if thieves were to steal platinum from a bank using a small truck with a maximum payload capacity of 700 lb , how many 1 l bars of the metal could they take?

Answer:

  -9/8

Step-by-step explanation:

You want a full simplification of ...

  [tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}[/tex]

The relevant rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  log(a^b) = b·log(a)

  logₐ(b) = log(b)/log(a)

  [tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}=\dfrac{3}{4}\log_{\frac{4}{9}}\left(\dfrac{27}{8}\right)=\dfrac{3}{4}\cdot\dfrac{\log\dfrac{27}{8}}{\log\dfrac{4}{9}}\\\\\\=\dfrac{3(\log(3^3)-\log(2^3))}{4(\log(2^2)-\log(3^2))}=\dfrac{3(3\cdot\log(3)-3\cdot\log(2))}{4(2\cdot\log(2)-2\cdot\log(3))}\\\\\\=\dfrac{9(\log(3)-\log(2))}{8(\log(2)-\log(3))}=\boxed{-\dfrac{9}{8}}[/tex]

__

Additional comment

We have reduced everything to the difference of the logs of 2 and 3. You could stop the reduction to smallest parts at any point where you recognize things that will cancel. You could write numerator and denominator in terms of powers of (3/2), for example.

The solution of the expression is 3m-5.

Basic Guidelines and Procedures for Condensing Any Algebraic Expression

step1:

(6m² -13m+5)/(2m-1): 3m-5

6m²  -13m+5/2m-1

factor 6m² -13m+5 : (2m-1) (3m-5)

=(2m-1) (3m-5)/2m-1

step2:

cancel the common factor 2m-1

=3m-5

The solution of the expression is 3m-5

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The inequality that represents the minimum number of points he must score on the remaining tests in order to get an A is 320 + n ≥ 389, n ≥ 69, where n is the number of points.

When we use ≥ symbol, as at least means greater than or equal to.

320 + n ≥ 389

Subtracting 320 on both the sides,

n ≥ 69,

n represents the score he must receive on the remaining tests. Then n + 320 represents his total score for the semester.

Thus, the required inequality is n ≥ 69, which means that n is the minimum scored points to get A.

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The number of algae after 7 days is approximately 70.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Given that,

Initial population of algae = 50

Percentage increase = 5%

To calculate the number of algae at any day, we need to find a formula.

Initial population = 50

After 1 day, population = 50 + (5% × 50) = 50 + (0.05 × 50) = 50 (1 + 0.05)

After 2 days, population = 50 (1 + 0.05)²

So, population after n days = 50 (1 + 0.05)ⁿ

Population of algae after 7 days = 50 (1 + 0.05)⁷

                                                      = 50 (1.05)⁷

                                                      = 70.355 ≈ 70

Hence there will be approximately 70 algae after 7 days.

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Sammy obtained a convenient sample.

The sampling method is biased because the students in the statistics class are not representative of the entire high school population. The sample only includes the students in one particular class and does not account for the experiences or characteristics of other students in the school.

68% is likely to be greater than the percent of all students at the high school who have a driver's license.

To avoid the bias, Sammy could use a more representative sample, such as a simple random sample or a stratified sample, to ensure that the sample includes a diverse group of students from various backgrounds, classes, and demographics. This would give a more accurate representation of the experiences and characteristics of the entire high school population.

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The following type of study can be concluded as an observational study.

An observational study is a type of study that is used to gather data on the characteristics and behaviors of a particular group of people or subjects without actively manipulating or interfering with the subjects.

This study can be used to suggest a causal relationship between increased stress and muscle cramps, but it cannot conclusively prove causality.

There are several reasons why this study design cannot be used to conclude a causal relationship. First, the study is a non-randomized, uncontrolled experiment, which means that there may be other factors that could be influencing the results.

For example, the subjects in the stress group may have other characteristics or preexisting conditions that are related to muscle cramps. Additionally, the study does not have a control group for comparison, so it is not possible to determine if the muscle cramps are caused by stress or by some other factor.

Second, the study design is a single-blind study, which means that only the subjects are not aware of their group assignment, but the experimenter knows which group the subjects are in. This can lead to bias in data collection, analysis, or interpretation.

Therefore, The following type of study can be concluded as an observational study.

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Answer:20

Step-by-step explanation:

you do it

The scale factor that takes quadrilateral T to quadrilateral U would be = 1.6

A scale factor is defined as the factor that is used to creat a similar shape of an object with a different dimension.

The formula that is used for the new object = original object × scale factor

The original object = quadrilateral T

The new object = quadrilateral U.

The scale factor the was used to form U using the length of the quadrilateral as 16;

16 = 10 * Scale factor

This gives

Scale factor = 16/10

Scale factor = 1.6

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[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \implies {\large \begin{array}{llll} y +2= \cfrac{1}{4} (x -8) \end{array}}[/tex]

The are of shade part of semi-circle is 75.36 cm^2.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Now,

Area of the shaded region=area of large semicircle-2*area of small semicircles

radius for large semicircle=7cm

radius for small semicircle=3.5cm

Therefore,

         Area of the shaded region=πR^2-2*πr^2

                                        =3.14(7^2-2*3.5^2)

                                         =3.14*(49-25)

                                         =3.14*24

                    Area of the shaded region =75.36 cm^2

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Answer:

y- intercept = 12, x- intercept = 4

Step-by-step explanation:

to find the y- intercept, the point where the line crosses the y- axis.

let x = 0 in the equation and solve for y

y = - 3(0) + 12 = 0 + 12 = 12

then y- intercept = 12

to find the x- intercept, where the line crosses the x- axis.

let y = 0 in the equation and solve for x

0 = - 3x + 12 ( subtract 12 from both sides )

- 12 = - 3x ( divide both sides by - 3 )

4 = x

then x- intercept = 4

Answer:

The dimensions are 3, 4 and 5 inches.

Step-by-step explanation:

Area = 1/2 * height * base

6 = 1/2 * h * b

h * b = 12.

As the hypotenuse is 5 inches long

H^2 + B^2 = 5^2

From the third line: h = 12/b, so we have
(12/b)^2 + b^2 = 25

144/b^2 + b^2 = 25

144 + b^4 = 25b^2

b^4 - 25b^2 + 144 = 0

Let B = b^2, so

B^2 - 25B + 144 = 0

(B - 16)(B - 9) = 0

B = 16, 9

So, b = 4, 3

h = 12/b

= 3 , 4.

Answer:

113.04

Step-by-step explanation:

see attached

Answer:

11 and 12

Step-by-step explanation:

Solving this would be the case of finding that square root of 131, then rounding both up and down.

First, to solve

The square root of 131 is 11.45

Now we take that 11.45 and round both up and down

Rounding down is 11 and rounding up is 12.

11 and 12 are next to each other, making them consecutive.

Answer:

I think its 11 and 12

Step-by-step explanation:

Therefore, the potential length of a triangle's third side is 17-11<x<17+11 is equals to 6 < x< 28.

A triangle's third side must always have a length that falls between (but not exactly equal to) the sum and difference of the other two sides. Consider the examples 2, 6, and 7 as an example. The third side length must therefore be larger than 4 and less than 8.

According to the Triangle Inequality Theorem, any two triangle sides must add up to more than the third side's length. To find the potential length of a triangle, multiply the sum of the two sides by the difference of the two sides.

Therefore, the potential length of a triangle's third side is 17-11<x<17+11.

= 6 < x< 28

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As a result, the third side of a triangle may be equal to 17-11<x<17+11 is equals to 6 < x< 28.

The third side of a triangle must always have a length that is between the sum and difference of the other two sides, but is not exactly equal to either. As an illustration, think about cases 2, 6, and 7. Therefore, the third side length must be more than 4 and lower than 8.

The Triangle Inequality Theorem states that any two triangle sides must add up to greater than the length of the third side. Multiply the sum of the two sides by the difference of the two sides to determine the potential length of a triangle.

Consequently, 17-11<x<17+11.= 6 < x< 28 is the possible length of the third side of a triangle.

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The trapezoid abcd median is 16 lengths long.

Regarding the query,

Considering that,

The trapezoid's area is equal to 80,

The trapezoid abcd is 5 inches tall.

Let a be the base of the trapezoid abcd.

So, b = a + 12 ,

In the formula Area of the trapezoid = A =(a+b)h/2, the value is substituted.

(a + a + 12)5/2 = 80

(2a + 12)5 = 160

2a + 12 = 160/5

2a + 12 = 32

2a =32 - 12

2a = 20

a = 20/2

a = 10 units

additional base is 10 + 12 = 22 units.

Therefore, the median's length will be equal to (10 + 22)/2.

= 32/2 = 16 units

As a result, the median's length is 16.

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Answer:

36 = 2 x 18

Step-by-step explanation:

The required interest rate would be 6.9% to the nearest tenth of a percent.

We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.

In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.

Plugging these values into the percent formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.

We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.

In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.

Plugging these values into the formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.

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If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.

In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.

The formula of area of rectangle is:

A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.

The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.

So, L + 2B = 200

Subtract L on both side, we get

2B = 200 - L

Divide by 2 on both side, we get

B = 100 - L/2

A = f(L)

A = L·(100 - L/2)

A = 100L - [tex]L^2[/tex]/2

Now finding the derivative.

A' = [tex]\frac{df(L)}{dL}[/tex]

A' = -L + 100

Let A' = 0

-L + 100 = 0

Subtract 100 on both side, we get

-L = -100

L = 100 feet

Now putting the value of L in B = 100 - L/2.

B = 100 - 100/2

B = 100 - 50

B = 50 feet

The maximum possible area of the corral = 100 × 50

The maximum possible area of the corral = 5000 Feet

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For the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.

What is quadratic equation?

The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients. Here, the variable "X" is unknowable.

ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

We have a quadratic equation;

2x² - 4x - 48 = 0

To find the value of x we have to follow these steps ;

(2x^2 -  4x) -  48  = 0

Pull out like factors :

2x^2 - 4x - 48  =   2 • (x^2 - 2x - 24)

x2 multiplied by 2x and 24

x^2 is the initial term, and it has a coefficient of 1.

The coefficient of the middle term, which is -2x, is 2.

"The constant," the final term, is -24.

⇒ x^2 - 6x + 4x - 24

⇒   (x+4)  •  (x-6)

⇒ 2 • (x + 4) • (x - 6)  = 0

therefore x+4 = 0

 x = -4

and   x-6 = 0

Add  6  to both sides of the equation :

                     x = 6

Hence, for the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.

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Answer:

84

Step-by-step explanation:

x/2=3*28/2=3*14 = 42

x=84

The time it takes for the wave to travel from point A to point B is 0.0086 seconds.

Assuming the question is referring to a sinusoidal wave with a frequency of 50 Hz, we can use the wave speed formula to calculate the time it takes for the wave to travel from point A to point B.

Wave speed (v) = frequency (f) x wavelength (λ)

Since the frequency is given as 50 Hz, we need to determine the wavelength to find the wave speed.

To calculate the wavelength, we can use the distance between two consecutive points on the wave that is in phase, such as points A and D or B and C. From the given information, we know that the distance between A and D or B and C is one wavelength. Therefore, we can calculate the wavelength as follows:

wavelength (λ) = distance between A and D or B and C = 10 m - 3 m = 7 m

Using the wave speed formula and the calculated wavelength, we can find the wave speed:

v = f x λ = 50 Hz x 7 m = 350 m/s

Now we can use the wave speed formula to find the time it takes for the wave to travel from point A to point B:

v = d / t

where d is the distance between A and B (which is 3 m) and t is the time it takes for the wave to travel that distance.

Rearranging the formula, we get:

t = d / v = 3 m / 350 m/s = 0.0086 s

Therefore, the time it takes for the wave to travel from point A to point B is 0.0086 seconds.

To find the amplitude of the wave, we would need additional information, as the amplitude is the maximum displacement of the wave from its equilibrium position.

As for whether points A and B are in phase, we need to compare the phase difference between the two points to the wave period. The period of a wave is the time it takes for one complete oscillation, and it is given by:

period (T) = 1 / frequency (f) = 1 / 50 Hz = 0.02 s

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Answer:

In a rhombus, all sides are equal. Therefore, you can set WV (s+12) and UV (3s) equal to each other.

s+12 = 3s

Subtract s from both sides, so the variables are all on one side.

12 = 2s

Divide both sides by 2 to isolate the variable.

6 = s

UV = 3s

UV = 3(6)

UV = 18

Answer:42 miles

Step-by-step explanation: She runs 3 times a week so 2  1/3 times 3 is equal to 7.

7x6=42

Answer:

see explanation

Step-by-step explanation:

a translation [tex]T_{(-5,-4)}[/tex]

means subtract 5 from the original x- coordinate and subtract 4 from the original y- coordinate.

A (2, - 1 ) → A' (2 - 5, - 1 - 4 ) → A' (- 3, - 5 )

B (- 4, - 2 ) → B' (- 4 - 5, - 2 - 4 ) → B' (- 9, - 6 )

C (3, 2 ) → C' (3 - 5, 2 - 4 ) → C' (- 2, - 2 )