Makayla wants to make 200 ml of a 18% saline solution but only has access to 8% and 24% saline mixtures. Which of the following system of equations correctly describes this situation if x represents the amount of the 8% solution used, and y represents the amount of the 24% solution used?
O a.) 0.24x +0.08y= 0.18(200) x+y = 200 O b.) 0.08x +0.24y = 200 x+y=0.18(200) O c.) 0.08x+0.24y = 0.18(200) x+y=200 O d.) 0.24x +0.08y = 200 x+y=0.18(200)

Answer:

y=2x-2

Step-by-step explanation:

formula for the equation of a line is y=mx+b

formula for slope is (y2 - y1)/(x2-x1)

which makes the slope 2 (m=2)

then calculate for b which is -2

finally the formula is y = 2x - 2

The standard deviation of the sample of monthly salaries is 2.74

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.

>Standard deviation gauges a dataset's dispersion from its mean.

>It is determined as the variance's square root.

Mean  = [tex]\frac{(8+6+12+11+13)}{5} = 10[/tex]

Variance = [tex]\frac{((8-10)^{2}+(6-10)^{2}+(11-10)^{2}+(13-10)^{2} )}{(5-1)} = 6[/tex]

Standard deviation = [tex]\sqrt{7.5} = 2.7386[/tex]

when rounded off to two decimals 2.7386≈2.74.

The standard deviation of the sample of monthly salaries is 2.74

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Answer:

equal 3/8 or 0.375 siuuuuu

The length of the hypotenuse of the right triangle is 4.1in

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

In trigonometry, if θ is the angle opposite the 4 in line, then sinθ= opp/hyp

cosθ=adj/hyp

tanθ= opp/adj

to find the hypotenuse

sin80= 4/hyp

hyp= 4/sin80

hyp = 4/0.985

therefore the hypotenuse = 4.1 in

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Answer:

  (-6, -2)

Step-by-step explanation:

For points A(-10, 2) and B(-3, -5), you want the point P that makes AP/PB = 4/3.

Using (x, y) for the coordinates of P, we have ...

  AP/PB = 4/3

  ((x, y) -(-10, 2))/((-3, -5) -(x, y)) = 4/3

This simplifies to ...

  (x+10, y-2)/(-3-x, -5-y) = 4/3

Cross multiplying gives ...

  3(x +10, y -2) = 4(-3 -x, -5 -y)

  (3x+30, 3y-6) = (-12-4x, -20-4y)

Treating these equations separately, we have ...

  3x +30 = -12 -4x   ⇒   7x = -42   ⇒   x = -6

  3y -6 = -20 -4y   ⇒   7y = -14   ⇒   y = -2

The point that partitions the segment is (-6, -2).

__

Additional comment

The point that partitions AB in the ratio m/n is ...

  P = (mB +nA)/(m+n)

  P = (4(-3, -5) +3(-10, 2))/(4+3) = (-12-30, -20+6)/7 = (-42, -14)/7 = (-6, -2)

Above, we started from the basic requirement, rather than using the formula that results from that requirement.

Answer:

appt

Step-by-step explanation:

No solution: 1/2y + 3.2 = 20, 15/2 + 2z -1/4 = 4z + 29/4 - 2z, 1.1 + 3/2x + 2 = 3.1 + 3/4x, and 4.5r = 3.2 + 4.5r. One solution: 2x + 4 = 3x + 1/2

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

If the value of the variable is zero, then the no solution.

If the value of the variable is one, then the one solution.

If the value of the variable is infinity, then the infinite many solutions.

No solution: 1/2y + 3.2 = 20, 15/2 + 2z -1/4 = 4z + 29/4 - 2z, 1.1 + 3/2x + 2 = 3.1 + 3/4x, and 4.5r = 3.2 + 4.5r.

One solution: 2x + 4 = 3x + 1/2

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2000/3

Hope it helps

Mark Brainlist

The ratio of the length of the piece of wire to the length of the rope to the length of the piece of string is 6:5:1.5

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Let the length of the rope = x

Length of a piece of wire = (5/6)x

Length of a piece of string = (1/4)x

Length of the piece of string = 4.5cm

This can be written as,

4.5cm = (1/4)x

45/10 x 4 = x

x = 9 x 2

x = 18 cm

Now,

Length of the rope = 18 cm

Length of a piece of wire = 5/6 x 18 = 15 cm

Now,

Length of the rope : Length of a piece of wire : Length of a piece of string

18:15:4.5

We can simplify the ratio as,

Taking out the common factor 3.

6:5:1.5

Thus,

The required ratio is 6:5:1.5

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Answer:

xx=5 and yy=6

Step-by-step explanation:

Hope it helps you

Answer:

y is equal to or greater than 1x

Step-by-step explanation:

Answer:

4cdb ( 6 − 9c )

Step-by-step explanation:

24cd = 4cd × 6

36c²d = 4cd × 9c

24cd − 36c²d = 4cd ( 6 − 9c )

Answer:

-4

Step-by-step explanation:

I use this equation to solve it^^

This person has walked a total of 21 miles and the total displacement vector for this walk is 13.153 in northeast direction by the concept of distance and displacement.

Unaffected by direction, distance describes an object's entire movement. Displacement, in contrast, refers to a shift in an object's position. Because of this, the primary distinction between distance and displacement is that one is a scalar and the other is a vector.

According to question let us determine the total distance 2 miles+3 miles+6 miles+7 miles+3 miles =21 miles

So, this person has walked a total of 21 miles

Now let us find displacement vector as follows:

Divide into parts: Each leg on the Southeast and Southwest diagonals is the hypotenuse, therefore multiply by (2) /2.

x-axis is given as 2+3*(√ (2) /2) +0 -7(√ (2) /2) +3 =1.464

Similarly, y-axis is given as 0- 3(√ (2) /2)- 6- 7(√ (2) /2) +0=-13.071

The coordinates of the given ques are as follows: <1.464, -13.071>

By Pythagoras theorem, the hypotenuse of the given coordinates is 13.153 in northeast which is our required displacement.

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Answer:

answer in image blow

Step-by-step explanation:

The {-4, 0, 1} represents members of the domain of the graphed function.

What is the domain of the function?

A function is a mathematical object that accepts input, appears to apply a rule to it, and returns the result.

A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result.

The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs.

The range refers to the outputs which are actually used.

We have,

collection of the ordered pairs represents a function:

{(4, 19), (-2, 77), (0, 10), (1/2, 9/5), (1, 10), (-3, 0), (100, 100)

a) Domain of the function is:

{ -2, -3, 0, 1/2, 1, 4, 100}.

b) Range of the function is:

{ 0, 9/5, 10, 19, 77,  100}.

Hence, the Domain of the function is { -2, -3, 0, 1/2, 1, 4, 100} and the Range of the function is {0, 9/5, 10, 19, 77,  100}.

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Answer:

Below

Step-by-step explanation:

h = height = 0 when it hits the ground

sooooo...

  0 = -16t^2 + 20t + 1200   <==== you equation ommited the t' s  and 20t

           Use Quadratic Formula   a = -16    b = 20   c = 1200

                           to find t = 9.3 s

The translated vertices from the given vertices are:

A(3, -4) → A'(-2, -6)

B(-4, -2) → B'(-9, -4)

C(1, 1) → C'(-4, -1)

The translation rule for the coordinates of a graph is given by

(x, y) → (x + a, y + b)

Here the coordinates (x, y) are translated by (a, b) units.

The given vertices of a ΔABC are:

A(3, -4), B(-4, -2), and C(1, 1)

If the vertices are translated by T(-5, -2) units, then the new vertices after translation are calculated by using the rule (x, y) → (x + a, y + b). Here (a, b)  is (-5, -2).

Thus,

A(3, -4) → (3 - 5, -4 - 2) ⇒ A'(-2, -6)

B(-4, -2) → (-4 - 5, -2 - 2) ⇒ B'(-9, -4)

C(1, 1) → (1 - 5, 1 - 2) ⇒ C'(-4, -1)

Therefore, the translated version of the ΔABC is ΔA'B'C' and its vertices are A'(-2, -6), B'(-9, -4), and C'(-4, -1).

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The interquartile range (IQR) is a measure of dispersion, which is a measure of how spread out a data set is. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

Q1 = ( n +1 ) / 4th observation

    = ( 9 + 1) / 4

    = 2.5 th obseravation

That is the average of 2nd and 3rd observations.

Q1 = 2

Q3 = 3 ( n + 1) / 4 th observation

     = 3 ( 9 + 1) / 4

     = 7.5 th observation

That is the average of the 7th and 8th observation

Q3 = 5.5

Interquartile range = Q3 - Q1 = 5.5 - 2 = 3.5

In this data set, the first quartile is the average of the second and third observations (2), and the third quartile is the average of the seventh and eighth observations (5.5). Subtracting the first quartile from the third quartile gives us an IQR of 3.5. This means that the values in the data set are spread out over a range of 3.5 dollars.

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Answer:

Step-by-step explanation:

You want to identify the equations that are quadratic in form.

A polynomial equation is "quadratic in form" if the powers of the variables are integer multiples of {0, 1, 2}, or some subset of these that includes 2. That is, it will be "quadratic" if some substitution z = f(x) is possible such that the resulting equation in z is a polynomial equation of degree 2.

Term are degrees 0, 2, 4, so this is "quadratic in form". The substitution z=x^2 will give a quadratic in z.

Term degrees are 1 and 4, so this is not quadratic.

The substitution z = (x+5)^2 is suggested by the 4th-power term, but the remaining terms cannot be written as a linear function of z. This is not quadratic.

This is a straight quadratic equation. One could substitute z=2x+4, but that is not necessary. This is "quadratic in form."

Term degrees are 0, 2, 4, so this is "quadratic in form."

Term degrees are 1, 2, 4, so this is not quadratic.

A problem that could be solved by multiplying (−3) × (−6) is "the product of -3 and -6"

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

(-3) x (-6)

In the above expression, we can see that

-3 and -6 are multiplied

This means that the problem is a product expression

And a problem that can represent (-3) x (-6) is "the product of -3 and -6"

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Assume "in the event that p, q" is the given contingent assertion "in the event that ∼q, ∼p" is its contrapositive assertion. Consider the situation in which the conditional statement "if p, then q" serves as its converse statement.

Reversing the two statements that make up a categorical or implicational statement yields its opposite in logic and mathematics. The opposite of the implication P Q is Q P.

The converse statement (q p) and inverse statement (p q) of a conditional statement p q are equivalent to one another. The statement p q and its counter positive counterpart, q p, are equivalent.

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The length, b, which is the longest side of the triangle, can be found to be 13.172 cm.

To find the area of 22.4 cm², the formula used was:
Area = 1/2 x a x b x Sin(C)

Using this formula, we can find the value of side a to be :
22.4 = 1/2 x 3.7 x a x Sin(97°)

a = 12. 199 cm

We can then use the Cosine rule to find the value of b, which is the longest side:

b² = a² + c² - 2 x a x c x Cos(B)

b = √ ( a² + c² - 2 x a x c x Cos(B))

b = 13. 172 cm

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The total maximum electrical work the battery could perform during discharge is 11 kj.

When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is actually a function. Simply drawing a vertical line will reveal whether the graph is a function if it touches it once. The graph is not a function if the vertical line is higher. A function is defined technically as a relationship between a set of possible outputs and a set of inputs, where each input is associated to exactly one outcome.

Given

Work is dependent on power.

Power is function on voltage.

Voltage is linear, according to the query, so:

V(t) = at + V

a = Slope

a = 0.70 - 1.45/3600s

P(t) = V*I = V(t) *I (I= 2850 mA)

Then,

W= ∫03600 P(t) dt

=  ∫03600 ( at +1.45 )*I dt

= I × ∫03600 ( at +1.45 )dt

W= 2.850( a*36002 /2  + 1.45*3600)

W = 11

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The cost for a child ticket was $4 less than the cost of an adult ticket.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the cost of adult tickets be x.

The 5 children received a 20% discount on their tickets.

So;

x-20% of x

= (x-20/100) × x

= x-0.2x

= 0.8x

Here, 4x+5×0.8x=160

⇒ 4x+4x=160

⇒ 8x=160

⇒ x=20

So, the cost of children is 20-20% of 20

= 20-0.2×20

= 20-4

= 16

Therefore, the cost for a child ticket was $4 less than the cost of an adult ticket.

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a. The response variable in this study is the draft.

The response variable is the variable that is being measured or predicted in a study. It is also known as the dependent variable. The treatments are the standard hitch and the new hitch. The experimental units are the 25 randomly selected points in each plot.

b. Yes, randomization was used properly in this study.

By randomly assigning one plot to use the standard hitch and the other plot to use the new hitch, the researcher is ensuring that any difference in draft observed between the two plots is not due to any other factors besides the hitch.

c. No, replication was not used properly in this study. Replication involves taking multiple measurements of the same treatment to ensure that any observed differences between treatments are not due to random variation.

By only taking 25 measurements of each treatment, it is impossible to determine whether any observed differences are due to the treatment or just random variation.

d. Plot of land is a confounding variable in this experiment.

This is because the two plots may differ in soil type, terrain, and moisture, which can all affect the draft. This means that any observed difference in draft between the two plots may be due to the hitch, but it may also be due to the difference in environment between the two plots.

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Answer:

136 in^2

Step-by-step explanation:

The rectangle withOUT the missing part is 20 X 8 = 160 in^2

  now subtract the 4-12 traingle

           160   -   1/2 (4 X 12) = 136 in^2

Answer:

area of triangle = 1/2bh

= 1/2(4)(20-8)

= 1/2(4)(12)

= 24 in²

area of rectangle = lw

= 20(8)

= 160 in²

answer

= area of rectangle - area of triangle

= 160 - 24

= 136 in²

Step-by-step explanation:

Answer: The wording may be confusing, but the problem is simple.

All they are asking you to do is to plot those x-y value pairs as data points on a graph. Doing that is very basic to science. In science, you put your data on a chart and look at how it shapes up to draw conclusions.

So your first point has x=325.0 and y=1.10,

your second point has x=348.9 and y=1.40, and so on.

If using pencil and paper, your best bet is to use graphing paper, or at least grid paper. Then your first step would be setting up the scale on the axes. You need to fit points with y values between 0.25 and 1.40, so you may want to set the scale on the y-axis so it covers the range from 0 to 1.6 at least (maybe even 0 to 2). Your x values are between 230.0 and 348.9, so you could set up your x-axis so that it includes 0 to 360 (or 0 to 400). Alternatively, you may not include x values all the way down to zero and set your x scale from 200 to 360 only,

The conclusion that you would draw from your plot is that the power seems to vary linearly with speed. The data points are almost in a straight line. They are not perfectly aligned, of course. There is always some variability in accurate data, but you can see a trend. You could draw a line that seems to fit the points best and use it to predict that the power at 250 rpm would be 0.44 hp for example.

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

While D is a given factor for any number, 3 is the only number that 9 and 12 can be evenly divided by.

Answer:

14

Step-by-step explanation:

[tex]\frac{90n+90n}{n+1}=168 \\ \\ 180n=168n+168 \\ \\ 12n=168 \\ \\ n=14[/tex]

Answer:

Step-by-step explanation:

Let the sum of the original list of n numbers be S. The average of the list is given by:

average = S/n

Since the average is 90, we can write:

90 = S/n

Multiplying both sides by n, we get:

90n = S

After the number 90n is added to the list, the average of the list becomes 168. The sum of the list is now S + 90n. The number of elements in the list is now n+1. The average of the list is given by:

average = (S + 90n) / (n+1)

Since the average is 168, we can write:

168 = (S + 90n) / (n+1)

Multiplying both sides by n+1, we get:

168(n+1) = S + 90n

Substituting for S using the equation S = 90n, we get:

168(n+1) = 90n + 90n

Simplifying, we get:

168n + 168 = 180n

Subtracting 168n from both sides, we get:

168 = 12n

Dividing both sides by 12, we get:

14 = n

Therefore, n = 14.