Answers
The angle of elevation from point C to point A is [tex]32^{\circ}[/tex]
Solution:
Given that we have to find the angle of elevation from point C to Point A
Given in figure that, angle A = [tex]58^{\circ}[/tex]
Given is a right angled triangle ABC where angle B = [tex]90^{\circ}[/tex]
We have to find angle C
The angle sum property of a triangle states that the angles of a triangle always add up to 180°
Therefore, in given triangle ABC
angle A + angle B + angle C = 180
[tex]58^{\circ} + 90^{\circ} + C = 180^{\circ}[/tex]
[tex]148^{\circ} + C = 180^{\circ}\\\\C = 180^{\circ} - 148^{\circ}\\\\C = 32^{\circ}[/tex]
Therefore angle C = [tex]32^{\circ}[/tex]
Related Questions
Help me this is worth a lot of points
Answers
Answer:
Area of ABCD = 100m²
Step-by-step explanation:
Area of a square is the square of the side.
A = s²
A = (10m)² = 10²m² = 100m²
Answer:
Area of ABCD = 100m²
Step-by-step explanation:
Dylan uses the expressions (x^2 -2x+8) and (2x^2 + 5x - 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan’s room ?
Answers
[tex]2x^4 + x^3 - x^2 +54x - 56[/tex] expression represents the area of Dylan’s room
Solution:Given that,
Length of room = [tex]x^2 -2x+8[/tex]
Width of room = [tex]2x^2 + 5x - 7[/tex]
To find: Expression that the area (lw) of Dylan’s room
Since bedroom is generally of rectangular shape, we can use area of rectangle
The area of rectangle is given as:
[tex]\text {area of rectangle }=\text { length } \times \text { width }[/tex]
Substituting the given expressions of length and width,
[tex]area = (x^2 -2x+8)(2x^2 + 5x - 7)[/tex]
We multiply each term inside first parenthesis with each term inside the second parenthesis.
So it becomes,
[tex]2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56[/tex]
Now combine like terms,
[tex]2x^4 + x^3 - x^2 +54x - 56[/tex]
Thus the above expression represents the area of Dylan’s room
Answer:
c
Step-by-step explanation:
What is the greatest common factor of 9 and 5
Answers
Answer:45
Step-by-step explanation:5 10 15 20 25 30 35 40 45
9 18 27 36 45
The greatest common factor of the number 9 and 5 is 1.
To find the greatest common factor (GCF) of 9 and 5, determine the largest number that evenly divides both 9 and 5.
The factors of 9 are 1, 3, and 9.
The factors of 5 are 1 and 5.
From these lists, the only common factor of 9 and 5 is 1.
Therefore, the greatest common factor of 9 and 5 is 1.
Learn more about greatest common factor here:
https://brainly.com/question/29584814
#SPJ6
You moved within a short walking distance to work and you no longer need to spend the $20 per week budgeted for bus
fare. Considering this, what is your new weekly budget surplus if your previous surplus was $175?
a) $30
b) $66
Oc) $120
O d) $195
Answers
you used to have $175 extra a week and now you have $20 more. 175+20= 195
Write an equation with a slope of 1/2 and a Y intercept of -2
Answers
Step-by-step explanation:
y=1/2×-2 @$@@$@$@$@%@%@%#_##%#%
HELP ME 20 POINTS!!!!!
Consider the characteristics of the graph. Which statement DOES NOT describe the data set?
A) The interquartile range (IQR) is 13.
B) The data is skewed right.
C) The data is skewed left.
D) The median is 50.
Answers
Answer:
B) The data is skewed right.
Step-by-step explanation:
The data is not skewed right. You can tell because the left side of the box is longer than the right, meaning that it is skewed left.
Answer:
B) The data is skewed right.
Step-by-step explanation:
The data is skewed right does not describe the data.
In this set of data, the left side tail is longer.
There are 100 freshman students at a school. The probability that a freshman plays a sport is 0.55. The probability that a freshman plays a musical instrument is 0.34. The probability that a freshman plays both a sport and a musical instrument is 0.15. What is the probability that a freshman student at this school plays either a sport or a musical instrument?
Answers
The probability that a freshman student at this school plays either a sport or a musical instrument is 0.74
Step-by-step explanation:
The addition rules in probability are:
P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen at the same time)P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they have at least one outcome in common)∵ The probability that a freshman plays a sport is 0.55
∴ P(sport) = 0.55
∵ The probability that a freshman plays a musical instrument is 0.34
∴ P(music) = 0.34
∵ The probability that a freshman plays both a sport and a musical
instrument is 0.15
∴ P(sport and music) = 0.15
To find the probability that freshman student at this school plays either a sport or a musical instrument use the second rule above because it is non-mutually exclusive
∵ P(sport or music) = P(sport) + P(music) - P(sport and music)
∴ P(sport or music) = 0.55 + 0.34 - 0.15
∴ P(sport or music) = 0.74
The probability that a freshman student at this school plays either a sport or a musical instrument is 0.74
Learn more:
You can learn more about the probability in brainly.com/question/9178881
#LearnwithBrainly
The probability that a freshman student at this school plays either a sport or a musical instrument is indeed 0.74
To find the probability that a freshman student plays either a sport or a musical instrument, we can use the principle of inclusion-exclusion for probability.
The principle states that for any two events A and B, the probability of the union of A and B is given by:
[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]
Let event A be the event that a freshman plays a sport, and event B be the event that a freshman plays a musical instrument.
We are given the following probabilities:
P(A) = 0.55 (the probability that a freshman plays a sport)
P(B) = 0.34 (the probability that a freshman plays a musical instrument)
P(A and B) = 0.15 (the probability that a freshman plays both a sport and a musical instrument)
Using the principle of inclusion-exclusion, we calculate the probability Upon reviewing the calculation, it appears there was an error in the final step.
The correct calculation should be:
[tex]\[ P(\text{either A or B}) = P(A \cup B) \][/tex]
[tex]\[ P(\text{either A or B}) = 0.74 \][/tex]
Therefore, the probability that a freshman student at this school plays either a sport or a musical instrument is indeed 0.74, not 0.64 as initially stated.
The final answer is [tex]\(\boxed{0.74}\).[/tex]
A car can hold gallons of fuel. It contains gallons of fuel. How much more fuel is needed to fill the car?
Answers
Question:
A car’s gas tank can hold 11 9/10 gallons of gasoline. It contains 8 3/4 gallons of gasoline. How much more gasoline is needed to fill the tank?
Answer:
[tex] 5\frac{3}{20}[/tex] more gasoline is needed to fill the tank?
Step-by-step explanation:
Given:
Capacity of the car tank = 11 9/10
Quantity of fuel already present = 8 3/4
To Find:
Quantity needed to fill the tank = ?
Solution:Let the quantity of the gasoline needed to fill the tank be x
Then
x = total capacity of the tank - quantity of fuel already present in the tank
x = [tex]11 \frac{9}{10}[/tex] - [tex]8 \frac{3}{4}[/tex]
x = [tex]\frac{119}{10}[/tex] - [tex]\frac{27}{4}[/tex]
x = [tex] 11.9[/tex] - [tex]6.75[/tex]
x = 5.15 or [tex] 5\frac{3}{20}[/tex]
Last week, it rained x inches. This week, the amount of rain decreased by 5% Which
expressions represent the amount of rain that fell this week? Select all that apply.
A. g - 0.05
B. g - 0.05g
C. 0.95g
D. 0.058
E. (1 – 0.05)g
Answers
Hope it helps u..............
PLS HELP
What is the perimeter of the rhombus below?
A. [tex]8\sqrt{5}[/tex]
B. [tex]5\sqrt{8}[/tex]
C. [tex]4\sqrt{5}[/tex]
D. [tex]5\sqrt{4}[/tex]
Answers
Answer:
8√5 units.
Step-by-step explanation:
See the diagram in the coordinate plane attached.
A rhombus has four equal sides and to find the perimeter of the rhombus we have to measure any of the sides of the figure of the rhombus.
The coordinates of the topmost point are (-1,-1) and that of the rightmost point are (3,-3).
Therefore, side length of the rhombus will be
[tex]\sqrt{(- 1 - 3)^{2} + (- 1 - (- 3))^{2}} = \sqrt{20} = 2\sqrt{5}[/tex] units.
So, the perimeter of the rhombus will be (4 × 2√5) units = 8√5 units. (Answer)
The distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] on a coordinate plane is given by
[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]
IF THIS WRONG I FAIL!!!!
Matt has started a car washing business to save money for college. Each week, he
washes 3 more cars than he did the week before.
Part A: Matt started by washing 6 cars his first week in business. Write an explicit formula that can be used to find the number of cars he washed on any given week.
Part B: Part B: How many cars will Matt wash on his 11th week in business?
Answers
Part B: 3(11)+6
Not a 100% sure but hope this helps
Answer:
Part A:
An= 6 + 3(n-1)
Part B:
36 cars
Given: x - 5 > -10.
Choose the solution set.
{xIXER, X<-15)
O {xIXER, x>-5)
O {xIXER,x<5)
{XIXER, x> 15)
Answers
Answer:
The solution set is given as:
B) [tex]\{x|x\epsilon R, x>-5\}[/tex]
Step-by-step explanation:
Given inequality:
[tex]x-5>-10[/tex]
To find the solution set for the given inequality.
Solution:
We have : [tex]x-5>-10[/tex]
Solving for [tex]x[/tex]
Adding 5 both sides.
[tex]x-5+5>-10+5[/tex]
[tex]x>-5[/tex]
Thus the solution set is all real numbers greater than -5. This can be given as:
[tex]\{x|x\epsilon R, x>-5\}[/tex]
Solve Ixl<13{(-13, 13}
{xl-13
[XIX<-13 or x 13)
Answers
Answer:
-13 < X < 13
Step-by-step explanation:
It is given |X| < 13.
Note that we have: |x| < a, for any real number 'a', then it equals:
-a < X < a.
So, in this case, |X| < 13 should be equal to -13 < X < 13.
Hence, the answer.
evaluat5-44*(-0.75)-18/ 2/380.8+(-4/5)
Answers
Answer:37.17 or 37.1763655462
Explanation:i just did the equation and evaulated it it's hard to explain sorry
Answer:
i dont know know because i have the same question but a little different its 5-44*(-0.75)-18 / 2/3 *.8 - 4/5
Step-by-step explanation:
Find the solutions to x2 = 18.
Answers
Answer:
6^3
Step-by-step explanation:
Ape-x
The solutions are [tex]\(x = 3\sqrt{2}\)[/tex] and [tex]\(x = -3\sqrt{2}\)[/tex]. Each represents a square root of 18.
To find the solutions to [tex]\( x^2 = 18 \)[/tex], you need to take the square root of both sides of the equation.
[tex]\[ x = \pm \sqrt{18} \][/tex]
[tex]\[ x = \pm 3\sqrt{2} \][/tex]
So, the solutions to [tex]\( x^2 = 18 \)[/tex] are [tex]\( x = 3\sqrt{2} \)[/tex] and [tex]\( x = -3\sqrt{2} \).[/tex]
11. If line a is parallel to line b, solve for x:
(7x + 11)
(10x - 43)
Answers
To find the value of x for parallel lines with expressions (7x + 11) and (10x - 43), set them equal and solve the resulting equation, which gives x = 18.
If line a is parallel to line b and we have the expressions (7x + 11) for line a and (10x - 43) for line b, then the corresponding angles formed by these lines and a transversal would be equal. To solve for x, we set the two expressions equal to each other because the slopes of parallel lines are equal. The equation would be 7x + 11 = 10x - 43.
Subtract 7x from both sides: 11 = 3x - 43.Add 43 to both sides: 54 = 3x.Divide both sides by 3: x = 54 / 3.Therefore, x = 18.This is the value of x that makes the two expressions equal, thus confirming the lines are parallel.
Given the diagram below, what is sin (30°) ?
Answers
Answer:
A. 1/2.
Step-by-step explanation:
The ratio of the sides of a 30-60-90 triangle is 2:1:√3 where 2 is the hypotenuse. 1 is the shortest leg and √3 is the longest leg.
In the diagram we see that the longest leg is opposite the 60 degree angle.
So the longest leg is 3.5√x and the shortest leg ( from applying the ratios) = 3.5√x / √3.
and the hypotenuse is 2 * 3.5√x / √3 (using the ratios again).
So sin 30 = shortest leg / hypotenuse = 3.5√x / √3 / 2 * 3.5√x / √3
= 1/2.
The owner of Ray’s Deli wants to find out if there is a relationship between the temperature in summer and the number of glasses of lemonade he sells. From the data shown in this scatter plot, you can tell that the A) hotter the temperature, the more lemonade was sold. B) cooler the temperature, the more lemonade was sold. C) most lemonade was sold when temperatures were above 90°F. D) data shows no relationship between temperature and lemonade sales.
Answers
Answer:
D) data shows no relationship between temperature and lemonade sales.
Step-by-step explanation:
There is no correlation between temperature and lemonade sales. Sometimes two variables are not related. The data shows no relationship between temperature and lemonade sales.
The correct option will be D) data shows no relationship between temperature and lemonade sales.
What is the significant use of graphs in real life?Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.
Given, The owner of Ray’s Deli wants to find out if there is a relationship between the temperature in summer and the number of glasses of lemonade he sells.
Since,
There is no correlation between temperature and lemonade sales. Sometimes two variables are not related. The data shows no relationship between temperature and lemonade sales.
Therefore, The correct option will be D) data shows no relationship between temperature and lemonade sales.
Learn more about graphs here:
https://brainly.com/question/17267403
#SPJ6
Select the correct answer.
During the summer, Jody earns $10 per hour babysitting and $15 per hour doing yardwork. This week she worked 34 hours and earned $410.
If x represents the number hours she babysat and y represents the number of hours she did yardwork, which system of equations models
this situation?
A.
X+ y = 34
10x+ 15y = 410
OB. X + y = 410
10x + 15y = 34
C.
X+ y = 34
15x+10y= 410
OD. x + y = 410
15x+10y = 34
Answers
Answer:
A
Step-by-step explanation:
x+y=34 (add the seperate hours together to get the total amount of hours)
10x+15y=410 (multiply the money made each hour by the hours worked and add them together to get the amount of money joy made)
The system which creates a mathematical representation of the given condition will be X+ y = 34 and 10x+ 15y = 410 so option (A) will be correct.
How to form an equation?When trying to set up or construct a linear equation to fit a real-world application, identify the known quantities and use the unknown quantity as a variable.
In other words, an equation is a set of variables that are constrained through a situation or case.
x = number of hours babysitting.
y = number of hours yard work.
Given that
She worked a total of 34 hours
So x + y = 34 will be the correct formation.
Jody earns $10 per hour babysitting
So a total of 10x money Jody will earn through babysitting.
$15 per hour doing yardwork
So a total of 15x money Jody will earn through yard work.
Given that
A total of $410 Jody earned so
10x + 15y = 410 will be the correct formation.
For more about the equation
brainly.com/question/2263981
#SPJ5
Determine the radius, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic
inches and a height of 3.3 inches.
Answers
The radius of can is 2.524 inches
Solution:
Given that large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches
To find: Radius
Given a large can of tuna fish, we know that can is generally of cylinder shape, we can use the volume of cylinder formula,
The volume of cylinder is given as:
[tex]\text{ volume of cylinder}= \pi r^{2} h$[/tex]
Where,
"r" is the radius of cylinder
"h" is the height of cylinder
[tex]\pi[/tex] is a constant equal to 3.14
Substituting the given values in above formula,
[tex]66 = 3.14 \times r^2 \times 3.3\\\\66 = r^2 \times 10.362\\\\r^2 = \frac{66}{10.362}\\\\r^2 = 6.369\\\\r = 2.524[/tex]
Thus the radius of can is 2.524 inches
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
see explanation
Step-by-step explanation:
The diagrams show triangular figures
The first figure has 1 dot
The second has 1 + 2 = 3 dots
The third has 3 + 3 = 6 dots
The fourth has 6 + 4 = 10 dots
Note the pattern is + 2 , + 3, + 4
Thus the fifth pattern is 10 + 5 = 15 dots
Elyse has $18 on a gift card that she can use to rent movies online. The graph at the right shows the amount of money remaining on her gift card ba. sed on the number of movies she rents. Find the unit rate of the graph, and describe what it means in the context of the situation.
Answers
Answer:
see the explanation
Step-by-step explanation:
The complete question in the attached figure
Let
x ----> the number of movies
y ----> the amount of money remaining on her gift card
we know that
The slope of the linear equation is equal to the unit rate
take two points from the graph
(0,18) and (2,12)
Find the slope
[tex]m=(12-18)/(2-0)[/tex]
[tex]m=(-6)/(2)=-\$3\ per\ movie[/tex] ---> is negative because is a decreasing function
That means -----> Each movie she rents cost her $3, so her gift card balance will decrease $3 for every movie rented
The linear equation is equal to
[tex]y=-3x+18[/tex]
For y=0
[tex]0=-3x+18[/tex]
[tex]x=6[/tex]
so
6 is the maximum number of movies that Elyse can rent on line
The unit rate is the ratio of the change in the y-coordinate value to the change in the x-coordinate value between any two strategically chosen points. Elyse's unit rate represents the cost per movie rental.
Explanation:While the graph isn't directly available, the principle to find the unit rate of the graph is the same. The unit rate is the ratio of the change in the vertical (y-axis) value to the change in the horizontal (x-axis) value between any two distinct points on the graph. In the context of Elyse's movie rentals, the unit rate would represent the cost per movie.
To calculate this, you'd subtract the y-coordinate value of the second point from the y-coordinate value of the first point. This represents the change in the balance of the gift card. Then you'd subtract the x-coordinate value of the second point from the x-coordinate value of the first point, representing the number of movies rented. Dividing the change in balance by the number of movies gives the cost per movie, which is our unit rate.
For example, if she had $12 after renting 2 movies and $6 on her card after renting 4 movies, the unit rate would be computed as: (12 - 6) / (4 - 2) = $3 per movie. This means that for every movie that Elyse rents, she spends $3 from her gift card.
Learn more about Unit rate here:https://brainly.com/question/11258929
#SPJ3
Find the product of x2 + 2x - 4 and 3x .
Answers
Answer:x4+2x3+7x2+6x+12
Step-by-step explanation:
A circle has a radius of 30cm what is the area
Answers
r = 30 cm
formula: A = πr²
A = πr²
A = π30²
A = 900π
if π = 3.14, then the answer is 2,826 cm
if π is not defined, the answer is 2,827.43 cm
Richard has four times as many marbles as john. if Richard have 18 to John they would have the same number. how many marbles has each?
Answers
Answer:
The number of marbles Richard has 24 and John has 6.
Step-by-step explanation:
Richard has four times as many marbles as john.
If Richard have 18 to John they would have the same number.
Now, to find number of marbles each has.
Let the marbles of John be [tex]x[/tex].
And the marbles of Richard be [tex]4x.[/tex]
According to question:
[tex]4x=x+18.[/tex]
Subtracting both sides by [tex]x[/tex] we get:
[tex]3x=18.[/tex]
Dividing both sides by 3 we get:
[tex]x=6.[/tex]
Marbles of John = [tex]6.[/tex]
Marbles of Richard = [tex]4x=4\times 6=24[/tex]
Therefore, the number of marbles Richard has 24 and John has 6.
Final answer:
John has 12 marbles, and Richard has 48 marbles, as Richard has four times as many as John, and giving John 18 marbles would equalize their amounts.
Explanation:
To find the answer, we need to set up an equation based on the information provided: Richard has four times as many marbles as John, and if Richard gives John 18 marbles, they would have the same number.
Let's denote the number of marbles John has as J. Then Richard has 4J marbles. If Richard gives 18 marbles to John, Richard would have 4J - 18 marbles, and John would have J + 18 marbles. According to the problem, after the exchange, they have an equal number of marbles, so we can write the equation:
4J - 18 = J + 18
Solving for J, we move all the J terms to one side and numeric terms to the other side:
4J - J = 18 + 18
3J = 36
Dividing both sides by 3, we get:
J = 12
So, John has 12 marbles. Since Richard has four times as many, he has 4 x 12 = 48 marbles. Therefore, Richard has 48 marbles and John has 12 marbles.
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
7x+3y= 30
-2x+3y= 3
ОА. (3, 5)
ОВ. (3, 3)
Ос. (6, 5)
D. (6, 3)
Answers
Explanation:
7x+3y=30
-2+3y=3
Choose a variable to eliminate (We’ll choose Y)
(7x+3y=30) -> 7x+3y=30
(-2x+3y=3) -1 -> 2x+-3y=-3
The -3y camels the other 3y, combine the equations
9x=27
Divide both sides by 9
9x/9 = 27/9
x = 3
Back to 7x+3y= 30
Substitute the x with 3
7(3)+3y= 30
21+3y= 30
Move the constant to the other side
21+3y=30
-21 -21
3y=9
Divide both sides by 3
3y/3 = 9/3
y = 3
Four students graphed one linear function each. Which student graphed a linear function with a y-intercept at -4?
Answers
Answer:
who ever line crosses the y-axis at -4.
Step-by-step explanation:
Answer:
Ellis so c
Step-by-step explanation:
Otto's investment portfolio consisted of shares of internet stock and copper stock. During the year, the value of his internet shares increased $10\%$, but the value of his copper shares decreased from $\$10{,}000$ to $\$9{,}000$. During the same year, the total value of his portfolio increased by $6\%$. What was the dollar value of his internet shares at the end of the year?
Answers
Answer:
44000
Step-by-step explanation:
Let w be the initial value of Otto's internet stock, in dollars. At the beginning of the year, the total value of his portfolio is w+10,000 dollars. At the end of the year, the total value of his portfolio is 1.1w+9,000 dollars. Since increasing by 6% is equivalent to multiplying by 1.06, we have
1.06(w+10,000)=1.1w +9,000
Distributing and collecting terms, we find w=40,000. At the end of the year, his internet stock is worth 40,000* 1.1=44,000 dollars.
*credits: AoPS
the cost of two pies and five cakes is $45.25. the cost of 2 pies and three cakes is $39.75 find the cost of each pie and each cake
Answers
Answer:
cost of each pie = $15.75
cost of each cake = $2.75
Step-by-step explanation:
Let x be the Pie and y be the cake.
Given:
The cost of two pies and five cakes is $45.25,
[tex]2x+5y=45.25[/tex]-----------(1)
The cost of 2 pies and three cakes is $39.75
[tex]2x+3y=39.75[/tex]--------------(2)
Now we subtract equation 2 from equation 1.
[tex]2y=5.5[/tex]
[tex]y=\frac{5.5}{2}[/tex]
y=2.75
Now we substitute the value of y in equation 1.
[tex]2x+5\times 2.75=45.25[/tex]
[tex]2x+13.75=45.25[/tex]
[tex]2x=45.25-13.75[/tex]
[tex]2x=31.5[/tex]
[tex]x=\frac{31.5}{2}[/tex]
x=15.75
So, The cost of each pie is $15.75
And the cost of each cake is $2.75
Final answer:
To find the cost of each pie and cake, two equations were set up based on the total cost of pies and cakes. By subtracting the second equation from the first, the cost of one cake was determined to be $2.75. Subsequently, the cost of one pie was calculated to be $15.75.
Explanation:
Calculating the Cost of Pies and Cakes
We have two equations based on the information provided:
2P + 5C = $45.25
2P + 3C = $39.75
Where P represents the cost of one pie, and C represents the cost of one cake. To solve for P and C, we can subtract the second equation from the first:
2P + 5C - (2P + 3C) = $45.25 - $39.75
2C = $5.50
C = $5.50 / 2
C = $2.75
Now that we know the cost of one cake, we can substitute C in one of the equations to find P:
2P + 5($2.75) = $45.25
2P + $13.75 = $45.25
2P = $45.25 - $13.75
2P = $31.50
P = $31.50 / 2
P = $15.75
Therefore, the cost of each pie is $15.75 and the cost of each cake is $2.75.
Every student in the senior class is taking history or science. There are $200$ seniors in the class. If there are $126$ seniors taking history and $129$ seniors taking science, how many students are taking both history and science?
Answers
Answer: 55
Step-by-step explanation:
126+129= 255
255-200=55
55 students are taking both history and science.
To solve this, we set up the problem as follows: Let H represent the set of students taking history, S represent the set of students taking science, and N represent the total number of seniors. We're given that N = 200, |H| = 126 (the number of students taking history), and |S| = 129 (the number of students taking science). The number of students taking both can be found by adding the number of students in sets H and S and subtracting the total N. This calculation is often represented by the formula |H ∩ S| = |H| + |S| - N, where |H ∩ S| is the number of students taking both history and science.
Using the formula, we calculate: |H ∩ S| = 126 + 129 - 200 = 55. Therefore, 55 seniors are taking both history and science.