A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 140 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?

Answers

Answer 1
Let x be the number of ounces of Solution A that the scientist uses, and let y be the number of ounces of Solution B that she uses. We can set up the following system of equations to represent the given information:

0.65x + 0.90y = 140 * 0.80 = 112
x + y = 140

To solve this system of equations, we can first multiply the second equation by -1 and add the resulting equations:

-1 * (x + y = 140)
-x - y = -140

0.65x + 0.90y = 112
-x - y = -140

-0.35x - 0.10y = -28

Next, we can divide both sides of the second equation by -0.1 to get rid of the fractional coefficient:

-0.35x - 0.10y = -28
(-0.1/-0.1) * (-0.35x - 0.10y) = (-0.1/-0.1) * -28
-3.5x - y = -28

Finally, we can add the resulting equations to eliminate one of the variables:

-3.5x - y = -28
0.65x + 0.90y = 112

0.35x + 0.90y = 84

Dividing both sides by 0.35, we find that x = 240.

Substituting this value back into the equation x + y = 140, we find that y = -100. Since y represents the number of ounces of Solution B, this is not a valid solution. This means that there is no solution to the system of equations, and the scientist cannot obtain a mixture that is exactly 80% salt using these two solutions.

Related Questions

Identify the sequence that lists sides of STU in order from shortest to longest

ST, UT, SU

UT, SU, ST

SU, ST, UT

SU, UT, ST

Answers

On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit

what is triangle?

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

the sum of the areas of the circle, the triangle, and the square.

Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.

A = 210-123 = 87 sq unit

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A tile is a square with an area of 64 cm square

Answers

Answer:

To find the perimeter, we will first find the side of the square tile.

Area - side ×side64 = side×side64=side² 8×8= side8=side Side = 8 cm.

Now,let us find perimeter.

Perimeter - 4 ×side=4×8= 32cm Perimeter - 32cm.

Through (-2,-1) and perpendicular to the graph of F(x) - 1/5x + 1 ( function notation)

Answers

The equation of line that passes through (-2,-1) and is perpendicular to f(x) = (-1/5)x + 1 is f(x) = 5x + 9.

What is the equation of line that passes through the given point and is perpendicular to f(x) = (-1/5)x + 1?

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the graph

f(x) = (-1/5)x + 1

Using the slope intercept, slope m is -1/5

The equation of a perpendicular line to f(x) = (-1/5)x + 1 must have a slope that is the negative reciprocal of the graph.

Slope of perpendicular line = -1 / (-1/5)

Slope of perpendicular line = 5

Plug the slope m = 5 and point (-2,-1) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - (-1) ) = 5( x - (-2) )

( y + 1 ) = 5( x + 2 )

y + 1 = 5x + 10

y = 5x + 10 - 1

y = 5x + 9

f(x) = 5x + 9

Therefore, the equation of the perpendicular line is f(x) = 5x + 9.

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Solve for each variable.
Explain how as well please
I will give brainlist if you give me an answer and not a link or something weird

Answers

Answer:

a = 38⁰

b = 54⁰

c = 54⁰

Step-by-step explanation:

a + 142⁰ = 180⁰ because a straight line = 180⁰

b + 38⁰ + 88⁰ = 180⁰ because the angles of a triangle equal 180⁰, and the missing measurement = 38⁰ because it is a vertical angle to angle a

c + 88⁰ = 142⁰ because the angles are corresponding angles

60, 80, 100
Right traingle

Answers

Yes it is a right triangle

John made a kite with all four sides the same length, as shown below. What is the perimeter of the kite?



help ple

Answers

Answer:

A

Step-by-step explanation:

The formula to find the perimeter of a rhombus is p=4a

and 4 times 1 2/3= 4 2/3


Two functions are shown below.
f(x) = 3x2 + 14x - 5
g(x) = 11x + 13
Select (click) the points at which the graphs of the two functions intersect.
(5,0)
(-3, -20)
(2, 35)
(6, 79)

Answers

Answer: (-3,20) (2,35)

Step-by-step explanation: well if the 2 is an exponent then this is the answer, I don’t know the step by step though sorry. <3

an open concrete tank is internally 1m wide, 2m long and 1.5m deep, the concrete being 10cm thick. Calculate the capacity of the tank in litres​

Answers

The capacity of the tank is 3000 liters

Calculations and Parameters

We would first find the volume of concrete:

(0.1*1.5*1*2)+(0.1*1.5*2(0.1*2))*2)+(0.1*1.2*2.2)

=0.3+0.66+0.264

=[tex]1.224 m^3[/tex] of concrete

The capacity of the tank in liters:

1x2x1.5

=[tex]3m^3[/tex] or 3000 liters

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In ABC segment DC bisects /_C and divides AB into segment AD and BD. CD = 6 units and AC = 8.5, then which statement would
justify that ACD - BCD?

Answers

Answer:

ABC=BCD wtdf

Step-by-step explanation:

In the ΔTUV below, find the m∠U to the nearest degree

Answers

Answer:

∠U=70°

Step-by-step explanation:

[tex]Cos~U=\frac{32^2+40^2+42^2}{2(32)(40)}[/tex]

[tex]Cos~U=43/128[/tex]

∠ U=  [tex]Cos^{-1}(43/28)[/tex]

∠ U= [tex]70[/tex]

------------------------

hope it helps...

have a great day!!!

Answer:

∠U=70°

Step-by-step explanation:

hope it helps

Find the value of each variable for each circle. Show your work

Answers

The values of the variables in the circles are

Circle 1: a = 34 degreesCircle 2: a = 58 degrees, b = 90 degrees and c = 61 degrees

How to determine the values of the variables in the circles?

From the question, we have the following parameters that can be used in our computation:

Circles and missing angles (see attachment for the figures)

Circle 1

To determine the unknown variable (a), we make use of the following theorem

The angle subtended by an arc at the circumference is twice the angle subtended at the circumference

Mathematically, this means that

a = 2 * 17 degrees

Evaluate the product

a = 34 degrees

Circle 2

To determine the unknown variable (a), we make use of the following theorem

The angle at the circumference in a semicircle is 90 degrees.

Mathematically, this means that

b = 90 degrees

Also, we have

a + 122 degrees = 180 degrees

Evaluate

a = 58 degrees

Using the theorem in (a), we have

b + a/2 + c = 180

This gives

90 + 58/2 + c = 180

Evaluate the like terms

c = 61 degrees

Hence, the angle c is 61 degrees

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g(x) = (2 (x+3))^3 + 4

Answers

.....................................

Can someone help me with this? It's urgent.

Answers

The table is filled as described , shown below.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

Rate per hour is $11.25

Number of regular hours is 40

Payment for regular hours:

time multiply with payment=

40*$11.25 = $450

Again, we have,

Rate per overtime hour:

$11.25*1.5 = $16.875 ≈ $16.88 (rounded up)

Number of overtime hours:

48.5 - 40 = 8.5

Payment for overtime hours:

$16.88*8.5 = $143.48

Now, we get ,

Gross payment is the sum of regular and overtime payments:

$450 + $143.48 = $593.48

Hence, he would get $593.48

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jaden makes 63% of the free throws he shoots. About how many shots do you predict he will have to take to make 15 free throws?

Answers

Answer:

I don't understand

Step-by-step explanation:

but hope u will understand

Answer:

3

Step-by-step explanation:

Please help no links look at picture ^^

Answers

Answer:

i cant see it

Step-by-step explanation:

9. Find the range, mean, median, and mode of the following data set. 5, 17, 21, 21, 7, 13, 1, 3 a. Range 20 Mean 11 Median 10 Mode 21 c. Range 20 Mean 10 Median 10 Mode 21 b. Range 24 Mean 11 Median 10 Mode 21 d. Range 20 Mean 11 Median 21 Mode 21​

Answers

Range: 20
Mean: 11
Median: 10
Mode: 21

P
Jimmy tried to solve the system of equations below, but he made an error
S 2.0
y=18
y= 40 +2
His work is shown. Find the error he made. Explain the error and show how to solve the sysm correctly.
1. 2.0 - 4.3 + 2 = 18
2.-2x = 16
3. = -8
4. y=4(-8) + 2
5. Y = -32 +2
6. y=-30
7. Check: 2 (-8) - (-30) = 18
8.
- 16 + 30 = 18
9 14 + 18
His mistake was on Line
because he should have
The correct solution is

Answers

Answer:

"His mistake was on line 1. He didn't distribute the negative sign (indicating a -1) to everything in the equation for y."

The correct solution is: x = -10, y = -38

Step-by-step explanation:

2x - y = 18

y = 4x + 2

Substitute the given value for y into the first equation:

2x - (4x + 2) = 18

2x - 4x - 2 = 18 ** here, he didn't distribute the (-) to everything in the parentheses that represents y

-2x -2 = 18

add 2 to both sides

-2x = 20

divide by -2

x = -10

-------------------

solve for y

y = 4x + 2

y = 4(-10) + 2

y = -40 + 2

y = -38

------------------

Check the math:

2x -  y = 18

2(-10) - (-38) = - 20 + 38 = 18

What is 5 times the quotient of 3 and 5?

Answers

Answer: 3

Step-by-step explanation:

5 X 3/5 = 3

suppose 210 subjects are treated with a drug that is used to treat pain and 53 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20​% of users develop nausea.​

Answers

find the missing length of the right triangle. round to the nearest tenth use the rounded values to calculate the next value, round your final answer to the nearest tenth 40° 20° 15

A manufacturer produces safety jackets for competitive fencers. These jackets are rated by the minimum force, in newtons, that will allow a weapon to pierce the jacket. When the production process is operating correctly, it produces jackets that have ratings with an average of 840 newtons and a standard deviation of 14 newtons.FIE, the international governing body for fencing, requires jackets to be rated at a minimum of 825 newtons.To check if the process is operating correctly, a manager takes a random sample of 49 jackets from the process, rates them, and calculates the mean rating for jackets in the sample, which turns out to be 830 newtons. She is confident that the standard deviation of the process is at the specified value of 14 newtons.What is the p-value of the appropriate test if she wants to check if the production process currently meets the FIE standards

Answers

Answer:

0

Step-by-step explanation:

H0 : μ = 840

H1 : μ < 840

Sample size, n = 49

Standard deviation, s = 14

Test statistic = (xbar - μ) ÷ (s/√(n))

Test statistic = (830 - 840) ÷ (14/7)

Test statistic = - 10 / 2

Test statistic = - 5

The Pvalue ;

Pvalue = P(Z < - 5) = 0 (Z probability calculator)

The Pvalue = 0

evaluate: a+b/c if a = -6,b = -4 and c= -2

Answers

Answer:

5

Step-by-step explanation:

-6+(-4)/-2

-6-4/-2

-10/-2

5

Apskaičiuokite pavaizduoto kūgio tūrį. Laikykite, kad π≈3

Answers

Answer:

Say wahhhhh!

Step-by-step explanation:

Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa. how many dvds does marissa own?

Answers

The number of Dvds owned by Maarissa is 45

How to find the number of dvds?

The given parameters that will guide us in finding the number  of dvds owned by marissa are

Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.

Let the number of dvds owned by Marissa be x

Nymber of dvds owned by Kyle be y

This implies that  x+y = 66 ............................1

also, 2y + 3 = x ..................................................2

Substitute x = 2y + 3 in equation 1

= 2y + 3+y =66 Collecting like terms

⇒ 3y = 63

Making y the subject of the relation we have y=21

Recall that  2y + 3 = x

That means x = 2(21) + 3

x=45

Therefore Marrissa owns 45 dvds

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Ms. Sharon bought 84 litre of cooking oil. She used 1/3 of it on Monday and another 20 litre
of it on Tuesday.
a) How much oil she used on Monday?
b) How much cooking oil did she use altogether?
c) How much cooking oil was left with her?
d) Write the fraction of cooking oil left with her

Answers

a) Ms. Sharon used 84 / 3 = <<84/3=28>>28 litre of oil on Monday.
b) Ms. Sharon used 28 + 20 = <<28+20=48>>48 litre of oil altogether.
c) Ms. Sharon has 84 - 48 = <<84-48=36>>36 litre of oil left with her.
d) The fraction of cooking oil left with her is 36 / 84 = <<36/84=6/14>>6/14.

The perimeter of a rectangle is 408cm and the length is 134cm. Find the rectangle’s width.

Answers

Answer: 70 cm

Step-by-step explanation: perimeter = 2*width + 2*length

408 = 2*width + 2*134

408 = 2*width + 268

Subtract 268 from both sides.

140 = 2*width

DIvide both sides by 2

Width = 70 cm

Answer:

The width of the rectangle is 70 cm

Step-by-step explanation:

Given,

The perimeter of a rectangle is 408 cmThe length is given as 134 cm

To Find : The width of the rectangle

As we know, the formula to find the Perimeter of the rectangle is

[tex]P = 2(l+b)[/tex]

Now the Perimeter is given and the length

[tex]408 = 2(134 + b)[/tex]

Now using distributive property

[tex]408 = 268 + 2b[/tex]

[tex]408 - 268 = 2b[/tex]

[tex]140 = 2b[/tex]

[tex]\frac{140}{2} = b[/tex]

[tex]70cm = b[/tex]

Hence, the width of the rectangle is 70 cm

Find two Equivalent fractions of 4/2

Answers

Answer:

40/20 & 22/11

Step-by-step explanation:

To find an equivalent fraction to 4/2, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:By dividing the original fraction by 2, we get:4 ÷ 2 / 2 ÷ 2 = 21. By multiplying the original fraction by 2, we get:4 × 2 / 2 × 2 = 8/4. Here is the full list of equivalent fractions to 4/2. 2/1, 4/2, 6/3, 8/4, 10/5, 12/6, 14/7, 16/8, 18/9, 20/10, 22/11, 24/12, 26/13, 28/14, 30/15, 32/16, 34/17, 36/18, 38/19, 40/20...

1. Find the focus of the parabola that has vertex (-7, 2), opens vertically, and passes through the point (-5,0).

Answers

Veterx id 7 opens vertically passes fhtought the point

Rosa Bought some place mats costing $17.16 and some napkin ring’s costing $10.36.If there were 4 place mats and 4 napkin ring’s what was the total cost for 1 place mat and 1 napkin ring?


Brian is trying to lose at least 2 pounds a week by eating less and walking 2 miles each day. For the past 3 weeks,he lost 2.4 pounds,1.9,and 3.2 pounds. what was the average number of pounds he lost?


Can someone answer these?

Answers

9514 1404 393

Answer:

$6.882.5 pounds

Step-by-step explanation:

1. In this case, it appears that "some" means "4". The total cost of 4 place mats and 4 napkin rings is apparently ...

  $17.16 +10.36 = $27.52

Then the total cost of 1 of each is 1/4 this amount, or ...

  $27.52/4 = $6.88

__

2. The average of three numbers is their sum, divided by 3.

  (2.4 + 1.9 + 3.2)/3 = 7.5/3 = 2.5

Brian lost an average of 2.5 pounds per week.

Circle C has radius 8 ft with an arc AB intercepted by a central angle of pi/4 radians. What is the length of arc AB expressed in
terms of pi?

Answers

Answer:

b

Step-by-step explanation:

The arc length is, 720 ft.

How to find the relation between angle subtended by the arc, the radius and the arc length?

[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]

The superscript 'c' shows angle measured is in radians.

If radius of the circle is of r units, then:

[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]

Length of an arc is given by:

l = r Ф .....[1]

where r is the radius of the circle and  Ф is the angle in radian.

From the given information;

In a circle with a radius 8 ft with an arc AB intercepted by a central angle of pi/4 radians.

r = 8 ft and radian pi/4

Substitute these values in [1] we have;

l = r Ф

l = 8 x pi/4 ft.

l = 4 pi

l = 4 x 180

l = 720 ft

therefore, the arc length  is, 720 ft.

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Find mZRTS.
R
112°
S
T

Answers

Answer:

RTS=(180-112)/2

=68/2

=34

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June, 3, 8, 2.Which statement best explains what is shown in their data?Choose the correct answer.ResponsesA.The beautyberry relies on wind to spread its seeds.B..The beautyberry relies on one type of animal to eat the berries.C.The beautyberry uses asexual reproduction to make new plants.D.The beautyberry increases its chances of reproduction because its berries do not all become ripe at the same time. please help me! paraphrase this article! Please make it at least in a paragraph!:Aside from being nutritious, potatoes are also incredibly filling.In one study, 11 people were fed 38 common foods and asked to rate foods based on how filling they were. 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