There are 84 ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.
acc to our question-
Number of commities: If now any sinyour then N1 = C6,4 = 15. If one sinyour then number of commities is =N2 = C4,1C6,3 = 4·20 = 80.hence,There are 84 ways.
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(sec(t)-cos(t))/sin(t)
The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)
How to simplify trigonometric ratios?There are different trigonometric ratios such as;
sin x
tan x
cos x
sec x
cosec x
cot x
Now, we want to simplify the trigonometric expression;
(sec(t) - cos(t))/sin(t)
We know that;
sec (t) can be written as 1/cos t
Thus;
(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t
= (1/(sint cos t) - cos t/ sin t
= (1 - cos²t)/(sin t cos t)
= sin²t/(sin t cos t)
= sin t/cos t
= tan t
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a percentage distribution is given below for the size of families in one u.s. city. size percentage 2 42.8 3 21.1 4 19.2 5 11.6 6 3.3 7 2.0 a family is selected at random. find the probability that the size of the family is 4 or more. round your result to three decimal places.
The probability that the size of the family is 4 or more rounded to three decimal places is 0.361.
Given that families are selected at random, to find the probability that the size of family 4 we need to select and add those probabilities whose family size is more than and equal to 4.
P(X ≥ 4) = P(4) + P(5) + P(6) + P(7)
P(X ≥ 4) = 19.2 + 11.6 + 3.3 + 2.0
P(X ≥ 4) = 36.1
Since we need the answer rounded off to three decimal places, we can divide the answer by 100 which will give the final answer which is 0.361.
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Select the two values of x that are roots of this equation. x2 + 3x – 5 = 0
The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
What are the two values of x which are root of the given quadratic equation?It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.
Recall that the roots of quadratic equations are given by the formula;
x = {-b ± √(b² - 4ac)} / 2a
Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.
Therefore, the roots are as follows;
x = {-3 ± √(3² - 4•1•-5)} / 2(1)
x = (-3 ± √29)/2
Therefore, the required roots are;
x = (-3 + √29)/2 and x = (-3 - √29)/2
Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
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Graph the line with the equation y=− 6/1x +1
Answer:
The answer is (1, 6)
Step-by-step explanation:
Fill the empty slots by dragging tiles from the left to show the
next step for solving the equation.
Use the information in the problem to write an equation.
Then use the equation machine to help you solve it.
8 years ago Marcus was 12 years old. How old is he
now?
8
y
8
12
12
Marcus is
years old
Show result
The age of Marcus now is 20 years as 8 years ago Marcus was 12 years old.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.
Let his age now be x.
x-8=12
x=20
Marcus is currently 20 years old, although he was 12 years old eight years ago.
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a package of 4 erasers costs $0.39. At this rate, how much would 54 erasers cost, in dollars and cents?
Answer:
Step-by-step explanation:
5 dollars and 25 cents
The parabolic path of a performer who is shot out of a cannon, where y is the height (in feet) and x is the horizontal distance traveled (in fleet), has a vertex of (60,50) and a y-intercept of (0,30). Write an equation of the parabola. The performer lands in a net 80 feet from the cannon. What is the height of the net?
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}[/tex]
which of the following is a reason why a researcher might choose to conduct a double-blind placebo control group study? a. to control for regression to the mean b. to control for observer bias c. to eliminate testing effects d. to prevent attrition
A double-blind placebo control group study is used to control for observer bias and eliminate testing effects. So option c is correct.
A double-blind placebo control group study is one in which subjects are randomly assigned to either a control group, who receive a placebo, or an experimental group, who receive the treatment being studied. The researcher is not aware of which subjects are in which group, and neither are the subjects. This design is used to control for observer bias and eliminate testing effects.
This type of study is important because it allows researchers to test the efficacy of a new treatment without the risk of bias. By eliminating the possibility that the researcher or the subjects will know who is receiving the treatment and who is receiving the placebo, any expectations or preconceptions about the treatment can be avoided. This type of study is also important because it helps to control for the placebo effect, which is the phenomenon whereby subjects in the control group may experience some benefits from the placebo itself.
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what is 15.0782 rounded to
the nearest 10
Reason:
The digit in the tens place is 1. Just to the right is 5, which tells us to bump the 15 up to 20.
We can say that 15.0872 is closer to 20, than it is to 10.
Be sure not to mix up "tens place" with "tenths place".
The round-off from the number 15.0782 to the nearest 10 will be 20.
What is rounding off to the number?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.
Given that the number is 15.0782. The round-off to the nearest 10 will be 20 for the number.
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jacob has a jar of nickels and dimes. he has twice as many nickels as dimes. he has 310. how many of each type of coin does he have
No. of coins in jar of nickels is 207 and of dimes is 103.
Let the no. of coins of dimes = x
No. of coins of nickels = 2x
Total = 310
x + 2x = 310
3x = 310
x = 310/3
= 103.33
≈ 103
No. of coins of dimes = 103
No. of coins of nickels = 310 - 103
= 207
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2x + y = 1
-2y + 5z = -5
3x + 4z = -2
Answer:
y=5 x= -2 z=1 the procedure Is in the picture
6 x 7/8
(six x seven eighth's) This is a review for last year but I forgot how to do it also can you show how you got it please?
Answer:
5 1/4 // 5.25
Step-by-step explanation:
convert 6 into a fraction:6/1 x 7/8multiply numerators by numerators, and denominators by denominators42/8 (6 x 7 = 42, 8 x 1 = 8)Simplify the fraction using the Lowest Common Multiples42/8 --> 21/4 convert the improper fraction into a mixed number:5 1/4OR
5.25Answer:
5 1/4
Step-by-step explanation:
You want the product of 6 and 7/8.
Product with a fractionYour written-out version of the question gives you a clue how to solve it:
six times seven eighths
The associative property of multiplication lets you rearrange this to ...
(six times seven) eighths = forty-two eighths
That is, the product is formed by multiplying the integer by the numerator, and expressing the whole thing over the denominator:
[tex]6\times\dfrac{7}{8}= \dfrac{6\times7}{8}=\dfrac{42}{8}\\\\=\dfrac{40+2}{8}=\dfrac{40}{8}+\dfrac{2}{8}=5+\dfrac{1}{4}\\\\=\boxed{5\dfrac{1}{4}}[/tex]
Improper fractionThe improper fraction is converted to a mixed number by looking at the quotient and remainder from the division: 42/8 = 5 r 2 = 5 2/8 = 5 1/4.
__
Alternate solution
Sometimes, it can be helpful to look at the problem another way.
6 × 7/8 = 6 × (1 -1/8) = 6 -6/8
= 6 -3/4 = 5 1/4
questions 1-4: the number of classes (x) a student takes in a given semester follows the following probability distribution: x 0 1 2 3 4 5 p(x) 0.4 0.25 0.15 0.08 0.02 ??? what is the expected number of classes a student will take in a given semester?
The expected number of classes a student will take in a given semester is 1.89
How calculate the expected value of x?Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.
Given :
x| 0 1 2 3 45
p| 0.4 0.25 0.15 0.08 0.02
where x = number of classes
p = probability
The expected value of x, E(x) =Σ xp
E(x) = (0×0.4) + (1×0.25) + (2×0.25) + (3×0.08) + (45×0.02)
E(x) = 0 + 0.25 + 0.5 + 0.24 + 0.9
E(x) = 1.89
Therefore, the expected number is 1.89.
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What transformation occurs from the graph y = x² to the graph of y = (x − 5)² + 7?
A a vertical shift up 5 units and a horizontal shift right 7.
B a vertical shift down 5 units and a horizontal shift right 7
C a vertical shift up 7 units and a horizontal shift left 5
D a vertical shift up 7 units and a horizontal shift right 5
The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
What do we mean by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.So, the transformation from:
y = x² to y = (x - 5)First, plot both graphs.
(Refer to the graph attached below)
Now, notice that the graph of the function y = (x - 5)² + 7 has shifted vertically upwards by 7 units and horizontally right by 5 units.Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
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if a factory can make 600 nails every 3 minutes, how long would it take to make 27,000 nails?
Answer:
2 hours 15 minutesStep-by-step explanation:
Conditions Given:A factory makes 600 nailsFor making 600 nails the factory takes 3 minutesTo Find:Time taken by the factory to make 27000 nailsSolution:Given,
No. of nails the factory makes = 600
Time taken by the factory to make 600 nails = 3 minutes
So,
Time taken by the factory to make 1 nail = [tex]\frac{3}{600}[/tex] minutes
∴ Time taken by the factory to make 27000 nails
= ( [tex]\frac{3}{600}[/tex] × [tex]27000[/tex] ) minutes
[On simplifying]= ( [tex]\frac{1}{2}[/tex] × [tex]270[/tex] ) minutes
[On further simplifying]= 135 minutes
Or,
As we know , [ 1 minute = [tex]\frac{1}{60}[/tex] hour]
So, 135 minutes = [tex]\frac{135}{60}[/tex] hours
[On simplification]= 2.25 hours
Now, [1 hour = 60 minutes]
0.25 hours = [tex]\frac{1}{4}[/tex] hours
= [tex]\frac{1}{4}[/tex] × 60 minutes
= 15 minutes
Hence,
The time taken by the factory to make 27000 nails is 2 hours 15 minutes (Ans)
Answer:
2.25 hours or 2 hours 15 minutes
Step-by-step explanation:
600 nails / 3 minutes = 200 nails / minute
27,000 nails / 200 nails/minute = 135 minutes
1 hour = 60 minutes
135 minutes × 1 hour / 60 minutes = 2.25 hours
2.25 hours = 2 hours + 0.25 hours × 60 minutes/hour = 2 hours 15 minutes
Answer: 2.25 hours or 2 hours 15 minutes
The president of the Huerta Middle School science club suggested a field trip to the local
aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who
goes.
Write an equation showing how the total cost, y, depends on the number of students going,
X.
Do not include dollar signs in the equation.
►
y =
The equation that shows the total cost, depends on the number of students going is y = 21.25 + 14.75x
Equation:
An equation is made up of two expressions connected by an equal sign.
For example, y = 3x + 6 is an equation.
Given,
The president of the Huerta Middle School science club suggested a field trip to the local aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who goes.
Here we need to find the equation that shows the total cost depends on the number of students.
Let us consider x be the number of students and y be the cost for x number of students.
Here we know that, there is one club advisor whose ticket cost is $21.25 and the cost per student is $14.75.
So, based on these details, the equation for the total cost is calculated as,
=> y = 21.25 + 14.75x
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Which equation represents a line which is perpendicular to the line y=-4x-5?
A.x+4y=−32
B.4x+y=3
C.4x−y=−4
D.4y−x=4
manufacture of a certain component requires three different machining operations. machining time for each operation has a normal distribution, and the three times are independent of one another. the mean values are 15, 20, and 30 min, respectively, and the standard deviations are 2, 1, and 1.8 min, respectively. what is the probability that it takes at most 1 hour of machining time to produce a randomly selected component? (round your answer to four decimal places.)
The probability that it takes at most 1 hour of machining time to produce a randomly selected component is 0.04074
we are provided with the independent time which are 15, 20, and 30 min and the respective standard deviations which are 2, 1, and 1.8 min.So the total mean X= 15+20+30 =65, as we know that
Variance = ( standard deviation )²
=> Variance = 2² + 1² + 1.8² = 8.24
since standard deviation = √variance
=>Standard deviation = 2.87
so the z score = X -mean /standard deviation
since here X = 1 hour = 60 mintues
z = 60-65/2.87 = -1.74216
So the probability, P( z≤ -1.74216) = 0.04074
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A store received shipment of 37 tvs valuad at 625 each what is the total value. Of the shipment
A store received shipment of 37 tvs valued at 625 each what is the total value of the shipment?
37 * $625 = $23,125
Baby lisa automatically turns her head in the direction of a touch on the cheek. This is the _____ reflex.
Turning of head is rooting reflex.
Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.
Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.
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A triangle has sides with lengths of 10 yards, 12 yards, and 14 yards. Is it a right triangle?
yes or no?
Answer:
No
Step-by-step explanation:
The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].
The square of the length of the largest side is [tex]14^2=196[/tex].
Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.
4 tins of soup have a total weight of 1120 grams
3 tins of soup and 5 packets of soup have a total weight of 1015 grams
work out the total weight of 5 tins of soup and 2 packets of soup
What is an equation of the line that passes through the point (2,-2)and is perpendicular to the line 5x-2y=4
Answer:
y=-0.4x - 1.2
which statement is not a step used when constructing an inscribed equilateral triangle ?
Use the compass to join the two circles together, this statement is not a step used when constructing an inscribed equilateral triangle.
What is known as a triangle?A polygon having three vertices and three sides are called a triangle. The triangle's angles are created by joining its three sides end to end at a single point.
The triangle's construction does not include claim D, which is the case. Use the compass to join the two circles together.
It is necessary to keep the compass at a width equal to the circle's radius and to position it at the point where the circle and radius connect while building an inscribed equilateral triangle.
Additionally, it's crucial to pivot an arc the radius's length away from the circle's point. It is not a part of the steps to join the two circles using the compass.
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help meeeeeeeeeeeeeee pleaseee
The following are features of the parabola shown in the diagram:
Vertex: (2, -1)
Axis of symmetry: x = 2
The parabola opens downward.
What is the Vertex of a Parabola?The vertex of a graph is the coordinates of the point where the tip of the parabola lies at.
What is the Axis of Symmetry of a Parabola?
The axis of symmetry of a parabola passes through the vertex and is it expressed as the x-coordinate of the vertex of the parabola.
The tip of the parabola shown in the image above is at (2, -1), and the parabola as can be seen opens downward.
Therefore:
The vertex of the parabola is (2, -1)
The axis of symmetry would be expressed as x = 2. The parabola opens downward as well.
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An expression is shown.
4x+2(9−3x)
Select all that are equivalent to the given expression.
-18x+54
-2(x-9)
-18(x-3)
10x+18
2(5x+9)
-2x+18
Answer:
-2x+18, and -2(x-9)
Step-by-step explanation:
4x+18-6x
4x-6x+18
-2x+18
-2(x-9)
-2x+18
The Coast Guard cutter Angelica travels at 30 knots from its home port of Corpus Christi on a course of 95 degrees for 2 hrs and then changes to a course of 185 degrees for 2 hrs. Find the distance and the bearing from the Corpus Christi port to the boat.
The distance and bearing of the boat from the port areas follows;
The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.
What is a bearing in mathematics?A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.
The speed at which the Coast Guard cutter travels = 30 knots
Bearing of the Coast Guard cutter Angelica = 95°
The time the coast guard travels in the initial direction = 2 hours
The direction the Coast Guard cutter changes to = 185°
Time of traveling in the new direction = 2 hours
30 knots = 55.56 km/hr
The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km
The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km
From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle
The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15
The distance f the boat from the port is approximately 157.15 kilometers
The base angles of an isosceles right triangle are 45°
Therefore, the bearing is 95° + 45° = 150°
The bearing from the port to the boat is 150°
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Jorge ha 173 fih for hi dog led team that he want to divide into maller piece how many piece of fih would there be if jorge divided eachfih into thenth
If the fishes are divided to be in tenths, then the total pieces of fishes that would be available would be 1730
How to solve for the pieces of fishIt is assumed that Jorge has 173 fish that he intends to cut up into smaller portions for his dog sled team.
The amount of fish pieces that would remain if Jorge divided each fish into tenths must be determined.
We are aware that there are 10 pieces to every fish.
There are a total of 173 fish available for the dog.
The product of the number of fish that are available and the number of pieces that each fish is divided into results in the total number of fish.
173 * 10
= 1730 pieces of fish.
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Complete question
Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
The normal price of a train ticket from Ashford to London is £34.20
Ross gets 1/3
off the price of his train ticket
Work out how much Ross pays for his ticket.
guys please help lol
Answer:
£22.80
Step-by-step explanation:
To work out how much Ross has to pay for his ticket, you first need to calculate how much the 1/3 of the full price is.
To do this, you divide the 34.20 by 3.
34.2 / 3 = 11.4
So Ross gets a discount of £11.40
To work out the price, that Ross has to pay, we substract the discount from the normal price:
34.2 - 11.4 = 22.8
So Ross pays £22.80 for his ticket.
One angle of an isosceles triangle measures 80°. What measures are possible for the other two angles? Choose all that apply.
80°,20° or 50°,50° are possible for the other two angles.
Given:
One angle of an isosceles triangle measures 80°.
we assumed that the 80° is one of the equal angles, then there is another 80° angle.That makes 160°.
Since a triangle always totals 180°,
180° - 160° = 20°.
if the 80° was the only different angle instead,the two remaining angles total:
180 - 80 = 100
Since we have two identical angles remaining, we need only divide the 100° in half to get the final answer:
100/2 = 50°.
Therefore 80°,20° or 50°,50° are possible for the other two angles.
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