Answer:
The lectures cost is $7.33 per hour
Step-by-step explanation:
* Lets explain how to solve the problem
- For the level 3 course the examination hours cost twice as much
as workshop hours
- The workshop hours cost twice as much as lecture hours
- There are examination hours , workshop hours and lecture hours
- There are 3 hr for examination, 24 hr for workshops and 12 hr
for lectures
* Let the cost of the lecture hours is $x per hour
∴ The cost of the lecture hours is x per hour
∵ The cost of workshop hours is twice the cost of lecture hours
∴ The cost of the workshop hours is 2(x) = 2x per hour
∵ The cost of examination hours is twice the cost of workshop hours
∵ The cost of the workshop hours is 2x
∴ The cost of examination hours is 2(2x) = 4x per hour
- The cost of the level 3 is the sum of the costs of the lecture hours,
workshop hours and examination hours
∵ There is 12 hours for lectures
∵ There is 24 hours for workshops
∵ There is 3 hours for examination
∵ The total cost of level 3 = 12(x) + 24(2x) + 3(4x)
∴ The total cost of level 3 = 12 x + 48 x + 12 x
∵ The total cost of level 3 = $528
∴ 12 x + 48 x + 12 x = 528
∴ 72 x = 528 ⇒ divide both sides by 72
∴ x = 7.33
∵ x is the cost of the lecture hours per hour
∴ The lectures cost is $7.33 per hour
two less than a number divided by four
Answer:
=x/4 - 2 (the third choice.
Step-by-step explanation:
Letting the number be x, the phrase two less than a number divided by four is expressed using the following steps:
We first take the the number x then divide by four then subtract 2.
The expression becomes:
(x/4) - 2
To solve an algebraic expression such as the one you described – "two less than a number divided by four" – you can follow these steps:
1. Start by identifying the variable, which is typically represented by "x." In this case, "a number" will be our variable "x."
2. The phrase "two less than" indicates a subtraction of two from a certain value. In algebraic terms, "two less than x" would be written as "x - 2."
3. Finally, the phrase "divided by four" tells us to take our result from step 2 and divide it by 4. So, we place the expression "(x - 2)" over 4, indicating division.
Putting it all together, the algebraic expression that represents the phrase "two less than a number divided by four" is:
(x - 2) / 4
To evaluate this expression for a particular value of x, you would substitute the value of x into the expression and then perform the calculation.
For example, if x is 10, you would evaluate the expression as:
(10 - 2) / 4
= 8 / 4
= 2
So, when x is 10, the value of the expression "two less than a number divided by four" is 2.
A paint box contains 12 bottles of different colors. If we choose equal quantities of 3 different colors at random, how many color combinations are possible? A. 479,001,600 B. 1,320 C. 220 D. 36
Answer:
C
Step-by-step explanation:
You are choosing 3 from a total of 12. Order does not matter. So you are working with combinations. The answer symbolically is
12C3
12C3 = 12!/(9!3!)
12C3 = 12 * 11 * 10 * 9!/(9! 3!)
12C3 = 12 * 11 * 10/6
12C3 = 2 * 11 * 10
12C3 = 220
========================================
We have 12 choices for the first selection, 11 for the second, and 10 for the third. There are 12*11*10 = 1320 permutations. If your teacher was asking about permutations, then you would be done at this point. However, your teacher is asking about combinations. With combinations, order does not matter.
For any group of 3 items, there are 3! = 3*2*1 = 6 ways to arrange this group. This means that we must divide 1320 over 6 to correct for the fact that we overcounted by a factor of 6
In this case,
number of combinations = (number of permutations)/6
number of combinations = 1320/6
number of combinations = 220
More generally, I'm using the connection that
nCr = (nPr)/(r!)
*****WILL GIVE BRAINLEST IF CORRECT******
Conner's work is correct. To combine and make it simple, you Multiply:
(3^5+9)+(6^8+10) which will equal 3^14 6^18.
But Jane's work, instead of adding, Jane multiplies. So, Conner is correct.
Hope that helped!
Alexa and Bart are arguing about who will do the dishes. How can they make
a fair decision?
Answer:
Flip a fair coin. It has a 50% chance of landing heads up and a 50% chance of landing tails up. Therefore, the person who will do the dishes will be chosen at random.
Answer:
B: Put each person's name on a separate piece of paper in a bag. Randomly draw a name. The person whose name is chosen does the dishes.
D: Roll a number cube. If the number rolled is even, Alexa does the dishes. If the number is odd, Bart does the dishes.
Step-by-step explanation:
I got it right:)
Melody lives due south of her cousins house and 40 miles due west of her grandparents house. One day she drove to her cousins house in a straight line from her grandparents house. How far did she drive?
Final answer:
Melody drove approximately 56.57 miles in total on her trip from her grandparents' house to her cousin's house by traveling in a straight line.
Explanation:
Melody drove a distance of 40 miles in a straight line from her grandparents house to her cousin's house. To find the total distance she drove, we can use the Pythagorean theorem as she traveled in a right-angled triangle.
Distance due south = 40 miles
Distance due west = 40 miles
Total distance driven = √(40² + 40²)
Total distance driven = √(1600 + 1600) = √3200
Total distance driven ≈ 56.57 miles
-4(w+2)+6w=
Can someone ease help me with this
Answer:
2w -8
Step-by-step explanation:
-4(w+2)+6w
Distribute the -4
-4w -8 +6w
Combine like terms
-4w +6w -8
2w -8
Answer:
Step-by-step explanation:
-4w-8+6w=0
8+2w=0
2w= -8
w= -4
!!PLEASE HELP I WILL MARK YOU BRAINLIEST!!!
In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
Answer:
You will use this formula x= -b +
[tex] x = - b + \sqrt{ { \: - 4ac}^{?} } [/tex]
Step-by-step explanation:
4n
[tex] {?}^{?} [/tex]
so you want to do n to the second power minus and minus 39 equals 0 so you using the quadratic formula
Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies
Louise mowed a neighbor's yard to earn \$25$25dollar sign, 25. She mowed a few more yards and earned an additional \$75$75dollar sign, 75. She continued to mow all of the yards each week for a total of 555 weeks, earning money at the same rate. At the end of the 555 weeks, she spent \$250$250dollar sign, 250.
Write a numerical expression with parentheses for the amount of money Louise has left.
Answer:
She has 250 dollars left
Step-by-step explanation:
The first lawn she gained 25 dollars
+25
Then she gained 75 dollars
+25 +75=100
She mowed lawns for 5 weeks making the same amount 5 weeks at 100 dollars
5*100 = 500
She earned a total of 500 dollars
She spent 250 dollars
500-250 = 250
She has 250 dollars left
How many months are in ¾ of a year
Answer:
9
Step-by-step explanation:
Answer:
9 months
Step-by-step explanation:
There are 12 months in a year
Multiply 12 months by 3/4
12 *3/4
36/4
9
There are 9 months in 3/4 of a year
A patient received 84 mL per hour of normal saline solution. How many liters did the patient receive in 24-hour period?
Answer:
2.106 liters
Step-by-step explanation:
24 * 84 mL = 2016 mL = 2.106 L
Answer: 84*24=2016
You multiply 84 by 24 to get 2016.
rounding 1137 to the nearest hundred
Answer:
1,100
Step-by-step explanation: The hundreds place is the second 1 from the left. That number will stay as it is or go up one number, based on the number to its right, which in this case is a 3. If the 3 is the number 5 or larger, then the 1 would round up to a 2, but since the 3 is less than 5, the 1 stays a 1. All numbers to the right of the place value you are rounding to become zeros.
Rounding 1137 to the nearest hundred:
Identify the hundreds place: 1137Look at the digit to the right of the hundreds place (3): since it's less than 5, round down to 1100x^5y^3/x^2-x-6 * x^2 -9/x^2y^4
[tex]\bf \cfrac{x^5y^3}{x^2-x-6}\cdot \cfrac{x^2-9}{x^2y^4}\implies \cfrac{x^5y^3}{x^2-x-6}\cdot \cfrac{\stackrel{\textit{difference of squares}}{x^2-3^2}}{x^2y^4} \\\\\\ \cfrac{x^5y^3}{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+2)}\cdot \cfrac{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+3)}{x^2y^4}\implies \cfrac{x^5y^3}{x+2}\cdot \cfrac{x+3}{x^2y^4}[/tex]
[tex]\bf \cfrac{x^5y^3}{x^2y^4}\implies \cfrac{x^5x^{-2}}{y^4y^{-3}}\cdot \cfrac{x+3}{x+2}\implies \cfrac{x^{5-2}}{y^{4-3}}\cdot \cfrac{x+3}{x+2}\implies \cfrac{x^3(x+3)}{y(x+2)}\implies \cfrac{x^4+3x^3}{yx+2y}[/tex]
If 5 cans of baked beans cost $2.85, how
many cans of baked beans can be bought
for $19.38?
Answer:
34 cans. If you set it up as ratios (5/2.85 = x/19.38), make the number of cans you need to know "x" and solve for x.
Final answer:
To determine how many cans of baked beans can be bought for $19.38, divide $19.38 by the cost of each can, which is found by dividing the total cost of 5 cans by 5. The result is that you can buy 34 cans of baked beans for $19.38.
Explanation:
To find out how many cans of baked beans can be bought for $19.38, we need to determine the cost of each can. Given that 5 cans of baked beans cost $2.85, we can divide the total cost by the number of cans to find the cost of each can: $2.85 ÷ 5 = $0.57 per can.
Next, we divide the amount of money we have, $19.38, by the cost of each can to find the number of cans we can buy: $19.38 ÷ $0.57 = 34 cans.
So, for $19.38, we can buy 34 cans of baked beans.
Find the least positive angle measurement that is coterminal with –100°.
Answer:
260 degrees is coterminal with -100 degrees.
Step-by-step explanation:
So a full rotation about a circle is 360 degrees.
So if we do 360+(-100) we get 260.
They will share the same terminal ray because if we go 100 clockwise from the initial ray that will be an angle coming counterclockwise 260 from the initial ray.
100+260=360.
Answer:
260°
Step-by-step explanation:
Co terminal angles are angle ± 360°n where n = 0, 1, 2, 3, ....
The least positive = - 100° + 360° = 260°
Find the slope of the line: 6x – 3y + 6 = 0
Answer:
m=2
Step-by-step explanation:
6x - 3y + 6 = 0
Subtract 6x from both sides.
-3y + 6 = -6x
Subtract 6 from both sides.
-3y = -6x - 6
Find the GCF of both sides by, which, in this case, is -3. Divide both sides by the GCF, -3.
y = 2x + 2
Since the formula for linear equations is:
y = mx + b , 2 in the slope.
Proportions in Triangles
Answer:
x =35.
Step-by-step explanation:
x / 20 = 14 / 8
Cross multiply:
8x = 20*14
8x = 280
x = 35.
The study of proportions in triangles involves understanding similar triangles' corresponding side ratios and how area scales with linear dimensions. The ratios help determine unknown lengths and compare triangles, and the square of the scale factor relates to how area changes.
Explanation:Understanding Proportions in Triangles
Proportions play a crucial role in the study of triangles, particularly when dealing with similar triangles. Similar triangles have corresponding sides that are in proportion and this concept can be applied in various problems to find unknown lengths or to compare triangles. For instance, if two triangles are similar, then the ratio of their corresponding sides are equal. This can be denoted as a₁ = A₁/A2 or a3 = A3/A2, where A1, A2, and A3 represent the lengths of the sides in one triangle, and a1 and a3 are the proportional sides in the other.
Area scaling is another important concept derived from proportions. If a triangle's sides are scaled by a factor, its area scales by the square of that factor. For example, if the sides of one triangle are twice as long as the sides of a similar triangle, the area of the larger triangle is four times greater, since 2 squared equals 4. This principle can be easily demonstrated by cutting the larger triangle into four smaller triangles identical to the original smaller one, showing that the larger triangle has four times more area as illustrated in fig. (b).
In summary, proportions are crucial when working with similar triangles and understanding how changes in linear dimensions affect the area of a triangle. When comparing triangles, the ratios of corresponding sides and areas can provide valuable insights and are foundational in various applications within geometry.
Mrs. Vanwhy made a two-way table to show which students made honor roll and which students study a foreign language.
Which is the best two-way table for Mrs. Vanwhy to organize her data?
Answer:
2
Step-by-step explanation:
did it on edge
Option (B) Column 1 has entries honor roll, foreign language, total. Column 2 is labeled not on honor roll. Column 3 is labeled no foreign language. Column 4 is labeled total is the correct answer.
What is table of values?A table of values is a set of ordered pairs usually resulting from substituting numbers into an equation (relation). By using this variable within the equation or in the other function, the value of the other variable or the missing number in the equation can be found easily.
For the given situation,
The diagram shows the two-way table.
Mrs. Vanwhy made a two-way table to show which students made honor roll and which students study a foreign language.
From the data, the table that shows all the required data for Mrs. Vanwhy to organize her data should consist of honor roll, foreign language, not on honor roll, no foreign language.
Hence we can conclude that option (B) Column 1 has entries honor roll, foreign language, total. Column 2 is labeled not on honor roll. Column 3 is labeled no foreign language. Column 4 is labeled total is the correct answer.
Learn more about table of values here
brainly.com/question/14695594
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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $35. For
one performance, 35 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $1125. What was the price of each kind of
ticket?
Answer:
Advance=15$
Same-day=20$
Step-by-step explanation:
Advance=15 Same-day=20
15*35=525
20*30=600
525+600=1125
WILL GIVE BRAINLEIST NEED TO TURN IN BY 9 P.M. PLS HURRY SUPER EASY.
Write a real-world problem in which you would solve the equation a+12=30.
Answer:
Brian has 12 apples. How many more apples does he need to have 30 apples in all?
Step-by-step explanation:
In this case "a" is the number of apples he needs to have 30 in all, and adding that to 12 results in the equation a + 12 = 30.
Hope this helps!
please need help asap !!!
two perpendicular Lines intersect at the origin. If the slope of the First line is -1/2, What is the equation Of The second Line?
Answer: y=2x
Step-by-step explanation: A perpendicular line is the opposite reciprocal of the slope. The opposite reciprocal of -1/2 is 2.
The equation of the second line is y=2x
#11 Mrs Owen ordered 500 chicken wings to be shared equally among 250 guests invited to her wedding anniversary party. However the turnout was less than expected and every guest ate one more chicken wing than originally planned. If there were 92 chicken wings left after the party, how many people attended Mrs. Owen’s party?
#12 The total number of cherries on a plate, in a cup and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Answer:
11: 136 people
12: 55 Cherries
A single card is drawn from a deck of 52 cards, find the following
probabilities:
a. result is a queen
b. result is a queen result is a face card
c. result is a heart
d. result is a heart | result is a red card
e. result is a heart result is a black card
f. result is a heart result is not a diamond
Answer:
a. 1/13
b. 1/78
c. 1/4
d. 1/12
e. 1/6
f. 1/4
Step-by-step explanation:
First, lets write some basic data
There are total 52 cards.26 cards are red and 26 cards are blackOut of 26 red cards; 13 cards are of diamond and 13 cards are of heartOut of 26 black cards; 13 cards are of spade and 13 cards are of clubsIn spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jacka. result is a queen
Each set has one queen; 1 of spade, 1 of clubs, 1 of heart, 1 of heart
There are total 4 queens
Total number of cards is 52
Probability = Number of favourable outcomes/total number of outcomes
Probability = 4/52
Probability = 1/13
b. result is a queen result is a face card
From my understanding, this question is result is a queen given that result is a face card.
Queen: 4 cards
Face card means King, Queen and Jack
Each set has one King, one Queen and one Jack
There are total 4 sets
Therefore, there are 4 Kings, 4 Queens and 4 Jacks
Face cards: 12-4 (because 4 queens have already been taken out) = 8
Total number of cards: 52-4 (because 4 queens have already been taken out) = 48
Probability (A|B) = P(A) * P(A|B)
P(A) = result is a queen = 4/52 = 1/13
P(A|B) = result is a face card = 8/48 = 1/6
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/13 * 1/6
Probability (A|B) = 1/78 or 0.01282
c. result is a heart
Out of the 52 cards, there are 26 red cards and out of the 26 red cards, there are 13 cards of heart
Heart = 13 cards
Total number of cards = 52 cards
Probability = Number of favourable outcomes/total number of outcomes
Probability = 13/52
Probability = 1/4
d. result is a heart | result is a red card
Result is a heart = P(A) = 13/52 = 1/4
Result is a red card=26/52 Total number of red cards is 26 but 13 cards (heart) are already taken out so 13 will be subtracted from the numerator and denominator
= 13/39 = 1/3
Result is a heart given that result is a red card P(A|B) = 1/3
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/4 * 1/3
Probability (A|B) = 1/12
e. result is a heart result is a black card
Result is a heart = P(A) = 13/52 = 1/4
Result is a black card=26/52 Total number of cards is 52 but 13 cards (heart) are already taken out so 13 will be subtracted from the denominator
= 26/39 = 2/3
Result is a heart given that result is a black card P(A|B) = 2/3
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/4 * 2/3 = 1/6
f. result is a heart result is not a diamond
Result is a heart = P(A) = 13/52 = 1/4
Result is not a diamond = there are 13 diamonds in a deck so cards that are not diamond are 52-13 = 39
Total cards = 52 - 13 (because hearts are already taken out) = 39
= 39/39 = 1
Probability (A|B) = P(A) * P(A|B)
Probability (A|B) = 1/4 * 1 = 1/4
!!
The probabilities of the given result in each subpart for deck of 52 cards can be given as following:
a. 1/13
b. 1/3
c. 1/4
d. 1/2
e. 0
f. 1/3
Following are the basics points need to know to solve this question:
There are total 52 cards.26 cards are red and 26 cards are black.Out of 26 red cards; 13 cards are of diamond and 13 cards are of heart.Out of 26 black cards; 13 cards are of spade and 13 cards are of clubs.In spade, clubs, heart and diamond there is one card of ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, King, Queen, Jack.a. Probability that the result is a queen
There are 4 queens in a standard deck of 52 cards. So the probability:
[tex]P(Queen) = \frac{ Number \ of \ Queens }{Total \ Cards} = \frac{4}{52} = \frac{1}{13}[/tex]
b. Probability that the result is a queen given the result is a face card
There are 12 face cards in a deck (3 face cards each for 4 suits: Jack, Queen, King). So, conditional probability:
[tex]P(Queen | Face Card) = \frac{ Number \ of \ Queens }{Total \ Face \ Cards} = \frac{4}{12} = \frac{1}{3}[/tex]
c. Probability that the result is a heart
There are 13 hearts in a deck. So the probability:
[tex]P(Heart) = \frac{ Number \ of \ Hearts }{Total \ Cards} = \frac{13}{52} = \frac{1}{4}[/tex]
d. Probability that the result is a heart given the result is a red card
Red cards consist of hearts and diamonds. There are 26 red cards, and half of them are hearts. So, conditional probability:
[tex]P(Heart | Red \ Card) = \frac{ Number \ of \ Hearts }{Number \ of \ Red \ Hearts} = \frac{13}{26} = \frac{1}{2}[/tex]
e. Probability that the result is a heart given the result is a black card
Black cards consist of spades and clubs. There are no hearts in black cards. So:
[tex]P(Heart | Black \ Card) = 0[/tex]
f. Probability that the result is a heart given the result is not a diamond
If the card drawn is not a diamond, it must be either a heart, club, or spade. There are 39 such cards. So:
[tex]P(Heart |Not \ a \ Diamond) = \frac{ Number \ of \ Hearts }{Number \ of \ Non-Diamond \ Cards} = \frac{13}{39} = \frac{1}{3}[/tex]
What is the solution to the equation 6x+2=9x-1
Answer:
1
Step-by-step explanation:
Combine like terms first by subtracting 6x from both sides.
[tex]6x+2=9x-1\\2=3x-1[/tex]
Next, add 1 to both sides.
[tex]2=3x-1\\3=3x[/tex]
Finally, divide both sides by 3.
[tex]3=3x\\1=x[/tex]
A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down. Which rule describes the translation?
Answer:
Because the translation is 4 units towards the right, it will be x + 4
and because it is 3 units down, it will be y - 3
(x,y) → (x + 4, y - 3)
Step-by-step explanation:
Final answer:
The translation of a triangle 4 units right and 3 units down is described by the rule (x, y) → (x+4, y-3).
Explanation:
The rule that describes the translation of a triangle 4 units to the right and 3 units down in the coordinate plane can be represented as (x, y) → (x+4, y-3). This represents a translation where each point (x, y) of the triangle is moved to a new point obtained by adding 4 to the x-coordinate and subtracting 3 from the y-coordinate. In terms of transformation geometry, this rule effectively shifts the entire shape without rotating, resizing, or otherwise distorting it.
Algebra 2 help? will give brainliest!
what is y=2x-5 and x+3y=27 graphed
Answer:
See attachment
Step-by-step explanation:
The first function is [tex]y=2x-5[/tex].
The slope is [tex]m=2[/tex] and the y-intercept is [tex]b=5[/tex].
The second equation is [tex]x+3y=27[/tex].
The slope intercept form is [tex]y=\frac{1}{3}x+9[/tex]
The slope is [tex]m=\frac{1}{3}[/tex] and y-intercept is [tex]b=9[/tex]
The graph of these two functions is shown in the attachment.
What is the maximum of f(x) = sin(x)?
Answer:
Sinx= 1(maximum value)
Step-by-step explanation:
Answer:
The maximum is 1
Step-by-step explanation:
-1<_sin(x)<_1
Range of sin(x)= [-1,1]
sin(x)= 1
f(x)=3.7-2x
g(x) = 0.25x-5
What is f(x) + g(x)
A) h(x)=3.95x-7
B) h(x)=8.7-2.25x
C) h(x)=-1.3-1.75x
D) h(x)=3.95-7x
Answer:
C) h(x)=-1.3-1.75x
Step-by-step explanation:
f(x)=3.7-2x
g(x) = 0.25x-5
f(x) + g(x) =3.7-2x + 0.25x-5
Combine like terms
= -1.75x - 1.3
Answer:
The answer is C.) h(x)=-1.3-1.75x
Step-by-step explanation: