a chef is going to use a mixture of two brands of Italian dressing the first brand contains 9% vinegar in the second bracket a 14% vinegar the chef wants to make 390 mL of dressing that is 12% vinegar how much of each brand should she use
Answers
Solution:
Let us denote
x = first brand
y = second brand
then, according to the problem we have the following system of linear equations:
x + y = 390 (EQUATION 1)
0.09 x + 0.14 y = 0.12(390) =46.8 (EQUATION 2)
Solving for y in equation 1, we get:
y = 390-x (EQUATION 3)
now, replacing the above y into equation 2, we get:
0.09 x + 0.14 (390-x) = 46.8
this is equivalent to:
0.09 x + 54.6 - 0.14x = 46.8
this is equivalent to:
54.6 - 46.8 = 0.14x - 0.09 x
this is equivalent to:
7.8 = 0.05 x
solving for x, we get:
\(x\text{ = }\frac{7.8}{0.5}\text{ = 15.6}\)thus, replacing the above x into equation 3, we get:
y = 390-x = 390-15.6 = 374.4
then, we can conclude that the correct answer is:
x = first brand = 15.6
y = second brand = 374.4
Related Questions
Can someone help with my math cw ?
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Answer:
Step-by-step explanation:
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i need help can someone please help me
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The measure of the angle m∠ZYX of the trapezoid is equal to 139°
What is a trapezoid?A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.
3x + 19 + x + 1 = 180°
4x + 20 = 180°
4x = 180 - 20 {collect like terms}
4x = 160
x = 160/4 {divide through by 4}
x = 40
m∠ZYX = 3(40) + 19 = 139°.
WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.
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Jay and Ted observed two points, P and Q, on a number line.
A number line is shown from negative 1 to positive 1 with increments of 1 over 8. The numbers negative 1, negative 6 over 8, negative 4 over 8, negative 2 over 8, 0, 2 over 8, 4 over 8, 6 over 8 are labeled on the number line. A point P is shown at the first tick mark to the left of 0, and a point Q is shown at the first tick mark to the right of 0.
Jay said that the absolute values of the numbers represented by the two points are the same.
Ted said that the absolute values of the numbers represented by the two points are different.
Which of the following explains who is correct? (1 point)
Jay, because each point is fraction 1 over 8 unit from 0
Jay, because the distance between the points is fraction 1 over 8 unit
Ted, because the points are on different sides of 0
Ted, because the points are at different locations on the number line
Answers
Jay, because each point is fraction 1 over 8 unit from 0.
What is absolute length?
One way to think about a number's absolute value is as its distance from zero on the real number line.In addition, the distance between two real numbers is the absolute value of their difference.For instance, the absolute value of 12:
Since each number is 12 units away from zero, it is clear that 12 and -12 both have the same absolute value, which is 12. In order to determine the absolute value of a negative number, simply remove the minus sign. Absolute value is always positive.Absolute value is the length from which the number is from 0 in this they are adding two so it would mean that they are both 1/8 away from 0.
Hence, Jay, because each point is fraction 1 over 8 unit from 0.
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A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 62% C: Scores below the top 38% and above the bottom 19% D: Scores below the top 81% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 77.5 and a standard deviation of 8.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answers
Answer:
The minimum score required for an A grade is 88.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
\(\mu = 77.5, \sigma = 8.6\)
Find the minimum score required for an A grade.
This score is the 100 - 12 = 88th percentile, which is X when Z has a pvalue of 0.88. So X when Z = 1.175.
\(Z = \frac{X - \mu}{\sigma}\)
\(1.175 = \frac{X - 77.5}{8.6}\)
\(X - 77.5 = 8.6*1.175\)
\(X = 87.61\)
Rounding to the nearest whole number:
The minimum score required for an A grade is 88.
Sixty men can build a wall in 40days but though they begin the work together, 55 men quit every ten days. The Time needed to build the wall is?
Answers
It would take 370 days to build the wall with the given conditions.
If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:
60 men x 40 days = 2400 man-days
However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.
The number of man-days required for the first 10 days is:
60 men x 10 days = 600 man-days
The number of man-days required for the second 10 days is:
5 men x 10 days = 50 man-days
The total number of man-days required for the first 20 days is:
600 man-days + 50 man-days = 650 man-days
The remaining work can be completed by the 5 men in:
2400 man-days - 650 man-days = 1750 man-days
Therefore, the total time needed to build the wall is:
20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days
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Which of the following points could be the initial point of vector v if it has a
magnitude of 10 and the terminal point (-3,3) ?
(-9,-5)
(-13,-7)
(0,2)
(-0.3,0.3)
Answers
The initial point of vector v if it has a magnitude of 10 and the terminal point (-3,3) is option B (-9,-5).
How to find the vector component?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
Given;
The magnitude of 10 and the terminal point (-3,3).
v = ai + bj
v = \(\sqrt{a^2 + b^2}\)
10 = \(\sqrt{a^2 + b^2}\)
AB = (-3 - a)i + (3 - b)j
If we put (-9,-5)then
AB = (-3 - a)i + (3 - b)j
AB = (-3 + 9)i + (3 + 5)j
AB = 6i + 8j
Put the value in the vector magnitude
10 = \(\sqrt{a^2 + b^2}\)
= \(\sqrt{6^2 + 8^2}\\\\\sqrt{36+ 64}\\\\\sqrt{100}\)
10 = 10
Thus, The correct option is B (-9,-5).
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Which of the lines below is a line of symmetry?
Answers
D. Red
Why:
Because it is the only symmetrical line
Help!!!! neeed someone to answer this question please!! its due today!
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Answer:
1.)
a.)The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations.
b.)Medications such as naproxen, ibuprofen, and acetaminophen are most effective in reducing pain and swelling associated with muscle-related lower back pain. However, OTC medication is less likely to alleviate symptoms that stem from nerve compression or disc problems.
Step-by-step explanation:
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What term has the y, in the equation 3y + 4 = x
Answers
-12 will be the term for y
Let us suppose that x= 0
then we will get
3y + 4 = x
and then it will be
3y+ 4 = 0
Now, we will move 4 to the right hand side and it being positive this side will become negative on right hand side
3y= -4
now,
3y = 1/4
y = 1/[4*3]
y=1/12
y= - 12
Hence the answer will be y= -12
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Please answer this Calculus webwork question about differential equations:
Answers
Answer:
a)
\(4ydy = xdx\)
\(2 {y}^{2} = \frac{1}{2} {x}^{2} + c\)
\( {y}^{2} = \frac{1}{4} {x}^{2} + c \)
\( {y}^{2} - \frac{1}{4} {x}^{2} = c \)
b)
c = 4, so
\( {y}^{2} = \frac{1}{4} {x}^{2} + 4\)
\(y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} \)
\(y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} \)
PLEASE HELP!!!!!!!!!!!!!
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Hope this helps!
What is the range of the function shown on the graph
Answers
Answer:
-2<=y<=-7
Step-by-step explanation:
HELPPPPPPP PLEASEEEEE
Answers
Answer:
D
Step-by-step explanation:
Let A be a 7×5 matrix with rank equal to 4 and let b be a vector in R8. The four fundamental sub- spaces associated with A are R(A), N(AT ), R(AT ), and N (A).
Answers
The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.
Given that
Dimension of matrix = 7×5
Rank of matrix = 4
The range space of A,
Which is a subspace of R, is known as R(A).
It is made up of all conceivable linear combinations of A's columns.
The dimension of R(A) = rank of A,
Which is 4 in this case.
The null space of the transpose of A,
Which is also a subspace of R, is designated as N(AT).
All potential answers to the equation ATx = 0,
Where x is a R column vector, are included in it.
N(AT) has a dimension = nullity of A,
which in this case is 3 in this example.
The range space of the transposition of A, is designated as R(AT).
The rows of A are arranged in all conceivable linear configurations.
The rank of A = 4
Thus it equal to dimension of R(AT).
N(A) is the null space of A.
Axe = 0, where x is a column vector in R, are included in it.
The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).
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What is the slope of the following graph?
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if you double a number and then add 36, you get 4 over 11 (4/11) of the original number,
what is the original number?
Answers
Answer:
The original number is -22
Step-by-step explanation:
We'll label our mystery number x.
2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22
Plug in to confirm
-44 + 36 = -88/11S
8 = 8
Need help with my geometry homework grade due to
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The surface area of the base ball to the nearest whole number is 26 in²
What is surface area of a sphere?A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a sphere is expressed as;
SA = 4πr²
where r is the radius and it's calculated as;
C = 2πr
9 = 2πr
r = 4.5/π =
SA = 4 π × (4.5/π)²
SA = 81/π
SA = 26 in²( nearest whole number)
Therefore the surface area of the sphere is 26 in²
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x^2 = 16, therefore x = 4.
Is this a valid conclusion? If not, give a counterexample.
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Kaley plans to increase the amount of food she feeds her puppy each day
by x ounces. The expression 3x + 18 represents the total weight of food, in
ounces, Kaley will need for her puppy for the next three days.
PART A: Rewrite the
expression as a product of two factors.
PART B: How many ounces of food did Kaley feed her puppy each day before she increased the amount? Explain how you know.
Answers
Part A; The rewritten expression is; 3(x+ 6)
Part B: The amount of ounces of food Kaley fed her puppy each day before she increased the amount is 18 ounces
Linear expressions;According to the question;
The expression 3x + 18 represents the total weight of food, in ounces, Kaley will need for her puppy for the next three days.Part A;
Rewriting the expression as a product of two factors; we have;
3(x+ 6)Part B;
According to the expression;
The amount of ounces of food Kaley fed her puppy each day before she increased the amount is 18 ounces
This is so because she increase the amount by x ounces per day for the next 3 days which represents 3x and we are left with 18 ounces.
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After a teacher handed out m packs of notebooks with c notebooks in each pac,he has
13 notebooks left. How many notebooks did he have?
Answers
Compute for the mean expenses of the XYZ Corporation given the following: Name Total Sales Total Expenses Quezon City 14,950.00 4,933.50 Caloocan City 18,290.00 6,035.70 Marikina City 37,200.00 12,276.00 Cebu City 18,900.00 6,237.00 Davao City 45,000.00 14,850.00 Mandaluyong City 23,000.00 7,590.00 Cavite 22,000.00 7,260.00 Laguna 21,000.00 6,930.00 Manila 66,000.00 21,780.00 Iloilo 34,000.00 11,220.00
Answers
The computed mean expenses of the XYZ Corporation based on the given information are 9,911.22.
What is the mean?The mean refers to the average value.
The mean is computed as the quotient that results from dividing the total value of the data set by the number of items in the set.
Name Total Sales Total Expenses
Quezon City 14,950.00 4,933.50
Caloocan City 18,290.00 6,035.70
Marikina City 37,200.00 12,276.00
Cebu City 18,900.00 6,237.00
Davao City 45,000.00 14,850.00
Mandaluyong City 23,000.00 7,590.00
Cavite 22,000.00 7,260.00
Laguna 21,000.00 6,930.00
Manila 66,000.00 21,780.00
Iloilo 34,000.00 11,220.00
Total 99,112.20
Mean Expenses = 9,911.22 (99,112.20 ÷ 10)
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A box of cereal weighs 600 grams. How much is this weight in pounds? (Note: 1 kilogram = 2.2 pounds)
Answers
Answer:
0.882
Step-by-step explanation:
Finds out how much grams equal lbs then do 400 times the number you just found then you get your answer
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A circle is divided into 4 slices. The slices are arranged into the shape shown.
What shape would you get closer to if you kept cutting the circle into more
and more slices?
A. A circle, and then a cone
B. A parallelogram, and then a rectangle
C. A parallelogram, and then a triangle
D. A triangle, and then a trapezoid
Answers
Answer:
B
Step-by-step explanation:
A p e x :3
Answer: B a parallelogram and then a rectangle
Step-by-step explanation:
which is the domain of f(x) = 4^x
will give brainlist!
Answers
Answer:
all real numbers
Step-by-step explanation:
The domain is the input values
All values for x are valid as inputs to the function
The net for a cylindrical candy container is shown.
net of a cylinder with diameter of both circles labeled 1.6 inches and a rectangle with a height labeled 0.7 inches
The container was covered in plastic wrap during manufacturing. How many square inches of plastic wrap were used to wrap the container? Write the answer in terms of π.
1.84π square inches
2.4π square inches
5.68π square inches
6.24π square inches
Answers
The wrap has an area of 1.12π square inches.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, The net of a cylinder with a diameter of both circles labeled 1.6 inches.
So, The complete circle or the circumference of the circle will be the length of the wrap which is,
= 2π×0.8.
= 1.6π and the height of the wrap is 0.7 inches.
Therefore, the area of the wrap is 1.6π×0.7 square inches.
= 1.12π square inches.
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Answer: The real answer is 2.4π square inches (B)
Step-by-step explanation:
(Get ready for a long explanation)
So, we are trying to find the Surface Area of the cylinder.
We need to use the formula (SA = 2πr^2 + 2πrh)
Looks like a very long formula, but let do it in parts.
So the first part is just finding the area of the circle and multiplying by 2 because there are two bases. The area formula for circles is (πr^2)
But this time put a 2 in there. (2πr^2)
Okay lets get started. The diameter is 1.6. The radius is half the diameter, so divide 1.6 by 2 and you will get 0.8 which is the radius.
Now times the radius by itself (0.8 * 0.8 = 0.64) Now times that by 2 (0.64 * 2 = 1.28) The answer should be in terms of pi so just put the pi symbol next to 1.28 (1.28π)
On to the next part, (2πrh) you are basically taking the circumference of either circle base, and multiplying that by the height, which is (0.7)
The formula for Circumference is (2πr)
We already have the diameter so we don't need times the radius by 2.
So take the diameter of the circle base (1.6) and multiply that by the height, which is (0.7)
(1.6 * 0.7 = 1.12π)
Now for the last part, we need to add the two values together to find the surface area.
The first value we found is (1.28π ) and the second is (1.12π)
Now add (1.28π + 1.12π = 2.4π)
Answer: 2.4π square inches
Sorry for the really long explanation. I took the same test and I got it right so here is proof that it is correct. Have a great day y'all.
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Answers
For example, suppose you have the Cartesian equation of a line in the form:
y = mx + b
and the equation of a plane in the form:
ax + by + cz + d = 0
To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.
Here's an example:
Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.
If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:
2(1) + 3(3) + 4z + 5 = 0
Solving for z, we find that z = -1.5.
Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.
If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.
AP STATISTICS HELP PLEASE!!!!
Answers
There are 8 measurements that fall between days 20 and 22, out of 25 total measurements. So the relative frequency is 8/25 = 0.32.
PLS HELP WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Find the measure of arc BC.
Answers
Answer: A 129
Step-by-step explanation:
Because the 2 chords are the same (lines in the circle), the 2 arcs are the same create an equation that makes them equal
3x+24 = 4x -11 >bring x to one side by subtracting both sides by 3x
24 = x -11 > add both sides by 11
35 = x
Now that we have solved for x you need to plug that back into the equation for BC
BC= 4x-11
BC = 4(35) - 11
BC = 140 - 11
BC = 129 >A
Last week, a chocolate shop sold 9 ounces of white chocolate. It sold 9 9/10 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?
please answer asap
Answers
Solving the Question
We're given:
9 ounces of white chocolate sold\(9\dfrac{9}{10}\) times as much milk chocolate as white chocolate soldIf the shop sold " \(9\dfrac{9}{10}\) times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.
Multiply \(9\dfrac{9}{10}\) by 9 ounces:
\(9\dfrac{9}{10}\times9\)
Convert the fraction into an improper fraction:
\(=\dfrac{99}{10}\times9\)
Multiply:
\(=\dfrac{891}{10}\)
AnswerThe shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.
The stem-and-leaf plots list the ages of the people in Lee’s study group and in Paul’s study group.
Which statement is NOT correct?
a. Paul’s group has a wider range of ages.
b. The data for Paul’s group has two modes.
c. The median age in both groups is 44 years.
d. The mean age in both groups is between 41 and 42 years.
Answers
The false statement from the stem-and-leaf plot is given as follows:
b. The data for Paul’s group has two modes.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
The mode of a data-set is the data-set that appears the most times in a data-set.
Hence, for Paul's group, the mode is given as follows:
44.
As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.
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