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?

The liners function are not direct variation

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation.

For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation

If b is directly proportional to a, then k is the constant of variation and the value of k = b/a for all value of b and a

In the problem, the variables are compared as follows

feet = k * sec

k = feet / sec

For the first values, k = 33 / 3 = 11

For the second values, k = 36 / 6 = 6

since 11 ≠ 6 the function is not a direct variation

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The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin. Option C

We can say that a relationship  is proportional when the relation does lead to a straight line graph and the graph would have to be able to pass through the origin.

Hence, even if we have a straight line graph but the graph does not pass through the origin of the graph then we can not say that the relationship that is existing between the coordinates that have been shown is proportional.

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now, this is implicit differentiation, so it comes with the assumption that "y" is a function in "x terms", as opposed to a plain vanilla variable, whilst "x" is just that, so

[tex]\cfrac{d}{dx}[x^2+y^4=20]\implies 2x+\stackrel{chain~rule}{4y^3\cdot \cfrac{dy}{dx}}=0\hspace{5em}\cfrac{d}{dx}\left[ 2x+4y^3\cdot \cfrac{dy}{dx}=0 \right] \\\\\\ 2+\stackrel{product~rule}{\left( 12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2} \right)}=0\implies 2+12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2}=0 \\\\\\ 2+12y^2\cdot \cfrac{dy}{dx}=-4y^3\cdot \cfrac{d^2y}{dx^2}\implies {\Large \begin{array}{llll} \cfrac{2+12y^2\cdot \frac{dy}{dx}}{-4y^3}=\cfrac{d^2y}{dx^2} \end{array}}[/tex]

Answer:

Step-by-step explanation:

An radical expression usually involves a radicand which is the number or expression inside the radical symbol √ and an index which is the number outside the radical symbol indicating the root, the radicand raised to the power of the reciprocal of the index.

But in the case of expression "U-2/5" it's not a radical expression as is. It's a fractional expression with variable U and a constant -2/5.

It can be written as √(U-2)/5 or U- √(2/5) if you want to express it as an radical expression.

Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]

Add the square of the scaling factor s to the area of ​​the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of ​​the figure after dilation Ad. a d = s2a p .

To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of ​​the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]

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P(1.6,-2.9) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Let L(3,−6), M(5,−3), N(8,−6) be the vertices of the given △LMN.

Let P(x,y) be the circumcentre of △LMN. Then,

PL = PM = PN

Also, PL² = PM² = PN²

PL² = PM²

(x-3)² + (y-(-6))² = (x-5)² + (y-(-3))²

(x-3)² + (y+6)² = (x-5)² + (y+3)²

x²-6x+9 + y²+12y+36 = x²-10x+25 + y²+6y+9

4x + 6y = -11   ---- (1)

Also, PM² = PN²

(x-5)² + (y-(-3))² = (x-8)² + (y-(-6))²

(x-5)² + (y+3)² = (x-8)² + (y+6)²

x²-10x+25 + y²+6y+9 = x²-16x+64 + y²+12y+36

6x - 6y = 27   ---- (2)

Solve (1) and (2) simultaneously by elimination:

6 × (4x + 6x = -11)

4 × (6x - 6y = 27)

24x + 36y = -66

24x - 24y = 108

subtract:

         60y = -174

         y = -174/60

         y = -2.9

Put y = -2.9 into (1):

4x + 6x = -11

4x + 6(-2.9) = -11

4x - 17.4 = -11

4x = 6.4

x = 1.6

Thus, the coordinates of the circumcentre of △LMN are P(1.6, -2.9)

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On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.

Permutations refer to the arrangements of objects in certain order or way.

The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.

The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.

The probability is obtained as 1 / ₉P₃

where;

₉P₃ = 9! / (9 - 3)!

₉P₃ = 9! / 6!

9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

6! = 6 * 5 * 4 * 3 * 2 * 1

₉P₃ = 504

Hence, the probability = 1/504

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Divide or multiply the output by a constant to expand or contract the graph in the y direction.

2f (x) is stretched by a factor of 2 in the y direction, and f (x) is contracted by a factor of 2 in the y direction (or stretched by a factor of ).

The y = f (x), y = 2f (x), and y = x graphs are shown here.

This is the difference quotient:

f (x + h) - f(x ) /h

quotient of difference

and f(x) = x3; thus, the difference quotient for this function is

(x + h)³ - x³ / h

quotient of difference.

The numerator can now be simplified by expanding (x + h)3 as (x + h)2(x + h), however I advise factoring (x + h)3 - x3 as a difference of cubes.

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Answer:

Its 1 because you are moving the digits 1 place to the right

Step-by-step explanation:

Answer:

The formula for finding Slope Intercept Form is y = mx + b.

Step-by-step explanation:

Y - Y coordinate

M - Slope

X - X coordinate

B - Y Intercept

This formula is used for finding the equation of a line.

Answer:

Step-by-step explanation:

-12

Answer:

A. Adjacent  

B. Complementary

C. Complementary

Step-by-step explanation:

Answer:

A 0.9102

Step-by-step explanation:

A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.

The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.

A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.

A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.

Hence, the correlation coefficient is A, 0.9102

The value of the variable 'x' is 273/27. Then the measure of the angle ∠DGH will be 2.43°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Then the equation is written as,

∠EFA + ∠DGF = 180°

x - 5 + 73x - 365 = 180°

74x = 550

x = 273/27

Then the measure of the angle ∠DGF is given as,

∠DGF = 73(273/27) - 365

∠DGF = 177.57°

Then the measure of the angle ∠DGH will be calculated as,

∠DGH + ∠DGF = 180°

∠DGH + 177.57° = 180°

∠DGH = 2.43°

The value of the variable 'x' is 273/27. Then the measure of the angle ∠DGH will be 2.43°.

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Answer:

27/8

Step-by-step explanation:

First, note that 3 3/8 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

3 = numerator

8 = denominator

To convert mixed number 3 3/8 to improper fraction, you follow these steps:

1. Multiply the whole number by the denominator

  3 × 8 = 24

2. Add the product from Step 1 to the numerator

   24 + 3 = 27

3. Write answer from Step 2 over the denominator

   27/8

The mixed number 3 3/8 converted to improper fraction is therefore :

27/8

On solving the provided question, we can say that - here the value of exponential equation is 648/1296 = 0.5

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

So, the equation is

[tex]3(2x^3y^5)^3/ (2x^6y^3)^4[/tex]

and x=y=1

so, 648/1296 = 0.5

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The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.

It is not always possible to interview or survey an entire population. Therefore, in many research studies, a portion of the population that is expected to represent the population is drawn and surveyed instead. The portion that is drawn is called the sample, and the method used to draw the sample is called the sampling method. Broadly, there are two types of sampling methods. The probability sampling method is a method wherein all members of the population have an equal probability to be selected to be included in the sample. The non-probability sampling method is a method wherein not all members of the population have an equal probability to be selected to be included in the sample. Instead, members are recruited into the sample based on the researcher's subjective and personal judgment.

Simple Random Sampling Method:

Simple random sampling method, sometimes abbreviated as SRS, is the purest form of probability sampling. Figuratively, it is like putting the names of the entire population in a hat and drawing each member from the hat with a blindfold. Therefore, every member of the population has an equal chance of being included in the sample.

Two-stage Cluster Sampling Method:

In the first stage of a two-stage cluster sampling method, the population is first divided into subgroups called clusters. For instance, the population is divided into subgroups based on geographic location. Unlike strata in stratified sampling, clusters are heterogeneous and each cluster is supposed to represent the heterogeneity of the population. These clusters are also known as primary sampling units or PSUs. In the second stage, the simple random sampling method is used to draw individuals from each of the PSUs to be included in the study sample.

Hence, The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.

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Answer:

To solve this problem, we can set up the following equation:

2.5 inches = 1,000 feet

We are told that the model is 18 inches high, so we can write the following equation:

18 inches = X feet

To solve for X, we can cross-multiply the equations to get:

(2.5 inches)X = (1,000 feet)(18 inches)

Simplifying this equation, we get:

X = 4,500 feet

Therefore, the height of the volcano is 4,500 feet.

Step-by-step explanation:

Complete the puzzles with values -4, 0, -3 and 2

Since each row, column, and diagonal adds up to the same total.

For the 1st row, the total is:

3 + (-2) + (-1) = 0

That means each row, column, and diagonal will always adds up to 0.

3 + w + 1 = 0

w = -3-1

w = -4

w + y + 4 = 0

-4 + y + 4 = 0

y = 0

-1 + 4 + t = 0

3 + t = 0

t = -3

1 + h + t = 0

1 + h + (-3) = 0

h -2 = 0

h = 2

(Check the attached image for labeling)

Thus, complete the puzzle with the values accordingly

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Answer:

10. Yes
11. No
12. Yes
13. Yes
14. No
15. No

Step-by-step explanation:

Use the vertical line test to determine whether or not a relation is a function. The vertical line test is when you draw a line through a relation and if that line intersects the relation more than ONCE, the relation is not a function.

10. Is a function, the vertical line only intersects the relation once.
11. Isn't a function, intersects the relation more than once.
12. Is a function, intersects the relation only once.
13. Is a function, only intersects the relation once.
14. Isn't the function, intersects the relation more than once.
15. Isn't a function, the relation intersects the function more than once.

Hope this helps.

Answer:

I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!

Answer:

- 420° =  -7/3 π ≈ - 2.333 π

Step-by-step explanation:

- 420° =  -7/3 π ≈ - 2.333 π

Coterminal angle in [0, 360°) range:

300°, located in the fourth quadrant.

Positive coterminal angles: 300°, 660°, 1020°, 1380°, 1740°...

Negative coterminal angles: -60°, -420°, -780°, -1140°

I hope this helps!1!!

-420° = -360° - 80° = -80°

-80° = 360° - 80° = 280°

Co terminal angle = 280° and -80°

5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.

5b) Under the lease, the customer saves $14,760.

5c) The lessee after returning the car has the following lease options:

6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.

6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.

6c) The monthly payment will be $567.26.

6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.

A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.

A car purchase can also be financed through loans, like home mortgages.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings from leasing = $14,760 ($36,160 - $21,400)

The value of the Honda Civic = $28,495

Harmonized Sales Tax (HST) = 13%

After-tax cost = $32,199.35 ($28,495 x 1.13)

Annual interest rate = 1.9% compounded monthly

Down payment = $6,000

Financing part = $26,199.35 ($32,199.35 -$6,000)

Financing period = 4 years

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 1.9%

PV (Present Value) = $26,199.35

FV (Future Value) = $0

P/Y (# of periods per year) = 12

C/Y (# of times interest compound per year) = 12

Results:

Monthly Payments (PMT) = $567.26

Sum of all periodic payments = $27,228.48

Total Interest $1,029.13

Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)

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The value of the x is 10.

What is the exterior angle theorem?

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

We have given,

angles of the triangle:

Interior angles :

∠D = 2x + 7,

∠E = 26°,

Exterior angle:

∠C = 6x - 7

To find x = ?

few common properties about the angles of a triangle:

A triangle has 3 internal angles which always sum up to 180 degrees.

It has 6 exterior angles and this theorem gets applied to each of the exterior angles.

Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.

Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.

So,

∠C  = ∠D + ∠E

6x - 7 = 2x + 7 + 26,

6x - 7 - 2x - 7 = 26,

4x - 14 = 26,

4x = 40

x = 40/4

x = 10,

Hence, the value of the x is 10.

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on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]

value of x from the given equation comes out to be 13.5

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Answer:

1/a³

Step-by-step explanation:

(1/a)³ = 1³/a³ = 1/a³