Three-fourths of the fudge at the fudge shop on Monday morning contain nuts. Helena works at the fudge shop and prepares 12 3/4 pounds of fudge containing walnuts to fulfill a special order Monday afternoon. With this additional amount of fudge, there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday (a) Write an inequality that represents the scenario. Begin by defining your variable. (b) Solve the inequality. Show your work. (c) Fudge is packaged into 1-pound boxes. What is the fewest number of boxes of fudge at the fudge shop Monday morning?
Answers
At least means less than or equal to.
Fewest means the smallest number of boxes.
12 3/4 +x ≥ 29 5/8
x ≥ 16 7/8
The fewest number of boxes would be almost ≅ 42 boxes
Part A:
Let x denote the amount of fudge at the shop.
Helena prepares 12 3/4 pounds of fudge containing nuts.
Mathematically, the total amount of fudge on Monday will be
12 3/4 +x
Of this amount of fudge there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday
12 3/4 +x ≥ 29 5/8
Part B:
The inequality can be solved
12 3/4 +x ≥ 29 5/8
x ≥ 29 5/8- 12 3/4
x ≥ 29- 12 5/8- 3/4 The whole numbers are subtracted and the fractions are solved separately to avoid long calculations.
x ≥ 17 (5-6)/8
x ≥ 17 - 1/8
x ≥ (136-1)/8
x ≥ (135)/8
x ≥ 16 7/8
Part C :
To find the number of boxes we divide the equal number of pounds .
12 3/4 + 29 5/8
12 + 29 3/4 + 5/8
41 11/8
42 3/8
The fewest number of boxes would be almost ≅ 42 boxes
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Related Questions
a tank truck holds 33.8 kl of oil. How many gallons does it hold
Answers
what’s the working out to this question as i know the answer is 2.94cm squared but the working out is wrong!
Answers
Answer:
2.94
Step-by-step explanation:
A = 6a²
6 × .7² = 2.94
.7 × .7 = .49
6 × .7 = 2.94
\( a = 6a {}^{2} \)
a is the side
area -6 x 0.7
An orchard sells 6 lb of apples for $13.50.There is a proportion relationship between the cost and the number of apples PLS HELP ME ASAP IT DUE IN 1 MIN
Answers
Answer:
Step-by-step explanation:
What is the area of the triangle?
Answers
Answer:
52
Step-by-step explanation:
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 302 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 89 mg of cholesterol. By eating 3 eggs and 1 cupcake, a child consumes 844 mg of cholesterol. How much cholesterol is in each item?
Answers
One egg contains 17.88 mg of cholesterol, one cupcake contains 83.33 mg of cholesterol, and one slice of pizza contains 27.22 mg of cholesterol.
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
Let's call the amount of cholesterol in one egg "x".
Then, the amount of cholesterol in one cupcake is "y" and the amount of cholesterol in one slice of pizza is "z".
From the first statement, we can set up the equation:
x + y + z = 302
From the second statement, we can set up another equation:
3y + 4z = 89
And from the third statement, we can set up a third equation:
3x + y = 844
Now we have three equations with three unknowns, so we can solve for the values of x, y, and z.
Starting with the third equation:
3x + y = 844
y = 844 - 3x
Next, we can substitute this expression for y in the first equation:
x + (844 - 3x) + z = 302
4x + z = -542
z = -542 - 4x
Finally, we can substitute these expressions for y and z in the second equation:
3y + 4z = 89
3(844 - 3x) + 4(-542 - 4x) = 89
2532 - 9x + -2168 - 16x = 89
536 - 25x = 89
25x = 536 - 89
25x = 447
x = 17.88
Hence, one egg contains 17.88 mg of cholesterol, one cupcake contains 83.33 mg of cholesterol, and one slice of pizza contains 27.22 mg of cholesterol.
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Almonds are sold in 8-ounce and 20-ounce packages. What is the least number of ounces you can buy of each package to have equal amounts of each package size?
The least number of ounces you can buy of each package to have equal amounts of each package size is ounces
Answers
Answer:
40
Step-by-step explanation:
\(8=2^3 \\ \\ 20=2^2 \times 5 \\ \\ \lcm(8,20)=2^3 \times 5=40\)
Which point would be a solution to the system of linear inequalities shown below?
Answers
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
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Can someone please answer and provide an explanation for these problems?
Answers
Step-by-step explanation:
The way you can think about volume is that we have some cross sectional area times the height of the solid.
27.
The volume of a square based pyramid is
\(v = {s}^{2} ( \frac{h}{3} )\)
where h is the height of the pyramid
s is the side length of the square base.
S=7
h=12
\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)
28. The volume of a rectangular prism
\(v = l \times w \times h\)
where l is length
w is width
h is height
\(v = 11 \times 11 \times 8 = 968\)
29.
Use the same formula in 27
\(v = 100(3) = 300\)
30.
Volume of a Cylinder is
\(v = \pi {r}^{2} h\)
where r is the radius of the circle
where h is the height
r is half of the diameter
The diameter is 22, thus the radius is 11.
\(v = {11}^{2} (8)(\pi)\)
\(v = 968\pi\)
pi is approximately 3.14
\(v = 3041.06\)
31. Volume of A Sphere
\( \frac{4}{3} \pi {r}^{3} = v\)
The radius is half of diamter, thus r=7
\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)
Expand and simplify (2x - 1)(x + 3)(x - 5)
Answers
Answer:
2x^3-5x^2-28x+15 -------------------------expanded
2x^3-5x^2-28x+15--------------------simplified
Step-by-step explanation:
\left(2x-1\right)\left(x+3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
simplyfied
\left(2x^2+5x-3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
=2x^3-5x^2-28x+15
Estimate 112% of 502. Round each number to the nearest ten.
Answers
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{112\% of 502}}{\left( \cfrac{112}{100} \right)502}~~\approx~~ 562.2\)
How tall is the tree?
5ft
35°
-20ft-
[?]ft
Round to the nearest foot.
Answers
Answer:
19
Step-by-step explanation:
tan35=x/20
20tan35=x
x=14.0041507641942
x+5=19.0041507641942
The nearest foot is 19
Look at this set of 7 numbers:
9 6 1 4982
By how much would the mode
increase if the number 3 were
added to the set?
Answers
Therefore, the mode will not increase and will still be 9.
What is mode?In statistics, the mode is the value that appears most frequently in a data set. It is one of the measures of central tendency, along with the mean and median. The mode is often used to describe the most common or popular value in a set of data. If a data set has more than one value that occurs with the same highest frequency, it is said to have multiple modes. If no value is repeated in the set, then it has no mode.
Here,
The mode is the number that appears most frequently in a set of numbers.
In the set {9, 6, 1, 4, 9, 8, 2}, the mode is 9 because it appears twice, which is more than any other number in the set.
If we add the number 3 to the set, then the new set becomes {9, 6, 1, 4, 9, 8, 2, 3}.
The mode of the new set will increase if the number 3 appears more times than any other number. However, since 3 is a new number that was not originally in the set, it cannot be the mode.
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The conversion of ammonium cyanide to urea is a second-order reaction. This means that the concentration C of ammonium cyanide at time t is given by 1/C = kt + 1/C0, where C0 is the initial concentration and k is the rate constant. Assume the initial concentration is known to be 0.1 mol/L exactly. Assume that time can be measured with negligible uncertainty.
a. After 45 minutes, the concentration of ammonium cyanide is measured to be 0.0811 ? 0.0005 mol/L. Estimate the rat? constant k, and find the uncertainty in the estimate.
b. Use the result in part (a) to estimate the time when the concentration of ammonium cyanide will be 0.0750 mol/L, and find the uncertainty in this estimate.
Answers
Answer:
your answer could be A
Step-by-step explanation:
what are exchange rates?
Answers
Answer:
Step-by-step explanation:
Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.
A class quiz has 5 multiple-choice questions and each question has 4 possible answers (A, B, C, or D). Which spinner would best simulate this scenario?
A spinner with 2 equal sections.
A spinner with 4 equal sections. (correct)
A spinner with 6 equal sections.
A spinner with 8 equal sections.
Answers
so your question is
A class quiz has 5 multiple-choice questions and each question has 4 possible answers (A, B, C, or D). Which spinner would best simulate this scenario?
A spinner with 2 equal sections.
A spinner with 4 equal sections.
A spinner with 6 equal sections.
A spinner with 8 equal sections.
Ur answer is B..... hope this helps .... please mark Brainliest , or u don't have to its fine
Find the numbers with the following property three times the sum of four and a number is less than seven times the same number
Answers
Let's represent the number with the variable "x". According to the given property, we can write the following equation:
3(x + 4) < 7x
Now, let's solve this inequality to find the range of numbers that satisfy the property.
3x + 12 < 7x
Subtract 3x from both sides:
12 < 4x
Divide both sides by 4 (since the coefficient of x is 4):
3 < x
So, the range of numbers that satisfy the given property is x > 3.
Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:
According to the problem, we know that:
3(4 + x) < 7x
Simplifying:
12 + 3x < 7x
Subtracting 3x from both sides:
12 < 4x
Dividing both sides by 4:
3 < x
So the number we're looking for must be greater than 3.
I need help please
here is the picture is about Row Ops
Answers
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
\(\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right]\)
Reducing row matricesFrom the question, we are to perform the given row operation on the given matrix
From the given information, the given matrix is:
\(\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right]\)
We are to carry out the operation
Add -4(row 1) to row 3
This means we should multiply row 1 by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result to row 3
4 -1 6 | -8
-4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
\(\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right]\)
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The administrator of a $200,000 trust fund must adhere to following guidelines.
a. The money may be invested in three different types of securities: a utilities stock paying a 9% dividend, an electronics stock paying a 4% dividend, and a bond paying 5% interest.
b. The amount invested in the stocks cannot be more than half the total amount invested; the amount invested in the utilities stock cannot exceed $40,000; and the amount invested in the bond must be at least $70,000.
c. The total amount need not be fully invested at any one time.
Required:
Setup an LP problem to maximize profit.
Answers
Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
- Write a two-column proof. Given BF bisects angle AFC and angle CFD congruent angle BFC. Prove angle AFB congruent angle CFD
Answers
Since BF bisects angle AFC, AFB and BFC would be the same angle. The sum of AFB + BFC + CFD = 180°. And since CFD is congruent to BFC, All the three angles are the same. So AFB would be equal to CFD
Question 3(Multiple Choice Worth 1 points)
(05.02 MC)
Solve the system of equations using substitution.
4x + 2y = 6
x = 2y + 4
(1, 1)
(2,-1)
(8,2)
(10,3)
Answers
Answer:
(2,-1)
Step-by-step explanation:
We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:
4(2y + 4) + 2y = 6
Simplifying the left side:
8y + 16 + 2y = 6
Combining like terms:
10y + 16 = 6
Subtracting 16 from both sides:
10y = -10
Dividing both sides by 10:
y = -1
Now that we know y, we can use the second equation to find x:
x = 2y + 4
x = 2(-1) + 4
x = 2
Therefore, the solution to the system of equations is (x, y) = (2, -1).
The correct answer choice is (2, -1).
Given the sequence defined by $a_n = 48 - 3n$, find all possible values of $k$ so that \[a_1 + a_2 + a_3 + \cdots + a_k = 330.\]
Answers
Answer:
k = 11 or 20
Step-by-step explanation:
The sum of terms of an arithmetic sequence is given by ...
Sn = (a1 +an)(n/2)
We want to find the value of n for a particular series to have a particular sum.
__
parametersThe series of interest is defined by ...
an = 48 -3n
so, the first term is ...
a1 = 48 -3(1) = 45
The k-th term is ...
ak = 48 -3k
__
sumThen the sum is ...
Sk = (45 +(48 -3k))(k/2)
We want this value to be 330, so we have ...
330 = (93 -3k)(k/2)
__
solution220 = (31 -k)k . . . . . . . . multiply by 2/3
k² -31k +220 = 0 . . . . . in standard form
We want factors of 220 that total 31.
220 = (1)(220) = (2)(110) = (4)(55) = (5)(44) = (10)(22) = (11)(20)
The last of these pairs totals 31, so we have ...
(k -11)(k -20) = 0 . . . . . factored form of the equation
k = 11 or k = 20 . . . . . values of k that make the factors zero
Possible values of k are 11 and 20.
Help with this question
Answers
Answer:
(x - 4)(x - 7)
Step-by-step explanation:
x² - 11x + 28
consider the factors of the constant term (+ 28) which sum to give the coefficient of the x- term (- 11)
the factors are - 4 and - 7 , since
- 4 × - 7 = + 28 and - 4 - 7 = - 11
then
x² - 11x + 28 = (x - 4)(x - 7) ← factored form
Consider the line y = 7x-3.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answers
Answer:
Gradient of parallel line= 7
Gradient of perpendicular line \( = - \frac{1}{7} \)
Step-by-step explanation:
The equation of the line is already in slope-intercept form (y= mx +c). This means that the coefficient of x is the gradient and the constant -3 is the y-intercept of the line.
y= 7x -3
Gradient= 7
Parallel lines have the same gradient.
Thus, the slope of the line parallel to this line is also 7.
The product of the gradients of 2 perpendicular lines is -1.
(Gradient of perpendicular line)(7)= -1
Gradient of perpendicular line
= -1 ÷7
\( = - \frac{1}{7} \)
Hello! :)
Parallel lines have the same slope.
If one line has a slope of 7, then the line parallel to it has a slope of 7 as well.
Now, perpendicular lines have slopes that are opposite reciprocals. It means we take the slope of one line, make it negative, and flop it over:
\(7\\-7\\-\frac{1}{7}\)
Hope it helps. Feel free to ask me if you have any questions.
~A determined teen
\(MagicalNature\)
In the accompanying diagram, angle ACD is an exterior angle of triangle ABC, angle A =3x, angle ACD is =5x, and angle B=50. What is the value of x ?
Answers
The value of x in the triangle ABC is 25.
How to find angles in a triangle?The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.
The exterior angle of the triangle is given as m∠ACD = 5x.
The sum of angle in a triangle is equals to 180 degrees. Therefore,
3x + 50 + (180 - 5x) = 180
3x + 50 - 5x + 180 = 180
3x - 5x + 50 + 180 = 180
-2x + 230 = 180
subtract 230 from both sides
-2x + 230 - 230 = 180 - 230
-2x = -50
divide both sidesby -2
-2x / -2 = -50 / -2
x = 25
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Helppppppp I’m on a time crunch
Answers
Answer:
55M
Step-by-step explanation:
Answer:
It might be 14.6
Step-by-step explanation:
nDont put this as the answer, I really dont know if its correct.
Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?
Answers
Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.
Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter
Time taken by Peter = 2PM - 10AM
= 4 hrs
Speed of Peter = 84 km/h
Distance travelled by Peter = speed × time
= 84 × 4
= 336 km
So, the distance between Town A and Town B = distance travelled by Peter = 336 km.
Now, we will calculate time taken by William.
Speed of William = 70 km / hr
Distance travelled by William = distance between Town A and town B = 336 km
Time taken by William = distance / speed
= 336 / 70 hr
= 4.8 hr
This can b converted into hrs and minutes
4.8 hr = 4 hr + 0.8 × 60
= 4 hr 48 mins
Time William took off = 10 AM - 1hr 25 mins
= 8:35 AM
Now, we will calculate the time William would reach town B.
Time = 8:35 + 4hr 48 mins
= 1:23 PM
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I need help with this
Answers
Answer:
1500
Step-by-step explanation:
Number of boxes = 12
Number of pencils in each box = 125
Total number of pencils
= 12 × 125
= 1500 pencils
1) 70% of what number is 28?
Answers
Answer: 40
Step-by-step explanation: 40*.7 is 28 so that's the answer. How I got the answer was I did 28/.7 to get 40
Hope this helps and brainliest would be appreciated
Reflections of Shapes
Graph the image of the figure using the transforma
1) reflection across the x-axis
Answers
A graph of the image of the figure after a reflection across the x-axis is shown below.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
By applying a reflection over or across the x-axis to triangle GLQ, we have;
(x, y) → (x, -y)
G (3, 4) → (3, -(4)) = G' (3, -4)
L (1, 2) → (1, -(2)) = L' (1, -2).
Q (4, -1) → (4, -(-1)) = Q' (4, 1)
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What is statistical power and how would you calculate it?
Answers
Answer:
The statistical power of a hypothesis test is the probability of detecting an effect, if there is a true effect present to detect. Power can be calculated and reported for a completed experiment to comment on the confidence one might have in the conclusions drawn from the results of the study.
I hope it's helpful!