Final answer:
To determine how much pasta salad is needed for 49 people when 5 pounds serves 14 people, calculate the proportion based on ounces, resulting in 17.5 pounds needed for 49 people.
Explanation:
If 5 pounds of pasta salad serves 14 people, the amount needed for 49 people can be calculated by setting up a proportion because the number of people and the amount of pasta salad are directly proportional. First, we convert 5 pounds of pasta salad to ounces, since the standard conversion is 1 pound = 16 ounces, so 5 pounds equals 80 ounces.
Next, we set up the proportion as follows:
14 people → 80 ounces of pasta salad
49 people → x ounces of pasta salad
To solve for x, you cross-multiply and divide:
14x = 80 * 49
x = (80 * 49) / 14
x = 280 ounces
Thus, you will need 280 ounces of pasta salad, which is equivalent to 17.5 pounds (since 280 ounces divided by 16 ounces per pound equals 17.5 pounds). Therefore, for a picnic with 49 people, you should bring 17.5 pounds of pasta salad.
Approximately what percentage of iq scores falls between 70 and 130?
Lee works at a job where her pay varies directly with the number of hours she works. Her pay for 6.5 hours is 49.40. Write a direct variation equation relating lee's pay x to the hours worked y. Then find her pay if she works 25 hours in a week
Final answer:
The direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x. Lee's pay for working 25 hours in a week is $190.
Explanation:
Let's define the direct variation equation:
y = kx
We can substitute the information given in the question:
When x = 6.5, y = 49.40
49.40 = 6.5k
k = 49.40 / 6.5
k = 7.60
Therefore, the direct variation equation relating Lee's pay (x) to the hours worked (y) is y = 7.60x.
To find Lee's pay if she works 25 hours, we can substitute x = 25 into the equation:
y = 7.60(25)
y = 190
Lee's pay for working 25 hours in a week is $190.
Landon babysits and works part time at tge water park over the summer. onw week, he babysat for 3 hours and worked at the water park for 10 hours and made 109$. the next week he babysat for 8 hours and worked at the water park for 12 hours and made 177$. how much does London make per hour at each job ?
1 define your variables ,- what are you solving for
2 set up equations - using the information given
3 solve the system using your method of choice
Answer:
Landon makes $10.5 per hour at babysitting and $7.75 per hour at water park.
Step-by-step explanation:
Let the amount made per hour in dollars for babysitting be = x
Let the amount made per hour in dollars at water park be = y
As per the condition, the equations form:
[tex]3x+10y=109[/tex] .......(1)
[tex]8x+12y=177[/tex] ......(2)
Multiplying (1) by 8 and (2) by 3, and subtracting (2) from (1), we get
[tex]44y=341[/tex]
=> y = 7.75
And [tex]3x+10(7.75)=109[/tex]
=> [tex]3x+77.5=109[/tex]
=> [tex]3x=109-77.5[/tex]
=> [tex]3x=31.5[/tex]
x = 10.5
Therefore, Landon makes $10.5 per hour at babysitting and $7.75 per hour at water park.
Solve 81^x = 27^x+2
X=1
X=2
X=5
X=6
The two-way table shows the number of sport utility vehicles with certain features for sale at the car lot.
What is the probability that a randomly selected car with no 4-wheel drive has third row seats?
0.3
0.4
0.7
0.8
Probability measures to determine the possibility of an event. In this case, the events are cars with no 4 wheels and cars with third row seats.
The probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3
Let:
[tex]A \to[/tex] A car with no 4-wheel drive
[tex]B \to[/tex] A car that has third row seats
The probability that a randomly selected car with no 4-wheel drive has third row seats is represented as:
[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]
From the 2-way table, we have the following parameters:
[tex]n(A\ n\ B) = 12[/tex]
[tex]n(A) = 40[/tex]
So, the probability is:
[tex]P(B|A)= \frac{n(A\ n\ B)}{n(A)}[/tex]
[tex]P(B|A)= \frac{12}{40}[/tex]
[tex]P(B|A)= 0.3[/tex]
Hence, the probability that a randomly selected car with no 4-wheel drive has third row seats is 0.3
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Need help please. Just need my answers checked. Thanks in advance. My answers are in brackets.
1. The coordinates of the vertices of ΔJKL are J(-5, -1) , K(0, 1) , and L(2, -5). Which statement correctly describes whether ΔJKL is a right triangle?
a. ΔJKL is a right triangle because JK is perpendicular to JL.
b. ΔJKL is a right triangle because JL is perpendicular to KL.
c. ΔJKL is a right triangle because JK is perpendicular to KL.
[ d. ΔJKL is not a right triangle because no two of its sides are perpendicular. ]
2. The coordinates of the vertices of ΔJKL are J(0, 2) , K(3, 1) , and L(1, -5). Drag and drop the choices into each box to correctly complete the sentences.
The slope of JK is [ -¹/₃ ], the slope of KL is [ 3 ], and the slope of JL is [ -7 ]. ΔJKL [ is ] a right triangle because [ two of these slopes have a product of -1 ].
answer choices: -3 ; 3 ; -7 ; -¹/₃ ; ¹/₇ ; is ; is not ; two of these slopes have a product of -1 ; no two of these slopes have a product of -1
3. The coordinates of the vertices of quadrilateral DEFG are D(-2, 5) , E(2, 4) , F(0, 0) , and G(-4, 1). Which statement correctly describes whether quadrilateral DEFG is a rhombus?
a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.
[ b. Quadrilateral DEFG is not a rhombus because there is only one pair of opposite sides that are parallel. ]
c. Quadrilateral DEFG is not a rhombus because opposites sides are parallel but the four sides do not all have the same length.
d. Quadrilateral DEFG is not a rhombus because there are no pairs of parallel sides.
The slopes of the sides are:
DE = -¹/₄
EF = 2
FG = -¹/₂
GD = 2
I'm debating between A and B.
4. The coordinates of the vertices of quadrilateral ABCD are A(-4, -1) , B(-1, 2) , C(5, 1) , and D(1, -3). Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is [ 1 ], the slope of BC is [ -¹/₆ ], the slope of CD is [ 1 ], and the slope of AD is [ -²/₅ ]. Quadrilateral ABCD [ is not ] a parallelogram because [ only one pair of opposite sides is parallel ].
answer choices: -²/₅ ; -¹/₆ ; 1 ; ³/₂ ; is ; is not ; both pairs of opposite sides are parallel ; only one pair of opposite side is parallel ; neither pair of opposite sides is parallel
5. The coordinates of the vertices of quadrilateral PQRS are P(-4, 2) , Q(3, 4) , R(5, 0) , and S(-3, -2). Which statement correctly describes whether quadrilateral PQRS is a rectangle?
a. Quadrilateral PQRS is not a rectangle because it has only two right angles.
b. Quadrilateral PQRS is a rectangle because it has four right angles.
c. Quadrilateral PQRS is not a rectangle because it has only one right angle.
d. Quadrilateral PQRS is not a rectangle because it has no right angles.
I'm not sure about this one.
Thanks again.
Answer:
#1) d. ΔJKL is not a right triangle because no two of its sides are perpendicular; #2) -1/3, 3, -7, is, two of these slopes have a product of -1; #3) a. Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length; #4) 1, -1/6, 1, -2/5, is not, only one pair of opposite sides is parallel; #5) c. Quadrilateral PQRS is not a rectangle because it has only one right angle.
Step-by-step explanation:
#1) The slope of any line segment is found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For JK, this gives us (1-1)/(-5-0) = 0/-5 = 0. For KL this gives us (1--5)/(0-2) = 6/-2 = -3. For LJ this gives us (-5-1)/(2--5) = -6/7. None of these slopes are negative reciprocals, so none of the angles are right angles and this is not a right triangle.
#2) The slope of JK is (2-1)/(0-3) = 1/-3 = -1/3. The slope of KL is (1--5)/(3-1) = 6/2 = 3. The slope of LJ is (2--5)/(0-1) = 7/-1 = -7. Two of these slopes have a product of -1, 3 and -1/3. This means they are negative reciprocals so this has a right angle; this means JKL is a right triangle.
#3) The slope of DE is (5-4)/(-2-2) = 1/-4 = -1/4. The slope of EF is (4-0)/(2-0) = 4/2 = 2. The slope of FG is (0-1)/(0--4) = -1/4. The slope of GD is (1-5)/(-4--2) = -4/-2 = 2. Opposite sides have the same slope so they are parallel.
Next we use the distance formula to find the length of each side:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Using our points, the length of DE is
[tex]\sqrt{(5-4)^2+(-2-2)^2}=\sqrt{1^2+(-4)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
The length of EF is
[tex]d=\sqrt{(4-0)^2+(2-0)^2}=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}[/tex]
The length of FG is
[tex]d=\sqrt{(0-1)^2+(0--4)^2}=\sqrt{(-1)^2+(4)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
The length of GD is
[tex]d=\sqrt{(1-5)^2+(-4--2)^2}=\sqrt{(-4)^2+(-2)^2}=\sqrt{16+4}=\sqrt{20}[/tex]
Opposite sides have the same length and are parallel, so this is a parallelogram.
#4) The slope of AB is (-1-2)/(-4--1) = -3/-3 = 1. The slope of BC is (2-1)/(-1-5) = 1/-6 = -1/6. The slope of CD is (1--3)/(5-1) = 4/4 = 1. The slope of DA is (-3--1)/(1--4) = -2/5. Only one pair of opposite sides is parallel, so this is not a parallelogram.
#5) The slope of PQ is (2-4)/(-4-3) = -2/-7 = 2/7. The slope of QR is (4-0)/(3-5) = 4/-2 = -2. The slope of RS is (0--2)/(5--3) = 2/8 = 1/4. The slope of SP is (-2-2)/(-3--4) = -4/1 = -4. Only one pair of sides has slopes that are negative reciprocals; this means this figure only has 1 right angle, so it is not a rectangle.
The answers provided for ΔJKL, ΔJKL as a right triangle, and quadrilateral ABCD are correct. For quadrilateral DEFG, the answer may be correct depending on side lengths, and for quadrilateral PQRS, slopes must be calculated to determine if it's a rectangle.
Explanation:To determine whether the given shapes are right triangles, rhombuses, rectangles, or parallelograms, we use properties such as the slopes of lines to check for perpendicularity, parallelism, and equal lengths.
For ΔJKL with vertices J(-5, -1), K(0, 1), L(2, -5), you calculated it's not a right triangle because none of the slopes of the sides are negative reciprocals of each other (indicating perpendicular sides). This is correct; no slopes have a product of -1, so answer (d) is correct.
In the second case, ΔJKL with vertices J(0, 2), K(3, 1), L(1, -5) has slopes -1/3, 3, and -7 for sides JK, KL, and JL respectively. Since -1/3 and 3 are negative reciprocals, ΔJKL is a right triangle due to the perpendicular sides JK and KL. So, the filled answers are correct.
Regarding quadrilateral DEFG, you might want to reconsider option (b), as you cannot determine whether it's a rhombus solely based on one pair of opposite sides being parallel. Instead, check if all sides have the same length using the distance formula, and if the opposite sides are parallel by comparing slopes. Since you didn't provide the side lengths, I will only address the slopes here, which you've noted. Answer (b) can be correct if the side lengths are not equal, but if they are, it should be (c).
For quadrilateral ABCD, your assessment of the slopes leads to the conclusion that it is not a parallelogram, which is correct as only one pair of opposite sides (AB and CD having a slope of 1) is parallel. The filled answers are appropriate.
Last, for quadrilateral PQRS, you must calculate the slopes of the sides to determine if the sides are perpendicular to each other by checking if the products of the corresponding slopes are -1. If the slopes of adjacent sides are negative reciprocals of each other, then PQRS has right angles, and it could be a rectangle. Calculate the slopes, and if none are negative reciprocals, then answer (d) is correct stating that PQRS is not a rectangle because it has no right angles.
Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
find the perimeter of ABC with vertices A (1,1), B (7,1), and C (1,9)
Answer:
24 unit
Step-by-step explanation:
Given,
The vertices of the triangle ABC are,
A (1,1), B (7,1), and C (1,9),
By the distance formula,
[tex]AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}[/tex]
[tex]BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}[/tex]
[tex]CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}[/tex]
Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit
You parents gave you $50 to take your brother and sister to the movies. Your ticket cost $7.25 and your siblings cost $4.25. If you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
Adults: 7.25
Seniors: 6.00
Children under 8: 4.25
Answer:
You bring home $14.25 with you.
Step-by-step explanation:
First we add the money spent in movie tickets and snacks.
Your ticket = $7.25
Brother's ticket = $4.25
Sister's ticket = $4.25
Soda and popcorn = $20.00
Total = 7.25 + 4.25 + 4.25 + 20.00 = $35.75
Your parents gave you = $50.00
You spent = $35.75
Balance = 50.00 - 35.75 = $14.25
You bring home $14.25 with you.
Try this trick out on a friend! Tell your friend to place a dime in one hand and a penny in the other hand. Explain that you can determine which hand is holding the penny. Here’s how to do it: a. Ask the friend to multiply the value of the coin in his or her RIGHT hand by 4, 6, or 8 and then to multiply the value of the coin in his or her LEFT hand by 3, 5, or 7. 2. b. Now ask the friend to add the two results together and tell you the total. c. If the total is EVEN, the penny is in the RIGHT hand. If the total is ODD, the penny is in the left hand.
The question involves a mathematical trick to determine the location of a penny based on the parity of a sum and a take-home experiment on the balancing of pennies and torque. Additionally, it touches upon probability in the context of half-life and independent probabilities.
Explanation:Understanding Coin Experiments and ProbabilityIn the trick described, you are presenting a simple mathematical puzzle to determine the location of a penny based on the parity of the sum of two numbers. This is an application of basic arithmetic operations and the concept of even and odd numbers. However, for the take-home experiment involving balancing pennies on a ruler, this is related to physics and moment of force (torque). In this experiment, to balance one penny placed 8 cm away from the pivot, you would need to find a position where the total torque caused by the two or three pennies counterbalances the torque caused by the single penny. This involves understanding the principles of levers and torque.
the half-life coin activity mentioned in the question is an example of using probability to model physical phenomena, specifically radioactive decay. It explores independent probabilities when flipping coins multiple times.
These experiments and demonstrations help to illustrate various scientific and mathematical concepts using coins, which are familiar objects, making them more approachable and relatable to students.
solve:512^x-2/(1/64)^3x-512
x = –1
x = 0
x = 1
no solution
The answer is x=1. Just did the assignment
The equation is a complex exponentiation problem that can be solved by simplifying and rearranging the equation. By plugging in the given potential solutions, it can be determined that x = -1 is the correct answer.
Explanation:This equation is an exponential equation. You can start solving by simplifying the bases, as both bases are actually the 2, but to different powers (512 = 2^9 and 1/64 = 2^-6). The equation can be rewritten as (2^9)^x - 2 = (2^-18)x - 512. Simplifying this gives 2^(9x) - 2 = 2^(-18x) - 512. From the options given (x = -1, 0, or 1), we can plug these into the simplified equation to see which one gives a valid solution. Plugging these values in reveals that x = –1 is the valid solution to the equation. None of the other choices work out correctly.
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A factory uses 15 pounds of steel for every 18 pounds of copper. How much copper will the factory use for 2,700 of steel. A.2,250lbs B.2,400lbs C.3,240lbs D.3,700lbs?
twenty-two pencils cost $0.60 less than $5 what is the cost per pencil?
Write a function rule the price p of a pizza is $6.75 plus $0.85 for each of the t toppings of pizza
Answer for 14 and 15 only
Find the measures of an angle and its complement if one angle measures 24 degrees
A bakery has prepared 320 ounces of bread dough. a machine will cut the dough into a loaf. the amount of d dough left after m minutes is given by the function d (m)=-5m+320. how many minutes will it take the machine to use all the dough? find a reasonable domain and range for this situation.
A. how many minutes will it take the machine to use all the dough?
We are given the formula:
d (m) = - 5 m + 320
To find for the value of m when all dough is used, we set d (m) = 0:
0 = - 5 m + 320
m = 320 / 5
m = 64 minutes
B. The domain is time and time can never be negative so it always starts at zero, so at time = 0, the range d (m) is:
d (m) = - 5 (0) + 320
d (m) = 320
The other domain and range is already described in (A.), when all dough is used up.
So the pair of reasonable domain and range is:
(0, 320), (64, 0)
Solve 6e^(x)-4e^(-x)=5. Solve for x and please describe how you got your answer.
For the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x, where a is a constant and a>1
It is given that,
6eˣ-4e⁻ˣ=5
Multiplying complete equation by eˣ
eˣ(6eˣ-4e⁻ˣ)=5(eˣ)
6(eˣ)(eˣ) - 4(e⁻ˣ)(eˣ) =5(eˣ)
6e²ˣ-4 = 5(eˣ)
6e²ˣ-5eˣ -4 = 0
Suppose y = eˣ
6y² - 5y -4 = 0
After solving the equation we get y = 4/3 and y = -1 / 2.As a result,
eˣ = 4/3
x = log(4/3)
x = 0.29
Thus, for the given equation 6eˣ-4e⁻ˣ=5 the value obtained after solving the equation will be x =0.29.
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algebra- you make a large pot of soup. You freeze the soup in small and medium containers. A small container holds 4 ounces and a medium container holds 6 ounces. The soup can fill 6 small containers and 10 medium containers.
A.Write an equation in standard form that models the possible combinations of small and medium containers that the soup can fill.
B. Graph the equation from part (a)
C. Find four possible combination.
A. Let us say that:
s = number of small containers
m = number of medium containers
From the given data, the total volume of soup is:
total soup = 4 ounces * 6 + 6 ounces * 10 = 84 ounces
So the equation is:
4s + 6m = 84
B. We rewrite the equation explicit to one variable, here we choose s:
4s = 84 – 6m
s = 21 – 1.5m
Then we assign several values for m starting at 0 to get the corresponding value of s then plot the graph. See the graph attached.
C. From the graph, we choose the pair of s and m that are whole numbers. The four possible combinations are:
21 small containers, 0 medium containers
15 small containers, 4 medium containers
9 small containers, 8 medium containers
3 small containers, 12 medium containers
WHAT IS 24.5 DIVIDED BY 7
Darryl has $5 left in his pocket. He spent $16 on a book, $20 on a compact disc, and $2 on a magazine. How much money did he have at the beginning of the day.
use the image above to write a conjecture about regular polygons and lines of symmetry
what 3 digits are in the ones/units period 4,083,817
∠E∠E and ∠F∠F are vertical angles with m∠E=9x+12m∠E=9x+12 and m∠F=3x+24m∠F=3x+24 .
What is the value of x?
Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F
Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24
Subtract both sides of the equation by 3x
6x + 12 = 24
Subtract 12 from both sides
6x = 12
Divide both sides by 6
x = 2
This should be your answer. Have an awesome day! :)
What is the y-intercept of the equation 4×+2y=12?
how do i factor x^3+3x^2
An auditor performs attribute sampling to test for proper cancellation of payment vouchers. in a sample population of 100, two vouchers are missing the proper cancellation, while one simply cannot be located. the error rate of the sample is
What construction can be used to identify a line of reflection?
Isa's calculator displays a number as 7.3579 E8. What is this number in standard form? Enter your answer in the box.
Suppose a coin is tossed 12 times and there are three heads and nine tails. how many such sequences are there in which there are at least five tails in a row?