A radiator has 20 L of a 52% antifreeze solution. How much must be drained and replaced by pure antifreeze to bring the concentration level up to 70%? 3.8 L of the 52% should be drained and replaced b

the slope of the line on the graph is 3 .

Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.

to find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .

the points i m choosing is (-2,0) and (-1,3)

now for finding the slope we will use the formula

m = (y2-y1)/(x2-x1)

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

m = 3 / 1

m = 3

so the slope of the line on the graph is 3 .

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Answer:

Infintely many solutions

Step-by-step explanation:

I'm going to assume that the capital y is equal to the lowerase y

if you subtract y and two from both sides in the second equation you get

-y=2x-2

you then divide by -1 to get it into a normal form

y= -2x+2

this is the same as the first equation, these lines are the same

Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = x^2, y = 0, x = 0, and x = 1 about the line x = 2 is (5/6)π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line, we use the method of cylindrical shells. The formula for the volume of a cylindrical shell is given as,
Volume = 2πrh * Δx

Where, r is the distance of the shell from the axis of rotation, h is the height of the shell, and Δx is the thickness of the shell. The factor 2π accounts for the entire circumference of the shell.
Example problem: Find the volume of the solid generated by rotating the region bounded by the curves y = x^2, y = 0, x = 0, and x = 1 about the line x = 2.
Solution:
Step 1: Draw the graph of the region to be rotated
Step 2: Identify the shell radius and height
For a shell at position x, the radius is given by r = 2 - x (the distance of the line x = 2 from the axis of rotation)
The height of the shell is given by h = x^2 (the difference between the top and bottom curves)
Step 3: Write the volume formula
Volume = 2πrh * Δx
Step 4: Integrate to find the total volume
The limits of integration are from 0 to 1 since the curves intersect at (0,0) and (1,1).
\(∫ 2π(2 - x)(x^2) dx from 0 to 1\)
= \(2π [∫ 2x^2 - x^3 dx from 0 to 1]\)
= \(2π [(2/3) - (1/4)]\)
= 2π [5/12]\(2π [5/12]\)
= (5/6)π cubic units
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Answer:

0<x<3 and 8<x<9

Step-by-step explanation:

Increasing intervals always relate to x-values. The increasing interval is from (0,3) and (8,9).

Answer:

.16

Step-by-step explanation:

So, we're looking for 0.4% of 40.  First, let's convert 0.4% to a decimal.  Since a percent is really just PARTS of one hundred, this decimal really means 0.4/100.  0.4 divided by 100 is 0.004.  Next, we need to figure out how to solve this problem!  To find a percent of a number, just multiply the percent (in decimal form) by the number!  So, we need to answer 0.004*40, which equals 0.16.

Answer: 0.16

A. The power of the two-tailed hypothesis test with α = .05 is 0.53.

B. The power of the one-tailed hypothesis test with α = .05 is 0.95.

A hypothesis test is used to make decisions about a population based on sample data. It involves specifying a null hypothesis, collecting data, and then assessing the data to either reject or accept the null hypothesis.

A. The power of the two-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- (1-α)\(^{1/2}\)

=1- (1-0.05)\(^{1/2}\)

=0.525

=0.53

This means that the researcher has an 53% chance of correctly rejecting the null hypothesis that there has been no change in the IQ over the past 10 years.

B. The power of the one-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- α

=1- 0.05

= 0.95

This means that the researcher has a 95% chance of correctly rejecting the null hypothesis that there has been no increase in the IQ over the past 10 years.

This is a higher power than the two-tailed test because the one-tailed test focuses on detecting an increase in the IQ, while the two-tailed test can detect both an increase or decrease in the IQ.

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He answers rounded to the correct number of decimals/sig. figs are:a. 15.0 b. 408.1 c. 369 d. 68.65

a. 12.5849+2.4Adding 12.5849 and 2.4 gives: 15. 0 (rounded to one decimal place)  b. 432.5−24.3984Subtracting 24.3984 from 432.5 gives: 408. 1 (rounded to one decimal place)  c. 246×1.5Multiplying 246 and 1.5 gives: 369 (no rounding required)  d. 974.59/14.2Dividing 974.59 by 14.2 gives: 68.65 (rounded to two decimal places)

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To find sin(t), cos(t), and tan(t) for the terminal point P(x, y) = (1/5, -2/6), we can use the trigonometric definitions based on the coordinates of the point.

First, let's find the values of sin(t) and cos(t):

sin(t) = y/r

cos(t) = x/r

where r is the distance from the origin to the point P, given by the formula:

r = sqrt(\(x^2\)+ \(y^2\))

In this case, x = 1/5 and y = -2/6. Let's calculate the values:

r = sqrt((\(1/5)^2\) + \((-2/6)^2\)) = sqrt(1/25 + 4/36) = sqrt(36/900 + 100/900) = sqrt(136/900) = sqrt(17/225) = sqrt(17)/15

sin(t) = (-2/6) / (sqrt(17)/15) = (-2/6) * (15/sqrt(17)) = -5/sqrt(17)

cos(t) = (1/5) / (sqrt(17)/15) = (1/5) * (15/sqrt(17)) = 3/sqrt(17)

Finally, we can calculate tan(t) using the formula:

tan(t) = sin(t) / cos(t)

tan(t) = (-5/sqrt(17)) / (3/sqrt(17)) = -5/3

Therefore, the values are:

sin(t) = -5/sqrt(17)

cos(t) = 3/sqrt(17)

tan(t) = -5/3

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The area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10 is 174/3 units².

To find the area of the region enclosed by the curves 10x=2y²+12y+19 and x=-4y-10, we need to solve this problem in the following way:

Since the curves are already in the form of x = f(y), we need to use vertical strips to find the area.

So, the integral for the area of the region is given by:

A = ∫a b [x₂(y) - x₁(y)] dy

Here, x₂(y) = 10 - 2y² - 12y - 19/5 = - 2y² - 12y + 1/2 and x₁(y) = -4y - 10

So,

A = ∫(-3)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy + ∫(-2)⁻²[(-2y² - 12y + 1/2) - (-4y - 10)] dy

=> A = ∫(-3)⁻²[2y² + 8y - 19/2] dy + ∫(-2)⁻²[2y² + 8y - 19/2] dy

=> A = [(2/3)y³ + 4y² - (19/2)y]₋³ - [(2/3)y³ + 4y² - (19/2)y]₋² | from y = -3 to -2

=> A = [(2/3)(-2)³ + 4(-2)² - (19/2)(-2)] - [(2/3)(-3)³ + 4(-3)² - (19/2)(-3)]

=> A = 174/3

Hence, the area of the region enclosed by the curves is 174/3 units².

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The correct answer is d) f^(-1)(x) = x/3, as it represents the Inverse relationship of y = 3x.

To find the inverse of a function, we need to switch the roles of x and y and solve for the new y.

The given function is y = 3x.

To find its inverse, let's swap x and y:

x = 3y

Now, solve this equation for y:

Dividing both sides of the equation by 3, we get:

x/3 = y

Therefore, the inverse function of y = 3x is f^(-1)(x) = x/3.

Among the given options:

a) f^(-1)(x) = 1/3x

b) f^(-1)(x) = 3x

c) f^(-1)(x) = 3/x

d) f^(-1)(x) = x/3

The correct answer is d) f^(-1)(x) = x/3, as it represents the inverse relationship of y = 3x.

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Determine the y-intercept of the equation -x + 2y = 10

a. 1

b.-10

C. 5

d. 2

__________________________________________

y-intercept is (0, b)

y = mx +b

-x + 2y = 10

2y = x +10

y = 1/2 x + 5

______________

if x= 0

y= 1/2 *0 +5

y= 5

____________________

The y-intercept is (0, 5 )

The answer is c

To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

Using the tangent function, we can set up the following equation: tan(40°) = opposite/adjacent. tan(40°) = distance between the buildings/20 meters. To find the distance between the buildings, we rearrange the equation: distance between the buildings = 20 meters * tan(40°). Using a calculator, we can evaluate the expression: distance between the buildings ≈ 20 meters * 0.8391 ≈ 16.782 meters. Therefore, the buildings are approximately 16.782 meters apart. To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

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it's true...........

Answer:

False

Step-by-step explanation:

Verified correct with test results.

The equation has x = 2 and x = 5. A valid solution for x is x = 5

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

√(x - 1) - 5 = x - 8

Add 5 to both sides

This gives

√(x - 1)  = x - 3

Square both sides

So, we have the following representation

x - 1 = x² - 6x + 9

Evaluate the like terms

x² - 7x + 10 = 0

This gives

(x - 2)(x - 5) = 0

Solve for x

x = 2 and x = 5

Testing the solutions, we have

√(2 - 1) - 5 = 2 - 8

-4 = -6 ---- falsee

√(5 - 1) - 5 = 5 - 8

-3 = -3 ---- true

Hene, the valid value of x is 5

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Answer:

Step-by-step explanation:

1. \(\sqrt{72}\)  break it apart so you can solve

   \(\sqrt{2} *\sqrt{36}\)

   \(\sqrt{2}\) * 6

   6\(\sqrt{2}\)

It's irrational. \(\sqrt{2}\) can not be written as a ratio.

2.

   rational

   a.  -9  

         3.0

         \(\frac{2}{5}\)

         2.4222...    2/90 = .22222....     36/90 = .4    180/90 = 2

                            2+36+180 = 218/90 which is a ratio, so it's rational

   irrational

   b.  \(\sqrt{8} = 2\sqrt{2}\)  

          \(\pi\)

3.

    6.51326.... and \(\sqrt{39}\)

The \(\sqrt{39}\) = 6.2445

Comparing to the 6.51326, it has a difference of 0.268262. Thus, 6.51326 is greater than square root of 39.

Answer:

Step-by-step explanation:

Rules:

Take out the GCF (greatest common factor)

a)  \(9m^{4} -9m^{3}\)             >take out GCF, what both terms can be divided by

  =9m³(m-1)                >when taking out GCF, divide both terms by GCF

b)  \(25x^{9}y^{10}-35x^{7}y^{5}\)    >GCF is \(=5x^{7}y^{5}\)

\(=5x^{7}y^{5}(5x^{2} y^{5}-7)\)

c)   (x-1)(x-1)-3(x-1)​        >GCF is (x-1)

  =(x-1) [(x-1) - 3]          >within the bracket you can combine like terms

  =(x-1) (x-4)

Step-by-step explanation:

A) 9m^4 - 9m^3 = 9m^3 (m - 1)

As for the number, you already took 9 out because it's common for both. As for the m, m^4 is the same as m×m×m×m. So the common between both is m×m×m = m^3.

B) 25x^9y^10 - 35x^7y^5 umm are you sure it's well written? How do you have a power in a power?

C) (x-1)(x-1)-3(x-1) = (x²-1x-1x+1) - (3x-3)

= x² - 2x + 1 - 3x + 3

= x² - 5x + 4

1. The random process: Roll the dice 10 times: even = make; odd = miss

2. Repeat the above process many times, such as 10,000 trials.

Probability is a scale from 0 to 1, with 0 denoting impossibility and 1 denoting certainty, that expresses the likelihood of an event occurring.

It aids us in making predictions and decisions based on uncertain or random outcomes by representing the relative frequency of an event's occurrence in a set number of trials.

Assuming that the player is able to make 50% of his three-point shots, we can model each shot as a Bernoulli trial with probability of success p=0.5.

To simulate this scenario using a die, we can roll a fair six-sided die 10 times and consider even numbers as a successful shot (making the shot) and odd numbers as a failed shot (missing the shot).

We then repeat this process many times, such as 10,000 trials, and count the number of times the player misses 7 or more shots in the first 10 attempts. We can use this count to estimate the probability of this outcome.

Therefore, the correct options for each step of the simulation are:

3. Count the number of trials where the player misses 7 or more shots in the first 10 attempts, and divide by the total number of trials (10,000) to estimate the probability.

If the probability is low (say, less than 5%), then we can conclude that missing 7 or more shots in the first 10 attempts is a surprising result, given the player's claim of making 50% of his three-point shots.

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The angular coordinate, angular velocity, and angular acceleration of the flywheel are: (a) At t = 0, θ = θ0 = 0.5 rad, ω = 0, and α = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = 4.116 rad/s, and α = -69.08 rad/s².

The given equation for the angular displacement of the flywheel is θ=θ0e(-3πcos(4πt)). Here, θ0 = 0.5 rad. To find the angular velocity and angular acceleration, we need to differentiate θ with respect to time.

θ = θ0e(-3πcos(4πt))

ω = dθ/dt = -12π²θ0e(-3πcos(4πt))sin(4πt)

α = d²θ/dt² = -48π³θ0e(-3πcos(4πt))(cos(4πt) - 2)sin(4πt)

Substituting t = 0, we get:

(a) At t = 0, θ = θ0 = 0.5 rad, ω = dθ/dt = 0, and α = d²θ/dt² = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = dθ/dt = 4.116 rad/s, and α = d²θ/dt² = -69.08 rad/s².

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The following statements can be concluded if ∠ABC and ∠CBD are a linear pair:

B. ∠ABC and ∠CBD are supplementary.

D. ∠ABC and ∠CBD are adjacent angles.

In Mathematics, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both form a linear pair. This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.

According to the linear pair theorem, ∠ABC and ∠CBD are supplementary angles because BDC forms a line segment. Therefore, we have the following:

∠ABC + ∠CBD = 180° (supplementary angles)

m∠ABC ≅ m∠CBD (adjacent angles)

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Answer:

10/15

simplest form:2/3

Step-by-step explanation:

Answer:

$125

Step-by-step explanation:

a rent collector is entitled to 2½% of all rents collected if he collected rents totaling $5,000.00 calculate his commission:

2 1/2% = 0.025

$5,000 * 0.025  = $125

Answer:

A.

they choose candidates before the general election

If a simple Pearson correlation value = .685, the percentage of variance accounted for by the correlation is 47%.

To determine the percentage of variance accounted for by a Pearson correlation coefficient, we need to square the correlation coefficient and multiply it by 100.

In this case, the given correlation coefficient is 0.685. Squaring this value gives us 0.469225. Multiplying this by 100, we find that the percentage of variance accounted for by the correlation is approximately 46.92%.

Therefore, the correct answer is c. 47%.

The squared correlation coefficient, also known as the coefficient of determination (\(r^2\)), represents the proportion of the variance in one variable that can be explained or accounted for by the linear relationship with the other variable. It indicates the strength and extent to which the two variables are related.

In this case, the \(r^2\) value of approximately 0.469225 means that approximately 46.92% of the variance in the dependent variable can be explained by the linear relationship with the independent variable. The remaining 53.08% of the variance is attributed to other factors or sources of variation that are not accounted for by the correlation.

Understanding the percentage of variance accounted for by a correlation is valuable in assessing the strength and meaningfulness of the relationship between variables. A higher \(r^2\) value indicates a greater proportion of variance explained, indicating a stronger and more predictive relationship between the variables.

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As per the given values, the value of α in this common base connection is 22.5.

IC = 0.9 mA

IB = 0.04 mA

A base is the arrangement of digits or letters and digits that a counting system employs to represent numbers. The collector current to base current ratio in a common base connection is known as the current gain, and is usually bigger than ten. It is required to divide IC by IB to obtain the value of α

Calculating the value of α -

α = IC / IB

Substituting the given values in the formula:

= 0.9 / 0.04

= 22.5

Therefore, after solving it is found that the value of α in this common base connection is 22.5.

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a) -3x + 7y = 28 -4x + 3y = 12

7y - 28 = 3x

x = (7y - 28)/3

Substitution

-4(7y - 28)/3 + 3y = 12

-4(7y - 28)/3 = 12 - 3y

-4(7y - 28) = 3(12 - 3y)

-28y + 112 = 36 - 9y

112 - 36 = 28y - 9y

76 = 19y

y = 76/19

y = 4

x = [(7*4) - 28)]/3

x = [28 - 28]/3

x = 0/3

x = 0 Result x = 0, y = 4

b) x + 3y = -7 -7x - 4y = -19

x = -7 - 3y

Substitution

-7(-7 - 3y) - 4y = -19

49 + 21y - 4y = -19

17y = -19 - 49

17y = -68

y = -68/17

y = -4

x = -7 - 3(-4)

x = -7 + 12

x = 4 Result x = 4, y = -4

c) 3x + 2y = 4 6x - 3y = -27

x = (4 - 2y)/3

Substitution

6(4 - 2y)/3 - 3y = -27

6(4 - 2y)/3 = -27 + 3y

6(4 - 2y) = 3(-27 + 3y)

24 - 12y = -81 + 9y

-12y - 9y = -81 - 24

-21y = -105

y = -105/-21

y = 5

x = (4 - 2(5))/3

x = (4 - 10)/3

x = -6/3

x = -2 Result x = -2, y = 5

d) It is not complete

e) -x + 4y = -5 x - 6y = 7

x = 7 + 6y

-(7 + 6y) + 4y = -5

-7 - 6y + 4y = -5

-6y + 4y = -5 + 7

-2y = 2

y = 2/-2

y = -1

x = 7 + 6(-1)

x = 7 - 6

x = 1 Result x = 1, y = -1