A box contains 3 plain pencils and 9 pens. a second box contains 7 color pencils and 3 crayons. one item from each box is chosen at random. what is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
16-2b=b+7
solve equation
Which set of points is not coplanar?
points A, B, E
points A, B, C, E
points B, C, D
points A, B, C, D
we know that
Coplanar points are three or more points which lie in the same plane. Remember that a plane is a flat surface which extends without end in all directions. Any three points in 3-dimensional space determine a plane.
case a) points A, B, E
Any group of three points determines a plane
so
The points A,B,E are coplanar
case b) points A, B,C,E
The four points do not belong to the same plane
so
The points A,B,C,E are not coplanar
case c) points B, C, D
Any group of three points determines a plane
so
The points B, C, D are coplanar
case d) points A,B, C, D
The base of the pyramid is a flat surface, the four points lie in the same plane
so
The points A,B, C, D are coplanar
therefore
the answer is the option
points A, B, C, E are not coplanar
15 oranges were purchased.
Cost per orange: $0.45
c = total cost of oranges
Which equation shows
the total cost of oranges?
Bob climbed down a ladder from his roof, while Rob climbed up another ladder next to him. Each ladder had 30 rungs. Thrir friend Jill recorded the following information about Bob and Rob: Bob Went down 2 rungs every second .Rob went up 1 rung every second . At some point , Bob and Rob were at the same height. Which rung were they on ?
The problem involves finding the time and the rung at which Bob and Rob meet. They both meet on the 10th rung after 10 seconds of Bob's descent and Rob's ascend on their ladders, moving at their respective rates.
Explanation:In this problem, we are asked to find the rung at which both Bob and Rob meet. Each ladder has 30 rungs. Bob is descending from 30 rungs, moving down 2 rungs every second. Rob is ascending from 0 rungs, moving up 1 rung every second. To determine where they meet, we need to find the time at which the rungs they're on coincide.
Bob goes down 2 rungs per second, so in 't' seconds Bob will be on the 30 - 2t rung. Similarly, Rob goes up 1 rung per second, so in 't' seconds Rob will be on the t rung. They meet when 30 - 2t equals t. Solving this equation gives us that t equals 10 seconds.
So at 10 seconds, they meet & the rung they're on is t = 10. Hence, Bob and Rob meet on the 10th rung.
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The cost of seeing a weekday show is 2/3 the cost of a weekend show. in one month, andy spent $42.50 for 4 weekday shows and 3 weekend shows. find the price of a weekday show and the price of a weekend show
Answer:
x = weekday shows
y = weekend shows
x = 2/3y
4x + 3y = 42.50
4(2/3y) + 3y = 42.50
8/3y + 3y = 42.50
8/3y + 9/3y = 42.50
17/3y = 42.50
y = 42.50 * 3/17
y = 127.50/17
y = 7.50
x = 2/3y
x = 2/3(7.50)
x = 15/3
x = 5
so weekday shows (x) cost $ 5 and weekend shows (y) cost $ 7.50
Step-by-step explanation:
For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)
Answer:
The required answer is: [tex]-x^2+2x+8[/tex]
Step-by-step explanation:
We have been given the two function:
[tex]f(x)=2x+1[/tex]
And [tex]g(x)=x^2-7[/tex]
We have to find (f-g)(x):
[tex](f-g)(x)=f(x)-g(x)[/tex]
[tex](2x+1)-(x^2-7)[/tex]
[tex]2x+1-x^2+7[/tex]
[tex]-x^2+2x+8[/tex]
We will get the quadratic expression after the prescribed operation been applied.
Hence, the required answer is: [tex]-x^2+2x+8[/tex]
given the function f(x)=3√x-2; What restriction is there on the value uner the square root symbol? In other words what can't you do with a square root expression? ...?
Answer:
x must be greater than or equals to 2
Step-by-step explanation:
Here we follow the rule , which says that , the term inside the square root must not be less than 0. It is because, square of any real number whether positive or negative always results in a positive real number. Hence , there can not be negative real number whose sqaure root exists.
Hence
In order to function to be defined ,
x-2>=0
Adding 2 on both sides we get
x>=2
Hence this is our condition.
a square is just big enough to contains a unit circle. what is radius of the largest circle in one of the corners in the square but outside the unit circle?
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.
5x+2y=21
-2x+6y=-34
...?
Answer:
The y-coordinate of the solution would be [tex]-\frac{64}{17}[/tex]
Step-by-step explanation:
Given system of equations,
5x+2y = 21 ----------(1)
-2x+6y = -34 ---------(2),
2 × Equation (1) + 5 × Equation (1),
We get,
4y + 30y = 42 - 170
34y = -128
[tex]\implies y = -\frac{128}{34}=-\frac{64}{17}[/tex]
What is the value of the function y = 2x - 3 when x = –1?
A.
–5
B.
2
C.
–1
D.
3
Solve for x.
A triangle is drawn with a midsegment. The midsegment is labeled 4 x minus 1 and the side of the triangle that is parallel to the midsegment is labeled 30.
30
15
7.75
4 Solve for x.
A triangle is drawn with a midsegment. The midsegment is labeled 4 x minus 1 and the side of the triangle that is parallel to the midsegment is labeled 30.
30
15
7.75
4
Liv wants to buy a new pair of jeans for an upcoming party. She finds a pair she likes that was originally priced at $50 and is now on sale for $42. What is the percent of discount for this item?
A.) 16%
B.) 18%
C.) 20%
D.) 25%
Classify the numbers as prime or composite
I am gonna give you classify three numbers as prime numbers and three numbers composite numbers, since you never mentioned about any specific numbers.
Prime numbers
1.3- it is a prime number because they only factors it has, is 1 and itself.
2.11- it is a prime number because you can only multiply by 11 or 1 to get 11.
3.13- it is a prime number because it only has 2 factors.
Composite numbers
1.4- it is a composite number because it has more than 2 factors.
2.8- it is a composite number because it has 1,2,4, and 8 as its factors.
3.14- it is a composite number because it has 1,2,7,and 14 as its factors.
what is the scietnific notation of 108,000,000?
...?
A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?
Answer:
[tex]\boxed{\boxed{a = 240, b = 1.16}}[/tex]
Step-by-step explanation:
General exponential function for growth or decay is,
[tex]y=a(1\pm r)^{x}[/tex]
Where,
a = initial value,
r = rate of change
+ is used for growth and - is used for decay.
As here, the number of birds increasing so, the exponential function is,
[tex]y=a(1+r)^{x}[/tex]
And initial value a = 240, r = rate of change = 16% = 0.16
Putting the values,
[tex]y=240(1+0.16)^{x}\\\\y=240(1.16)^{x}[/tex]
Comparing this with the given equation [tex]y=ab^{x}[/tex]
Hence, a = 240, b = 1.16
Answer:
The value of a is 240 and b is 1.16.
Step-by-step explanation:
Given,
The initial population of the birds = 240,
Annual rate of increasing = 16 %,
Hence, the population of birds after x years
[tex]P=240(1+\frac{16}{100})^x[/tex]
[tex]=240(1+0.16)^x[/tex]
[tex]=240(1.16)^x[/tex]
We can put P = f(x), ( because, f(x) also shows the population of birds after x years )
[tex]\implies f(x) = 240(1.16)^x[/tex] --------(1)
According to the question,
[tex]f(x) =ab^x[/tex] --------(2),
From equation (1) and (2),
a = 240 and b = 1.16
Write an equation to solve the problem.
Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 45 mi/h. When will they be 400 mi apart? ...?
ok guys this is for connexus introduction to solving equations: practice
1. B, h=2A/b 2. C, v=h+5t^2/t 3. D, 23 4. D, -81 5. A, 17/7 6. D, 8 7. A, 4 hours 8. C, width is 4.5; length is 7.5 9. C, never true 10. B, sometimes true
-hope this helps you guys out :3 your welcome
What is 3/5 as a decimal? answers:
a. 0.75
b. 0.3
c. 0.12
d. 0.15
Sydney is cutting the crust from the edges of her sandwich. The dimensions, in centimeters, of the sandwich is shown.
Which expression represents the total perimeter of her sandwich, and if x = 1.2, what is the approximate length of the crust?
Answer:
The answer is B. I looked at the picture of his problem. I just did the test.
I just knew the answer beforehand.
Step-by-step explanation:
How would the following numbers be represented in E notation?
3.287 x 10^6
A laptop computer is purchased for 2300 . After each year, the resale value decreases by 35% . What will the resale value be after 4 years?
round your answer to the nearest dollar ...?
What's the numerator for the following rational expression? G/h + 8/h = ?/h
Shuttle A departs every 8 minutes Shuttle B departs every 10 minutes and Shuttle C departs every 12 minutes. If all shuttles leave the airport at 4:00 P.M., at what time will they next leave the airport together?
Each face of a pyramid is an isosceles triangle with a 74° vertex angle. What are the measures of the base angles?
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
An isosceles triangle is a triangle whose two sides are equal and the angle opposite to the equal sides are equal.
The sum of the isosceles triangle = 180°
The base angle of the isosceles triangle for each face of a pyramid is 53°
What is a triangle?Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
An isosceles triangle is a triangle whose two sides are equal and the angle opposite to the equal sides are equal.
Now,
Vertex angle of the isosceles triangle = 74°
The sum of the isosceles triangle = 180°
Let the two equal base angles = x
x + x + 74° = 180°
2x + 74° - 180°
2x = 180 - 74
2x = 106
x = 53°
Thus,
The base angle of the isosceles triangle for each face of a pyramid is 53°
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I need help solving these please help...
A jeweler orders necklaces from a website that offers $6 shipping for any-size order. each necklace costs $7. the jeweler wants to know the total cost of ordering n necklaces.
Answer:
7n + 6.00
Step-by-step explanation:
A jeweler orders necklaces from a website that offers $6 shipping for any size order.
Each necklace costs $7.00
The jeweler wants to know the total cost of ordering 'n' necklaces.
Therefore the cost of the necklaces is
Total Cost = 7n + 6.00
capricia is using ribbon to create girls hair barrettes. she has a total of 64 yrds of ribbon with which to make her creations. Regular barrettes requires 1 yrd of ribbon and a deluxe of barrettes use 4 yds .
WRITE AN INEQUALITY
The inequality that represents the situation is 1*R + 4*D <= 64 which indicates that the total amount of ribbon used to make regular and deluxe barrettes should not exceed 64 yards.
Explanation:Let's denote the number of regular barrettes as R and that of deluxe barrettes as D. Each regular barrette requires 1 yard of ribbon and each deluxe barrette requires 4 yards of ribbon. We know that Capricia has a total of 64 yards of ribbon. Therefore, we can create the inequality as follows:
1*R + 4*D <= 64
This inequality states that the total amount of ribbon used for both the regular and the deluxe barrettes should not exceed 64 yards.
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if the difference in the side lengths of two squares is 10 and the sum of the side lengths is 18 what are the side lenghts
Order 51/62 32/43, and 74/87
a rectangle has a perimeter of 88 ft. if the ratio of its length to width is 9:2, what is its actual length and width