A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 70% salt. She wants to obtain 30 ounces of a mixture that is 60% salt. How many ounces of each solution should she use?

Answers

Answer 1

Answer:

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 180        y = 180 - x

.60x + .85y = .75(180)

.60x + .85y = 135      Multiply both sides of the equation by 100 to remove the decimal points.

60x + 85y = 13500

60x + 85(180 - x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces          

Step-by-step explanation:

Wyzant (ask an expert) solution on their website.


Related Questions

People were asked if they owned an artificial Christmas tree. Of 78 people who lived in an apartment, 38 own an artificial Christmas tree. Also it was learned that of 84 people who own their home, 46 own an artificial Christmas tree. Is there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees

Answers

Answer:

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Apartment:

38 out of 78, so:

[tex]p_A = \frac{38}{78} = 0.4872[/tex]

[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]

Home:

46 out of 84, so:

[tex]p_H = \frac{46}{84} = 0.5476[/tex]

[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]

Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:

At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:

[tex]H_0: p_A - p_H = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:

[tex]H_1: p_A - p_H \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]

[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]

[tex]z = -0.77[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.

Looking at the z-table, z = -0.77 has a p-value of 0.2207.

2*0.2207 = 0.4414

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Please help me! Thank you!
Find the length of BC
A. 27.22
B. 11.62
C. 22.02
D. 19.78

Answers

Answer:

B

Step-by-step explanation:

Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:

[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]

Solve for BC. We can take the reciprocal of both sides:

[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]

Multiply:

[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]

Use a calculator. Hence:

[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]

BC measures approximately 11.62 units.

Our answer is B.

Solve for x

Answer choices:
4
5
8
3
2

Answers

opposite angles are equal

[tex]\\ \sf\longmapsto 13x+19=84[/tex]

[tex]\\ \sf\longmapsto 13x=84-19[/tex]

[tex]\\ \sf\longmapsto 13x=65[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{65}{13}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

[tex]\boxed {\boxed {\sf x=5}}[/tex]

Step-by-step explanation:

We are asked to solve for x.

We are given a pair of intersecting lines and 2 angles measuring (13x+19)° and 84°. The angles are opposite each other, so they are vertical angles. This means they are congruent or have the same angle measure.

Since the 2 angles are congruent, we can set them equal to each other.

[tex](13x+19)=84[/tex]

Solve for x by isolating the variable. This is done by performing inverse operations.

19 is being added to 13x. The inverse operation of addition is subtraction. Subtract 19 from both sides of the equation.

[tex]13x+19-19= 84 -19[/tex]

[tex]13x= 84 -19[/tex]

[tex]13x=65[/tex]

x is being multiplied by 13. The inverse operation of multiplication is division. Divide both sides by 13.

[tex]\frac {13x}{13}= \frac{65}{13}[/tex]

[tex]x= \frac{65}{13}[/tex]

[tex]x= 5[/tex]

For this pair of vertical angles, x is equal to 5.

The data show the traveler spend- ing in billions of dollars for a recent year for a sample of the states. Find the range, variance, and standard deviation for the data.
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0

Answers

Solution :

Given data :

20.1     33.5     21.7      58.4     23.2     110.8     30.9

24.0    74.8     60.0

n = 10

Range : Arranging from lowest to highest.

20.1,   21.7,   23.2,    24.0,   30.9,    33.5,    58.4,    60.0,    74.8,   110.8

Range = low highest value - lowest value

           = 110.8 - 20.1

           = 90.7

Mean = [tex]$\frac{\sum x}{n}$[/tex]

         [tex]$=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$[/tex]

          [tex]$=\frac{457.4}{10}$[/tex]

         [tex]$=45.74$[/tex]

Sample standard deviation :

[tex]$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$[/tex]

[tex]$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$[/tex]  

      [tex]\sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}[/tex]

[tex]$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$[/tex][tex]$S=\sqrt{\frac{1}{9}(8026.96)}$[/tex]

[tex]$S=\sqrt{891.88}$[/tex]

S = 29.8644

Variance = [tex]S^2[/tex]

               [tex]=(29.8644)^2[/tex]

               = 891.8823

Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.

Answers

Answer:

c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

Step-by-step explanation:

Given :

Groups:

x1 = 69 ; s1 = 19 ; n1 = 38

x2 = 32 ; s2 = 14 ; n2 = 37

1 - α = 1 - 0.95 = 0.05

Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :

The confidence interval obtained is :

(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between

(24.32 ; 39.68) .

If g(x) = x^2 + 8x - 24 find the value of g(6)

Answers

Answer:

hope it helps you..........

Answer:

60

Step-by-step explanation:

g(x)= x^2 +8x - 24

Substitute x for 6 in the equation

g(6)= 6^2 + 8(6) - 24

= 36+48-24

= 60

Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?

Answers

Answer:

Step-by-step explanation:

I need help on this math problem ​

Answers

Answer:

for the first one, simply add g(x) and h(x) :

x+3 + 4x+1 = 5x + 4

the second one, you would multiply them :

(x+3)(4x+1) = 4x^2 + 13x + 3

the last one, you would subtract :

(x+3)-(4x+1) = -3x + 2

and then substitute 2 for 'x' :

-3*2 + 2 = -6 + 2 = -4

Answer:

1. 5x+4

2. [tex]4x^2+13x+3[/tex]

3. -4

Step-by-step explanation:

1. (x+3)+(4x+1)

Take off the parentheses and Add.

5x+4

2. (x+3)(4x+1)

Use the FOIL method to multiply.

[tex]4x^2+x+12x+3[/tex]

[tex]4x^2+13x+3[/tex]

3. First, set up the equation as (g-h)(x)

(x+3)-(4x+1)

x+3-4x-1

Solve.

-3x+2

Substitute in 2 for x.

-3(2)+2

-6+2

-4

A circular fence is being placed to surround a tree. The diameter of the
fence is 4 feet. How much fencing is used? *

Answers

Answer:

12.6 ft

Step-by-step explanation:

Write a rule to describe the transformation.
A. reflection across y=x
B. rotation 90º clockwise about the origin
C. rotation 180º about the origin
D. rotation 90º counterclockwise about the origin

Answers

Answer:

C. rotation 180º about the origin

Step-by-step explanation:

Given

Quadrilaterals GWVY and G'W'V'Y'

Required

Describe the transformation rule

Pick points Y and Y'

[tex]Y = (5,-4)[/tex]

[tex]Y' = (-5,4)[/tex]

The above obeys the following rule:

[tex](x,y) \to (-x,-y)[/tex]

When a point is rotated by 180 degrees, the rule is:

[tex](x,y) \to (-x,-y)[/tex]

Hence, (c) is correct

T
On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
TE
$
(S

Answers

9514 1404 393

Answer:

  $3277.23

Step-by-step explanation:

The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...

  A = P(1 +r/2)^(2t)

where P is the principal value.

For the given rate and time, this is ...

  A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23

The value of the CD at maturity will be $3277.23.

find an odd natural number x such that LCM (x,40)= 1400

Answers

The odd natural number x such that the LCM of x and 40 is 1400 is 35

Lowest Common Multiple

The least common multiple the lowest multiple of two or more numbers.

From the question, we need to determine the value of x of the LCM of the numbers is 1400

LCM (x,40) = 1400

Find a possible value of x

x = 1400/40

x = 35

Hence the odd natural number x such that the LCM of x and 40 is 1400 is 35

Learn more on LCM here: https://brainly.com/question/233244

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14. What, if any, is a real solution to 5x +1 +9 - 3?
1
C
D. There is no real solution.

Answers

I believe the question is:

What is the solution to 5x + 1 +9 - 3

In this case, we solve for X.

5x + 1 + 9 - 3

5x + 10 - 3

5x + 7

5x = -7

x = -7/5

Unfortunately, It is not one of the answer choices it looks like.

Maybe you should reword your question but hopefully this is correct.

If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5

The value of x in a given expression is -7/5.

We have given that,

5x + 1 + 9 - 3

We have to determine the value of x.

What is the variable?

A variable is any factor, trait, or condition that can exist in differing amounts or types. Scientists try to figure out how the natural world works

In this case, we solve for X.

5x + 1 + 9 - 3

5x + 10 - 3

5x + 7

5x = -7

x = -7/5

If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5.

Therefore we get the value of x is -7/5.

To learn more about the value of the variable visit:

https://brainly.com/question/5030068

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Study the scatterplot and trend line. Which two points can be used to find the equation of the trend line?

Which points are on the trend line?
(1, 30) and (9, 95)
(2, 30) and (6, 70)
(2, 45) and (8, 90)
(3, 50) and (7, 65)

Answers

Answer:

C

Step-by-step explanation:

Just trust

Answer:

C

Step-by-step explanation:

I did the assignment in edge and got it right.

Proof:

In an experiment, you choose to have two randomly assigned groups. In one, you take measurements both pretest and posttest; with the second, a posttest-only measure. This describes which task of conducting an experiment

Answers

Answer:

The answer is "Specific treatment levels".

Step-by-step explanation:

When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.

Find the sum of -3x^2-4x+3 2x^2+3

Answers

The answer is -x^2-4x+6

If a=120° , find the measure of angles b, c and d.
Explain your reasoning.

Answers

Answer:

b=120°

c=60°

d=60°

SEE THE IMAGE FOR SOLUTION

1/10 + 3/5
ANSWER QUICK PLS FIRST ANSWER GETS BRAINLIEST

Answers

3/5 is equal to 6/10 - always find a common denominator
So then you can easily add 1/10+6/10 which equals 7/10

Find the area If you get this correct i WILL GIVE YOU 100 POINTS

Answers

Answer:

Area of yellow portion =54 in

For what numbers is f(0) = sec 0 not defined? ​

Answers

Your mom your dad and you brother

Answer:

stundeez

Step-by-step explanation:

Nicki Minaj hdhsbskdhsnsk

please help me with this
——/———————-////—————-

Answers

Answer:

"C"

Step-by-step explanation:

-B means the B is in the opposite direction

a store sign reads "Take 75% of the original price when you take an additional 15% off the sale price, which is 60% off the original price." Is the stores sign accurate?

Answers

Answer:

The new price is 66% off the original not 75% off

Step-by-step explanation:

Let x be the original price

First take 60 percent off

x - x*60% = new price

x- .60x = .40x

The new price is .40x

Then take 15 % off

(.40x) - (.40x)*15%

.40x - .40x*.15

.40x - .06x

.34x

100 -.34 =.66

The new price is 66% off the original not 75% off

what is the absolute value of |9|?​

Answers

Answer:

9

Step-by-step explanation:

it's as simple as that 9 is 9 away from 0

9. absolute value. the answer is what ever is inside of the parallel lines. for example |-2| would be 2. so therefore the answer for your question is just 9. hope this helps!❤️

If 2x - 5y – 7 = 0 is perpendicular to the line ax - y - 3 = 0 what is the value of a ?

A) a =2/3

B) a =5/2

C) a = -2/3

D) a = -5/2

Answers

Answer:

D) a = - 5/2

Step-by-step explanation:

2x -5y - 7 = 0

5y = 2x - 7

y = 2/5 x - 7

the slope of this line is therefore 2/5 (factor of x).

the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.

What is the product of 2/5 × 3/4?

Answers

answer:
3/10 or 0.3
step-by-step explanation:
2/5 x 3/4
2 x 3
6
6/4
4 x 5
20
6/20
3/10

Answer:

3/10

Step-by-step explanation:

2/5*3*4

=6/20

=3/10

CAN SOMEONE HELP ME PLEASE CAN YOU FIGURE OUT WHERE I PUT 4 PI ON THE NUMBER LINE

Answers

Answer:

see below

Step-by-step explanation:

Pi is approximately 3.14

4*3.14 =12.56

So about halfway between 12 and 13

A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450 miles.

How many miles per hour is the superhero flying?

Answers

Answer:  4900 mph

Work Shown:

30 min = 30/60 = 0.5 hours

distance = rate*time

rate = distance/time

rate = (2450 miles)/(0.5 hours)

rate = (2450/0.5) mph

rate = 4900 mph

For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.

In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.

Answers

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

[tex]f(t) = 10000(0.9407)^t[/tex]

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

[tex]f(t) = f(0)(1-r)^t[/tex]

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that [tex]f(0) = 10000[/tex], thus:

[tex]f(t) = 10000(1-r)^t[/tex]

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

[tex]f(2) = 8850[/tex]

We use this to find 1 - r.

[tex]f(t) = 10000(1-r)^t[/tex]

[tex]8850 = 10000(1-r)^2[/tex]

[tex](1-r)^2 = \frac{8850}{10000}[/tex]

[tex](1-r)^2 = 0.885[/tex]

[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]

[tex]1 - r = 0.9407[/tex]

Thus

[tex]f(t) = 10000(1-r)^t[/tex]

[tex]f(t) = 10000(0.9407)^t[/tex]

Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)​

Answers

The equation has 2 valid solutions; no extraneous solutions

The given equation is:

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

First, we determine the solutions

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

Add 5 to both sides

[tex]\sqrt{x - 1} = x - 8 + 5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

Square both sides

[tex]x - 1 = (x - 3)^2[/tex]

Expand

[tex]x - 1 = x^2- 3x - 3x + 9[/tex]

[tex]x - 1 = x^2- 6x + 9[/tex]

Collect like terms

[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]

[tex]x^2 - 7x + 10 = 0[/tex]

Expand again

[tex]x^2 - 2x-5x + 10 = 0[/tex]

Factorize

[tex]x(x - 2) -5(x -2)= 0[/tex]

Factor out x - 2

[tex](x - 5)(x -2)= 0[/tex]

Split

[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]

[tex]x= 5[/tex] or [tex]x = 2[/tex]

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

Read more about equations at:

https://brainly.com/question/2396830

Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

for plato users

Algebra 2, please help! thank you
The function y = 2 cos 3(x + 2π∕3) +1 has a phase shift (or horizontal shift) of

A) –2π∕3
B) 3
C) 1
D) 2

Answers

Answer:

-2pi/3

Step-by-step explanation:

y = 2 cos 3(x + 2π∕3) +1

y = A sin(B(x + C)) + D  

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

We have a shift to the left of 2 pi /3

Answer:

A

Step-by-step explanation:

The standard cosine function has the form:

[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]

Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.

We have the function:

[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]

We can rewrite this as:

[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]

Therefore, a = 2, b = 3, c = -2π/3, and d = 1.

Our phase shift is represented by c. Thus, the phase shift is -2π/3.

Our answer is A.

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