at a gas station, lora took 1/6 minute to fill 3/5 gallon of gas. at this rate, how many gallons of gas could lora fill in 1 minute?

The answer for this Simplifiction 4x3−12x24x2 7x−22x2−6x5x2 11x 2 using  BODMASS rule is -19316

=4*3-12*24*27*-22*2-6*5*211*2

=-19316

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Answer:

The equation of the line in slope-intercept form is: y = 1/3x + 2

To derive this equation, we first need to identify the slope of the line, which is given as 1/3. We then use the point (0,2) to find the y-intercept, which is 2. Finally, we substitute these values into the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we have m = 1/3 and b = 2, so the equation of the line is y = 1/3x + 2.

Alternatively, we could use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, we have (x1, y1) = (0,2) and m = 1/3, so the equation of the line is y - 2 = 1/3(x - 0), which simplifies to y = 1/3x + 2. This is the same result as before, but using a different method to derive the equation.

Step-by-step explanation:

The slope of the line is  4/3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

In the slope marked,

vertical length = change in y values = number of unit squares = 4

Horizontal length = change in x values = number of unit squares = 3

Slope= ( change in y values  )/ ( change in x values ) = 4/3

Thus, the slope = 4/3

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After 13 years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old iddm women, if the incidence rate remains constant over time.

In this question we have been given the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.

We need to find the number of years after which we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time.

Let n be the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females.

The probability of becoming blind over n years is 0.10

Given that the annual incidence rate of blindness per year was 0.74% IDDM females.

This means the rate r = 0.0074

For n years the annual incidence rate of blindness  0.0074n

We need to find the value of n,

0.0074n = 0.10

n = 13.51

n ≈ 13 years

Therefore, the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females = 13

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The complete question is:

A study [12] of incidence rates of blindness among insulin-dependent diabetics reported that the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.

After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time?

The measure of the supplementary angle for one of the base angles is 95°.

The supplementary angles are the angles whose sum is given as 180°. The sum of all angles on one side of straight line is also 180°

The measures of angles are given as  (4x + 5)°, (4x + 5)°and  10⁰ respectively.

Since, the sum of the angles of a triangle is 180⁰. The following equation can be written as,

(4x + 5)° + (4x + 5)° + 10⁰ = 180⁰

⇒ 8x = 160°

⇒ x = 20°

Thus, the angles can be written as 4 × 20 + 5 = 85° and 10° respectively.

Now, the measure of the exterior angle can be written as below,

⇒ 180° - 85° = 95°.

Hence, the measure of the exterior angle is given as 95°.

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After evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the main trigonometric identities.

We must apply the sine rule and the cosine rule to the non-right-angled triangles.

So, we have the function:

tan (15π - 2t)

Now, evaluate as follows:

(15π - 2t)

Rewrite using trigonometric identities:

- sin(2t)/cos(2t)

Rewrite using trigonometric identities:

- tan(2t)

Therefore, after evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

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(x+x/2)*3=105 is the equation for "three times the sum of a number and half the number equals 105."

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. 4 + 6 = 10 is an example of an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

Three more than twice the sum of a number and half the number equals 105,

The equation will be,

(x+x/2)*3=105

The equation for "Three more than twice the sum of a number and half the number equals 105" will be (x+x/2)*3=105.

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Parametric equations describe a physical situation only when we have to draw the coordinates of the figure which actually didn't have any such coordinates.

There are many reasons. The best way to answer any “why?” question in math is to work, at least a little, with the subject to see what it can do.

With parametric equations you will find that they simplify many problems that are a complex jumble of variables if viewed in rectangular coordinates.

To illustrate a very simple case:

Define a certain circle as: x^2 + y^2 = 25 in rectangular coordinates.

Switching to polar coordinates we have: x = 5*cos(theta) and y = 5*sin(theta).

We have parameterized an equation in two variables into two simpler equations in the one variable theta. We did this by finding a single variable (the parameter theta) that will show the behavior of x and y independently.

This can be a very powerful tool if we have an equation in many variables and can reduce it to many equations but in fewer variables.

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There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

H0:p1=0.5,p2=0.3,p3=0.2

Ha:At least one proportion is different from the stated proportions.

Null hypothesis indicate that proportions are same as stated.

Product observed(fo) pi Expected(fe) (fo-fe)^2/fe

Whole 74 0.5 154.50 41.943

Universal 71 0.3 92.70 5.080

Annuities 164 0.2 61.80 169.010

Total 309 1 309 216.033

Expected value for the number of customers who prefer Whole Life=309*0.5=154.50

Expected value for the number of customers who prefer Universal Life=309*0.3=92.70

Test statistic:

Chi square=216.033

df=3-1=2

critical Chi square value=CHIINV(0.01,2)=9.210

Reject the null hypothesis

Therefore, There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.

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The dimensions of the rectangular box is 2.

The base will be 4×4 and the height will be 2 (all numbers in feet)

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is

base+height×perimeter

=b2+4bh=48

From which we can determine:

h=48−b24b

The Volume of the box:

V(b)=b2h=b2⋅(48−b24b)

=12b−3b34

b=±4

Plugging this back into the formula

h=48−b24b

we get

h=2

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Answer:

Step-by-step explanation:

The length of AB will be 32

Given that,

AC=32

AD=8

∠ABC=90 degree

From the diagram, we can see that it is a right-angle triangle so we can use that trigonometry to find the value of AB.

We know that,

                     sinФ=[tex]\frac{perpendicular}{hypotenuse }[/tex]

Now using this formula we can find the value of AB. And we know that the value of sin90= is 1.

sin90=AB/AC

⇒1=AB/32

⇒32=AB

⇒AB=32

So the length of AB mean x is 32

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Answer:

8.98 miles/hour

Step-by-step explanation:

To find the speed of the vehicle in miles per hour, you can first convert the number of rotations per minute to the number of rotations per hour by multiplying it by 60. So, the number of rotations per hour is 800 rotations/minute * 60 minutes/hour = <<800*60=48000>>48000 rotations/hour.

Then, you can use the formula for the circumference of a circle to find the distance traveled by one of the wheels in one rotation: C = 2 * pi * r, where C is the circumference, pi is approximately 3.14, and r is the radius of the wheel. So, the circumference of each wheel is 2 * 3.14 * 16 inches = <<23.1416=100.48>>100.48 inches.

Then, you can use the formula for speed: distance traveled / time traveled. Since the distance traveled by one of the wheels in one rotation is 100.48 inches, and there are 48000 rotations per hour, the distance traveled by one of the wheels in one hour is 48000 rotations/hour * 100.48 inches/rotation = 4.81E5 inches.

To convert this distance to miles, you can divide it by the number of inches per mile: 4.81E5 inches / (12 inches/foot * 5280 feet/mile) = 8.98 miles/hour. This is the speed of the vehicle.

A line chart is the best chart to show trends over time. It shows trends and data variables clearly.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

We can deduce that a line chart is the best chart to show trends over time as it shows trends and data variables clearly and also assists readers with making predictions for the future. However, for a data set comparison being useful, you must use the same scale on both axes.

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16/25 as a percentage is 64%.

The number in the denominator is the one below the fraction line, while the number in the numerator is the one above the fraction line.

When we talk about percentages, we really mean that it's a subset of 100. Since the word "percent" refers to a hundred, 50% is equivalent to expressing 50/100 or 5/10 in fractional form.

Therefore, since 25 is the denominator in 16/25, we might change the fraction so that 100 is the denominator.

To do that, we divide 100 by the denominator:

100/25 = 4

Once we have that, we can multiply both the numerator and denominator by this multiple:

[tex]\frac{16}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{64}{100}[/tex]

Now we can see that our fraction is 64/100.

Thus, 16/25 as a percentage is 64%.

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The value of a for which v is a linear combination is given as follows:

a = -8.

v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.

From the vectors, the system is defined as follows:

From the first equation, the value of x is obtained as follows:

-x = -1

x = 1.

From the second equation, the value of y is obtained as follows:

2x - y = 4

2 - y = 4

y = 2 - 4

y = -2.

From the third equation, the value of z is obtained as follows:

5x + 4y - 3z = -6.

5 - 8 - 3z = -6

3z = 3

z = 1.

Then the value of a needed for the linear combination is of:

a = -x + 3y - z

a = -1 - 6 - 1

a = -8.

The problem is given by the image shown at the end of the answer.

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Answer: 312=(2)(2)(2)(3)(13)

Step-by-step explanation:

312  |  2

156  |  2

78   |  2

39   |  3

13    | 13

Hence, 312=(2)(2)(2)(3)(13)

Answer:

question 1: T
question 2: F
question 3: C

Step-by-step explanation:

Answer:

1. True

2. False

3. D. {2,4,9,16}

Step-by-step explanation:

⭐What is a function?

Therefore, #1 is a function because for every x-value, there is 1 y-value.

Therefore, #2 is NOT a function because 6 has 2 y-values, and 12 has 2 y-values.

⭐What is the range of a function?

Therefore, {2,4,9,16} is the range of #3 because it lists all of the y-values in ascending order.

The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.

Given:

radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.

we are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.

we have dr/dt = 6 in/min and dh/dt = -4 in/min

Volume, V = πr²h

Differentiate the above expression to get:

dV/dt = 2πrh dr/dt + πr² dh/dt

SUbstitute the value we get:

dV/dt = 2π(6)(18)(6) + π(6)²(-4)

= 4069.44 - 452.16

= 3617.28 in³ per minute.

The volume is increasing at a rate of  3617.28 in³ per minute.

Area = 2πr(h+r)

Differentiate the above expression:

dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}

dA/dt = 2π {(18+6)(6) + 6(-4+6)}

= 2π(144 + 12)

= 312π

= 979.68 in² per minute.

The area is increasing at a rate of 979.68 in² per minute.

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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.

Given:

The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.

We are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.

We have dr/dt = 6 in/min and dh/dt = -4 in/min

In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

Volume, V = πr²h

Differentiate the above expression to get:

dV/dt = 2πrh dr/dt + πr² dh/dt

Substitute the value we get:

dV/dt = 2π*6*18*6 + π*6² * -4

= 4069.44 - 452.16

= 3617.28 in³ per minute.

The volume is increasing at a rate of 3617.28 in³ per minute.

Area = 2πr(h+r)

Differentiate the above expression:

dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}

dA/dt = 2π {(18+6)(6) + 6(-4+6)}

= 2π(144 + 12)

= 312π

= 979.68 in² per minute.

The area is increasing at a rate of 979.68 in² per minute.

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The statement made by Erin about the triangles is false

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

As a general rule of dilation (i.e. scale factors),

The area of the image of the dilation is the square of the scale factor multiplied by the area of the pre-image shape

Mathematically, this is represented as

Area of the image of the dilation = scale factor² * Area of the pre-image shape

Using familiar terms, we have

Area of ∆XYZ = (31)² * the area of ∆ABC.

The above statement is true and it is not the same as Erin's statement

Hence, Erin is incorrect

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To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.

Given,

A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.

We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

Here,

To obtain the sample size,

n = z² pq / ME²

Where,

P is the proportion of voters

M. E is the margin of error.

q is the proportion of non-voters

z is the corresponding z score

The z score for the 95% confidence interval is 1.96.

n = 1.96² pq / 0.05²

n = 1536.64 pq

If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.

n = 1536.64 pq = 61.42

≈ 62 voters

Therefore,

62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

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The length of the YZ for the two similar triangles will be 9 inches.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Given that triangle, ABC is similar to triangle XYZ. The value of the side YZ will be calculated by the similarity property,

YZ / BC = XZ / AC

x / 3 = 15 / 5

x = ( 15 x 3 ) / 5

x = 3 x 3

x = 9 inch

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The speed of a point on the rim  is 2.44 m/s.

What is a quick answer for diameter?

The diameter is the distance along the circle's center that must travel in order to touch two points on its edge.

First convert diameter into radius

r = d/2 = 0.08/2 = 0.04 m

The moment of inertia of disc is given by

I = 0.5mr²

Where m is the mass and r is the radius of the disk

I = 0.5(0.1)(0.04)²

I = 0.00008 kg.m²

and since we are dealing with rotational motion then rotational kinetic energy is given by

E  =  0.5 I ω²

we have to separate ω

ω² = E/0.5 I

ω = √E/0.5 I

ω = √0.15/0.5(0.00008)

ω = 61.23 rad/sec

Finally we know that speed is given as

v = ω r

v = 61.23 (0.04)

v = 2.44 m/s

Therefore, the speed of a point on the rim  is 2.44 m/s.

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The complete question is -

A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim

The value of the x in g(h(x)) = 4 is 4 if the g⁻¹(4) = 2 and at x = 4 h(x) = 2 option (C) is correct.

The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The relation is,

g (h (x)) = 4

Now, Substitute x = 4;

LHS;

g (h (x)) = g (h (4))

            = g (2)

           = 4

Thus, The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

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Answer:

The lowest common denominator is 12

Step-by-step explanation:

Finding the lowest common denominator

Multiples of 6: 6,12,18,24

Multiples of 4: 4,8,12,16,20

The lowest common multiple is 12

The lowest common denominator is 12

Answer:

? = 6

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other 2 sides , then it divides those sides proportionally , that is

[tex]\frac{?}{15}[/tex] = [tex]\frac{4}{14-4}[/tex] = [tex]\frac{4}{10}[/tex] ( cross- multiply )

10? = 15 × 4 = 60 ( divide both sides by 10 )

? = 6

A test's large p-value does not necessarily mean that the null hypothesis should be accepted.

In a test, a low P-value will favor rejecting the null hypothesis.

The P-value approach evaluates whether something is "likely" or "unlikely," assuming that the null hypothesis is correct, by calculating the probability of observing a test statistic that is more extreme in the direction of the alternative hypothesis than the one actually seen. If the P-value is low, such as less than, it is "unlikely" (or equal to) α.

The null hypothesis is disregarded in favor of the alternative hypothesis if the P-value is less than (or equal to) α. Additionally, the null hypothesis is not disproved if the P-value is higher than α.

As a result, the right response is false.

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The correct option A: graph A, shows the logarithmic function;

f(x) = log₃x + 1

f(x) = log₃x + 1

f(1) = log₃1 + 1

f(1) = 0 + 1

f(1) = 1

(1, 1)

f(3) = log₃3 + 1

f(3) = 1 + 1

f(3) = 2

(3, 2)

Thus, the graph must contain the points   (1, 1), (3, 2).

Therefore, graph A define the given logarithmic function;

f(x) = log₃x + 1.

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