Zachary brought $38. 25 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1 6 as much as the souvenir, and the souvenir cost 3 4 the cost of the pass. Zachary had $4. 50 left over after buying these items
Answers
It is not possible for Zachary to buy a burger, a souvenir, and a pass with the given prices and have $4.50 left over.
What was the total cost of the burger, souvenir, and pass that Zachary bought at the state fair, if he had $4.50 left over and the burger was 1/6 as much as the souvenir, while the souvenir cost 3/4 the cost of the pass?Let's represent the cost of the souvenir as x.
Then, according to the problem:
The cost of the burger is 1/6 of the cost of the souvenir, which is (1/6)x.
The cost of the pass is 4/3 times the cost of the souvenir, which is (4/3)x.
The total cost of the burger, souvenir, and pass is equal to the amount Zachary brought to the state fair, which is $38.25.
Zachary had $4.50 left over after buying these items, so the cost of the burger, souvenir, and pass must be $33.75.
Putting all this information together, we can write an equation:
(1/6)x + x + (4/3)x = 33.75
Simplifying the left side of the equation:
(7/6)x = 33.75
Multiplying both sides by 6/7:
x = 30
Therefore, the cost of the souvenir is $30, the cost of the burger is (1/6) * 30 = $5, and the cost of the pass is (4/3) * 30 = $40.
To check that these values are correct, we can add them up:
30 + 5 + 40 = 75
And we can subtract the total cost from the amount Zachary brought:
38.25 - 75 = -36.75
Learn more about cost
brainly.com/question/30045916
#SPJ11
Related Questions
A shelf has four books on it. The weight, in pounds, of each of the four books on the shelf is listed below.
2.5, 3.2, 2.7, 2.3
Which inequality represent the weight, w, of any book chosen from the shelf?
A ) w > 2.3
B ) w < 2.4
C ) w > 3.2
D ) w < 3.3
Answers
Answer:
C ) w > 3.2
C ) w > 3.2
Step-by-step explanation:
Because 3.2 times 4 is 12.8.
3.2
+3.2
6.4
+3.2
9.6
+3.2
12.8
simplify the following expression. 5.3x − 8.14 3.6x 9.8 a. -2.84x − 1.66 b. 8.9x 1.66 c. -2.84x 17.94 d. 8.9x 17.94
Answers
The simplified expression is (-187.584x + 287.6672) / 6.8, which is equivalent to option A: -2.84x - 1.66.
To simplify the expression 5.3x - 8.14 / 3.6x - 9.8, we can first simplify the division by finding a common denominator for the fractions.
The common denominator for 3.6x and 9.8 is 3.6x * 9.8 = 35.28x.
Next, we can rewrite the expression using the common denominator:
5.3x * (35.28x/35.28x) - 8.14 * (35.28x/35.28x) / 3.6x * (35.28x/35.28x) - 9.8 * (35.28x/35.28x)
Simplifying further, we get:
(5.3 * 35.28x^2 - 8.14 * 35.28x) / (3.6 * 35.28x - 9.8 * 35.28x)
Now, we can simplify the numerator:
(187.584x^2 - 287.6672x) / (-6.8x)
Factoring out an x from the numerator, we have:
x(187.584x - 287.6672) / (-6.8x)
Finally, we can cancel out the x terms:
(187.584x - 287.6672) / -6.8
Therefore, the simplified expression is (-187.584x + 287.6672) / 6.8, which is equivalent to option A: -2.84x - 1.66.
To know more about simplified expression refer here:
https://brainly.com/question/29076148
#SPJ11
Select the correct answer.
The function g(x) = x2 is transformed to obtain function h:
h(x) = g(x − 3).
Which statement describes how the graph of h is different from the graph of g?
A.
The graph of h is the graph of g vertically shifted up 3 units.
B.
The graph of h is the graph of g horizontally shifted right 3 units.
C.
The graph of h is the graph of g horizontally shifted left 3 units.
D.
The graph of h is the graph of g vertically shifted down 3 units.
Answers
Answer:
B
Step-by-step explanation:
Given g(x) then g(x + a) is a horizontal translation of g(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
h(x) = g(x - 3) = (x - 3)² with a < 0
The graph of h(x) is the graph of g(x) horizontally shifted right 3 units
A manufacturer produces bearings, but because of variability in the production process, not all of the bearings have the same diameter. The diameters have a normal distribution with a mean of 1.8 centimeters (cm) and a standard deviation of 0.04 cm. The manufacturer has determined that diameters in the range of 1.72 to 1.88 cm are acceptable. What proportion of all bearings falls in the acceptable range? (Round your answer to four decimal places.)
Answers
To find the proportion of bearings that falls in the acceptable range of 1.72 to 1.88 cm, we need to calculate the area under the normal distribution curve between these two values.
Given:
Mean (μ) = 1.8 cm
Standard deviation (σ) = 0.04 cm
Range: 1.72 cm to 1.88 cm
To calculate the proportion, we need to find the z-scores corresponding to the lower and upper limits of the acceptable range. The z-score formula is:
z = (x - μ) / σ
For the lower limit (1.72 cm):
z1 = (1.72 - 1.8) / 0.04 = -2
For the upper limit (1.88 cm):
z2 = (1.88 - 1.8) / 0.04 = 2
Using a standard normal distribution table or a statistical software, we can find the area under the curve between these z-scores. The area between -2 and 2 represents the proportion of bearings falling within the acceptable range.
Looking up the z-scores in the standard normal distribution table, we find that the area between -2 and 2 is approximately 0.9545.
Therefore, approximately 0.9545 (or 95.45%) of all bearings fall within the acceptable range of 1.72 to 1.88 cm.
Approximately 95.45% of all bearings produced by the manufacturer fall within the acceptable range of 1.72 to 1.88 cm, based on the given mean and standard deviation. This indicates that the majority of the bearings meet the specified diameter criteria.
To know more about curve visit:
https://brainly.com/question/30465469
#SPJ11
A population with a mean of μ = 6 has ∑X = 42. How many scores are in the population?
N = 7
N = 252
N = 6/42 = 1/7
It cannot be determined from the information given.
Answers
It cannot be determined from the information given that how many scores are in the population. The given information is not sufficient to determine the total number of scores in the population.
What is a population?The term population is used in statistics to refer to the whole set of observations or scores of interest that have something in common. The population is the complete collection of data of all possible observations or scores that satisfy some given conditions.
The given information about the population is insufficient, since we are not aware of the total number of scores in the population .A population with a mean of μ = 6 has ∑X = 42 implies that the total sum of all scores is 42. Since the sum of all scores is equal to the sum of individual scores, we cannot say how many scores are in the population.
In fact, we can have different numbers of scores in the population with a sum of 42.For example, if we have 7 scores in the population, the sum of all scores will be 42. That is, 6+6+6+6+6+6+6=42. However, if we have 14 scores in the population, then the sum of all scores will be 42. That is, 3+3+3+3+3+3+3+3+3+3+3+3+3+3=42. Therefore, it is impossible to determine the number of scores in the population with only the given information.
To know more about statistics refer here :
https://brainly.com/question/30683316
#SPJ11
A storm that moved through several states at a speed of 60 miles per hour affected 219 miles of land. What did that make the storm
Answers
The longest tornado ever recorded spanned 219 miles of land as it swept through many states at a pace of 60 miles per hour.
What are the importance of vector calculus?A tornado could cause a natural disaster to wreak havoc in significant geographic areas.A violent column of air between a thunderstorm and the earth is what is known as a tornado.In severe tornadoes, winds exceeding 200 miles per hour (h) are not uncommon.In conclusion, the longest tornado ever recorded affected 219 miles of land as it swept through many states at a speed of 60 miles per hour.Mathematically, a tornado is vector calculus with a fury. Severe storms are the result of the interaction of the two scalar forces of pressure and humidity with the vector field known as wind.To learn more about tornado, refer to:
https://brainly.com/question/29099905
#SPJ4
Adam has 4 blue ping pong balls, 4 red ping pong balls, and 4 white ping pong balls. how many possible ways can the 12 ping pong balls can be arranged in a row?
Answers
There are 479,001,600 possible ways to arrange the 12 ping pong balls in a row.
To find the number of possible ways the 12 ping pong balls can be arranged in a row, we can use the concept of permutations.
Since all 12 ping pong balls are distinct (each color is unique), we can use the formula for permutations of distinct objects. The formula is:
nPr = n! / (n - r)!
Where n is the total number of objects and r is the number of objects taken at a time.
In this case, we have 12 ping pong balls, so n = 12.
To arrange all 12 ping pong balls in a row, we take all 12 balls at a time, so r = 12.
Plugging the values into the formula, we get:
12P12 = 12! / (12 - 12)!
= 12! / 0!
= 12!
The factorial of 12 (12!) is calculated as:
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Evaluating this expression, we find:
12! = 479,001,600
Therefore, there are 479,001,600 possible ways to arrange the 12 ping pong balls in a row.
Learn more about permutation at https://brainly.com/question/29990226
#SPJ11
Find the measure of each angle indicated.
Answers
Answer:
The answer is
\(48\)
Step-by-step explanation:
Greetings!!
N.B
Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Thus,
\(50 + 82 + x = 180 \\ 132 + z= 180 \\x = 180 - 13 \\ x = 48\)
Hope it helps!!!
porfis ayúdenme es para hoy
Answers
Answers:
1. V=triangle area × length
V=1/2×8×12×20
V=960in³
2. triangle area × length
Area of the triangle=1/2×4×11
A=22ft²
V=22×6
V=132ft³
3. b, volume always have cubic power (³)
4. d, same reason of question 3
Aline has a slope of -3 and a y-intercept of 3
what is the x-intercept of the line?
Answers
Answer:
(1,0)
Step-by-step explanation:
y = -3x+3
simple, to find the x-intercept, what does x equal for y to be 0?
when x is 1, y equals 0, so the x-intercept would be at (1,0)
(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR.P(1, 0, 1), Q(-2, 1, 3), R(4, 2, 5)
Answers
The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).
For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)
For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by
\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)
where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get
\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)
The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).
Learn more about area of triangle here:
https://brainly.com/question/19305981
#SPJ4
Which ordered pairs are solutions to the inequality?
y < -4x +11
O (-4.-11)
O (-1.5)
0 (0,0)
O (2,3)
Answers
Answer:
(-4,-11)
Step-by-step explanation:
-11<-4(-4)+11
-11<16+11
-11<27 which is true
What is 88.2 rounded to the nearest whole number?
Answers
Answer:
88
Step-by-step explanation:
if the decimal is below 5 then round down
Answer:
88
Step-by-step explanation:
2 is less than 5, therefor it would be rounded to 88. If a number higher than five or five was in two's place it would be rounded to 89.
in the diagram below the lager angle is 4 times bigger than the smaller angle.find larger angle
Answers
Let the smaller angle be
\(=x\)The larger angle is 4 times bigger than the smaller angle means
\(\begin{gathered} \text{larger angle =y} \\ \text{Therefore,} \\ y=4\times x \\ y=4x \end{gathered}\)Concept:
The sum of two or more angles on a straight line is always 180°
Therefore,
\(x+y=180^0\)By substituting the value of y=4x in the equation above, we will have
\(\begin{gathered} x+4x=180^0 \\ 5x=180^0 \\ \text{divide both sides by 5} \\ \frac{5x}{5}=\frac{180^0}{5} \\ x=36^0 \end{gathered}\)substitute the value of x= 36° in y=4x to find the value of the bigger angle
\(\begin{gathered} y=4x \\ \text{when x=36} \\ y=4\times36 \\ y=144^0 \end{gathered}\)Hence,
The larger angle is =144 °
OPTION D IS THE CORRECT ANSWER
express 6160 as a product of their prime factor
Answers
→ The process of finding the Prime Factors of 6160 is called Prime Factorization of 6160.
→ To get the Prime Factors of 6160, you divide 6160 by the smallest prime number .
→ Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with..;-
• Prime Factorization process creates what we call the Prime Factor Tree of 6160:... see the above attachment ↑ ...• All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 6160... See here:
6160 ÷ 2 = 30803080 ÷ 2 = 15401540 ÷ 2 = 770770 ÷ 2 = 385385 ÷ 5 = 7777 ÷ 7 = 1111 ÷ 11 = 1All the prime numbers you used to divide above are the Prime Factors of 6160. Thus, the Prime Factors of 6160 are:
2, 2, 2, 2, 5, 7, 11.Hope this helps you :) ...
#Carry on learning# :)...
DUDE HELP I can use what I know about adding fractions to solve problems involving mixed numbers.
A.
strongly agree
B.
agree
C.
disagree
D.
strongly disagree
Answers
Answer:
C. Disagree
Explanation:
Because when you're adding mixed fractions, you don't just make them/find there denominator's equivalent/LCM and them, you have to first convert them to improper fractions.
Hope this helps
Anna is following this recipe to make biscuits.
Anna uses 550 g of sugar.
How many grams of oats will she need?
Recipe: Makes 24 biscuits
125 g margarine
100 ml syrup
275 g oats
110 g sugar
55 g chocolate
Answers
Answer:
Anna will need 1375 g of oats
110:275
550:x
To find x,we do (275*550)/110
Which is 1375gs of oats
Regina works at Runza and her current paycheck is $590. If this was $50 less than twice the amount of her last paycheck, what was the amount of her last paycheck?
Answers
Answer:
1130
Step-by-step explanation:
twice as much would be 1180 and then take away 50 is 1130
Suppose you have drawn two cards: 10 of clubs and 4 of hearts. You now draw a third card from the remaining 50. What is the probability that the sum of all three cards is strictly larger than 21
Answers
The probability that the sum is strictly larger than 21 is P = 0.46
How to find the probability?
We already have a 10 and a 4, so: 10 + 4 = 14
To sum more than 21, we need to draw at least an 8.
On the deck there are:
6 cards equal or larger than 8 of diamonds.6 cards equal or larger than 8 of clubs.6 cards equal or larger than 8 of spades5 cards equal or larger than 8 of hearts (because we already drew the 10).So, 23 out of 50 cards meet our requirements. So the probability will be:
P = 23/50 = 0.46
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
In a flower display, there are spaces for 3 plants. If there are 9 plant options, how many different ways can the plants be arranged? Hint: Are repeats allowed?
Answers
There are different consecutive ways that the flowers can be planted:
3,9,15,21 and so on.
Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written sequentially, where the difference between the numbers is fixed and no number in between is skipped.
Given that:
Roses plants in 1st, 2nd, row are:
3,9 ,.....
Since difference between consecutive terms is same:
It is an AP
We have to find number of row in the flower bed:
Lets assume there are n rows in the flowers bed.
We know that:
aₙ = a + (n-1)d
and d = 9-3 = 6
Therefore, the next numbers can be:
3,9,15 ,21 ......
Learn more about Consecutive :
https://brainly.com/question/30679467
#SPJ4
Please help!
Worth 20
Answers
the Area will be 280 inch².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The base of triangle = 20inch
The height of triangle = 14inch
Area is = (base * height) = (20*14)
Area = 280 inch²
Hence the Area will be 280inch²
Learn more about triangles, by the following link
https://brainly.com/question/17335144
#SPJ1
which of the following is an area of mathematics that studies how competing parties interact
Answers
An area of mathematics that studies how competing parties interact is known as "game theory."
Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.
Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.
The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.
Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.
Learn more about outcomes here:
https://brainly.com/question/32511612
#SPJ11
use synthetic division
f(x)= 2×^3+X^2-8X+5 BY X+3
Answers
markdown
Copy code
_________
|2 1 -8 5|
|3 3 0 0|
|0 -3 -8 2|
|0 0 -24 6|
_________
The final row represents the polynomial 2x^2 - 3x - 24, which is the remainder. The quotient is 2x^2 + 3x + 3.
So, f(x) divided by x + 3 is equal to (2x^2 + 3x + 3) + (2x^2 - 3x - 24)/(x + 3).
Answer:
f '(x) =6x² +2x-8+5by
Step-by-step explanation:
QUADRATIC EQUATION â€" WORD PROBLEMS
The sum of two numbers is 5 and their product is â’84. Find these numbers
The answer is 12 , -7
I just need the steps
Answers
Answer: -7, 12
Step-by-step explanation:
a+b = 5
a*b = -84
a = 5-b
(5-b)*b = -84
-b^2 + 5b + 84 = 0
(-b - 7)(b + 12) = 0
The roots are -7 and 12.
I'm not sure what â€" stands for
Brainliest question please please help me please
Answers
Answer: C outside of the circle
Step-by-step explanation:
The answer is c because
point 4, -1 falls outside of the
circle.
Hope this helps :)
Answer:
Its on the circle
Step-by-step explanation:
vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a speed pass device affixed to the dashboard. data on a busy day for cars and trucks passing over the bridge are shown here. payment method live cashier speed pass total vehicle type car 35 67 102 truck 18 47 65 total 53 114 167 what percentage of vehicles are trucks, given that they use speed pass?
Answers
The percentage of vehicles that are trucks and given that they use speed pass is 38.92%.
The percentage of all vehicles that are trucks is determined using the information provided in the table.
There are 167 vehicles in total, 65 of which are trucks that use the speed pass device. Thus, the percentage of vehicles that are trucks and use speed pass is as follows:
Speed pass truck percentage = (65 / 167) * 100 = 38.92%.
As a result, the percentage of all vehicles that are trucks and use speed pass is the percentage of speed pass trucks, which is 38.92%.
To know more about percentage click here:
https://brainly.com/question/29306119?
#SPJ11
Find the m ∠ G in DEG , if the m ∠ E = 118° and m ∠ D = 44°. i need this fast guys.
Answers
Answer:
18
Step-by-step explanation:
Answer: I think it may be 18.
Step-by-step explanation: The reason is because, 118 plus 44 equals 162. 180-162=18
The lifespan of a car battery averages 5 years. Suppose the battery lifespan follows an exponential distribution. What is the probability that the battery lasts more than 3 years
Answers
The probability that battery lasts more than 3 years is \(e^{-0.6 }\).
Parameter of Exponential Distribution
It is given that the average lifespan of the car battery = 5 years
⇒ μ = 5
And, we have to find the probability that the car battery lasts more than 3 years.
Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,
1/ λ = μ
⇒ λ = 1/5
Calculating the Probability
The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.
P(N>3) = 1 - P(N≤3)
P(N>3) = 1-F(4)
Here, F is the exponential distribution for the lifespan of the car battery.
P(N>3) = 1-(1-e^(-λn))
P(N>3) = \(e^{-3/5}\)
Thus, the required probability is,
P(N>3) = \(e^{-0.6 }\)
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
if y=e^nx then d^ny/dx^n
Answers
To find the nth derivative of y = e^(nx) with respect to x, we can use the power rule and the chain rule repeatedly. The nth derivative will involve a combination of exponential and polynomial terms.
Let's start by finding the first derivative of y with respect to x:
dy/dx = d/dx (e^(nx)) = ne^(nx)
The second derivative can be found by differentiating ne^(nx) with respect to x:
d^2y/dx^2 = d/dx (ne^(nx)) = n^2e^(nx)
We can continue differentiating and find the nth derivative:
d^ny/dx^n = d/dx (n^(n-1)e^(nx)) = n^n e^(nx)
The nth derivative of y = e^(nx) simplifies to n^n e^(nx), which involves the original exponential term e^(nx) multiplied by a polynomial factor n^n. Thus, the nth derivative contains both exponential and polynomial components.
Learn more about derivatives here: brainly.com/question/25324584
#SPJ11
mZADB = m/BDC and CD1 AE, which is a valid conclusion?
DB bisects/ADC
I ZADB and/ADF are supplementary angles
11 ZADB and/BDC are complementary angles
Olonl
I and II
OI and III
O I, II, and Ill
3
C
K-
Answers
the correct answer is option I as ∠ZADB and ∠ADF are supplementary angles.
Based on the given information, m∠ZADB = m∠BDC and CD is parallel to AE. A valid conclusion would be:
I. ∠ZADB and ∠ADF are supplementary angles.
This is because when a transversal line intersects two parallel lines, alternate interior angles are congruent. Since m∠ZADB = m∠BDC, and ∠BDC and ∠ADF are alternate interior angles, they are congruent. Additionally, since ∠ZADB and ∠BDC form a straight line, ∠ZADB and ∠ADF are supplementary angles.
So, the correct answer is I.
learn more about angles here:
https://brainly.com/question/31645384
#SPJ11