The probability of grabbing one blue pen from the given box of 12 pens.
As given in the question,
Total number of given red pens in a box = 4
Total number of given blue pens in a box = 3
Total number of given black pens in a box = 5
Total number of pens in a given box = 4+ 3+ 5
= 12
Total number of grabbing one pen from the box = ¹²C₁
Total number of grabbing one blue pen out all the pens in the box
= ⁴C₀ × ³C₁ × ⁵C₀
Probability of selecting one blue pen from the box
= (Total number of favourable outcomes )/ ( total number of outcomes)
= ( ⁴C₀ × ³C₁ × ⁵C₀ ) / ( ¹²C₁ )
= ( 1 × 3 × 1 ) / 12
= 3/12
= 1 / 4
Therefore, the probability of grabbing one blue pen from the box of 4 red, 3blue and 5 black pens is equal to ( 1/4 ).
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Graph the following features: Y intercept = -3 Slope = 4/5
The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the equation A is y = mx + b
The y intercept of the line b = -3
The value of b = -3
The slope of the line m = 4/5
The value of m = 4/5
Now , substituting the values in the equation of line , we get
y = mx + b
y = ( 4/5 )x + ( -3 )
y = ( 4/5 )x - 3
The graph of the equation y = ( 4/5 )x - 3 is given below
Therefore, the value of the equation of line A is y = ( 4/5 )x - 3
Hence , The equation of line where the y intercept is -3 and slope is 4/5 is
y = ( 4/5 )x - 3
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(10)
Write the equation
of the line in
Slope-Intercept
Form.
Answer: y= -3x -1
Step-by-step explanation: y=mx+b
The Y-intercept is at (0,-1), so b is -1
The slope is rise/run, and the graph is down 3, right 1, so the slope is -3/1
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Si en un Salón hay 25 estudiantes de los cuales 12 son varones ¿Cual es la razón de varones a hembras?
La razón que buscamos para los números de estudiantes es:
12:13
¿Cual es la razón de varones a hembras?Sabemos que si de un numero N podemos separar 2 grupos, de tal forma que hay a elementos del grupo A y b elementos del grupo B, la razon de el grupo A al grupo B es a:b
En este caso sabemos que hay 25 estudiantes y hay 12 varones, entonces hay:
25 - 12 = 13 "hembras"
Entonces la razon que buscamos es:
12:13
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In the coordinate plane, the point X(-4,-2) is translated to the point X'(-6,-5) . Under the same translation, the points Y(0,0) and Z(-2,2) are translated to Y' and Z' , respectively. What are the coordinates of Y' and Z' ?
Under the same translation as X and X' the coordinates of Y' = (-2, -4) and Z' = (-4, -1)
What is translation of a point in coordinate system?
A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.
According to the given question:
It is given about the points X (-4, -2) and X' (-6, -5).
We see that the translation is moving -2 units horizontally to the left and -3 units vertically down.
Therefore, the point Y(0,0) is translated to Y'(0-2,-1-3) = Y'(-2,-4)
and the point Z(-2,2) is translated to Z'(-2-2,2-3) = Y'(-4,-1).
Hence, under the same translation Y' = (-2, -4) and Z' = (-4, -1)
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For a family living in Southern Mississippi, the probability of owning a dog is 0.4, the
probability of owning a cat is 0.5, and the probability of owning both a cat and a dog is
0.12.
What is the probability that a family living in Southern Mississippi owns a cat or a dog?
Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is [tex]0.78[/tex].
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The meaning of probability is basically the extent to which something is likely to happen.
Here given that,
For a family living in Southern Mississippi, the probability of owning a dog is [tex]0.4[/tex], the probability of owning a cat is [tex]0.5[/tex], and the probability of owning both a cat and a dog is [tex]0.12[/tex].
Probability od owing a dog is
[tex]P(A)=0.4[/tex]
Probability of owing a cat is
[tex]P(B)=0.5[/tex]
Probability pf owing both a cat and a dog is
[tex]P(A[/tex]∩[tex]B)=0.12[/tex]
As we know,
[tex]P(A[/tex]∪[tex]B)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]
[tex]P(A[/tex]∪[tex]B)=0.4+0.5-0.12[/tex]
[tex]P(A[/tex]∪[tex]B)=0.78[/tex]
Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is [tex]0.78[/tex].
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A company sold 7.1 million items in a two-year period. Sales increased by 100,000 the second year. How many were sold the second year?
Answer:
I think it's 3650000
Step-by-step explanation:
7.1 mil ÷ 2 = 3550000
3550000 + 100000 = 3650000
Quanta Indutrie old $325,000 of conumer electronic during July under a nine-month warranty. The cot to repair defect under the warranty i etimated at 4. 5% o-
the ale price. On November 11, a cutomer wa given $220 cah under term of the warranty
The journal entry for the July 31 sales and November 11 cash payment is shown below .
In the question ,
it is given that ,
the amount for which Qantas Industries sold electronics during July under a nine-month warranty is = $325000 ,
cost to repair defects is = 4.5 percent of sales price .
So , the cost to repair is = 4.5% × 325000 = $14625 .
So , the journal entry for July 31 is
Warranty expense Debit 14625
Estimated warranty liability/warranty payable Credit 14625
and the journal entry for November 11 is :
Estimated warranty liability /warranty payable Debit 220 ,
Cash Credit 220 .
Therefore , the Journal entry is shown above .
The given question is incomplete , the complete question is
Qantas Industries sold $325,000 of consumer electronics during July under a nine-month warranty. The cost to repair defects under the warranty is estimated at 4.5% of the sales price. On November 11, a customer was given $220 cash under terms of the warranty. Provide the journal entry for the estimated warranty expense on July 31 for July sales. Provide the journal entry for the November 11 cash payment .
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what is this in Algebra tiles (x-1) (x+3)
please help me.
The area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.
Given that, the dimensions of a rectangle (x-1) and (x+3).
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, the area of a rectangle
= (x+3)×(x-1)
= x²+3x-x-3
= x²+2x-3
Hence, the area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.
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"Your question is incomplete, probably the complete question/missing part is:"
Find the area of a rectangle with the dimensions (x-1) and (x+3).
Alex has $600 in her checking account. She wants to spend a part of this money on a computer.
She wants to have at least $250 left in her checking account after buying the computer. Write an
inequality that can be used to find t, the amount of money in dollars that Alex can spend on the
computer, and solve fort.
Amount of computer can be 350 or more than 350.
What do you mean by inequality?
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.
Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.
It is given that Alex has $600 in her checking account and She wants to have at least $250 left in her checking account after buying the computer.
Let the amount of computer be t
According to the question , inequality become:
600 - t ≥ 250
600 - 250 ≥ t
350 ≥ t
Therefore, amount of computer can be 350 or more than 350.
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In the following diagram, AD || BC and AB || DC.
Prove angle A is congruent to angle C
solve for b in the trapezoid.
180 - 57 = 123 ( ALLIED ANGLE )
Will swims a total of 45.6 laps in 2.85 hours. How many laps does he swim each hour?
The number of swims that Will swims by using decimal divisions is 16 laps in each hour.
What is decimal division?
When dividing decimals, the divisor must be converted to a whole number by moving the decimal point to the right. The dividend's decimal point is then carried up to the same number of places to the right, and the resulting numbers are divided in the same manner as regular long division.
Given, Will swims a total of 45.6 laps in 2.85 hours
That is, 2.85 hours = 45.6 laps
or, 1 hour = 45.6/2.85 = 16 laps
Hence, he swims 16 laps each hour.
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how many solutions does the equation 4+3−1=2(2+2)−2 have?
Answer:
1
Step-by-step explanation:
This equation only has 1 solution
#12: A train left Philadelphia at 8 AM on July 1st. It traveled
2,864 miles to Portland, Oregon, arriving at 9AM on July 4th.
What was the average rate of change of the train in miles per
hour?
Round to the nearest hundredth
Answer: 39.23 miles per hour
Step-by-step explanation:
1 day = 24 hour
3 days = 72 hours
Add one more hour for both to get to 9 AM, so it will take 73 hours to get there.
Now we find the average rate of change.
We take 2864 divided by 73 = 39.23 miles per hour
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
AD = 12 and EA = 13, solve for AC. Round your answer to the nearest tenth if
necessary.
The line AC from the diagrammatic expression of the tangent of the circle shows that line AC is 24.0
What is the tangent of a circle?A tangent of a circle is a line that intersects the circle at a single point. The site at which the tangent intersects the circle is referred to as the site of tangency.
From the given information:
Line |CD| = Diameter
Line |EA| = radius = 18
Line |DB| = 12
Then, we can infer that line EA = DE since they are both (radii of the circle.)
Line |DE| = |EA| = 18
By using the formula for Pythagoras' theorem, we can find line |EA|.
hyp² = opp² + adj²
where;
Line |BE| = hypotenuse = DB + BE = 12 + 18 = 30
Line |AB| = opposite (x) = ???
Line |EA| = adjacent = 18
Thus;
30² = x² + 18²
900 = x² + 324
-x² = -900 + 324
x = √576
x = 24.0
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2) Solve: 115 − 10 = −12 − 5(2 − 6)
Answer:
False
Step-by-step explanation:
Simplify 115 − 10 : 105Subtract the numbers 115 − 10 = 105
2.Simplify 12 − 5(2 − 6) : 8
105=8
this shows that the sides are not equal so it is false
a paddle wheel on a boat is 4 feet in diameter. the fins along the outer edge travel at a speed of 1.3 feet per second. how long does it take the paddle wheel to complete 100 full revolutions ? round to the nearest second.
_ minutes and _ seconds.
Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:
C = 2π * 2 = 8π feet
To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):
100 * 8π feet / 1.3 feet per second = 615.38 seconds
Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.
For the function f(x) shown graphed below, over which of the following intervals is f(x) <0?
The function f(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.
What is graph?Graph is a mathematical representation of a Networks and it's describes the relation between lines and points.
The graph of the function f(x) is given.
The following steps can be used in order to determine the interval for f(x):
Step 1 - The value of f(x) means the value of y.
Step 2 - The value of f(x) is positive when the graph of f(x) is in the first or in the second quadrant.
Step 3 - So, according to the graph function f(x) is positive when the value of x is in between -3 and 5.
Therefore, the correct option is 3).
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Andrew just started a running plan where he runs 12 miles the first week and then increases the number of miles he runs by 5% each week. If he keeps up this plan for 10 weeks, how many total miles would Andrew have run, to the nearest whole number?
Answer:
18 miles.
Step-by-step explanation:
You start with 12 miles and then you first need to figure out what 5% of that is by doing the equation x/12 = 5/100 and you will then get .6. Then you multiply that number by 10 (one for each week) getting 6. Then you add the 6 to your starting total to get 18.
A semicircle is divided into two circular sectors of which one is 4/5 of the other. The radius of the circle measures 18cm. Calculate the length of the two arcs and the area of the two circular sectors
The length of the two arcs and the area of the two circular sectors can be calculated as follows:
Since the semicircle is divided into two circular sectors, each sector has an angle of 180/2 = 90 degrees. Therefore, the smaller circular sector has an angle of 90 * (4/5) = 72 degrees, and the larger circular sector has an angle of 90 - 72 = 18 degrees.
The length of the arc of a circle is equal to the circumference of the circle multiplied by the ratio of the central angle of the arc to 360 degrees. Therefore, the length of the smaller arc is 18 * pi * (72/360) = 8pi cm, and the length of the larger arc is 18 * pi * (18/360) = 2pi cm.
The area of a circular sector is equal to the area of the circle multiplied by the ratio of the central angle of the sector to 360 degrees. Therefore, the area of the smaller circular sector is 18^2 * pi * (72/360) = 288pi cm^2, and the area of the larger circular sector is 18^2 * pi * (18/360) = 72pi cm^2.
Therefore, the length of the two arcs is 8pi cm and 2pi cm, and the area of the two circular sectors is 288pi cm^2 and 72pi cm^2.
Find the three consecutive integers such that the smallest and three times the largest is 330. What is the smallest integer?
The smallest integer out of the three integers is 109
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
Three consecutive integers:
x, x+1, x+2
The sum of the integers,
x+(x+1)+(x+2) = 330
3x + 3 = 330
3x= 327
x= 327/3
x= 109
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A taxi ride in a large city costs $2.75 plus 5 for each mile traveled. write an equation to represent the situation where D is the distance traveled and see is the total cost of the trip. if Brandon traveled 9.5 miles by taxi how much was the cost C of his taxi ride?
Answer: $50.25
Step-by-step explanation:
First, we will write an equation to represent this situation.
C = $2.75 + $5D
Next, we will substitute 9.5 miles into D and solve.
C = $2.75 + $5D
C = $2.75 + $5(9.5)
C = $50.25
Answer:
(a) c = 2.75 + 5d
(b) $50.25
Step-by-step explanation:
(a)
The information tells us the following:
Cost of a taxi ride = $2.75 + (5 * number of miles travelled)
We can use the variables c and d to represent the descriptions:
c = 2.75 + 5d
(b)
Substitute 9.5 into the equation as d:
c = 2.75 + 5(9.5)
Simplify:
c = 2.75 + 47.5
c = 50.25
Therefore, the cost of a 9.5 mile ride is $50.25.
solve for 2x² = 80?
Answer:
x=2√10,−2√10
Step-by-step explanation:
a prestigious program accepts 2 out of every 9 applicants per yer. if the program accepted 360 applicants, how many applicants were not accepted?
If a prestigious program accepts 2 out of every 9 applicants per year than the program will accept 360 applicants out of 1620.
What is ratio math example?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
What is a equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
the ratio is given:
2/9 = 360/x
solving for the value of x;
x/9=360/2
x=(180)9
x=1620
this is the required value of applicants that were not accepted.
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what is the answer of this question?
Step-by-step explanation:
The given mass of the Earth is 5.972 × 10²⁴
The given mass of the Jupiter is 1.898 × 10²⁷
Now,
1.898 × 10²⁷ ÷ 5.972 × 10²⁴
= 0.3178 × 10³ = 317.8
Thus, Jupiter is 317.8 heavier than Earth
You have rented a moving truck to move into your first apartment. ABC truck has interior dimensions of 168 inches times 96 inches times 77 inches. The dimensions of your storage boxes are 24 inches times 13 inches times 28 inches. Determine how many boxes can fit into the truck.
Find the scale factor
Please help me!
Answer:
[tex]\frac{7}{5}[/tex] or 7:5
Step-by-step explanation:
You are going from the smaller triangle to the larger.
Let x = the scale factor. Find two corresponding sides that you know both lengths.
50x = 70 Divide both sides by 50
x = [tex]\frac{70}{50}[/tex] Divide both the numerator and denominator by 10
[tex]\frac{7}{5}[/tex]
Nora placed 12 cans in each box.How many boxes will she need if she has 240 cans?
Answer:
20 boxes
Step-by-step explanation:
12 cans = 1 box
240 = x
apply rule of three
(240/12) x 1 = x
20 = x
Answer:
She will need 20 boxes
Step-by-step explanation:
Take the total number of cans and divide by the number of cans per box
240/12
20
She will need 20 boxes.
1. Line L contains points (4, -1) and (4,9). Point P has coordinates (1,6)
The distance between the point and the line is 3 units.
Find the equation for line L
Begin by finding the slope of the line through the given points, (4,-1) and (4,9) ; its intercept:
m = (y₂ - y₁) / (x₂ - x₁)
= (9 - (-1) ) / 4 - 4
= 10 / 0
= Undefined
Because the slope is undefined, then line L is a vertical line which has an x-intercept of (4,0):
x=4
Because, line L is vertical, then the line w perpendicular to it is a horizontal line that passes through (1,6)(1,6) so its equation is y=6. Hence, L and w intersect at (4,6) which we will denote as Q.
The perpendicular distance is the distance from point P(1,6) to point Q(4,6) which is simply the absolute value of the difference of the x-coordinates:
d = | 1 - 4 |
= |-3|
= 3
Hence, The distance between the point and the line is 3 units.
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.... i need help past due