula
d=30*t
d=30t
If the Dad stands 6 feet above the ground, we have
[tex]\frac{25-6}{30}[/tex]
=[tex]\frac{19}{30}[/tex]
Therefore the pear will be 19/30 feet in the air if the Dad sees him and catches it at 6 feet above the ground.
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PS bisects ∠QPR . Complete the proof that ∠PSR ≅ ∠PSQ .
The proof is shown in the image.
Reasons for statement
Any line that bisects an angle divides the angle into two equal parts The two lines are congruent by cpct as the triangles are congruent The angle subtended the bisector line divides equally into two angles. Also, the triangles are congruent so angle QPS = angle RPS by cpct The common line between congruent triangles is the same Triangles are congruent by side angle side rule Angles are equal by corresponding parts of the congruent triangle rule.To know more about congruent triangles,
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Two basketball players are trying to have the most
points per game for the season. The current leader has
2112 points in 77 games and the second place player
has 2020 in 74 games. How many points per game did
the leading team score?
Helpppppp
The leading team has scored 0.13 points per game for the season that the second place player.
What is PPG Statistics?
The average number of points a player scores in a game of a sport, over the course of a series of games, a season, or a career, is known as points per game, or PPG, and it is an important statistic. By dividing the total points by the number of games, it is calculated. Basketball and ice hockey are two sports that frequently use PPG statistics.First, consider the PPG of the current leader of the season from among the two basketball players.
The total number of points obtained by the current leader is equal to 2112.
The total number of games played by the current leader is equal to 77.
The points per game obtained by the current leader can be calculated as follows,
PPG = Total Points Obtained / Total Number of Games
[tex]\implies PPG=\frac{2112}{77}\\\implies PPG=27.42[/tex]
Now, consider the PPG of the second place player for the season.
The total number of points obtained by the second place player is equal to 2020.
The total number of games played by the second place player is equal to 74.
The points per game obtained by the second place player can be calculated as follows,
PPG = Total Points Obtained / Total Number of Games
[tex]\implies PPG=\frac{2020}{74}\\\implies PPG=27.29[/tex]
Subtracting the points per game of both players, we get
[tex]27.42-27.29=0.13[/tex]
Hence, the leading team has scored 0.13 points per game (PPG) for the season compared to the second place player.
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Using the normal distribution, it is found that a student has to score 0.675 standard deviations above the mean to be publicly recognized.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
z=x-nuo/sigmaIt measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The top 25% is at least the 100 - 25 = 75th percentile, which is X when z has a p-value of 0.75.Looking at the z-table, z = 0.675 has a p-value of 0.75.Hence, a student has to score 0.675 standard deviations above the mean to be publicly recognized.To know more about Standard deviation here
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can someone help quick? someone gave me the answer but didn’t explain. what’s the inequality? where do i graph this? please give the right answers only
An inequality that represents the height h, in inches, of a person allowed to ride rollar coaster is h ≥ 48
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Let h represent for the height of any member allowed to ride rollar coaster
From the question we know that everyone's height must be greater that 48 inches.
It means the inequalities would be
h ≥ 48 tall inches
Thus, an inequality that represents the height h is h ≥ 48
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The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
Answer:
182 feet
Step-by-step explanation:
Taking the fact that 112/40 = 2.8, you would need to multiply the miles per hour by 2.8 to get the feet needed.
Why is that, well I cant really explain...its just math and it works out /:
The graph shows a system of inequalities.
Graph of two inequalities.
Which system is represented in the graph?
y > x2 + 4x – 5
y > x + 5
y < x2 + 4x – 5
y < x + 5
y ≥ x2 + 4x – 5
y ≤ x + 5
y > x2 + 4x – 5
y < x + 5
The system of inequalities shown by the graph are
y > x² + 4x – 5y > x + 5How to identify inequality graphsThere are some points that help in interpreting inequality graphs.
The first part is to arrange the equation in the form so that y is the subject of the formula and to the left
Then watch out for dashed lines or solid lines
dashed lines means there is no equality sign in the inequality > OR <solid line means there is equality in the inequality ≤ OR ≥Another part is the shaded portion
shading above the line defines greater thanshading below the line defines less thanEquipped with tis information, it is clear that the two lines of the graph are both dashed and shaded above the line,
Hence we look out for equations having no equality sign in the inequality and due to the shading must be greater than.
This makes the first option the best choice
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A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.
The correct answer is option B which is -1.67 is the expected value.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
You have a higher probability of losing money than gaining it due to the distribution of probability.
There are more chances to lose than win.
As a result, you are expected to lose money.
Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.
Hence, the correct answer is option B which is -1.67 is the answer.
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Answer:
You will Gain 5 points.
Step-by-step explanation:
Got it right on the test!
Data regarding fuel efficiency of an 18-wheel truck were collected. The graph shows the correlation between the average speed above 40 miles per hour (in miles per hour) and the money spent on gas (n dollars): Estimate the average rate of change from x = 5 to x = 9.
The average rate of change of the function at the interval x = 5 to x = 9 is 1.25
How to determine the average rate of changeThe interval is given as
x = 5 to x = 9
From the question (see attachment), we have the following parameters that can be used in our computation:
x = 5 and y = 15
x = 9 and y = 20
This means that
f(5) = 15 and f(9) = 20
The average rate of change is then calculated as
Average rate of change = [f(9) - f(5)]/[9 - 5]
Substitute the known values in the above equation, so, we have the following representation
Average rate of change = [20 - 15]/[9 - 5]
Evaluate
Average rate of change = 1.25
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12. The number of liters of fuel used on a trip
varies directly with the number of miles traveled. If
a 120 mile trip requires 12.5 liters of fuel, how
many liters are required for a 504 mile trip?
Answer:
Step-by-step explanation:
using excel lookup functions, add new fields to the invoice data by bringing in information from the other data sheets
To pull values from another worksheet, we need to follow these steps:
Select cell C3 and click on it.
Insert the formula: =VLOOKUP(B3,'Sheet 2'!$ B$3:$C$7,2,0)
Press enter.
Drag the formula down to the other cells in the column by clicking and dragging the little “+” icon at the bottom-right of the cell.
How do I add a LOOKUP field in Excel?
Open Design View on the table. Click a cell in the Field Name column in the first available empty row, and then type a field name for the lookup field. Select Lookup Wizard from the drop-down list by clicking the arrow after clicking in the Data Type column for that row.
To compute values in several columns, the VLOOKUP function may be used in conjunction with other functions like the Sum, Max, or Average. Since this is an array formula, all we need to do to make it function is hit CTRL+SHIFT+ENTER at the conclusion of the formula.
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A random sample of size 36 is taken from a population with mean µ = 15 and standard deviation σ = 8. What is the probability that the sample mean is greater than 16?
Answer:
Below
Step-by-step explanation:
Deleted
What is the inverse of f(x)=2x+9?
Answer:Find the Inverse f (x)=-2x+9Find the Inverse f (x)=-2x+9 f (x) = −2x + 9 f (x) = - 2 x + 9 Write f (x) = −2x+ 9 f (x) = - 2 x + 9 as an equation. y = −2x+9 y = - 2 x + 9 f (x) = −2x + 9 f (x) = - 2 x + 9 Write f (x) = −2x+ 9 f (x) = - 2 x + 9 as an equation. y = −2x+9 y = - 2 x + 9
Step-by-step explanation:
Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².
What is Area :The space around a shape's perimeter or boundary is known as its area. To determine the areas of various forms, many mathematical formulae are available.
Area of circle = πr², where r is the radius of the circle. Area of rectangle = lb, where l = length and b = breadth.Here we have
composed of a rectangle and two semicircles.
Dimensions of the rectangle are,
Length = 14 and breadth = 4
=>Area of the rectangle = 14 × 4 = 56 units²
If we join the two semicircles,
we will have one circle with a diameter of 4 units
=> As we know Radius of the circle = Diameter/2
=> Radius of circle = 4/2 = 2 units
=> Area of the circle = 2πr
= [tex]2 \times\frac{22}{7} \times 2[/tex] = 12.56 unit²
Area of the figure = Area of rectangle + Area of the circle
= 56 units² + 12.56 unit²
= 68.56 unit²
Therefore,
The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².
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If u(x) = -2x² +3 and V(x) =
X
what is the range of (u.v)(x)?
The range of u(x) = {-15, -5,1,3,1, -5, -15} and range of v(x)= {-3,-2, -1,0,1,2,3} for the domain of x = { -3,-2,-1,0,1,2,3}
What is domain and range?The domain of a function is defined by the set of the values of independent variables and the ranges are the set of values of dependent variables.
The domains act as an input of function where ranges act as an output.
How to find domain and range?We select domain randomly as domain are the set of independent variables. But how will be the ranges must depend on the function given us.
we are given 2 function u(x) = -2x²+3 and v(x)
for the 1st function the set of domain and ranges are different, but the domain and ranges have the same values for the 2nd function.
we select domain x= {-3, -2, -1, 0, 1, 2, 3}
the ranges for u(x) ={ -15, -5, 1, 3, 1, -5 , -15}
because, u(-3) = -2(-3)²+3 = -15
u(-2) = -2(-2)²+3 =-5
u(0) = 3
similarly, for the same set of x value, v(-3) = -3
v(-2) = -2
v(0) =0
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A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N). A support cable running to the ground is inclined 71° from the horizontal.
Find the tension in the support cable. Give answer to the nearest whole number.
The tension in the support cable is 2731 N
How to find the tension in the support cable?Given that:
A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N) and a support cable running to the ground is inclined 71° from the horizontal.
This can sketch as shown in the attached image. Considering the image:
T is the tension in the support cable
Using trigonometric ratio:
cos 71° = 889/T (adjacent/hypotenuse)
T = 889/cos 71°
T = 2731 N
Therefore, the tension in the support cable is 2731 N
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is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation.
Answer:
Not parallel.
Step-by-step explanation:
Given:
m∠9 = 110°m∠8 = 70°Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Angles 9 and 10 form a linear pair:
⇒ m∠9 + m∠10 = 180°
⇒ 110° + m∠10 = 180°
⇒ m∠10 = 70°
Angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
As line p is parallel to line q, and according to the vertical angles theorem and the corresponding angles postulate:
m∠1 = m∠6 = m∠9 = m∠14 = 110°m∠2 = m∠5 = m∠10 = m∠13 = 70°m∠3 = m∠8 = m∠11 = m∠16 = 70°m∠4 = m∠7 = m∠12 = m∠15 = 110°If line a was parallel to line b, then according to the corresponding angles postulate:
m∠1 = m∠3 = m∠6 = m∠8m∠2 = m∠4 = m∠5 = m∠7As m∠1 ≠ m∠8 and m∠2 ≠ m∠7 then lines a and b are not parallel.
Solve the equation for v.
0.5v + 0.03 > 2.83
v > 1.3
v < 1.3
v > 5.6
v < 5.6
Answer:
[tex] \huge{ \boxed{v > 5.6}}[/tex]
Step-by-step explanation:
[tex]0.5v + 0.03 >2.8[/tex]
In order to solve this inequality, first subtract 0.03 from both sides of the inequality to isolate 0.5v
[tex]0.5v + 0.03 - 0.03 > 2.83 - 0.03 \\ 0.5v > 2.8[/tex]
Next divide both sides by 0.5
[tex] \frac{0.5v}{0.5} > \frac{2.8}{0.5} \\ v > 5.6[/tex]
We have the final answer as
[tex] \bold{v > 5.6}[/tex]
the first term of an arithmetic sequence is -27. the common difference of the sequence is 6. What is the sum of the first 50 terms
Answer: 6000
Step-by-step explanation:
The formula for the first [tex]n[/tex] terms of an arithmetic sequence with first term [tex]a[/tex] and common difference [tex]d[/tex] is [tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex].
In this question, [tex]a=-27, d=6, n=50[/tex].
So, [tex]S_{50}=\frac{50}{2}[2(-27)+(50-1)(6)]=6000[/tex].
A side of the triangle below has been extended to form an exterior angle of 156°. Find the value of x.
The value of x inside the triangle is 24°
How to calculate the value of x(angle)?
A straight line's total number of angles adds up to 180°. Supplementary angles are two angles whose sums equal 180 degrees. Angles are referred to as neighbouring if they have a similar vertex and side.A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight.Angles in a straight line are the total of all the angles that can be arranged in a straight line. Straight line angles add up to 180°.The angle of the straight line = 180°
156° + x = 180°
x = 180° - 156°
x = 24°
Hence, the value of x inside the triangle is 24°.
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The equation of the graph
is y = pq* where p and q are
positive constants.
Find the values of p and q.
PLS HURRY The chances of finding a rare card in a pack of trading cards can be represented with the equation y equals one-fifteenth times x, where y represents the number of rare trading cards and x represents the number of packs of trading cards. Determine how many rare trading cards you would find if you bought 90 packs of trading cards.
6
15
1,350
one-fifteenth
If you bought 90 packs of trading cards then Rare trading cards are 6
What is probability?The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
If the conditions are met, Y = 1/15 * X = 90 , then Y = 1/15 x 90 Y = 6.
A deck of cards has 52 cards. Therefore, 52 outcomes overall.
The number of positive results is 4 (as there are 4 kings in a deck)
Hence, there is a chance that this will happen.
P(E) = 4/52 = 1/13.
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