How many ounces of a 28% alcohol solution and a 40% alcohol solution must be combined to obtain 51 ounces of a 32% solution?

Answer:

There might be an error in the question, the result below should be the correct answer. It is not possible for a^2+b^2+c^2 to be the answer.

(a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2

Step-by-step explanation:

(a+b+c)(a-b+c) = a^2 - ab +ac + ba - b^2 +bc + ca - cb + c^2 (expanding the two terms in brackets first)

Since ab = ba, ac = ca and bc = cb,

-ab and ba can be cancelled out

bc and -cb can be cancelled out

Hence, (a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2

This is what I have obtained through expansion, then simplification by cancelling out the common terms.

Could you help check the question again?

If you double the amount of fluid ounces, the amount of cups also double

There is a proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.

The donation is proportional to the dinner bill

The donation for a dinner bill of $50 is $9

If there are 8 fluid ounces in one cup

8 : 1 = 16 : x

8/1 = 16/x

8 × x = 16 × 1

8x = 16

x = 16/8

x = 2

The difference between weight = 1

The difference between cost = $0.68 - $0.47

= $0.21

$0.89 - $0.68

= $0.21

$1.10 - $0.89

= $0.21

Cost of mailing 6-ounce letter

1 : 0.47 = 6 : x

1/0.47 = 6/x

1 × x = 6 × 0.47

x = $2.82

The donation for a dinner bill $50 is

Dinner bill : donation

25 : 4.50 = 50 : x

25/4.50 = 50/x

25 × x = 50 × 4.50

25x = 225

x = 225/25

x =$ 9

Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.

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The XYZ coordinates are read as x-axis, y-axis and z-axis respectively.

Here we know that the x-axis is the horizontal line along which the wall to your left and the floor intersect where as the y-axis is the horizontal line along which the wall to your right and the floor intersect and the z-axis is the vertical line along which the walls intersect.

Here we also know that x-coordinate is measured along the east west axis, the y-coordinate is measured along the north south axis, and the z-coordinate measures height or elevation.

And it is used for a three-dimensional structure where the x-axis and y-axis represent the first two dimensions and the z-axis is the third dimension.

And in a graphic image, the axes x and y denote width and height and the z denotes depth.

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[tex]T=2\pi \sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\sqrt{\cfrac{L}{g}}\implies \cfrac{T}{2\pi }=\cfrac{\sqrt{L}}{\sqrt{g}}\implies T\sqrt{g}=2\pi \sqrt{L} \\\\\\ \sqrt{g}=\cfrac{2\pi \sqrt{L}}{T}\implies (\sqrt{g})^2=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2\implies g=\left( \cfrac{2\pi \sqrt{L}}{T} \right)^2 \\\\\\ g=\cfrac{(2\pi \sqrt{L})^2}{(T)^2}\implies g=\cfrac{4\pi ^2L}{T^2}[/tex]

On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts

data across time numbers about the population

The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.

Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.

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Answer:

320 sq in

Step-by-step explanation:

SA(rect prism) = 2(lw)+2(wh)+2(lh)

= 2(12·7)+2(7·4)+2(12·4)

= 2(84)+2(28)+2(48)

= 168+56+96

= 320

Answer:

3.5. 2.2.

x 4. x 1 1

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

14.0. 22

220

24.2

Step-by-step explanation:

answer for me is 38.2

are you sure ur math is right?

The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.

The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.

Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.

The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.

Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .

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A domain has [-1, 1]

Now, According to the question:

Let's know:

How do you find the domain?

Let y = f(x) be a function with an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using for that purpose a value for x then that chosen x-value is said to belong to the domain of f.

A square root with a negative number under the root cannot produce a real number. This means that [tex]1-x^2[/tex] must be greater than or equal to zero.

Squaring a real number will always produce a positive number, so [tex]x^{2}[/tex]must be equal to or smaller than 1. This means x is between 0 and 1, giving the domain of [0,1].

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The complete question is this ;

What is the domain of [tex]\sqrt{1-x^2}[/tex]

Answer:

<x=28 degrees

Step-by-step explanation:

Since we know line KL and FG are perpendicular, and DE and FG are parallel, then KL and DE must also be perpendicular.

Angles GCA, JCB, IAE, and CAD are all the same angle. Angles IAD, EAC, GCJ, and ACB are all the same angle. Since DE and KL are perpendicular, then angles KAD, KAE, EAL, and DAL all are 90 degrees, or right angles.

Because we know all this, we can take the angle of KAD, 90 degrees, and subtract 62 from it to find the angle of IAD. This is 28 degrees. Since angle IAD is equal to angle GCJ, which is also angle x, angle x is 28 degrees.

Hope this helps! Please mark me Brainliest!

Answer:

Step-by-step explanation:

Answer:

take a better picture

Step-by-step explanation:

Nobody can see that ;-;

Answer:

It is one of the 4 answers the question gives.

Step-by-step explanation:

Answer: -120

6 less than is 6 - and 3 times a number 42 is 3 x 42 so...

6 - (3 x 42) = -120

Answer:

its B hope this helps byee

pls mark me brainless.

Answer:

B

Step-by-step explanation:

Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it

According to our question-

x is the quantity of oranges.

y is the quantity of apples.

Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.

Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.

0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).

x + y = 15

0.5x + 0.65y = 9.00

As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).

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Answer: R A C P J

Step-by-step explanation:

Answer:

Yes it is because it is a straight line.

(I hope it helps, because i'm just learning about this meself so...)

F:4+4=8

A:23+8+4=35

H:53+3+28=84

I:11+17+93=121

I:24+8+3=35

I think that is all correct

Answer:

A, 6, 8, 10

Step-by-step explanation:

since you know that it is a right triangle, you can use pythagorean theorem, which states that A^2+B^2=C^2. so you add the squares of the smaller numbers, then take the square root of that number to get the answer. it is guess and check, but its a good theorem to know.

6^2=36

8^2=64

36+64=100

√(100)=10

Answer:

A and D

Step-by-step explanation:

we can find out the polynomial by the degree of the Polynomial.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

Types of polynomial

Depending upon the number of terms, polynomials are divided into the following categories:

1-Monomial

2-Binomial

3-Trinomial

4-Polynomial containing 4 terms (Quadronomial)

5-Polynomial containing 5 terms (pentanomial ) and so on.

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The original price of the case of candles before markup was $8.50.

Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:

Original price = Marked up price / (1 + markup percentage)

In this case, the original price would be:

$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50

So the original price of the case of candles before markup was $8.50.

Thus, Original price is $8.5

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Answer:

[tex]A=-3[/tex]

[tex]C=6[/tex]

[tex]B=4[/tex]

[tex]D=9[/tex]

Step-by-step explanation:

From the question we are told that:

Center of hyperbola at ( 6 , 9 )

Focus of hyperbola at ( 11 , 9 )

Vertex of hyperbola at ( 9 , 9)

Equation of hyperbola [tex]\frac{(x-C)^2}{A^2} -\frac{(y-D)^2}{B^2}=1[/tex]

Generally the C and D of the hyperbola equation is mathematically given by

[tex]Centers (6,9)[/tex]

[tex]C=6[/tex]

[tex]D=9[/tex]

Generally the A and B a of the hyperbola equation is mathematically given by

 [tex]A=x_c-x_v[/tex]

 [tex]A=6-9[/tex]

 [tex]A=-3[/tex]

 [tex]C'=x_c-x_f[/tex]

 [tex]C'=6-11[/tex]

 [tex]C'=-5[/tex]

Therefore with Center,Focus ,Vertex on the same line

 [tex]B^2=C'^2-A^2[/tex]

 [tex]B^2=(-5^2)-(-3^2)^2[/tex]

 [tex]B^2=(25)-(9)[/tex]

 [tex]B^2=16[/tex]

 [tex]B=4[/tex]

Answer:

72in^2

Step-by-step explanation:

Area of triangle:

base*height/2

Area = 16*9/2

Area = 72in^2

Answer:

8.9 ft. (Option C)

Step-by-step explanation:

Here, we are given a right angled triangle. We are asked to find the value of perpendicular (y).

We'll be using pythagoras property.

According to the pythagoras property, sum of the squares of base and perpendicular is equivalent to the square of hypotenuse.

Here,

→ H² = B² + P²

→ H² - B² = P²

→ (12 ft)² - (8 ft)² = y²

→ 144 ft² - 64 ft² = y²

→ 80 ft² = y²

→ √(80 ft²) = y

→ 8.94427191 ft = y

→ 8.9 ft = y

[tex] \therefore [/tex] Value of y is 8.9. (Option c)

Answer:

24 feet

Step-by-step explanation:

factors that produce an area of 32:

1x32  Would give a perimeter of 66

2x16  Would give a perimeter of 36

4x8  Would give a perimeter of 24

The residual values are -0.1, 3.8, 0.32, and 0 respectively for the given coordinate pairs.

A residual is a difference between the observed value (y) and the predicted value (y-hat) for a given x value. To find the residual for each coordinate pair (x,y), we need to substitute the x value into the equation for the line of best fit and calculate the difference between that value and the observed y value.

The equation for the line of best fit is y = 1.1x + 3.4

The residual for each coordinate pair (x,y) is given by -

Residual = Yactual - y

A. (5, 8.8) ; Yactual = 8.8

Residual = 8.8 - (1.1(5) + 3.4) = - 0.1

B. (2.5, 9.95) Yactual = 9.95

Residual = 9.95 - (1.1(2.5) + 3.4) = 3.8

C. (0, 3.72) Yactual = 3.72

Residual = 3.72 - (1.1(0) + 3.4) = 0.32

D. (1.5,5.05)​ Yactual =

Residual = 5.05 - (1.1(1.5) + 3.4) = 0

It's worth noting that residuals are used to measure how well the line of best fit represents the data set. The residuals should be as close to zero as possible, indicating that the line of best fit is a good representation of the data set.

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The complete question is -

The line of best fit for a data set is y=1.1x+3.4. Find the residual for each of the coordinate pairs, (x,y).

A. (5, 8.8)

B. (2.5, 9.95)

C. (0, 3.72)

D. (1.5,5.05)​

The angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.

The angles of a triangle are determined by the triangle's side lengths. This is known as the Law of Cosines. To determine the angles of a 5-12-13 triangle, we can use the Law of Cosines formula:

Cos(A) = (b² + c² - a²) / 2bc

In this equation, A is the angle opposite side a, b is the angle opposite side b, and c is the angle opposite side c. In a 5-12-13 triangle, a = 5, b = 12, and c = 13.

Using the Law of Cosines formula, we can calculate the angle A:

Cos(A) = (12² + 13² - 5²) / 2(12)(13)

Cos(A) = (144 + 169 - 25) / 156

Cos(A) = 278 / 156

Cos(A) ≈ 1.78

Using a calculator, we can calculate the angle A:

A = cos-1 (1.78)

A ≈ 81.19°

Using the same Law of Cosines formula, we can calculate the other two angles of the triangle:

Cos(B) = (a² + c² - b²) / 2ac

Cos(B) = (5² + 13² - 12²) / 2(5)(13)

Cos(B) = (25 + 169 - 144) / 65

Cos(B) = 50 / 65

Cos(B) ≈ 0.77

Using a calculator, we can calculate the angle B:

B = cos-1 (0.77)

B ≈ 48.76°

We can also calculate the angle C:

Cos(C) = (a² + b² - c²) / 2ab

Cos(C) = (5² + 12² - 13²) / 2(5)(12)

Cos(C) = (25 + 144 - 169) / 60

Cos(C) = 10 / 60

Cos(C) ≈ 0.17

Using a calculator, we can calculate the angle C:

C = cos-1 (0.17)

C ≈ 9.98°

Therefore, the angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.

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Answer:

The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

Answer:

0.22268

Step-by-step explanation:

z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

At least means equal to or greater than 67 inches

z = 67 - 64.97/2.66

z = 0.76316

P-value from Z-Table:

P(x<67) = 0.77732

P(x>67) = 1 - P(x<67) = 0.22268

The probability that the selected woman will have a height of at least 67 inches is 0.22268

Step-by-step explanation:

A variable that can have any value between two given value is known as continuous variable, while a variable have only integer values is a discrete variable

The correct values are;

(c) (i) The probability of a height of at least 67 is 0.2263

(ii) The answers do not match due to the difference between the discrete and normal probability models

(d) (i) A probability that can be found using the discrete model but not the normal model is P (H = 60)

The probability of an exact value using the normal distribution is zero

(ii) A probability that can be found using the normal model but not the discrete model is P(H = 56)

The value is for height of 56 inches is not given on the histogram and therefore

The reason the above selections are correct is follows:

(c) (i) Using the normal probability model, we have;

The mean = 64.27 inches, the standard deviation = 2.66 inches

The z-score for the height of 67 inches is given as follows;

[tex]z = \mathbf{\dfrac{x - \mu}{\sigma}}[/tex]

Therefore, we have;

[tex]z = \dfrac{67 -64.97}{2.66} \approx 0.7632[/tex]

From the z-score table, the probability P(x < 67) = 0.7737

P(x > 67) = 1 - P(x < 67) = 1 - 0.7737 = 0.2263

The probability of a height of at least 67, by the normal model = 0.2263

(ii) Based on the histogram, we have;

The probability of at least 67 = The area of the bars equal to and larger than 67 = (0.11 + 0.07 + 0.05 + 0.02 + 0.01 + 0.01) × 1 = 0.27

The probability of a height of at least 67 = 0.27

The answer in part (c-i) and the answer in part (a) using the histogram do not match

The reason they do not match is that the normal model used in part c is

based on normal probability, which focuses on future events, using the

normal model which is a continuous probability model, while the value of

probability calculated using the histogram is based on the relative

frequency, which focuses on historical values, based on the discrete model

(d) (i) An example of a probability that can be found using the discrete model but not the normal model is the probability that the height of a woman is a discreet single value such as 65 inches

Therefore, using the discreet model, we have;

P(H = 65) = 0.18

Using the continuous model, we have;

P(H = 65) = 0

This is so because the continuous model is given by the area under the curve, which for a single value is infinitesimally small

(ii) An example of a probability that can be found using the normal model but not the discrete model is the probability of the height of a woman selected is 56 inches, P(H = 56) is not given in the histogram

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