Answer:
Green Pens : 21
Step-by-step explanation:
Let the number of
green pens = x
Three more blue pens than green pens translates to
=> number of blue pens = number of green pens + 3
=> blue pens = x + 3
Total number of pens = blues + green = x + 3 + x = 2x + 3
Probability of taking 2 green pens:
The first time a green pen is taken out, the probability
P( 1s green pen) = Number of green pens/Total number of pens
= [tex]\dfrac{x}{2x + 3}[/tex]
After the first green pen is removed, the number of green pens will be one less and so will the total number of pens
Number of green pens = x - 1
Total number of pens = 2x + 3 - 1 = 2x + 2
P(second green pen | first green pen)
[tex]=\dfrac{x-1}{2x + 2}[/tex]
P(2 green pens) = P(first green pen) x P(second green pen)
[tex]= \dfrac{x}{2x + 3} \times \dfrac{x-1}{2x + 2}\\\\=\dfrac{x(x -1)}{(2x +3)(2x+2)}[/tex] [1]
Probability of 2 blue pens
P( 1st blue pen) = number of blue pens/total number of pens
[tex]=\dfrac{x + 3}{2x + 3}[/tex]
P(second blue pen = (number of pens remaining if first was blue) ÷ total number of pens - 1
If the first pen taken was blue then there will be 2x + 3 - 1 blue pens out of a total of 2x + 3 - 1 pens
P(2nd blue pen | first blue pen)
[tex]=\dfrac{x + 2}{2x + 2}[/tex]
[tex]\text{P(2 blue pens)} =\dfrac{x + 3}{2x + 3} \times \dfrac{x + 2}{2x + 2}[/tex][tex]=\dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex] [2]
The probability of either 2 green pens or 2 blue pens is the sum of the two probability expressions [1] and [2]
[tex]= \dfrac{x(x -1)}{(2x +3)(2x+2)} + \dfrac{(x + 3)(x+2)}{(2x + 3)({2x + 2})}[/tex]
[tex]= \dfrac{x(x - 1)+ (x + 3) (x +2)}{(2x + 3)(2x + 2)}\\\\\\= \dfrac{2x^2+4x+6}{(2x + 3)(2x + 2)}\\\\\\\\[/tex]
Numerator: factor out 2 to get 2(x² + 2x + 3)
denominator = 4x²+10x+6 = 2 (2x² + 5x + 3)
2 of numerator and 2 of denominator cancel out to give the final expression:
[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3}[/tex]
But we are given that the probability of picking 2 pens of the same color = 27/55
This will give us:
[tex]\dfrac{x^2\:+\:2x\:+\:3}{2x^2+\:5x\:+\:3} = \dfrac{27}{55}[/tex]
Cross-multiplying we get
[tex]55\left(x^2+\:2x\:+\:3\right)=27\left(2x^2+\:5x\:+\:3\right)[/tex]
=> [tex]55x^2+110x+165 = 54x^2+135x+81[/tex]
Grouping like terms and simplifying gives
[tex]x^2-25x+84=0[/tex]
This is a quadratic equation which can be solved using a scientific calculator (as I did)
The solution set is
x = 21, x = 4
Remember x = number of green pens. We can ignore x = 4 because the total number of pens given by the expression 2x + 3 will be less than 12 and we are told there are more than 12 pens total
So the solution is x = 21 (number of green pens)
Number of blue pens = x + 3 = 21 + 3 = 24
Answer: Green Pens : 21 and Blue Pens: 24
Passes through (9, 0) and (0, -3).
do you mind explaining with the answer so that i’ll understand it and be able to continue without being confused? thank you! :)
Answer: y = (1/3)x - 3
Step-by-step explanation:
It passes through -3 at 0, so we know the y = mx + b form will include -3
Next, we want to find the slope:
Change in y = 0 - -3 = 3
Change in x = 9 - 0 = 9
Change in y / Change in x = slope
3/9 = 1/3
Work out the value of (6.31 x 10^5) + (2.6 × 10^1)
Give your answer in standard form.
Answer: 16,406,000
Step-by-step explanation:
First, multiply 6.31 and 2.6 to get 16.406. Then, add 10^5 and 10^1 to get 10^6.
It should now look like this, 16.406 x 10^6
The number has to be between 10 and 1 so you need to make it smaller by moving the decimal point over once to the left. It should now be 1.6406. But, you can't leave the exponent at 10^6 so, you need to make it bigger since you made the number smaller.
Your answer should now look like this, 1.6406 x 10^7
Since it needs to be in standard form, move the decimal point 7 times to the right since it is a positive number.
So, your answer is: 16,406,000
Omar has been training for the Candlewood Footrace. The first week he trained, he ran 7 days and took the same two routes each day: 3 miles around the track before work and a longer route through his neighborhood after work. By the end of the week, Omar had run a total of 63 miles.
Which equation can you use to find how many miles, x, Omar ran each day after work?
The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
The total number of days he run = 7 days
Total distance he ran in one week = 63 miles
The distance he run before the work = 3 miles
The total distance he run before the work in one week= 7×3
= 21 miles
The total distance he run after the work = 63 - 21
= 42 miles
The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7
Substitute the values in the equation
= 42/7
= 6 miles
Hence, The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
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brian sells wholesome computer parts at a comission rate of 4% .what is his income last month if his total sales were 82,968.00
Brian's income last month t is $3,318.92
How to calculate the income ?The commission rate for the computer parts is 4%
The total sales for last month is 82,968.00
Brian income last month can be calculated as follows
Total sales × commission percentage
4/100 × 82,968
= 0.04 × 82,968
= 3,318.92
Hence Brian income for last month is $3,318.92
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True or false? If x>0, then x² > x.
Answer:
False
Step-by-step explanation:
It is false when x=1 because
[tex]1^{2} =1[/tex]
Use the equation below to find a, if b=3 and h=4
in a survey of group people showed that 60 liked tea, 45 liked coffee, 30 liked milk,25 liked coffee as well as tea,20 liked tea as well as milk,15 liked coffee as well as milk and 10 liked all the three. How many people were asked this question?
Answer:
85 people were surveyed
Step-by-step explanation:
Let n(X0 represent the number of people who belong in set X
We have 3 sets here
T = set of all people who like tea
C = set of all people who like coffee
M = set of all people who like milk
From the info given
n(T) = 60
n(C) = 45
n(M) = 30
The intersection of the sets are
n(C ∩ T) = 25
n(T ∩ M) = 20
n(C ∩ M) = 15
n(C ∩ T ∩ M) = 10
The number of people who were asked this question is given by
n(T U C U M)
= n(T) + n(C) + n(M) - n(C ∩ T) - n(T ∩ M) - n(C ∩ M) + n(C ∩ T ∩ M)
= 60 + 45 + 30 - 25 - 20 - 15 + 10
= 85
Venn Diagram is attached
5
How many 14-pound hamburgers can you make from 312 pounds of ground beef?
You can make ? hamburgers.
Answer:
You can make 22 burgers.
Step-by-step explanation:
If you have 312 pounds of ground beef and burgers are 14 pounds, divide 312 by 14 ( 312 / 14). This gives you an answer of 22.28 You will have leftovers because 14 does not go into 312 perfectly. You can also check the answer by doing multiplication ( 22 * 14) which gives you 308. You cannot have another burger because 308 + 14 = 322 which is over the amount of beef you have.
in 1 year the water level of a lake changes by -3/8 inch
Answer:
-3÷8 or -0.375
Step-by-step explanation:
-3÷8÷1=-3÷8×1÷1=-24÷8=-3
micah is 111 of 282828 students in a class. micah's teacher is going to randomly select 333 students from their class to visit a classroom of younger students. what is the probability micah is included in the group of students chosen?
0.71% is the probability micah is included in the group of students chosen.
Describe probability using an example?
By dividing the number of favorable outcomes by the total number of possible outcomes, probability—the likelihood that an event will occur—is determined.The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails.the probability micah is included in the group of students chosen =
3/28 = 10.71%
The probability of her getting picked is unlikely.
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The complete question is -
Micah is 1 of 28 students in a class. Micah's teacher is going to randomly select 3 students from their class to visit a classroom of younger students. What is the probability Micah is included in the group of students chosen?
What is the Process for performing the transformation on a coordinate plane using rigid transformations
Flipping and Stretching is the Process for performing the transformation on a coordinate plane using rigid transformations.
A rigid transformation of a geometric object preserves distance between each pair of points of the object. In other words, rigid transformations preserve the shape and size of an object. For example, a rigid transformation of a triangle preserves both the measure of the angles and the lengths of the sides of the triangle. Think of rigid transformations of a shape as being like taking a cardboard cutout of the shape. The shape can be moved around, rotated, and flipped from one side to the other, but the shape itself does not change.
There are rules associated with rigid transformations. A rigid transformation is some function F from a set X to itself such that F preserves the distances between two points. Let d(x ,y) be the distance between two points. Then, to write the definition in mathematical notation, if d(x ,y) = d(F(x),F(y)) for all points x and y, then F is a rigid transformation.
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in exercises 17–30, (a) find the function’s domain, (b) find the function’s range, (c) describe the function’s level curves, (d) find the boundary of the function’s domain, (e) determine if the domain is an open region, a closed region, or neither, and (f) decide if the domain is bounded or unbounded.
The domain of f { (x,y) ∈ R² x² + y² < (3/5)² } is bounded.
What does the math term domain mean?
Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.Given f(x,y) = [tex]\frac{1}{\sqrt{9 - 25x^{2} - 25y^{2} } }[/tex]
a) the domain of f is the value of ( x, y) for which 9 - 25x² -25y² >0
9 - 25x² -25y² ⇒ 9/25 > x² + y² ⇒ x² + y² < (3/5)²
∴ domain of f = [ (x,y) ∈ R² : x² + y² < (3/5)²}
B) Let z = f = [tex]\frac{1}{\sqrt{9 -25x^{2} - 25y^{2} } }[/tex]
its range is { z ∈ R² : 3z > 1}
c) let f = k ⇒ k = [tex]\frac{1}{\sqrt{9 - 25x^{2} - 25y^{2} } }[/tex]
k² ( 9 - 25x² - 25y²) = 1 = 9 - 25x² - 25y² = 1/k²
⇒ 25x² + 25y² = 9 - 1/k² ⇒ x² + y² = 1/25( 9 - 1/k²)
The level curves are circles for different k values .
d) The boundary of the function's domain
= { (x,y) ∈ R² x² + y² = (3/5)²}
e) Since x² + y² < (3/5)² is the circular open disk , the domain of f is an open set
f) The domain of f { (x,y) ∈ R² x² + y² < (3/5)² } is bounded.
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(-8,5); y= -4x+2 find the parallel equation
Answer: y=-4x-27
Step-by-step explanation:
[tex]y=mx+b[/tex]
Lines are parallel if their slopes are equal
[tex]y=-4x+2[/tex]
⇒ m=-4
⇒ y=-4x+b
A line passes through (-8.5)
⇒ x=-8 y=5
[tex]5=-4(-8)+b\\5=32+b\\5-32=32+b-32\\-27=b[/tex]
So, y=-4x-27
Is 9 11/13 bigger than 9.79
[tex]9\frac{11}{13}[/tex] is bigger than 9.79
The mixed fraction = [tex]9\frac{11}{13}[/tex]
The mixed fraction is the fraction that expressed with its quotient and remainder. The mixed fraction is the combination of a whole number and a simple fraction
Simple fraction is the fraction that has whole numbers as the numerator and denominator.
The decimal number is a number that has whole and the fractional parts are separated by a decimal point
First we have to convert the mixed fraction into simple fraction
[tex]9\frac{11}{13}[/tex] = 128/13
Next we have to convert the simple fraction into decimal form
Divide 128 by 13
The result will be
128/13 = 9.85
Hence, [tex]9\frac{11}{13}[/tex] is bigger than 9.79
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4/6 - 3/6p=16/6 what is p
20 points
Answer:
-4
Step-by-step explanation:
4/6 - 3/6p=16/6
Multiply each side by 6
4 - 3p = 16
Subtract 4 from both sides
-3p = 12
Divide both sides by -3
p = -4
Answer:
-4
Step-by-step explanation:
Solving for 'p':[tex]\sf \dfrac{4}{6}-\dfrac{3}{6}p=\dfrac{16}{6}[/tex]
To find the value of 'p', isolate 'p',
[tex]\sf \dfrac{-3}{6}p=\dfrac{16}{6}-\dfrac{4}{6}\\\\[/tex]
[tex]\sf = \dfrac{12}{6}[/tex]
= 2
[tex]\sf p = 2* \dfrac{6}{-3}\\\\ p = 2 *(-2)\\\\p = -4[/tex]
Help please whoever awnsers correctly I will put as brainliest!!
Based on the fact that the triangles are similar, the length of x is 7.2 cm and the length of y is 7.4 cm
How to find the lengths?If the triangles are similar then it means that the difference between their dimensions can be found by a scale factor.
The scale factor is:
= Dimension of larger similar side / Dimension of smaller similar side
= 11.6 / 5.8
= 2
With a scale factor of 2, then x is:
= 3.6 x 2
= 7.2 cm
The value of y would be:
= 14.8 / 2
= 7.4 cm
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on jan 22 0217 the cost to mail a letter in the us was raised from 47 to 49 centrs. find the relative change in the cost
The relative change is 2%.
What is relative change?In contrast to the reference value, the absolute change's size is expressed as a fraction called the relative change: relative change = absolute change reference value = new value reference value reference value. The absolute change is expressed as a percentage of the value of the indicator in the prior period, or "relative change" expresses the absolute change as such. When measuring indicators in percentage terms, such as the unemployment rate, absolute and relative change principles also apply. To determine the absolute change, subtract the starting value from the ending value. Simply deduct 1,000 from 1,100 to arrive at 100 in the example. The student population increased by 100 pupils throughout the course of the year because this is the absolute change.
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Given the sequence:
5, 12, 19, 26, 33 ...
1. Determine the function that represents this sequence?
2. What is the 30th term of this sequence?
Answer:
Step-by-step explanation:
solve the value equation -6 | 2x+7|=-90
The value of equation is 4,-11
What is algebraic expression ?When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement. Let's say James and Natalie were tinkering with matchsticks when they had the idea to arrange the sticks into number patterns. James used four matchsticks to make the numeral 4 in the air. Adding three additional matchsticks allowed Natalie to create a pattern with two 4s. They understood that they may continue to add three matchsticks each round to make a total of four. They deduced from this that, generally speaking, 4+ 3(n-1) sticks are required to create a pattern with n numbers of 4s. The algebraic statement 4+ 3(n-1) is referred to here.
Given that : the equation -6 | 2x+7|=-90
-6 | 2x+7|=-90
|2x +7|=[tex]\frac{-90}{-6}[/tex]
|2x +7|=15
2x + 7 =±15
2x + 7 = 15 ... (i)
2x = 8
x =4
2x + 7 = -15....(ii)
2x = -22
x =-11
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Which is a correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” when n = 4?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.
The correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” is "StartFraction n cubed Over 16 EndFraction minus 2 + 8"
The correct answer option is option a
The value of the expression when n = 4 is 10. option D
How to write algebraic expressionThe unknown number = nQuotient means divisionquotient of a number cubed and sixteen
= n³ / 16
two less than the quotient of a number cubed and sixteen
= (n³ / 16 - 2)
two less than the quotient of a number cubed and sixteen, increased by eight”
= (n³ / 16 - 2) + 8
If n = 4
(n³ / 16 - 2) + 8
= (4³ / 16 - 2) + 8
= (64/16 - 2) + 8
= (4 - 2) + 8
= 2 + 8
= 10
In conclusion, the expression can be written as "StartFraction n cubed Over 16 EndFraction minus 2 + 8"
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If f (x) = 4x² + 3x - 5, then f(x+h)-f(x)/ h is equal to which of the following?
Answer:
Option 3
Step-by-step explanation:
[tex]f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h-5 \\ \\ f(x+h)-f(x)=4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5) \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5)}{h}[/tex]
Please help me with this question!
The two swimming pools will have same amount of water using this equation, where x represents the time in minutes
3300 - 24x = 3696 - 35x
How to find the equation when the two pools will have same amount of waterinformation given in the question is as follows
the first pool had 3300 liters of water and drains at a rate of 24 liters per minute
the second pool had 3696 liters of water and drains at a rate of 35 liters per minute.
The given information implies that
every minute in x minutes 24x liters of water is drained from the first tank.
3300 - 24x
Similarly, in the second tank in x minutes 35x liters of water in drained from the second tank
3696 - 35x
The tanks will have equal volume of water when the two equations are equal
3300 - 24x = 3696 - 35x
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Find and interpret the slope. The number of cubic feet of watery In a reservoir x hours after the water starts flowing into the reservoir Is a linear function. The points (40,2,000) and (60, 3,000) are on the line of the function. The slope ls which means that the amount of water in the reservoir is increasing at a rate of cubic feet each hour.what is the y- intercept? what is the x- intercept?
The slope of a line (m) given two points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with (40,2,000) and (60, 3,000):
[tex]m=\frac{3000-2000}{60-40}=\frac{1000}{20}=50[/tex]The slope ls 50 cubic feet/hour which means that the amount of water in the reservoir is increasing at a rate of 50 cubic feet each hour.
Slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept. Replacing with m = 50 and point (40, 2000), e get:
200050()40
2000
2000 - 2000 = b
0 = b
Then the y-intercept is point (0, 0) which is also the x-intercept
The equation is:
y = 50x
Solve one sixth times quantity x plus 18 end quantity equals negative 5.
x = −48
x = −138
x = 12
x = 18
pls hurry
Answer:
(a) -48
Step-by-step explanation:
You want the solution to the equation 1/6(x +18) = -5.
2 Step equationThe first step to solving this can be to multiply both sides by 6, eliminating the fraction:
x +18 = -30
The second step can be to isolate the variable by subtracting 18 from both sides.
x = -48
The solution is x = -48.
__
Additional comment
Sometimes you may want to simplify the equation before you start the solution process. Here, you can also start by eliminating parentheses:
1/6x +3 = -5
Now, subtracting 3 gives ...
1/6x = -8
Finally, multiplying by 6, we have ...
x = -48
<95141404393>
Simplify 3(2x-5) - (1-3x)
6x-15 - 1 - 3x
6x - 16
Why is this wrong
Answer:
6X-15-1-3X=3X-16
6-3=3
Raise 7 to the 2nd power, then add the result to b
(7)^2 +
2nd power means squaring a number and since you need to do that first, it goes in brackets.
answer: 49 + b, or just 7^2 + b
explanation: 7^2 = 7x7, so it is equal to 49. then add b to 49
Look at the image for the problem, also round to the nearest hundredth if necessary.
ANSWER
[tex]V=3052.08ft^3[/tex]EXPLANATION
We want to find the volume of the sphere.
The volume of a sphere is given as:
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]where r = radius of the sphere.
Therefore, we have that the volume of the sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot9^3 \\ V=3052.08ft^3 \end{gathered}[/tex]That is the volume of the sphere.
Latisha has $40 in her checking account. She makes a withdrawal of $20 and then writes a check for $40. Then she deposits $30.
If Latisha has $40 in her checking account and she makes a withdrawal of $20 and then writes a check for $40, then she deposits $30, then the amount she has in her checking account is $10
The amount she has in her checking account = $40
The amount she withdraw from her account = $20
The amount she writes a check = $40
The deposited amount = $30
To find the final checking account balance we have to use the arithmetic operations
The final balance amount = The amount she has in her checking account -The amount she withdraw from her account - The amount she writes a check + The deposited amount
= 40-20-40+30
= $10
Hence, by using arithmetic operations, if Latisha has $40 in her checking account and she makes a withdrawal of $20 and then writes a check for $40, then she deposits $30, then the amount she has in her checking account is $10
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C
A
O 49°
50°
B
If mBD = 23°, and mZBED=16°, what is mï?
27.5°
55°
D
DE
The arc angle AC is measured as 55 degrees.
How to find arc angle?If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.
Therefore, the secants intersect outside the circle at point E.
The arc angle AC can be found as follows:
Therefore,
m∠BED = 1 / 2 (arc angle AC - arc angle BD)
arc angle AC = x
arc angle BD = 23 degrees.
m∠BED = 16 degrees.
m∠BED = 1 / 2 (arc angle AC - arc angle BD)
16 = 1 / 2 (x - 23)
16 = 1 / 2x - 23 / 2
16 + 11.5 = 0.5x
27.5 = 0.5x
x = 27.5 / 0.5
x = 55 degrees.
Therefore,
arc angle AC = 55 degrees.
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1.8 as decimal in it simplest form
Answer:
1.8 = 9
5
= 14
5
as a fraction