How many gallon of a 14%-alt olution mut be mixed with 6 gallon of a 25%-alt olution to obtain a 20%-alt olution?

The area of the rectangle is 72 cm^2.

Let's call the side length of each square s.

Since the perimeter of each square is 24 cm, then each side measures 24 cm / 4 = 6 cm.

So the length of the rectangle is 2s = 2 * 6 cm = 12 cm.

And the width of the rectangle is s = 6 cm.

Therefore, the area of the rectangle is A = l * w = 12 cm * 6 cm = 72 cm^2.

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The area of the rectangle is 72 square centimeters.

The rectangle is formed by placing two identical squares side by side the perimeter of each square is 24 cm.

Remember that for a square of sidelength S, the perimeter is P = 4*S

Then the sidelength of the squares is

24cm = 4*S

24cm/4 = 6cm = S

When we place these two squares together, we will have a rectangle of 6cm by 12cm, and the area is the product of the dimensions, then the area is:

A = 6cm*12cm = 72cm²

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My puppy is racing away from me at a rate of 200 feet per minute, while I am moving at a rate of 270 feet per minute. Yes, you will catch the puppy after 4 minutes

What is the relation between time and distance?

The relation between time and distance is defined as the ratio of speed and distance. We stand in the frame of reference where he is still, in this frame the speed of the puppy will be equal to the speed of the puppy in our previous frame plus the speed of him in the previous frame (because they are running in opposite directions). Speed =  270 - 220 = 50 feet per minute. My puppy is running away at a speed of 220 feet per minute. The distance between him and puppy = 200 feet Speed of him = 270 feet per minute.

For example if a car travels for 2 hours and covers 120 miles we can work out speed as 120 ÷ 2 = 60 miles per hour. The units of the the distance and time tell you the units for the speed.

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There are 640 students are expected to choose chocolate as their favorite ice cream.

How many students are expected to choose chocolate as their favorite ice cream flavor if there are 700 students in the school?

Total number of student =700

no of students are expected to choose chocolate as their favorite ice cream be x

school are randomly selected and asked about their favorite ice cream flavor =60

60+x=700

x=700-60=640

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Answer:

Step-by-step explanation: just / the $7.04 by 8 since there is 8 bars then boom

You can determine if the inverse of a polynomial function is a function by using the Horizontal Line Test on the inverse.

The Horizontal Line Test is a graphical method that can be used to determine whether a given function is one-to-one, meaning that for each output value, there is at most one input value that maps to it.

If the inverse of a polynomial function is a function, it must pass the Horizontal Line Test, meaning that no horizontal line intersects the graph of the inverse more than once.

In other words, if the inverse of a polynomial function passes the Horizontal Line Test, it is guaranteed to have an inverse, which will be a function itself. If the Horizontal Line Test fails, then the inverse is not a function and does not have an inverse.

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We can see that p-q = 1, which implies that p and q are directly related.

(a) If x and y are inversely prοpοrtiοnal, then we knοw that xy = k fοr sοme cοnstant k.

If [tex]x^p[/tex] and [tex]y^q[/tex] are alsο inversely prοpοrtiοnal, then we can write [tex](x^p)(y^q) = k'[/tex] fοr sοme cοnstant k'. Using the inverse prοpοrtiοnality relatiοn, we get:

[tex](x^p)(y^q) = k'[/tex]

[tex](xy)^pq = k'[/tex]

[tex](k)^pq = k'[/tex]

[tex]k^(pq-1) = k'[/tex]

Frοm this equatiοn, we can see that pq-1 = 0, which implies that pq = 1. Therefοre, p and q are inversely related.

(b) If x and y are inversely prοpοrtiοnal, then we knοw that xy = k fοr sοme cοnstant k.

If [tex]x^p[/tex] and [tex]y^q[/tex] are directly prοpοrtiοnal, then we can write [tex](x^p) = k'(y^q)[/tex] fοr sοme cοnstant k'. Using the direct prοpοrtiοnality relatiοn, we get:

[tex](x^p) = k'(y^q)[/tex]

[tex](xy)^p = k'(y^q)(k)[/tex]

[tex]k^p = k'(y^{(q-1)})[/tex]

[tex]k^{(p-q)} = k'[/tex]

Frοm this equatiοn, we can see that p-q = 1, which implies that p and q are directly related.

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The area under the curve y = 3x³ + 4x from x = 1 to x = 2 is 4 square units.

A curve is a continuous, smooth, and often repeating shape in the plane or in space. It is a geometric object that can be described mathematically by an equation or a set of points.

In mathematics, curves are used to model real-world phenomena and to study geometric and mathematical properties. For example, curves can be used to describe the shape of objects, the path of moving objects, or the graph of a mathematical function.

There are many types of curves, including lines, circles, ellipses, parabolas, hyperbolas, and spirals, among others. Each type of curve has unique properties and characteristics, and they are studied and used in different ways in different fields of mathematics and science.

In physics, curves are used to describe the motion of objects and the behavior of physical systems. For example, the trajectory of a projectile can be modeled by a parabolic curve, while the path of a planet around the sun can be modeled by an elliptical curve.

To find the area under the curve y = 3x^3 + 4x from x = 1 to x = 2, we can use the definite integral:

∫[1,2] (3x^3 + 4x) dx

To evaluate this integral, we can use the power rule for integration: ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.

Using this rule, we get:

∫ (3x³ + 4x) dx = ∫ 3x³ dx + ∫ 4x dx = x^4/4 + 2x² + C

Evaluating this definite integral from x = 1 to x = 2, we get:

[tex][x^{\frac{4}{4}+2x^{2} } ]2-[x^{\frac{4}{4}+2x^{2} } ]1=(2^{\frac{4}{4} }+22^{2} ) -(1^{\frac{4}{4} } +21^{2} )=\frac{21}{4}-\frac{16}{4}=4[/tex]

So the area under the curve y = 3x^3 + 4x from x = 1 to x = 2 is 4 square units.

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The initial rate of c production is -0.100k, where k is the rate constant of the reaction.

The rate of production of c (δ[c]/δt) can be determined using the equation of the rate of reaction [tex]\ce{A + B - > C}[/tex] . The rate of reaction is given by

[tex]\begin{equation} \frac{\delta[C]}{\delta t} = -k[A][B]\end{equation}[/tex]

where k is the rate constant of the reaction. If the initial concentrations of a and b are given, the rate of c production can be calculated.

In this problem, the initial concentration of a and b are given as [a] = 0.200 M and [b] = 0.500 M. Therefore, using the equation given above, the initial rate of c production is

[tex]\begin{equation} \frac{\delta[C]}{\delta t} = -k[A][B] = -k(0.200)(0.500) = -0.100k\end{equation}[/tex]

Therefore, the initial rate of c production is -0.100k, where k is the rate constant of the reaction.

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Answer:

Step-by-step explanation:

Take any two pairs of coordinates to find the slope.

The forumla for slope is (y2-y1)/(x2-x1)

Wil will choose the points (2,10) and (4,20)

Therefore:

m = (20-10)/(4-2)

m = 5

The weight of a hamburger can be considered a continuous random variable.

A random variable is a mathematical representation of a random phenomenon.

In probability and statistics, the weight of a hamburger can be used to illustrate the concepts of discrete and continuous random variables.

A discrete random variable is one that can only take on specific, distinct values.

For example, the number of hamburgers sold at a fast food restaurant in one day could be considered a discrete random variable, as the number of hamburgers sold can only be a whole number.

On the other hand, a continuous random variable is one that can take on an infinite number of values within a given range.

The weight of a hamburger could be considered a continuous random variable, as the weight of a hamburger can take on any value within a certain range, such as between 0.1 and 0.5 kilograms.

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The mystery number 'm' that satisfies the stated conditions is - 8.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, Tameeka's mystery number be 'm'.

So, When you add 16 to mystery number then subtract 20,

m + 16 - 20,

you get the same result as when you add mystery number to itself, then add 20 and subtract 16,

m + m + 20 - 16.

Therefore,

m + 16 - 20 = m + m + 20 - 16

m - 4 = 2m + 4.

- m = 8.

m = - 8.

So the Tameeka’s mystery number (m) is -8.

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The Fahrenheit value is 97.52

How To Convert 36.4 °C to °F?

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The coach made a mistake in converting the average rate from miles per hour to feet per second. To convert miles per hour to feet per second, the formula is (miles per hour) x (5280 feet/mile) / (60 minutes/hour) = (feet per second).

However, the coach used a different conversion factor, which resulted in an incorrect value. This incorrect value led the coach to conclude that Aliza was not running fast enough, when in reality, the actual rate could be higher than 8.2 feet per second.

Therefore, the coach made an error in the conversion factor used and in the conclusion based on the incorrect converted value.

The two equations are y = - 1 and y = (1/5)x - 12/5 and the solution to the system is (7, - 1).

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The first line passes through (- 1, 0) and (2, - 1).

Slope(m) = (- 1 + 1)/(2 - 0).

Slope(m) = 0.

- 1 = 0(2) + b.

b = - 1.

y = - 1.

A horizontal line at y = - 1.

The second line passes through (4, - 2) and (- 3, - 3).

Slope(m) = (- 3 + 2)/(- 3 - 4).

Slope(m) = - 1/- 5.

Slope(m) = 1/5.

- 3 = (1/5)(- 3) + b.

b = 3/5 - 3.

b = (3 - 15)/5.

b = - 12/5.

y = (1/5)x - 12/5.

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Madeline should not ask for the loan

1. With college loan:

DTI  = 43.9%    

2. Without the college loan

DTI = 29.3%

Calculate the DTI for both scenaries, with and without the college loan.

DTI = (monthly debt payments) / (gross monthly income) × 100

                                   With college loan     W/O college loan

Monthly debt payments($)

      Taxes                                    145                              145

      Credit card                            90                                95

       College loan                        120                                  0

               Sub-total                    360                              240

Montly gross income ($)             820                              820

1. With college loan:

DTI  = (360/820)×100 = 43.9%    

2. Without the college loan

DTI = (240/820)×100 = 29.3%

There are several rules to assess if a DTI is good or not.

Some of those rules include that:

A DTI without a mortgage should be below 28%, thus 29.3% is slightly over the limit.

A DTI with a mortgage should be below 43%, thus 43.9% is slightly over the lilmit.

The 20% rule states that the debt without a mortgage should be no more than 20 percent of the annual income after taxes.

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To convert cups to pounds, you can use the following conversion factor   1 cup = 0.5 pounds

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thats how u calculate this Use the angle fact that angles in a full turn add to 360°. To work the bearing, subtract 130° from 360°. 360° – 130° = 230° and so, the bearing of A from B is 230°.

Rounding off to the nearest whole number, the value of the investment at maturity would be $15,108.

What is the whole number?

A whole number is a positive integer that has no fractional or decimal component. Whole numbers include 0, 1, 2, 3, 4, and so on.

The formula to calculate the future value of an investment is given by: y = a (1 + r)t, where y is the future value, a is the initial investment, r is the rate of return as a decimal, and t is the time in years.

In this case, the initial investment is $7,000, the rate of return is 10% (or 0.10 as a decimal), and the time in years is 14. So, the calculation would be:

y = $7,000 * (1 + 0.10)^14

y = $7,000 * 1.10^14

y = $7,000 * 2.151373

y = $15,108.16

Rounding off to the nearest whole number, the value of the investment at maturity would be $15,108.

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The number of students that answered Malachi's question is 20 students.

A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous or discrete data. It is a bar graph that displays the number of data points within specified ranges or bins, allowing for the observation of patterns, trends, and anomalies in the data.

The height of each bar in the histogram represents the frequency of data within the corresponding bin or range, providing a visual representation of the distribution of the data.

In this case, we have that the number of students that answered the question are;

1 + 4 + 10 + 4 + 1 = 20 students

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Answer:

20

Step-by-step explanation:

i got it correcttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

The is used as a measure of to overcome the range is influenced too much by .

?

are then selected as 3 points such that

they create four groups in the data, each groups approximately possessing 25% of the data.

(inter quartile range) is defined as the between third and first quartile.

Since, range is used as a measure of to overcome the difficult of the range.

The interquartile range can be affected by , so the IQR (interquartile range) is used as a better of the range.

Hence, The interquartile range is used as a measure of variability to overcome the range is influenced too much by

Learn more about here:

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The interquartile range is used to overcome the difficulty of range as a measure of variability which is affected by outliers.

The range is a measure of variability which is determined by calculating the difference between the highest and lowest values in a dataset. However, this measure of variability can be affected by outliers - values that are unusually high or low. For example, if a dataset includes one value that is much higher than the rest, then the range will be much higher than it would be without the outlier. The interquartile range is used to overcome this difficulty by ignoring the outliers when calculating the range. It is calculated by dividing the data into quartiles and then subtracting the lower quartile from the upper quartile. This gives a more reliable measure of variability as it ignores the outliers and is not affected by them.

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Answer:

The part to whole ratio for n sixth-grade band to t total sixth graders is

n/t.

What is ratio?

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics as well as in science.

In our daily life, we use the concept of ratio and proportion such as in business while dealing with money or while cooking any dish, etc.

Now,

Given There are n sixth-grade band members and t total sixth graders

Therefore, part-to-whole ratio = n/t.

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The value of the double integral is [tex]$-\frac{\pi}{12}$[/tex].

We are given that;

∫∫D^y^dA where d is the set of points (x, y)

0 ≤ 2x/ π ≤ y, y ≤ sin x

Now,

We can see that x varies from 0 to [tex]\pi[/tex], and for each fixed x, y varies from [tex]\frac{2x}{\pi} to \sin x[/tex]. Therefore, we can write the double integral as:

[tex]$$\iint_D y \, dA = \int_0^\pi \int_{\frac{2x}{\pi}}^{\sin x} y \, dy \, dx$$[/tex]

Now we can evaluate the inner integral with respect to y:

[tex]$$\int_{\frac{2x}{\pi}}^{\sin x} y \, dy = \frac{y^2}{2} \bigg|_{\frac{2x}{\pi}}^{\sin x} = \frac{\sin^2 x}{2} - \frac{2x^2}{\pi^2}$$[/tex]

Plugging this result into the outer integral, we get:

[tex]$$\iint_D y \, dA = \int_0^\pi \left( \frac{\sin^2 x}{2} - \frac{2x^2}{\pi^2} \right) dx = \frac{1}{4} \int_0^\pi (1 - \cos 2x) dx - \frac{2}{\pi^2} \int_0^\pi x^2 dx$$[/tex]

Using the antiderivatives of [tex]\cos 2x[/tex] and x^2, we get:

[tex]$$\iint_D y \, dA = \frac{1}{4} (x - \frac{1}{2} \sin 2x) \bigg|_0^\pi - \frac{2}{\pi^2} (\frac{x^3}{3}) \bigg|_0^\pi =\frac{\pi}{4} - 0 - 0 + 0 - \frac{2}{\pi^2} (\frac{\pi^3}{3}) + 0 =\frac{\pi}{4} - \frac{2\pi}{3} =-\frac{\pi}{12}$$[/tex]

Therefore, by integral the answer will be [tex]$-\frac{\pi}{12}$[/tex].

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An equation that represents the Kim's and her sister's age combined is,

x + k = n.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Let k represents Kim's age, and x represents her sister's age.

Let the combined age is n.

Then,

an equation that represents the Kim's and her sister's age combined is,

x + k = n.

Therefore, the equation is x + k = n.

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Answer:

Below

Step-by-step explanation:

See diagram below   solve the angles in order 1-2-3-4-5-6

as shown in the diagram:

Answer:

85 degrees

Step-by-step explanation:

Okay, let's have a look at the triangle on the left.
We can see an exterior angle of 115 degrees, adjacent to the interior angle.
Thus, as they both form a line (180 degrees), Interior angle = 180 - 115
= 65 degrees
We know that all the angles of the triangle equal 180.
Now to find the remaining angle of the triangle on the left,
180 - (85 + 65) = 30 degrees

Moving towards the center, we have our interior triangle angle (30 degree), a 90 degree angle and an interior angle of the triangle on the right. So, as they all form a line, the interior angle of the triangle on the right will be
180 - (90 + 30) = 60 degrees

Also, on top of the triangle on the right, we have a 115 degree exterior angle again.
Repeating our first step, the interior angle would be 65 degree

Now to find the remaining angle of the triangle on the right,
180 - (30 + 65) = 95 degrees

This angle forms a line with another angle exterior to this one, so again,
180 - 95 = 85 degrees

Hope this helps

the integral value of = ∫ √3 9 arctan( 1 x) dx is: 9 {√3x/6 - π/4 + 1/2 ln 2}

Integration in mathematics is a technique for integrating or adding up the parts to get the total. By breaking down the functions into their component pieces, differentiation is carried out in reverse. The summation under a broad scale is found using this approach. The process of combining smaller parts or information from various subsystems into a single operational unit is known as integration. By breaking down the functions into their component pieces, differentiation is carried out in reverse. The summation under a broad scale is found using this approach.

Given that,

= [tex]\int\limits^{\sqrt{3}}_1{9arc\tan(1/x)} \, dx[/tex]

= [tex]9\int\limits^{\sqrt{3}}_1{tan^{-1}(1/x)} \, dx[/tex]

= [tex]9\int\limits^{\sqrt{3}}_1{cot^{-1}(x)} \, dx[/tex]

[As here we use tan⁻¹(1/x) = cot⁻¹x]

We integrate cot⁻¹x by parts by taking cot⁻¹x as I function.

= [tex]9{[cot^{-1}(x)\int\limits\, dx]{^\sqrt{3}} _1 - \int\limits^\sqrt{3}} _1 {d/dx (cot^{-1}x \int\limits\, dx }[/tex]

= 9 {√3x/6 - π/4 + 1/2 ln 2}

Thus, the integral value of = ∫ √3 9 arctan( 1 x) dx is: 9 {√3x/6 - π/4 + 1/2 ln 2}.

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The volume of the solid obtained by rotating the region bounded by x = y² and x = 1 − y² about x = 4 is 16.

The volume of a solid obtained by rotating a region about a line is calculated by using the method of cylindrical shells.

In this problem, we are given the region bounded by the curves x = y² and x = 1 − y², and we are asked to find the volume of the solid obtained by rotating this region about the line x = 4

Next, we set up a coordinate system with the y-axis being the axis of rotation and the x-axis being the height of the cylindrical shell.

We will be rotating the region about the line x = 4, so the width of the cylindrical shell is 4 - y².

The height of the cylindrical shell is the change in x from one shell to the next, which is given by the bounds of the region. The circumference of the shell is

=> 2πy,

and the width of the shell is 4 - y².

We integrate the product of these three quantities over the bounds of the region to find the total volume of the solid.

This integration can be done using a definite integral, with the bounds being the y-coordinates of the two points where the curves intersect.

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Based on the residual plot, it is possible to determine whether a regression model is a good fit or not.

A residual plot is a scatterplot of the residuals (the differences between the actual values and the predicted values) against the predicted values. A good regression model should have residuals that are randomly distributed around zero and have roughly equal variance across the range of predicted values.

If the residuals form a pattern, such as a U-shape or a curve, it indicates that the model is not a good fit for the data. Additionally, if there are outliers or extreme values in the residual plot, it suggests that the model may not be appropriate for those observations.

Correct Question :

Based on the residual plot, how do you think that regression model is a good fit?

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