10 is the probability that hamid guesses both answers correctly .
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
the likelihood that Hamid will correctly guess both answers
= 2/5x1/4 = X
= 0.4x0.25 = X
= 0.1 = X
= 0.1x 100 = 10
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This graph shows fuel consumption for a car during a test run. Three of the statements are true. Which is NOT?
Line graph. X axis labeled miles; y axis labeled gallons. Line with upward arrow extends from point where X and Y axes connect (0, 0) with one marked coordinate (73.5, 3.5).
The car used 312 gallons of gas to go nearly 75 miles.
The car used 70 gallons of gas to go 3 miles.
The car used gas at a unit rate of 21 miles per gallon.
At this rate, it would take 4 gallons of gas to travel 84 miles.
In the graph showing fuel consumption for a car during a test run the correct statement is
At this rate, it would take 4 gallons of gas to travel 84 miles.How to find the correct statementThe information given in the problem will help to find the equation of the graph in the form
y = mx + c
definition of variable to suit the problem
y = output variable = number of gallons
m = slope
x = input variable = number of miles
c = y intercept
The slope
= (3.5 - 0) / (73.5 - 0)
= 0.05
the y intercept is 0
the equation of the line is y = 0.05x
Only option the last option fits the equation as shown
number of gallons = 0.05 * number of miles
= 0.05 * 84 miles
= 4.2 gallons
= 4 gallons
hence the last option is the correct choice
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2
Write the answer in each blank.
Of these numbers
745 281 578 170
is the smallest
is the largest
Answer:
170 is the smallest
745 is the largest
Step-by-step explanation:
It is what it is
there are 498 identical plastic chips numbered 1 through 498 in a box. what is the probability of reaching into the box and randomly drawing a chip number that is greater than 315? express your answer as a simplified fraction or a decimal rounded to four decimal places.
The probability of reaching into the box and randomly drawing a chip number that is greater than 3150 is 0.3675
In this question we have been given there are 498 identical plastic chips numbered 1 through 498 in a box.
We need to find the probability of reaching into the box and randomly drawing a chip number that is greater than 315
Total number of chips = 498
so, n(S) = 498
Let event A: drawing a chip number that is greater than 315
The number of chips greater than 315:
498 - 315 = 183
So, n(A) = 183
The probability of reaching into the box and randomly drawing a chip number that is greater than 315 using the formula of probability,
p(A) = n(A)/n(S)
p(A) = 183/498
p(A) = 0.3675
Therefore, the required probability is 0.3675
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Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each. Let x represent the number of apples and y represent the number of mangos she can buy.
Problem part 1: Mia has $20 to spend. Which inequality can be used to represent this situation?
Problem part 2: If Mia decided to buy 3 mangos, determine the maximum number of apples that she could buy.
The inequality that can be used to represent this situation is 2x + 1.50y ≤ 20.
The maximum number of apples she can buy is 7 apples.
How to represent inequality?Mia went into a grocery store and where they sell apples for $2 each and mangos $1.50 each.
where
x = number of applesy = number of mangoesTherefore, let's represent the inequality when Mia has to spend 20 dollars.
2x + 1.50y ≤ 20
If Mia decide to buy 3 mangoes , the maximum number of apples she can buy can be calculated as follows:
2x + 1.50y ≤ 20
2x + 1.50(3) ≤ 20
2x + 4.5 ≤ 20
2x ≤ 20 - 4.5
2x ≤ 15.5
x ≤ 15.5 / 2
x ≤ 7.75
Therefore, the maximum she can buy is 7 apples.
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miley believes that listening to white noise can enhance verbal exam performance. she takes a random sample of college students and randomly assigns each student to one of two groups-the quiet group and the white noise group. the quiet group is asked to take a verbal exam in a completely silent classroom. the white noise group is asked to take the same exam in a classroom in which white noise is playing in the background. all students have one hour to complete the exam. miley will then compare the mean exam score for the two groups. suppose miley makes a type i error. in terms of the scenario, what would this mean?
A Type I error in this scenario would mean that Miley would conclude that the noise impacts the students when in fact it doesn't.
What are Type I errors and Type II errors?The definitions of Type I errors and Type II errors are presented as follows:
Type I: Rejection of a true null hypothesis, meaning that the null hypothesis is true, but a sample gives you enough evidence to reject it.Type II: Non-rejection of a false null hypothesis, meaning that the null hypothesis is false, but the sample does not give you enough evidence to reject it.The hypotheses tested in this problem are given as follows:
Null hypothesis: not enough evidence to conclude that there are differences in the exam scores.Alternative hypothesis: enough evidence to conclude that there are differences in the exam scores.A Type I error would mean that she rejected a true null hypothesis, meaning that Miley would conclude that the noise impacts the students when in fact it doesn't.
(rejected null hypothesis means that there is enough evidence to conclude that there are differences).
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To secure a 500-meter radio tower against high winds,
guy wires are attached to the top of the tower. Each wire
forms a 15° angle with the top of the tower. Find the length
of the wire from the tower to its anchor in the ground.
Answer: To find the length of the wire from the tower to its anchor in the ground, you can use the formula for the length of a side in a 30-60-90 triangle. Since the angle between the wire and the tower is 15°, the angle between the wire and the ground is 75° (90° - 15°). This means that the wire and the tower form a 30-60-90 triangle.
In a 30-60-90 triangle, the side opposite the 30° angle is half as long as the hypotenuse, and the side opposite the 60° angle is half as long as the side opposite the 90° angle. Since the wire is the hypotenuse of the triangle, and the wire is opposite the 60° angle, the length of the wire from the tower to its anchor in the ground is half as long as the hypotenuse.
Therefore, the length of the wire from the tower to its anchor in the ground is 500/2 = 250 meters.
Construct a triangle with sides
equal to a and b and and having angle c included as the angle
The triangle with sides a and b and angle c is added as an attachment
How to construct the triangle with the given propertiesFrom the question, we have the following parameters that can be used in our computation:
Triangles with the following properties
Side lengths = a and b
Angle between the side lengths = C
The above parameters mean that
Side length BC = aSide length AC = bVertex C = Angle CAlso, the other angles and sides can be derived from the above parameters
So, we have
Side length AB = cVertex A = Angle AVertex B = Angle BNext, we construct the triangle
See attachment for the triangle
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Salma finds some nickels and pennies
under the couch cushions. How much
money (in dollars) does she have if she
has 100 nickels and 150 pennies? How
much money (in dollars) does she have if
she has a nickels and y pennies?
Total value, 100 nickels and 150
pennies (dollars):
Total value, x nickels and y pennies
(dollars):
Answer:
$6.50
0.05x + 0.01y
Step-by-step explanation:
There are 100 pennies in a dollar. So each penny is 1/100 = $0.01
Each nickel is worth 5 pennies. So there are 20 nickels per dollar and therefore each nickel is worth 20/100 = $0.05
If you have 100 nickels, this works out to 0.05 x 100 = $5.00
If you have 150 pennies this works out to 0.01 x 150 = $1.50
Total value = 5 + 1.50 = $6.50
If you have x nickels and y pennies then that, inn dollar amount, would work out to
0.05x + 0.01y
How do I solve -3x-2y=5 and get the initial value and rate of change.
Answer:
-3/2
Step-by-step explanation:
[tex]-3x-2y=5 \\ \\ 3x+2y=-5 \\ \\ 2y=-3x-5 \\ \\ y=-\frac{3}{2}x-\frac{5}{2}[/tex]
A photo is 16in long and 126cm wide.what is the approximate area of the picture in square feet?
The picture has the dimension of a rectangle and will have the area of 66.166 in square feet.
How to calculate for the areaWe have to convert the length and width to be in same unit, before calculating for the area by multiplying the length by the width, and then convert the result to be in square feet.
1 cm = 0.394 inches
126 cm = 126 × 0.394 inches
126 cm = 49.644 inches
So the picture has length 16 inches and width 49.644 inches
area of picture = 16 inches × 49.644 inches
area of picture = 794.304 square inches
1 inch = 0.0833 feet
794.304 square inches = 794.304 × 0.0833 square feet
794.304 square inches = 66.166 square feet.
In conclusion, the picture has an area of 66.166 square feet.
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CHALLENGE:
Combine like terms:
3y + 4xy + x + 2y + 2xy + x + 10 + 1
Answer: 2x+6xy+5y+11
Step-by-step explanation:
Two cities are 145 miles apart. A truck travels this distance in 2.5 hours. A car is 1.5 times as fast as the truck. How long does it take the car and the truck to meet if they leave at the same time and travel toward each other
The time it will take the car and truck to meet is 5hours
What is velocity?Velocity is the rate of change of displacement with time. It is a vector quantity and it is measured in meter per seconds but it can also be measured in other units like kilometers per hour and miles per hour.
Velocity = displacement/time
the velocity of the truck is 145/2.5 = 58miles per hour
the car is 1.5 times faster than the truck
this means the velocity of the car is 58× 1.5= 87miles per hour
displacement = velocity×time
total displacement = 145miles
displacement of car = 87t
displacement of truck = 58t
using addition of vectors
145=87t-58t
145= 29t
t = 145/29
t= 5hours
therefore at 5hours the car and the truck will meet
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Help meee please !!!???
Answer:
Step-by-step explanation:
it is c
Which equations are true for x = –2 and x = 2? Select two options
O x2 – 4 = 0
O x2 = –4
O 3x2 + 12 = 0
O 4x2 = 16
O 2(x – 2)2 = 0
The only two options with equations that are true for x = –2 and x = 2 are;
Option A: x² - 4 = 0
Option D: 4x² = 16
How to identify the correct domain value?The domain of a function is the set of all input values for which the function is possible.
Now, we are given the domain values as x = –2 and x = 2.
a) x² - 4
f(-2) = (-2)² - 4
= 0
f(2) = (2)² - 2
= 0
b) x² = -4
f(-2) = (-2)²
= 4
f(2) = (2)²
= 4
c) 3x² + 12
f(-2) = 3(-2)² + 12
= 24
f(-2) = 3(2)² + 12
= 24
d) 4x²
f(-2) = 4(-2)²
= 16
f(2) = 4(2)²
= 16
e) 2(x - 2)²
f(-2) = 2(-2 - 2)²
= 32
f(2) = 2(2 - 2)²
= 0
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Veronica used this figure in her proof of the Pythagorean theorem.
Sum of the square of a and square of b should be equal to the square of c of pythagoras theorem is incorrect.
What is Pythagoras' theorem?
Pythagoras' theorem states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse (longest side). Mathematically, it can be expressed as a2 + b2 = c2, where a and b are the lengths of the two shorter sides and c is the length of the hypotenuse.
hypotenuse²=opposite side²+Adjacent side²
Substitute the variables
So, c² = a² + b²
So, option c, which is the sum of the square of a and square of b should be equal to the square of c is correct.
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If 400 m long fencing wire is required to surround a square flower garden 2 times, find length of the garden. -Maths Links Book 6 Approved by CD
Answer:
garden=400/2
=200
4× side = perimeter=200
So, =200/4
=50 m.
Step-by-step explanation:
Answer:
Length of garden is 50 m.
Step-by-step explanation:
Fence required for 1 time,
→ 400 ÷ 2
→ 200 m
Perimeter of square formula is,
→ P = 4 × L
Now length of the garden will be,
→ P = 4 × L
→ 200 = 4L
→ 4L = 200
→ L = 200/4
→ [ L = 50 m ]
Hence, length of garden is 50 m.
PLEASE HELP ME!!!!!! THIS IS DUE ON FRIDAY!!!!!! (There is another part)
Answer:
it's c trust me I had the same problem
someone please help me with this question it’s my last one!
Answer:
Step-by-step explanation:
okay so what I would do is multiply the denominator of 3 from 2/3 by 4 to get 12. So what you do to the bottom you have to do to the top so that fraction 2/3 will turn to 8/12.
Then I would multiply the denominator of 4 from 1/4 by 3 to get also get 12. And again what you do to the bottom you have to do to the top. So that fraction will be 3/12.
Ten you add them 8/12 + 3/12 = 11/12
Answer = 11/12
suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked. (i) define the random variable of interest and state how the variable is distributed. (ii) determine the expected value of the random variable and interpret the expected value in context.
i) The random variable is the number of suspicious transmissions reviewed until finding the first blocked one and the random variable is distributed usinng geometric distribution
ii) The expected value of the random variable: 2.5 which means the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.
In this question we have been given a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history.
Based on past history, the specialist blocks 40 percent of the suspicious transactions.
so, p = 0.40
i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one.
We will use a geometric distribution to model the first transmission.
ii. We know that according to the geometric model the expected value of the random variable would be.
E(X) = 1/p ,
= 1/0.4
= 2.5
This means, the specialist will review 2.5 suspicious transactions on average before finding the first transmission that will be blocked.
Therefore, i) the random variable: the number of suspicious transmissions reviewed until finding the first blocked one.
ii) the expected value of the random variable: 2.5
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The complete question is:
At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions.
Suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked.
(i) Define the random variable of interest and state how the variable is distributed.
(ii) Determine the expected value of the random variable and interpret the expected value in context.
Brendan deposited $3,967 in an account earning 5% interest compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
The interest earned in 5 years is $1096.
What is interest?Interest is the fee a business pays a lender (creditor) to borrow money.
Given that, Brendan deposited $3,967 in an account earning 5% interest compounded annually.
A = P(1+r/100)ⁿ
n = 5, r = 5% = 0.05, P = 3967 and a = amount earned
A = 3967(1+0.05)⁵
A = 3967(1.05)⁵
A = 5063
Interest earned = amount - principal
Interest = 5063-3967
Interest = $1096
Hence, Brendan earned $1096 as interest.
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Answer:
$1096.01
Step-by-step explanation:
Which ordered pair is a solution of the
equation?
-3x + 5y = 2x + 3y
Answer:
Solve the equation for [tex]{y}[/tex].
[tex]y=\frac{5x}{2}[/tex]
Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.
Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(0,0)}[/tex]
Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex](1,\frac{5}{2})[/tex]
Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(2,5)}[/tex]
These are three possible solutions to the equation.
[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]
please help me I don’t get this
The operations between functions are:
a) h(f(3)) = 5
b) (f×g)(4) = -8
c) f( g(h(0))) -1
How to operate with functions?
The first thing we want to find is a composition, we want to find:
h(f(3))
That means that we need to evaluate h(x) in f(3), look at the graph and you can see that f(3) = -4
Replacing that we get:
h(f(3)) = h(-4)
And on the graph, we can see that h(-4) = 5
then h(f(3)) = 5
b) Now we have the product:
(f×g)(4) = f(4)*g(4)
Again, looking at the graph:
f(4) = -4
g(4) = 2
Then:
(f×g)(4) = f(4)*f(4)
(f×g)(4) = -4*2
(f×g)(4) = -8
c) Finally we have other composition:
f( g(h(0)))
So we have 2 compositions, first we find:
h(0) = 5
f( g(h(0))) = f(g(5))
Then:
g(5) = 0
f( g(5)) = f(0)
Finally, look at the graph and you can see that f(0) = -1
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By rounding to 1 significant figure, estimate
101
×
52
The significant figure by multiplying 101 with 52 is 5000.
What is significant figures?The number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value is referred to as significant figures. At the first non-zero digit, we begin counting significant figures.A number's first significant figure is the first digit that is not zero.To round to the nearest one, ten, hundred, thousand, and so on, change all digits to the right of the rounding digit to zeroes.Here given,
101 x 52
Round 101 to 100 and 52 to 50, then multiply together to get 5000.
Significant Figures: 1
Decimals: 0
The significant notation: 5e+3
Therefore the significant notation is 5000.
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(5 points)
If ABCD is a parallelogram, what is the measure of
D
A/9x + 5
16x
C
B
If ABCD is a parallelogram, then the measure of D is 68
From the property of parallelogram the opposite angels are equal so < DAB = < DCB so < DAB will become 16x.9x + 5 + 16x(<DAB) = 180 ....... because it is straight line.
25x + 5 = 180
25x = 180 - 5
25x = 175
x = 7
now let's substitute in the angle < DAB( 16x): 16 × 7= 112To get < ADC lets use the property of parallelogram which says that adjacent angles are supplementary. which means<ADC+ <DAB= 180
<ADC+ 112 = 180
< ADC= 180 - 112
< ADC = 68
Therefore, the measure of D is 68
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Geometry
It’s a a kite. Looking for x and y
We have to find the values of x and y. We know that one pair of opposite angles of a kite are equal. We know that the sum of all the angles of a quadrilateral is equal to 360 degrees. Therefore, the values of x and y are 80° and 110°.
A kite is a quadrilateral with two pairs of adjacent sides, congruent. A kite also has perpendicular diagonals, where one bisects the other. You can use either of these things to determine if a quadrilateral is a kite.
What is a kite in geometry terms?
The most general definition that is typically used: A kite is a quadrilateral in which one of its diagonals is its axis of symmetry. This definition is equivalent to the following one: A kite is quadrilateral that has two pairs of equal adjacent sides.
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(HELP-)
On the day of the test, the teacher instructed the students to take out at least 3 pencils from their backpacks.
Determine which inequality represents this scenario.
3 < p
3 > p
3 ≥ p
3 ≤ p
Chad purchased a new dirt bike for a competition. The salesperson recommended that the tires maintain an air pressure of at least 12psi for good traction on the riding surface.
Determine which inequality represents the salesperson's recommendation.
number line with open circle on the number 12 and line shaded to the left
number line with closed circle on the number 12 and line shaded to the left
number line with closed circle on the number 12 and line shaded to the right
number line with open circle on the number 12 and line shaded to the right
Ms. Rumble's history class conducted interviews with their grandparents for a class project. The grandparents at least 89 years old knew that Amelia Earhart was the first woman to fly solo across the Atlantic Ocean.
Determine the graph to represent this scenario.
number line with open circle on the number 89 and line shaded to the right
number line with closed circle on the number 89 and line shaded to the right
number line with closed circle on the number 89 and line shaded to the left
number line with open circle on the number 89 and line shaded to the left
Wyatt had to climb the stairs to ride the waterslide. The top of the waterslide was more than 56 feet from the ground. Which graph represents this inequality?
number line with open circle on the number 56 and line shaded to the left
number line with closed circle on the number 56 and line shaded to the left
number line with a open circle on the number 56 and line shaded to the right
number line with an closed circle on the number 56 and line shaded to the right
Zan took her dog, Simba, to the dog park on Saturday afternoon. There were more than 20 dogs running around the park when they arrived.
Determine which inequality describes the dogs at the park.
d < 20
d > 20
d ≥ 20
d ≤ 20
The inequality which can represent the above scenario is 3 ≤ p
What is Inequality ?
In mathematical expressions, inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. The symbols we will use in this instead of equals to are Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.
≤ - less than or equal to
≥ - greater than or equal to
≠ - Not equal
Main Body:
Given:
On the day of the test, the teacher instructed the students to take out at least 3 pencils from their backpacks.
To find:
Determine which inequality represents this scenario.
Let us know about Inequality
In the given scenario,
The teacher asked the to take out at least 3 pencils from their backpacks. which the students can take out 3 pencils or 2 or 1 pencil (which is less than 3) but not greater than 3.
Therefore,The inequality which can represent the above scenario is 3 ≤ p
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Please help
The linear combination method gives a solution of (-4,2) for which a of these systems of linear equations?
A) 3x+13y=14
6x+11y=-2
B)4x+5y=12
8x+3y=-4
C) 5x+4y=12
7x+8y=12
D) 10x+3y=8
17x+6y=10
Please show your work
Using the provided points, Applying the substitution of the points in these system of linear equations. The equations which satisfies the points are the required answer. The answer is A) 3x+13y =14 and 6x+11y=-2
What is a equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What do you mean by system of linear equation?The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.
point = (-4,2)
for option A) 3*-4 +13*2 =14
14=14
and 6*-4 + 11*2 = -2
-2 = -2
For other options these equality doesn't holds.
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4 Describe at least two different transformations or sequences of transformations that
transform square A to square B.
The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0).
Does the order of transformations matter in functions?
Order is not important. According to algebra, y=12f (x3). Our four transformations are (1), (3), (2), and (4); all four are in the x direction. When we combine a stretch and a translation in the same direction, the sequence counts.
The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.
ABCD can be transformed to A'B'C'D' by ...
rotation 90° CCW about the point (-1, -1)
Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...
reflection across the line y=x
reflection across the line x=-1
Complete question: A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.
b.) There is more than one way to transform quadrilateral ABCD into quadrilateral A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
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Please help me with this
What is the answer to 21≥3(a−7)+9
