The costs for the given candy are $7 for strawberry taffy and $6 for banana taffy. By writing equations and simplifying them, we get the requiredd values.
How to solve two equations?To solve two equations,
Rewrite one of the equations for one of its variables.Substitute it in the other equation.On simplifying, we get a value for one variable.Then, substitute in one of the equations, and we get another variable.This method of solving is called the substitution method.Calculation:It is given that, two friends visited a taffy shop.
Winton bought - 2 kg of strawberry taffy and 1 kg of banana taffy for $20.
Audrey bought - 4 kg of strawberry taffy and 4 kg of banana taffy for $52.
Then, we can write the above information into equations as
2S + B = 20 ...(1)
4S + 4B = 52 ...(2)
Where S represents strawberry taffy and B represents banana taffy.
From (1), we can write
B = 20 - 2S
Then, on substituting in (2), we get
4S + 4(20 - 2S) = 52
⇒ 4S + 80 - 8S = 52
⇒ -4S = 52 - 80 = -28
⇒ 4S = 28
∴ S = 7
Thus, the cost of strawberry taffy is $7.
On substituting S = 7 in (1), we get
2(7) + B = 20
⇒ 14 + B = 20
⇒ B = 20 - 14
∴ B = 6
Thus, the cost of banana taffy is $6.
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A ladder is leaning against the side of a 10 m. House. If the base of the ladder is 3 m. Away from the house, how tall is the ladder?.
The length of ladder leaning against the side of a house is 10.44 m .
As shown in the figure below h is the length of the house so we have to find h .
the ladder form a right angled traingle where base of the ladder is 3 m.
and the height of wall to which ladder is leaning against is 10m. and the ladder is the longest side of the right angled traingle i.e Hypotenuse
so we wil use Pythagoras theorem to find the longest side of ladder + wall system
so for a right angled traingle Pythagoras theorem states that
[tex]h^2 = p^2 + b^2[/tex]
where h=Hypotenuse ,p=perpendicular , b=base.
so we have to find h given p= 10m ,b=3m
so putting the values of p and b in the above equation we get
[tex]h^2 = 10^2 +3^2 =109[/tex]
so
[tex]h=\sqrt{109} = 10.44 m[/tex]
so the length of ladder is 10.44 m
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Which statement is true?
Answer:
Correct Statement : The y- intercept of Function A is greater than the y- intercept of Function B
Given m\parallel nm∥n, find the value of x and y. (3x-19)° (2x+1)° (5y+19
Answer:
Step-by-step explanation:
3x - 19 = 2x + 1
x - 19 = 1
x = 20
2(20) + 1 + 5y + 19 = 180
40 + 1 + 5y + 19 = 180
41 + 5y + 19 = 180
5y + 19 + 41 = 180
5y + 60 = 180
5y = 120
y = 24
Plllssssss help In which function has f(x) been shifted up 2 units and to the right 7 units?
O f(x - 7) + 2
O f(x- 2) + 7
O. f(x + 2) + 7
O. f f(x + 7) - 2
Identify the angles shown
A. Corresponding angles
B. Alternate interior angles
C. Same side interior angles
D. Alternate exterior angles
Help!!!
a deck of playing cards contains 52 cards, four of which are aces. what is the probability that the deal of a five-card hand provides a pair of aces?
The probability that the deal of a five-card hand provides a pair of aces is 0.0399
In this question, we have been given a deck of playing cards contains 52 cards, four of which are aces.
We need to find the probability that the deal of a five-card hand provides a pair of aces.
The sample space for given experiment is: choosing 52 cars choosing 5.
n(S) = 52C_5
We need to find the chance of getting a pair of aces, there are 4 aces in the pack on 2 of them.
So, n(A) = 4C_2
So that means there are 48 cards left which are not aces in the pack and want 2 of those.
So, the required probability is:
P(A) = (4C_2 * 48C_3) / 52C_5
P(A) = (6 * 17296) /2598960
P(A) = 103776 / 2598960
P(A) = 0.0399
Therefore, the required probability is 0.0399
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the booking limits for four fare classes in a flight are given as . (a) what is the available capacity for these four classes, i.e., what is the booking limit for classes {1, 2, 3, 4}? [ select ] (b) from this available capacity, how many seats are protected for class 1, i.e., what is the protection level for class 1?
The function available capacity for the four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are protected for class 1. 40 + 40 + 40 + 40 = 160
The booking limits for the four fare classes in a flight are given as 40, 40, 40, and 40, respectively. This means that the available capacity for these four classes is 40 seats each. The protection level for class 1 is 40 seats, meaning that 40 seats are specifically reserved for passengers in class 1. This ensures that passengers in class 1 are guaranteed at least 40 seats on the flight. The protection level for the other classes is also 40 seats each, ensuring that at least 40 seats are available for each class. This allows airlines to ensure that all of their classes have sufficient seating capacity for their passengers. 40 + 40 + 40 + 40 = 160
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HELP PLEASE Note: For questions 22-25, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer.
Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday she restocked her supply and sold 0.85 of the boxes of cheeses. On which day did Marietta sell more boxes? Explain.
She sold more cheese boxes on Tuesday.
What is comparison?Comparing numbers in maths is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday, she restocked her supply and sold 0.85 of the boxes of cheeses.
On Monday = 7/9 = 0.777
On Tuesday = 0.89
Since, 0.89 > 0.777
Hence, she sold more on Tuesday.
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This number line models the division problem 13÷6 . What is the quotient?
Answer: About 2.2
Step-by-step explanation: Since 13 divided by 6 is 2.16 repeating, you can use the 6 to round up the 1, making it about 2.2
Please help me with this
Answer:
d = 0
Step-by-step explanation:
7.5d = 2.5d
Divided both sides by factors and we get
d = 0
two of the nine insist on sitting side-by-side. in how many ways can the nine be seated together in a row?
A group of nine people can now be seated in a row in 40320 different ways.
The two people who insist on sitting next to one other can be situated in one of two ways. The remaining seven people can be seated in seven different ways.
As a result, the total number of ways in which the nine persons can be seated in a row is 1 x 7! = 40320.
In this situation, the two people who dislike each other can be seated in
(7-1)! different ways.
The remaining seven people can be seated in seven different ways.
As a result, the total number of possible combinations for seating 9 individuals in a row is (7-1)! x 7! = 40320.
A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.
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Look at this diagram:
The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,
Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to 180°
Thus, the solution of the angles is shown above.
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Which ratio is equivalent to 3/15 ?
If X + 2 y = 5, then X + 2 (3 + y) =
Answer:
11
Step-by-step explanation:
x + 6 + 2y
x + 2y + 6
x + 2y = 5
5 + 6 = 11
find the surface area?
Surface area implies the external surface that bounds a given shape. The surface area of the shape is 384 sq in.
The surface area of a shape is the external side of the shape that can be seen. Sometimes, a given shape may have different shapes that forms its surface area.
From the given question,
i. The area of triangular surface = 1/2 * base* height
= 1/2*12*8
= 48
Area of the triangular surface = 48 sq in.
ii. The area of its rectangular sides = length * width
= 9* 10
= 90
Area of its rectangular sides = 90 sq in.
iii. The area of its base = length * width
= 9 * 12
= 108
Area of its base = 108 sq in.
Therefore,
the surface area of the shape = (2*48) + (2*90) + 108
= 96 + 180 + 108
= 384 sq in.
The surface area of the given shape is 384 square inches.
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Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
One week a student exercised 3 hours at school and another of an hour at
home. If of the student's total exercise came from playing basketball, how
much time did the student spend playing basketball that week? Enter your
answer in hours; do not include units in your answer.
The number of hours in a week a student played basketball is [tex]11\frac{3}{8}[/tex].
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.
Also given that 1/4 of the exercise of a student came from playing basketball.
Therefore, Time playing basketball is one-fourth of the total time exercised which is,
= (3 + 1/4)×(1/4).
= (13/4)×(1/4).
= (13/8).
Therefore, In a week the student played (13/8)×7.
= 91/8.
= [tex]11\frac{3}{8}[/tex].
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which document do you need to have on hand when preparing to file your tax return? a. auto insurance card b. birth certificate c. driver’s license d. form w-2 e. form w-4
The document do you need to have on hand when preparing to file your tax return is W-2
What is a tax return?A tax return is a form or forms filed with a tax authority that reports income, expenses, and other pertinent tax information.
To file your return, you'll need the following on hand: Your W-2: This form will come from your company and list not only your salary for the year, but the amount of taxes withheld along the way. You're required to file your W-2 along with your taxes, so if you're a salaried employee, this form is non-negotiable.
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w is proportional
to √x
x is decreased by 9.75%
Work out the percentage decrease in
W.
Answer:
To determine the percentage decrease in W when x is decreased by 9.75%, we need to first determine the relationship between w and x. Since w is proportional to the square root of x, we can write an equation to represent this relationship as follows:
w = k * √x
where k is the proportionality constant.
If the value of x is decreased by 9.75%, we can write the new value of x as follows:
x' = x * (1 - 0.0975) = x * 0.9025
Substituting this expression for x' into the equation above, we get:
w' = k * √(x * 0.9025)
To determine the percentage decrease in w, we can divide the new value of w by the original value of w and multiply by 100% to get the percentage change, or:
percentage decrease in w = (w' / w) * 100%
Substituting the expressions for w' and w into this equation, we get:
percentage decrease in w = [(k * √(x * 0.9025)) / (k * √x)] * 100%
Simplifying this expression, we get:
percentage decrease in w = (√(0.9025)) * 100%
Since the square root of 0.9025 is approximately 0.95, we can say that the percentage decrease in w is approximately 5%. This means that the value of w decreases by approximately 5% when the value of x decreases by 9.75%.
A typical tip in a restaurant is 15% of the total bill. If the bill is $150, what would the typical tip be?
he typical tip would be $
Answer:
22.5
Step-by-step explanation:
total bill =$150
tip percentage =15%
now,
tip money = 15% of $150
=150×15/100
=2250/100
=$22.5
Tritan purchaed a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a contant rate. If the value of the car wa \$10,400$10,400 in the year 2006, then what would be the predicted value of the car in the year 2016, to the nearet dollar?
Tritan purchased a new car in 2000 for $22,800. The value of the car ha been depreciating exponentially at a constant rate then the Cost of the car in year 2016 will be $2811.
Cost price of the car = $22800
Value of the car has been depreciating exponentially, so the formula for value of the car after t years,
Here P(t) = Final value after t years
A = Cost price or initial value
r = rate of depreciation
t = duration in years
r = 100(1 - 0.87737)
r = 12.26%
Now cost of the car in year 2016 (After 16 years)
P(16) = 2810.99
= $2811
Therefore, cost of the car in year 2016 will be $2811.
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A contractor bought 10.8 ft2 of sheet metal. he has used 2.3 ft2 so far and has $153 worth of sheet metal remaining. The equation 10.8x - 3.2x= represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
10.8 - 2.3 = 8.5ft2 amount of $153
Can i use proportion for this?
8.5/153 : 1/x
8.5x = 153
x = 18
The cost of metal per square foot is $18.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-4) The instantaneous rate of change of f(x)=x³−5 at (2,3) is:
a) 4
b) 12
c) 48
d) 60
The instantaneous rate of change of f(x) = x³ − 5 at (2,3) is (b) 12
How to determine the instantaneous rate of changeFrom the question, we have the following parameters that can be used in our computation:
Function: f(x) = x³ − 5
Point = (2, 3)
Differentiate the function to get the instantaneous rate
This is represented as
f'(x) = 3x²
Substitute 2 for x in the equation
The 2 is coming from the x-coordinate in (2, 3)
So, we have
f'(2) = 3(2)²
Evaluate
f'(2) = 12
Hence, the instantaneous rate of change is 12
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Question 1-8
Cameron goes to the grocery store every 15 days. Brooks goes to the grocery store every 12 days. If both Cameron and Brooks go to the grocery
store today, how many days until they go to the grocery store on the same day again? Enter the answer in the box.
days
Answer:
60
Step-by-step explanation:
To find the least common multiple of 15 and 12, we can list the multiples of 15 and 12 and find the smallest number that appears in both lists:
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The least common multiple of 15 and 12 is 60, so Cameron and Brooks will go to the grocery store on the same day every 60 days.
If M.P. = Rs 1,530, S.P. = Rs 1,377, find the discount and discount percent.
Answer:
Discount = Rs 153,Discount % = 10%.------------------------------------------------
Given:
Marked price = Rs 1530,Sale price = Rs 1377.Find the discount:
1530 - 1377 = 153Find the discount %:
153/1530 * 100% = 10%Which division problem is represented in this model?
Answer:
try 5/15 or 1/15
Step-by-step explanation:
this is because it shows one shaded box we know it's a third out of just that one column
so you multiple a third by 5 and you get 15 what ever you do to the denominators you do to the numerator
Please help!! Find the equation of variation given that y varies directly with x and y is 25 when x is 5
Answer:
y=5x
Step-by-step explanation:
If y is 25 and x is 5
25 = 5 (5)
25=25
three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, but instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices. where should these slices be made in order to accomplish this?
As per the Newton's method, the equal ration of the Pizza is 3: 2: 3
In math, Newton's method states that a technique for solving equations of the form f(x)=0 by successive approximation
Here we have given that three calculus students entered a pizza parlor. they were quite hungry and ordered an entire pie, instead of having the pizza maker cut the pie in the usual manner they asked her to slice the pie into three equal areas using only two parallel slices.
And we need to find these slices be made in order to accomplish this
Here let us assuming that the pizza has unit radius, and the area of the pizza is π and each piece has to have area π/3.
Therefore, the given details is enough to find the height of a circle segment such that its area is one third of the original circle,
As per the Newton's method, we get the value of h as,
=> h ≈ 0.735068 ≈ 4492/6111,
Therefore the three slices have widths approximately proportional to 3:2:3.
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Given f (x) = 3x + 15, find a when f (x) = 51.
Answer: 168
Step-by-step explanation: f(51)= 3(51)+15, 3(51)=153. 153+15=168
Answer:
x = 12
Step-by-step explanation:
given
f(x) = 51
f(x) = 3x + 15
51 = 3x + 15
3x = 51 - 15
3x = 36
x = 12
x² : (x + 6) = 1 : 2
Find the possible values of x
Answer:
x= 2 and x= -(2/3)
Step-by-step explanation:
Step 1 :Multiply all terms by the same value to eliminate fraction denominators
x^2/ x+6 = 1/2
2(x+6)*(x^2/x+6) = 2(x+6) * 1/2
Step 2: Cancel multiplied terms that are in the denominator
2x^2= x+6
Step 3: Move terms to the left side
2x^2 - (x+ 6) = 0
Step 4: Distribute
2x^2 - x - 6 = 0
Step 5: Use the quadratic formula
x= ( - (-1) +- Squar((-1)^2-4*2(-6)) ) / 2*2
Step 6: Simplify
x= (1+- 7)/ 4
Step7: Separate the equations
x= (1+7)/ 4 and x= (1- 7)/ 4
Step 8: Solve that 2 small equation
x= 2 and x= -(3/2)
Answer:
x = - [tex]\frac{3}{2}[/tex] , x = 2
Step-by-step explanation:
x² : x + 6 = 1 : 2
express the ratio in fractional form
[tex]\frac{x^2}{x+6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x² = x + 6 ( subtract x + 6 from both sides )
2x² - x - 6 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 6 = - 12 and sum = - 1
the factors are - 4 and + 3
use these factors to split the x- term
2x² - 4x + 3x - 6 = 0 ( factor the first/second and third/fourth terms )
2x(x - 2) + 3(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(2x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]
suppose one individual is randomly chosen. find the probability that this person has an iq greater than 95.
The probability that this person has an IQ greater than 95 =62.93%
What is probability?The area of mathematics known as probability is concerned with the outcomes of random events. Probability refers to a chance or potential for something to happen. It explains the likelihood that a specific event will take place.
We frequently say things like, "It will probably rain today," "He will probably pass the test, "There is very little chance of getting a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for all of the words chance, doubt, maybe, likely, etc. in these sentences.
In essence, probability is the ability to forecast an outcome based on the variety and quantity of potential outcomes or the analysis of historical data.
Let X be the IQ
IQ is normally distributed with a mean of 100 and a standard deviation of 15.
a) the probability that this person has an IQ greater than 95
=62.93%
b) the probability that this person has an IQ less than 125
=4.75%
c) Sample size =500
No of people = 0.2486(500) =124.3
d)
No of persons = 0.0047(500) = 2.35
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