Which situation could best be represented by this linear equation?
2.75x + 3.25y = 215
Answers
answer is the last one (D)
Answer:
The correct option 4.
Step-by-step explanation:
The given equation is
[tex]2.75x+3.25y=215[/tex] .... (1)
Let x is the number of pretzels sold and y is the number of popcorn bags sold.
Total sales is defined as
[tex]Sales=C_1x+C_2y[/tex] ... (2)
From (1) and (2) it is clear that,
The cost of each pretzel is $2.75 or 275 cents. The cost of each popcorn bag is $3.25 or 325 cents ($1 = 100 cents). Total sales is $215.
[tex]325-275=50[/tex]
Pretzels cost is 50 cents less than popcorn bags. The variable x represents the number of pretzels sold and y represents the number of popcorn bags sold. The total sales was $215.
Therefore the correct option 4.
Related Questions
Trygg has 3/4 package of marigold seeds. He plants 1/6 of those seeds in his garden and divides the rest equally into 10 flower pots. What fraction of a packege of seeds is planted in each flower pot? Show your work.
Answers
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
We are given that
Trygg has package of marigold seeds=[tex]\frac{3}{4}[/tex]
He plants seeds in garden=[tex]\frac{1}{6}\times \frac{3}{4}=\frac{1}{8}[/tex]
Remaining seeds=[tex]\frac{3}{4}-\frac{1}{8}=\frac{5}{8}[/tex]
He divide remaining seeds equally into 10 flower pots.
We have to determine the fraction of a package of seeds is planted in each flower pot.
Seeds in each pot=[tex]\frac{\frac{5}{8}}{10}=\frac{1}{16}[/tex]
Hence, seeds planted in each pot=[tex]\frac{1}{16}[/tex]
Find the missing numbers 85,95, _ ,100,105, _
Answers
Note that 85 plus 5 is 90; 90 plus 5 is 95; 95 plus 5 is 100; 100 plus 5 is 105.
This is just an example to show you one possibility.
This is an arith. sequence ONLY IF you add the SAME number each time to find the next term of the sequence.
if you have 12 fish and 6 drown how many do you have left?
Answers
Cody saves all his nickles. Today he is getting them out of his piggy bank and wrapping them to take to the bank. He finds he has 360 nickels. It takes 40 Nicole's to fill each paper wrapper and make a roll. How many wrappers does he need? Explain how you solved this problem and how you know your answer is correct.
Answers
Divide 360 by 40
360/40 = 9
Cody needs 9 wrappers.
3rd grader explanation:
Explain that Cody wants to divide 360 into __ groups of 40.
Use an illustration of separating things into equal groups (you can simply use separating 6 objects into equal groups of 2).
Explain that subtraction, multiplication, or addition will not help.
Tell him/her to use division.
Although 360 and 40 are large numbers, explain that the 0's can be removed into 4 and 36.
36 / 4 = 9
Since the answer is 9, Cody needs 9 wrappers.
Have an awesome day! :)
Glenda began the day with a golf score of -6 and ended with a score of -10. Which statement represents her golf score for that day?
A) -6 - ( - 10) = 4
B) - 10 - ( - 6) = - 4
C) - 6 + ( - 10) = - 16
D) - 10 + ( - 6) = - 16
Answers
She started with -6 and ended up with -10 so her score was 4 less than what she started with so it is -4
Which statement best describes one of these transformations? Triangle 1 is rotated to result in triangle 2. Triangle 1 is dilated to result in triangle 3. Triangle 1 is reflected to result in triangle 4. Triangle 1 is stretched to result in triangle 5.
Answers
Answer:
Triangle 1 is rotated to result in triangle 2.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
GOT IT RIGHT
Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system. x < 2 and y ≤ 4x + 1
(5, 6)
(5, –2)
(–3, –15)
(1, 11)
Answers
x < 2
y ≤ 4x + 1
Graph the lines:
x = 2
y = 4x +1
The solution to the system of inequalities is the shaded region shown in the graph below.
Test the given points to see whether they fall within the solution region.
Point Pass/Fail
-------- --------------
(5,6) Fail
(5,-2) Fail
(-3,-15) Pass
(1,11) Fail
Answer: (=3, -15)
Two redwood trees are the same height. A third tree's height is x feet. The first tree is 50 feet more than three times the height of the third tree. The second tree is 100 feet taller than twice the height of the third tree. What is the height, in feet, of the third tree? A. 150 B. 50 C. 200 D. 100
Answers
3rd tree = x
1st tree = 3x+50
2nd tree = 2x+100
3x+50 = 2x+100
subtract 50 from each side
3x= 2x+50
subtract 2x from each side
x = 50
so 3rd tree = 50 feet tall
Answer is B
Bill worked 24 hours last week and earns $8.25 per hour. Use front-end estimation to find an estimate of the total amount of money he earned.
Answers
Answer:
The total amount of money he earned was $160
Step-by-step explanation:
Bill worked 24 hours last week
He earns $ 8.25 per hour.
We have to use front-end estimation, we have to round to the first number all the values. So. Bill worked h = 20 hours and he earns 3 =$8 per hour.
Total amount (T) wil be the hours (h) multiplied by the earning (e)
T = h*e
T = (20 hours)(8 $/hours)
T = 160 $
After using front-end estimation, we can conclude that Bil earned $160.
labored 24 hours remaining week
He earns $ 8.25 in step per hour.
We should use the front-stop estimation, we have to round to the first number of all of the values. So. invoice worked h = 20 hours and he earns 3 =$eight according to an hour.
the entire amount (T) can be the hours (h) extended through the earning (e)
T = (20 hours)(eight $/hours)
T = 160 $
After using front-end estimation, we will conclude that Bil earned $one hundred sixty.
How do you calculate front-end estimation?front-cease estimation is a particular way of rounding numbers to estimate sums and variations. to apply the front-end estimation, add or subtract the handiest of the numbers in the finest location cost. Then upload the decimals rounded to the closest 10th.
what are front-end estimation examples?
In the front-cease estimation, we replace the original quantity with quite a number it is close by but the handiest has one non-zero digit. as an example, 20, three hundred, -50, 1,000, eighty,000. Take the quantity 32; the selections to update it with are 30 or forty (they both have the handiest one non-0 digit).
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A four person relay team completed a race in 72.4 seconds. On average what was each runner's time?
Answers
72.4/4=18.1
Answer:
i believe it's 18.1
Step-by-step explanation:
WILL GIVE BRAINEST
Which system of inequalities is shown?
Answers
The system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have a graph shown in the picture,
As we can see in the picture there two lines are shown which represent the inequality and the shaded region is the solution to the pair of the linear inequality.
y > x and
y > 4
Thus, the system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.
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A sample of n = 9 scores has a variance of s2 = 36. what is the estimated standard error for the sample mean? 1 2 4 16
Answers
σ² = 36, the variance
n = 9, the sample size.
The standard deviation is
σ = 6
By definition, the standard error is
σ/√n = 6/3 = 2
Answer: 2
Help!
Math Torture!
Adam is constructing an equilateral triangle. He has already constructed the line segment and arcs shown.
What should Adam do for his next step?
A. Place the point of the compass on point X and draw an arc, using a width for the opening of the compass that is greater than 12XR.
B. Place the point of the compass on point X and draw an arc, using XR as the width for the opening of the compass.
C. Use the straightedge to draw XR←→ and XS←→.
D. Use the straightedge to extend RS¯¯¯¯¯ in both directions.
Answers
Answer:
C. Use the straightedge to draw XR←→ and XS←→.
Step-by-step explanation:
Adam has drawn the arcs by using RS distance as the radius of the circle and mid points as R and S.
So the point X is the same distance from R and S.
So now Adam has to use the straightedge to draw XR←→ and XS←→.
Then, XR = XS = RS
So it is an equilateral triangle.
Therefore, the correct answer is C.
Adam should do for his next step to use the straightedge to draw [tex]\( XR \)[/tex] and [tex]\( XS \).[/tex] The option (C) is correct.
The construction process for the equilateral triangle:
To construct an equilateral triangle using a straightedge and compass:
Construct [tex]\( XR \)[/tex]: Adam has already constructed segment [tex]\( XR \).[/tex]
Draw [tex]\( XS \)[/tex]: Using the straightedge, Adam should draw a line segment [tex]\( XS \)[/tex] from point [tex]\( X \)[/tex] to another point [tex]\( S \)[/tex] such that [tex]\( XS = XR \)[/tex]. This ensures that two sides of the equilateral triangle are equal in length.
Draw [tex]\( RS \)[/tex]: After drawing [tex]\( XS \)[/tex], Adam should use the straightedge to draw segment [tex]\( RS \)[/tex], completing the equilateral triangle [tex]\( \triangle XRS \).[/tex]
This method aligns with the steps typically used in geometric constructions to form an equilateral triangle: ensuring that all three sides are equal in length by first establishing two sides of equal length and then completing the triangle.
Therefore, upon reconsideration, option (C) is indeed the correct next step for Adam to construct his equilateral triangle.
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $30 per foot, and the fencing for the east and west sides costs $15 per foot. If I have a budget of $120 for the project, what are the dimensions of the garden with the largest area I can enclose?
Answers
The largest rectangular orchid garden that can be enclosed within a $120 budget, considering the given costs of fencing, has dimensions of 2 feet by 2 feet, resulting in an area of 4 square feet.
You wish to create a rectangular orchid garden with the house forming the northern boundary, and you're working with a budget of $120 for fencing. The cost per foot for the southern boundary is $30, and for the east and west sides, it's $15 each. We need to determine the dimensions that maximize the area.
Let's denote the width of the garden (east and west sides) as w feet, and the length (only the southern side, as the northern side is the house) as l feet. The total cost of fencing is therefore the sum of the costs for all three sides: Cost = $30l + 2($15w), which simplifies to Cost = $30l + $30w. Since your budget is $120, we can write the equation $30l + $30w = $120, which simplifies further to l + w = 4.
To find the dimensions that give you the largest area, we need to maximize the area A of the rectangle, which is A = l imes w. Substituting w with 4 - l (from our previous equation), we get A = l imes (4 - l). To find the maximum area, take the derivative of A with respect to l and set it to zero, solving for l. This gives us l = 2 feet. Substituting back, we find w = 2 feet as well.
The dimensions for the garden that will give you the largest enclosed area within a $120 budget are 2 feet in width by 2 feet in length, resulting in an area of 4 square feet.
Figure ABCDE is the result of a 180° rotation of Figure LMNOP about the point. Which angle in the pre-image corresponds to ∠B in the image? Enter your answer in the box.
Figure L M N O P is rotated 180 degrees about a point resulting in image A B C D E.
Answers
Answer: ∠M in the pre-image corresponds to ∠B in the image.
Step-by-step explanation:
When we look at the figures , we can see that the three vertices B , C , D are one side as vertices to M , N ,O .
Clearly , vertex C corresponds to vertex N ( presents in the middle )
Also, point B is at the right from point C .
In Figure L M N O P , vertex M is at the right from vertex N .
Thus , vertex M corresponds the vertex B.
It means ∠M in the pre-image corresponds to ∠B in the image.
An angle measures 54 less than the measure of a complementary angle. What is the measure of each angle?
Answers
A shop advertised a 22%-off sale. If a coat originally sold for $257, find the decrease in price and the sale price
Answers
I suck at word problems help
Answers
hope this helped
Find the length of the curve. r(t) = 3 i + t2 j + t3 k, 0 ≤ t ≤ 1
Answers
[tex]\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=1}\|\mathbf r'(t)\|\,\mathrm dt=\int_{t=0}^{t=1}t\sqrt{9t^2+4}\,\mathrm dt=\frac{13\sqrt{13}-8}{27}[/tex]
To determine the length of the curve, we find the derivative of the given vector function, compute its magnitude, and then compute the integral of the magnitude from 0 to 1. This involves calculus techniques.
Explanation:To find the length of the curve, we have to compute the integral of the magnitude of the derivative on the interval from 0 to 1. First, we find the derivative of r(t) = 3 i + t^2 j + t^3 k which is r'(t) = 2t j + 3t^2 k. The magnitude of r'(t) is |r'(t)| = sqrt((0)^2 + (2t)^2 + (3t^2)^2) = sqrt(4t^2 + 9t^4). Thus the length of the curve is the integral of this magnitude from 0 to 1: ∫ from 0 to 1 of sqrt(4t^2 + 9t^4) dt. This integral can be evaluated using techniques from calculus.
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joe is using his allowance money to download songs from the internet. he can download them at a rate of eight songs every 10 minutes. Jasmine, who is downloading songs with the money she made from her part time job, can download at a rate of 12 songs every 15 minutes. Who is downloading songs faster?
Answers
Joe: 8 songs in 10 minutes = 8/10 = 0.8 songs per minute
Jasmine: 12 songs in 15 minutes = 12/15 = 0.8 songs per minute
they are downloading at the same speed
Henry is making a corn grits recipe that calls for 14 cup of corn grits for every 12 cup of water. How much water will he need if he uses 112 cups of corn grits? Enter the number in the box
Answers
To find this answer you have to first divide the 112 cups of corn grits by 14, your answer will be 8. Next you multiply 8 by the cups of water per 14 cups of corn grits which is 12 cups of water (8x12) which gives you your answer of 96 cups of water.
On your last credit card statement, you had a previous balance of $98.14, payments of $10, a periodic rate of 1.34 percent, and new charges totaling $34.89. What is your new balance?
A. $88.14
B. $100.58
C. $124.21
D. $189.35
Answers
what is the answer 4(6/10−1/5)+0.4=
Answers
The task here is EVALUATION: Finding the value of a mathematical expression.
Use Order of Operations rules. Often dubbed "PEMDAS," these rules start by emphasizing that anything enclosed inside parentheses MUST be done first. Next come mult. and di. Last are add'n and subt'n.
In 4(6/10−1/5)+0.4, we MUST combine 6/10 and -1/5 FIRST.
That's the same as 3/5-1/5, or 2/5. Then the problem looks like:
Evaluate: 4(2/5)+0.4
Now, we MUST multiply before adding or subtracting. We get
8/5 + 4/10, or 16/10+4/10 = 20/10, or 2 (answer).
Or in shorter answers 2
If p(a) = 0.65, p(b) = 0.58, and p(a and
b.= 0.76, then p(a or
b.is:
Answers
The value of P( a or b)= 0.47.
what is Conditional Probability?The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.
Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.
Given:
p(a) = 0.65, p(b) = 0.58, and p(a and b)= 0.76
Now, using the formula
P(a∪b) = P(a) + P(b) - P(a∩b)
= 0.65 + 0.58 - 0.76
= 0.47
Hence, the value of P( a or b)= 0.47.
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Evaluate the triple integral of f(x,y,z)=z(x2+y2+z2)−3/2f(x,y,z)=z(x2+y2+z2)−3/2 over the part of the ball x2+y2+z2≤49x2+y2+z2≤49 defined by z≥3.5z≥3.5. ∫
Answers
[tex]f(x,y,z)=z(x^2+y^2+z^2)^{-3/2}=\dfrac z{(x^2+y^2+z^2)^{3/2}}[/tex]
(as opposed to subtracting 3/2, say)
Convert to spherical coordinates, taking
[tex]\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
Now when [tex]z=\dfrac72[/tex], below the "cap" of the ball we have a right triangle with hypotenuse coinciding with the ball's radius and a leg of length [tex]\dfrac72[/tex], with the angle between them [tex]\varphi[/tex] satisfying
[tex]\cos\varphi=\dfrac{\frac72}7=\dfrac12\implies\varphi=\cos^{-1}\dfrac12=\dfrac\pi3[/tex]
Furthermore, when [tex]z=\dfrac72[/tex], we have
[tex]\dfrac72=\rho\cos\varphi\implies\rho=\dfrac72\sec\varphi[/tex]
Call the cap [tex]C[/tex]. Then the triple integral over [tex]C[/tex] is
[tex]\displaystyle\iiint_Cf(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=7/2\,\sec\varphi}^{\rho=7}\frac{\rho\cos\varphi}{(\rho^2)^{3/2}}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi[/tex]
[tex]=\displaystyle2\pi\int_{\varphi=0}^{\varphi=\pi/3}\int_{\rho=7/2\,\sec\varphi}^{\rho=7}\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi[/tex]
[tex]=\displaystyle\pi\int_{\varphi=0}^{\varphi=\pi/3}\sin2\varphi\left(7-\dfrac72\sec\varphi\right)\,\mathrm d\varphi[/tex]
[tex]=\displaystyle\frac{7\pi}2\int_{\varphi=0}^{\varphi=\pi/3}(2\sin2\varphi-\sin2\varphi\sec\varphi)\,\mathrm d\varphi=\frac{7\pi}4[/tex]
To evaluate a triple integral over a region of a sphere, we switch to spherical coordinates. We then express the integrand and the limits of the variables in terms of these new coordinates. Don't forget the Jacobian when changing variables.
Explanation:The subject is a mathematical problem that requires evaluating a triple integral over a specific part of a ball in three-dimensional space. The function to integrate is f(x,y,z)=z*(x2+y2+z2)-3/2 and the region of integration is defined as the part of the sphere with radius 7 (x2+y2+z2<=49) in which z >= 3.5. Unfortunately, the solution to such a problem requires advanced mathematical skills and knowledge, such as spherical coordinates and integration techniques, which cannot be elaborated within the word limit here.
However, to solve such problems, you typically switch to spherical coordinates, where x=r*cos(theta)*sin(phi), y=r*sin(theta)*sin(phi), z=r*cos(phi). Then, you express your function and the limits of your variables r, theta, and phi in terms of these new coordinates. You need to consider the Jacobian determinant when changing variables. Eventually, you integrate over the specified region. The solution needs careful elaboration of every step due to the complexity of the integral.
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Rajendra has 14 4/5 pounds of trail mix. He is putting them into bags that hold 1 1/2 pounds each. Does he have enough trail mix to completely fill 8 bags?
Answers
~PutarPotato
Answer: Yes , Rajendra has enough trail mix to completely fill 8 bags.
Step-by-step explanation:
Given : Total trail mix Rajendra has = [tex]14\dfrac{4}{5}[/tex] pounds
Convert [tex]14\dfrac{4}{5}[/tex] into improper fraction.
[tex]14\dfrac{4}{5}=\dfrac{(14)(5)+4}{5}=\dfrac{74}{5}[/tex]
Amount of mix in each bag = [tex]1\dfrac{1}{2}[/tex] pounds.
[tex]=\dfrac{1(2)+1}{2}=\dfrac{3}{2}[/tex] pounds
Then, the total number of bags can be filled by the trail mix Rajendra has
= Total trail mix ÷ Amount of mix in each bag
[tex]=\dfrac{74}{5}\div\dfrac{3}{2}[/tex]
[tex]=\dfrac{74}{5}\times\dfrac{2}{3}=\dfrac{148}{15}=9.86666666667\approx9[/tex]
It means Rajendra has enough trail mix to fill 9 bags.
Since 9 > 8
Therefore , Rajendra has enough trail mix to completely fill 8 bags.
I need help! Rewrite each product below using Distributive property.
a: 18(26)
b: 6(3405)
c: 21(35)
Thanks!!!p
Answers
a. 18(26) →18 × 26 = 468
b. 6(3405) → 6 × 3405 = 20,430
c. 21(35) → 21 × 35 = 735
The numbers in bold are the answers. Hope this helps and have a phenomenal day!
By using distributive property, the answers are :(a)468, (b) 20430, (c) 735.
Explain, distributive property.Distributive property is the mathematical property to solve expressions in the form of a(b + c), in which firstly bracket term is solve and then other terms are solved.
(a)
The given term is,
18(26),
According to distributive property, bracket changes in multiply.
Therefore, 18(26)⇒18×26=468.
(b)
The given term is,
6(3405),
According to distributive property, bracket changes in multiply.
Therefore, 6(3405)⇒6×3405=20430.
(c)
The given term is,
21(35),
According to distributive property, bracket changes in multiply.
Therefore, 21(35)⇒21×35=735.
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Which number is a factor of 20 and also a prime number?
A.
4
B.
5
C.
7
D.
10
Answers
thus B is your Answer.
What is the solution set of {x | x < -5} ∩ {x | x > 5}?
Answers
Mara ran 3 km north and then 4 km east. She will finish her run by running directly home. What was the total distance of her run?
Answers
Here's a crash course: any length of a side (a) squared plus the other side of a triangle (b) squared is equal to the long side (c) squared. This also works if you're trying to find the length of the diagonal of a square.
So, if Mara ran 3 km north then 4 km east, you would come out with the equation:
3^2+4^2=c^2
Solve using order of operations.
3^2+4^2=c^2
9+16=c^2
25=c^2
5=c
This is the length of the run directly home. To get the total distance run, just add up all the sides of her triangle-shaped run.
3+4+5=12
She ran 12 km.
Hope this helps!
The total distance of her run is 12 Km and this can be determined by using the Pythagorean theorem.
Given :
Mara ran 3 km north and then 4 km east.Mara will finish her run by running directly home.The following steps can be used in order to determine the total distance of Mara run:
Step 1 - The Pythagorean theorem can be used in order to determine the total distance of her run.
Step 2 - The Pythagorean theorem is given below:
[tex]\rm H^2 = P^2+B^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 3 - Now, substitute the values of the known terms in the above expression.
[tex]\rm H^2 = (3)^2+(4)^2[/tex]
H = 5 Km
Step 4 - So, the total distance of Mara run is given below:
Total distance = 5 + 4 + 3 = 12 Km
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