a chef is going to use a mixture of two brands of italian dressing. the first brand contains 5% vinegar and the second brand contains 15% vinegar. the chef wants to make 300 milliliters of a dressing that is 9% vinegar. how much of each brand should she use?
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The chef will end up with 300 mL of a dressing that is 9% vinegar. Let's calculate how much vinegar will the dressing have:
Therefore,
[tex]v=\frac{300\times9}{100}\rightarrow27[/tex]He'll have 27mL of vinegar.
Now, we know that x mL of the 5% dressing plus y mL of the 15% one will give the chef a total of 27mL of vinegar. Therefore,
[tex]\begin{gathered} x(\frac{5}{100})+y(\frac{15}{100})27 \\ \\ \rightarrow0.05x+0.15y=27 \end{gathered}[/tex]And that x mL of the 5% dressing plus y mL of the 15% one will give the chef a total of 300mL of dressing. Therefore,
[tex]x+y=300[/tex]We have a system of equations:
[tex]\mleft\{\begin{aligned}0.05x+0.15y=27 \\ x+y=300\end{aligned}\mright.[/tex]Let's clear y from equation 2 and replace in equation 1:
[tex]\begin{gathered} x+y=300\rightarrow y=300-x \\ \\ 0.05x+0.15y=27\rightarrow0.05x+0.15(300-x)=27 \\ \rightarrow0.05x+45-0.15x=27\rightarrow-0.10x=-18\rightarrow x=\frac{-18}{-0.10} \\ \\ \rightarrow x=180 \end{gathered}[/tex]Thereby,
[tex]\begin{gathered} y=300-x\rightarrow y=300-180 \\ \\ \rightarrow y=120 \end{gathered}[/tex]The chef would have to use 180mL of the dressing that's 5% vinegar, and 120mL of the one that's 15% vinegar.
Related Questions
On a construction site, a winch is used to wind cable onto the drum of the winch
Answers
Solution
Formula
[tex]P=\frac{K}{D}[/tex]Given parameters
[tex]\begin{gathered} P=8400 \\ D=3 \end{gathered}[/tex][tex]3in\text{ =0.25foot}[/tex]Now, substitute the given parameters into the formula
[tex]\begin{gathered} 8400=\frac{K}{3} \\ \\ K=8400\times0.25 \\ K=2100 \end{gathered}[/tex]The final answer
2100 foot -pounds
Answer the questions below using the given scatter plot. a. The scatter plot shows what kind of association?Circle one. Positive, Negative, Noneb. Finish the following sentence.As the number of peaches sold_________,the price of peaches____________.
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a) The scatter plot shows a negative association
b) As the number of peaches sold increases, the price of peaches decreases
given BD is the angle bisector of ABC complete the flowchart proof below .Note that the last statement and reason has been filled for you
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Box 1:
Statement
[tex]\bar{BD}\text{ bisects }\angle ABC[/tex]Reason
Given
Box 2 (left):
Statement
[tex]\bar{AD}\cong\bar{CD}[/tex]Reason
A segment bisector divides a segment into two congruent segments
Box 3:
Statement
[tex]\bar{BD}\cong\bar{BD}[/tex]Reason
Reflexive property
Box 4:
Statement
[tex]\angle ADB\text{ }\cong\text{ }\angle CDB[/tex]Reason
All right angles are congruent
Martina purchased a prepaid card for $30. Long distance calls cost 11 cents a minute using this card. Martina used her card only once to .ake a long distance call. If the remaining credit on her card is $28.46, how many minutes did her call last.
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we get that
[tex]\begin{gathered} 28.46+0.11t=30 \\ t=\frac{30-28.46}{0.11}=14 \end{gathered}[/tex]so her call last 14 minutes
Find the standard deviation of the data set.**Round your answer to the nearest hundredth.48, 30, 24, 42, 60, 24
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Ok, let's find the standard deviation of the data set:
Step 1: calculate the mean.
(48+30+24+42+60+24)/6=228/6=38
Step 2: calculate the square of the distance from the mean for each piece of data.
|48-38|²=10²=100
|30-38|²=8²=64
|24-38|²=14²=196
|42-38|²=4²=16
|60-38|²=22²=484
|24-38|²=14²=196
Step 3: add the values that resulted from step 2.
100+64+196+16+484+196=1056
Step 4: divide by the number of data.
1056/6=176
Step 5: take the square root.
√176≈13.27
Finally we obtain that the standard deviation is 13.27.
Geometry - Triangles > Interior angles of a trlangle 20. The three angles of a triangle measure x°, yº and 17. Which of the following statements must be true? y=180- x+y=17 y+x= 180 - 17 y=x+ 17
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Given:
Three angles of a triangle are x°, y° and 17°.
The objective is to select the correct statement.
By the angle sum property of triangle, the sum of all the angles of a triangle will be 180°.
Then, the sum of given three angles will be,
[tex]\begin{gathered} x\degree+y\degree+17\degree=180\degree \\ x\degree+y\degree=180\degree-17\degree \end{gathered}[/tex]Hence, the correct statement is y+x=180-17.
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
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We have the expressions:
[tex]y>2x+4[/tex][tex]y+x\le6\Rightarrow y\le6-x[/tex]Now, we will graph:
Since it is an intersection, we will graph the values contained by both inequalities.
b.) What does the point (2.1, 18.6) represent? Select]
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Based on the information of the graph, you can notice that the point (2.1 , 18.6) corresponds to point B.
The point (2.1 , 18.6) means that for 2.1 free throw attemps per game, there are approximately 18.6 points per game.
1500.000 to the nearest hundredth
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1500.000 to the nearest hundredth is 1500.00
Given that there is a zero in the thousandths position, the zero in the hundredths position is rounded to zero.
whats 9 9/35- 6 8/10
Answers
You have the following expression:
9 9/35 - 6 8/10
In order to simplify the prevous expression, first convert the mixed number to normal fractions, just as follow:
9 9/35 = 9/1 + 9/35 = (315 + 9)/(35) = 324/35
6 8/10 = 6/1 + 8/10 = (60 + 8)/10 = 68/10 = 34/5
next, subtract the previous result:
324/35 - 34/5
multiply the second fraction by 7/7 to obtain two homogeneus fractions:
(34/5)(7/7) = 238/35
then, you have
324/35 - 34/5
= 324/35 - 238/35
= (324 - 238)/35
= 86/35
Hence, the simplied expression is 86/35
Answer:
For decimals, it is: 2.45714285714
For fractions, it is: [tex]2\frac{22857142857}{50000000000}[/tex]
Step-by-step explanation:
Please brainliest.
Sanford's gym coach made him run 20 laps on a 600-m track. How many kilometers did he run? How many miles? Round youranswers to two decimal places, if necessary.wSanford rankilometers, which ismiles.Х5HELP?? Stuck
Answers
First, determine how far he ran in meters
20 laps * 600 meters
12000 meters
We can find the number of kilometers by using the conversion factor 1000meters = 1 km
12000meters * 1 km/1000m = 12 km
Now we can convert km to miles
1 km = .62137119 miles
12 km * .62137119 miles/ 1 km
7.45645428
Rounding to 2 decimal places
7.46 miles
Can you please help me complete. I am reviewing for a final
Answers
Given:
Kayakers pulling a raft. One kayaker pulls with a force of F1=(190, 160) and the other kayaker pause with a force of F2=(128, -121)
Required:
We need to find the angle between F1 and F2
Explanation:
[tex]undefined[/tex]Stan and Olga are considering buying a sheep farm. A surveyorhas supplied them with the given accurate sketch. Find the areaof the property, giving your answer in:km2
Answers
The approximate area of the property is;
[tex]75km^2[/tex]Here, we want to calculate the area of the property
Firstly, we can see that the farm is divided into two shapes (two triangles actually)
By finding the areas of the two triangles, adding tehm up, we will have the area of the farm
Firstly, we need to get all the sides of the triangles
Let us start with the triangle below
It is simply the length of the diagonal QS
We can find this by the use of cosine rule
We have this as;
[tex]\begin{gathered} p^2=q^2+s^2-2qsCosP \\ p^2=8^2+12^2\text{ -2(8)(12)Cos70} \\ p^2\text{ = 64 + 144 - 65.67} \\ p\text{ = 11.93 km} \end{gathered}[/tex]Now, by using this calculated diagonal, we can get the missing side of the top triangle
We have the missing side calculated as follows;
[tex]\begin{gathered} q^2=r^2+s^2-2rsCosQ \\ q^2=11.93^2+10^2-2(11.93)(10)Cos30 \\ q^2\text{ = 35.69} \\ \text{q = 5.97 km} \end{gathered}[/tex]So, we now use Heron's formula for each of the two triangles before adding up
For triangle QPS, we have;
[tex]\begin{gathered} A\text{ = }\sqrt[]{s(s-a)(s-b)(s-c)} \\ a,b\text{ and c are the sides} \\ \text{s = }\frac{a+b+c}{2}\text{ = }\frac{8+12+11.93}{2}\text{ = 15.965} \\ \\ A\text{ = }\sqrt[]{15.965(15.965-8)(15.965-12)(15.965-11.93)} \\ A\text{ = }\sqrt[]{15.965(7.965)(3.965)(4.035)} \\ A=45.105km^2 \end{gathered}[/tex]For triangle QRS, we have;
[tex]\begin{gathered} A\text{ = }\sqrt[]{s(s-a)(s-b)(s-c)} \\ a,b,c\text{ are the sides} \\ s\text{ = }\frac{a+b+c}{2}\text{ = }\frac{10\text{ + 5.97+11.93}}{2}\text{ = 13.95} \\ \\ A\text{ = }\sqrt[]{13.95(13.95-10)(13.95-5.97)(13.95-11.93)} \\ A=29.803km^2 \end{gathered}[/tex]The area of the sheep farm is the sum of both areas
We have this as;
[tex]\text{Total area = 29.803 + 45.105 = 74.908 km}^2[/tex]The formula for the volume of a rectangular prism is V = lwh. What is the formula when solved for w?o202IhW=VwV?hVuw=
Answers
Formula for the Volume of rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h; \\ l\text{ is long} \\ w\text{ is width} \\ h\text{ is high} \end{gathered}[/tex]They ask you solve the expresion for w, that means that you have to find a expression like w=?
To do that, you should be move l and w to the other side of equation...
Start moving l,
Tell me, what is doing l to w.. what math operation...
??
Exactly, multiply.. the pass to other side to do the oposite operation.. in this case divide..like this..
[tex]\frac{V}{l}=w\cdot h[/tex]we do the same with h.. and thats all.. then we take:
[tex]\frac{V}{l\cdot h}=w[/tex]or the same
[tex]w=\frac{V}{l\cdot h}[/tex]That's your answer
A mountain bike has a cash price of $600,00. Eric purchases the bike by making a down payment of $18.00 and 24 payments of $33.71 Find the finance charge.O A $58200B. $227.04OC. $291.00 D. $18.00
Answers
From the statement, we know that:
• the original price of the bike is $600.00,
,• Eric purchases the bike by making a down payment of $18.00,
,• and 24 payments of $33.71.
The final price of the bike is the sum of the down payment and the 24 payments:
[tex]FP=\text{ \$18.00 }+24\times\text{\$33.71}=\text{ \$827.04.}[/tex]The finance charge is the difference between the final price and the original price:
[tex]FC=FP-OP=\text{ \$827.04}-\text{\$600.00}=\text{ \$227.04.}[/tex]AnswerB. $227.04
Asha has $100 on a movie theatergift card. Each time she buys a ticketto a movie it costs her $8.75. Writean equation that Asha can use to findX, the number of tickets she can buyif she wants to keep a $15 balance onthe gift card.
Answers
We can write an equation for the balance of the gift card.
We know that if she doesn't buy any ticket (x = 0), the balance will be $100, which is the initial balance.
Each increase in x, is a decrease of 8.75 for the balance. This represents the slope of the equation, as there is not other term.
Then, we can write the equation as:
[tex]y=100-8.75x[/tex]If she wants to know how many tickets she can buy to have a $15 balance (y = 15), we can use the equation as:
[tex]\begin{gathered} y=15 \\ 100-8.75x=15 \\ 100-15=8.75x \\ 85=8.75x \\ x=\frac{85}{8.75} \\ x\approx9.71 \end{gathered}[/tex]She can buy up to 9 tickets (if she buys 10 tickets, she will have less than $15).
Answer:
The equation is y = 100 - 8.75x.
X = 9 tickets for a balance of $15.
if ×=10 what is the value of 2×+5
Answers
In order to calculate the value of 2x + 5 if x=10, we would need to substitute in the expression 2x + 5 the variable x with the number 10.
Therefore, 2x + 5 if x=10 would be equal to:
2(10)+5=20+5=25
Therefore, the value of 2×+5 if x=10 would be 25
Which ordered pair is a solution to the system of equations?Note: Use the substitution method.{x=1/4y+2 and −4x+3y=4 (−1/12, −2/63 )(7/2, 6 )(5/4, 3 )(−1/4, 1 )
Answers
Given the system of equations
[tex]\begin{gathered} x=\frac{1}{4}y+2 \\ -4x+3y=4 \end{gathered}[/tex]Substitute x =1/4y+2 in the second equation
[tex]-4(\frac{1}{4}y+2)+3y=4[/tex]Simplify
[tex]\begin{gathered} -y-8+3y=4 \\ 2y-8=4 \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} 2y-8+8=4+8 \\ 2y=12 \\ \frac{2y}{2}=\frac{12}{2} \\ y=6 \end{gathered}[/tex]Then substitute y = 6 in x
[tex]x=\frac{1}{4}(6)+2=\frac{6}{4}+2=\frac{7}{2}[/tex]Answer: (7/2, 6)
I dont know how to find the mean or what a mean is
Answers
To find the mean simply add all the numbers, and then divide by how many numbers are.
We have 6 values (numbers)
-54 + (-32)+ (-70)+(-25)+(-65)+(-42)
-288
-288 /6 = -48
If a submarine is 80 m below sea level if it dives another 15 m, how far below sea level is the submarine now?
Answers
ANSWER
EXPLANATION
The submarine is initially 80 m below sea level.
It then dives another 15 m.
That means it goes 15 m lower than its original position.
Sea level is equivalent to 0 m.
Therefore, the submarine being initially 80 m below sea level means that it was at -80 m.
Now, it goes 15 m lower,
solve the right triangle and round decimal answers to the nearest tenthi know its either option a or c but im not 100% sure which one
Answers
Step 1
Name all sides
Hypotanuse = 16 side facing right angle
Opposite = y side facing given angle
Adjacent = x
90 +
Step 2
Find the values of x and y
[tex]\begin{gathered} \theta\text{ = 76} \\ \sin \theta\text{ = }\frac{\text{Opposite}}{\text{Hypotanuse}} \\ \sin 76\text{ = }\frac{y}{16} \\ 0.97\text{ = }\frac{y}{16} \\ \text{Cross multiply} \\ y\text{ = 0.97 x 16} \\ y\text{ = 15.52} \\ y\text{ = 15.5} \end{gathered}[/tex][tex]\begin{gathered} \cos \theta\text{ = }\frac{adjacent}{\text{hypotanuse}} \\ \cos 76\text{ = }\frac{x}{16} \\ 0.24\text{ = }\frac{x}{16} \\ \text{Cross multiply} \\ x\text{ = 0.24 x 16} \\ x\text{ = 3.8}5 \\ x\text{ = 3}.9 \end{gathered}[/tex]Addison Rae Drank 3.5 bottles of water Yesterday. Each bottle Contained 1.2 pints of water what was the number of pints of water Addison rae drank yesterday
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Find the points of inflection. f(x) = x3 + 3x2 - X - 24 O (-1,3) 0 (-1,0) O (1,8) 0 (-1, -21)
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a) what is KN+IKb)What is the coordinate of midpoint GO
Answers
Given the figure of a number line
a) We will find the value of KN+IK
As shown in the figure:
[tex]\begin{gathered} K=0 \\ N=3 \\ I=-2 \\ So, \\ KN+IK=0\times3+(-2)\times0=0+0=0 \end{gathered}[/tex]So, the answer will be KN+IK = 0
b) )What is the coordinate of midpoint GO
As shown:
[tex]G=-4,O=4[/tex]The midpoint =
[tex]\frac{-4+4}{2}=\frac{0}{2}=0[/tex]So, the answer will be the midpoint will be k = 0
Using the chart above of 500 people go in for surgery how many are going for eye surgery?
Answers
From the graph (a pie chart), we have that the percent of people that go to Eye Surgery is 5%.
We have that total is 500 people. We, therefore, need to get the 5% of 500 to get the number of those that go for eye surgery, then:
[tex]\frac{5}{100}\cdot500\text{ = 25}[/tex]Then, for eye surgery, we have 25 people in total, according to chart.
Which expression uses the commutative property to make it easier to evaluate ( – 5). 11. ? 3 5 11 O A. (-). 11 $). O B. (-6).3. OC. . 11.(-5) O D. (-5) 5.11 SUBN
Answers
I’m here to help you. Just give me a few mins to look over your question.
Step 01:
Data
(-6/5) *11 * 3/5
Commutative property
Step 02:
We must analyze the expressions to find the solution.
Commutative property
[tex]\frac{5}{3}\cdot11\cdot(-\frac{6}{5})[/tex]That is the solution .
A sporting goods salesperson sells 2 fishing reels and 5 rods for $365. Thenext day, the sales person sells 4 reels und 2 rods for S290. How much does each cost?(Solve by Setting-up a system of two equations in two variables)
Answers
Let's use the variable x to represent the cost of one fishing reel and the variable y to represent the cost of one rod.
If 2 fishing reels and 5 rods cost $365, we have the equation:
[tex]2x+5y=365[/tex]Then, if 4 reels and 2 rods cost $290, we have the second equation:
[tex]4x+2y=290[/tex]Let's divide the second equation by 2 and isolate the variable y:
[tex]\begin{gathered} 2x+y=145 \\ y=145-2x \end{gathered}[/tex]Then, let's use this value of y in the first equation:
[tex]\begin{gathered} 2x+5(145-2x)=365 \\ 2x+725-10x=365 \\ -8x=365-725 \\ -8x=-360 \\ x=45 \\ \\ y=145-2\cdot45 \\ y=145-90 \\ y=55 \end{gathered}[/tex]So the cost of one reel is $45 and the cost of one rod is $55.
I need help with this practice from my trigonometry prep book I attempted this previously, struggling, I got two answers and I’m not sure if I’m correct so I would like more clarification
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Therefore:
[tex]\cos (\alpha-\beta)=-\frac{63}{65}[/tex]Gerd is considering an account that earns 6% interest per annum compounded monthly. What is the annual percentage yield (APY)? Give your answer as a percent rounded to the nearest tenth (e.g. 5.1%). Do not include the percentage sign (%) in the answer box below.
Answers
Data
Interest = 6%
Annual percentage yield = ?
APY = (1 + r/n)^n -1 12 is because a year has 12 months
6% = 0.06
APY = (1 + 0.06/12) ^12 - 1
APY = (1 + 0.005)^12 - 1
APY = (1.005)^12 - 1
APY = 1.062 - 1
APY = 0.062 or 6.2%
mrs. Ruiz planted 14 flowers in three plots she planted 4 flowers in 1 blue pot and split the rest equally between 2 red plots add symbols to the equation below then solve the equation to find the number of flowers mrs. Ruiz planet and each of the two red plots
Answers
Total numbers of flowers = 14
4 flowers in the blue pot
Then, 14 - 4 = 10 plants
10 plants were equally planted in 2 red pots.
10 = 2r
r = 5 flowers
Mrs Ruiz planted 4 flowers in the blue pot and 5 flowers in each of the red pots.