Is this true? log(x) = logb(c) * log(x). For this question, first try several examples. Then prove it. See the proofs in the Basic Math lecture for ideas. (Hint: let
m = logb(x) and n=logb(c) and p = logc(x). Then use the definition of logarithms and rules of exponents to show m = np.

The number of bottles that would be left is 1

The given parameters are

Number of Bottles = 7

Number of Friends = 3

Assume that the bottles are to be shared among the friends only

The number of bottles that would be left is

Bottles left = Number of Bottles % Number of Friends

This gives

Bottles left = 7%3

Evaluate the modulo operation

Bottles left = 1

Hence, the number of bottles that would be left is 1

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The Area of the triangle with base 6 and height 4 is 12 square units.

Area of triangle with base "b" , and height "h" can be calculated using the formula

Area = 1/2*b*h  .

From the figure

It is given that height of triangle = 4

base of the triangle = 6

By using the formula for Area of the triangle we get ,

Area = 1/2*b*h

Substituting the value of base and height from above we get ,

Area= 1/2*6*4

=(6*4)/2

=24/2

=12

Therefore ,  the Area of the triangle with base 6 and height 4 is 12 Square units .

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You require the score of 78 to do equally well in exam 2.

To compare both the scores, we need to compute the z scores of both exams and then compare the values. The formula for z-score is:

Z = (X - μ)/σ

Where X = score obtained

           μ = mean score

          σ = standard deviation

For Exam 1:

Z = (91 - 79)/8

  = 12/8

Z = 3/2

To perform similarly well on the second exam, let x equal z 3/2.

For Exam 2:

Z = (x - 60)/12

3/2 = (x - 60)/12

By cross multiplying we get

2(x - 60) = 12 * 3

x - 60 = 36 /2

x - 60 = 18

x = 18 + 60

x = 78

Therefore, Consequently, you must achieve a score of 78 to perform equally well in Exam 2.

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They still loose 100 dollars

Answer:

The store lost $100....

Answer: use the 'grouping method' to get your answer (answer choice 'B')

Step-by-step explanation:

Take your first two terms, 2x^3 and 4x^2 and find a GCF. In this case, 2x^2 can go into both terms. Your first side should look like this 2x^2(x+2).

Take your last two terms (6x+12) and find a GCF. In this case, your GCF is 6 because both terms can fit into 6. Your second side should look like this 6(x+2).

We know we did this problem correctly because we can see that both parenthesis state the same thing, which is (x+2).

Your equation after finding a GCF in both sets should look something like this; 2x^2(x+2)+6(x+2).

Now, combine the 2x^2 and 6 together to get (2x^2+6) in one parenthesis set. Your second should include ONLY ONE of the '(x+2)'s.

Your final answer should look like this; (2x^2+6)(x+2). Therefore, your answer choice is 'B'.

Hope this helps, dawg.

a. The distance around the park is 180 yards

b. QM = 18 yards

c. It takes 49 minutes  to travel the entire distance

a. The distance around the yard is given as;

PQ + QR + PQ

Where;

Total = 40 + 70 + 70 = 180 yards

b. To determine QM, we use the Pythagorean theorem;

PQ² = QM² + 1/2 PR²

40² = QM² + (35. 5)²

1600 = QM² + 1260. 25

Make 'QM' the subject

QM² = 1600 - 1260. 25

QM = √339. 75

QM = 18 yards

c. Average speed = 150 yards/ per minute

Total distance = 180 yards

Time = Average speed/ distance

Time = 150/ 180

Time = 0. 8 3 × 60

Time = 49 minutes

Thus, the distance around the park is 180 yards

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=====================================================

Explanation:

"bisect" means to "divide in half"

So segment WY is split into two smaller equal pieces.

Segments WX and XY are the same length

WX = XY

6k+8 = 11k-12

6k-11k = -12-8

-5k = -20

k = -20/(-5)

k = 4

Answer:

128 feet

Step-by-step explanation:

8*16 is 128 feet

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given : A scientist had [tex]\frac{3}{4}[/tex] of a bottle of a solution.

The part of the solution she used in the experiment :  [tex]\frac{1}{6}[/tex]

The part of bottle she used is given by :

[tex]\frac{1}{6} *\frac{3}{4}[/tex]

= [tex]\frac{1*3}{4*6}[/tex]

= [tex]\frac{3}{24}[/tex]

Simplify = [tex]\frac{1}{8}[/tex]

Hence, she used [tex]\frac{1}{8}[/tex] of the bottle .

The answer for the given question is 59/90

A fraction is said to be in lowest terms when the greatest common factor (GCF) of the numerator and denominator is 1. Now that this is in mind, let's continue to solve.

Given, 5/9+1/10 and we have to convert or reduce it into the lowest terms.

So, let's proceed to solve this question

First add 5/9 and 1/10 i.e.,

= 5/9+1/10

Taken LCM of 9 and 10 which comes out to be 90.

Then, adding, we get

= 50+9/90

= 59/90

59/90 is already in its lowest form because the numerator and denominator have no common factor other than 1. So it's already at its most basic level.

Therefore, 59/90 is the required answer.

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The minute hand has moved 25 times out of a possible 60 from the top of the clock as of 4:25. 150 degrees is 25 multiplied by 6 degrees. Simply subtracting those degrees from the above calculation, the angle from the minute hand to the hour hand is equal to 360 degrees. 342.5 degrees is 360 minus 17.5.

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex. Using a protractor, angles are measured in degrees (°).

An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.

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Answer:

1 TABLET

Step-by-step explanation:

1 tablet should be given. The aim is to ensure that the amount of medicine you give matches what was prescribed. In order to do that, we must change either the amount we ordered or the amount that is available so that they are both measured in the same unit.

To decide the number of tablets that ought to be given, we have to be change over the accessible sum from grams to milligrams.

Given:

Ordered: 100 mg

Available: 0.1 g

1 g = 1000 mg

Converting the available sum to milligrams:

0.1 g * 1000 mg/g = 100 mg

Since the available amount is equal to the ordered sum, you'd have to be give 1 tablet.

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There are two ways to say 1900 in word form.

1900 = nineteen hundred

1900 = one thousand, nine hundred

Both are equally valid.

Answer: one thousand nine hundred

Step-by-step explanation:

Answer:

84 minutes

Step-by-step explanation:

360 per hour = 6 per min

140 per hour = 2 1/3 per min

Both together do 8 1/3 per min.

In 3 minutes, both machines together do 25 packages.

700/25 = 28.

In 3*28 minutes, which is 84 minutes, both machines together seal 700 packages.

Thanks!

Answer:

The slope is 4/5

y = 4/5x + 20

Step-by-step explanation:

Slope:

Change in y over the change in x

(4 - 8) / -20 - -15

-4 / -20 + 15

-4 /-5

4 / 5

Equation of the line:

You could use either point given.  I am going to use the point (-20,4)  I will use -20 for x and 4 for y.  I will use 4/5 as the slope.  I will need to solve for the y-intercept

y = mx + b

4 = (4/5)(-20) + b

4 = -16 + b  Add 16 to both sides

20 = b

The equation will be

y = 4/5x + 20

The factor (r + 3) is common. Then the greatest common factor will be (r + 3).

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expression is given below.

⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)

In both terms, the factor (r + 3) is common. Then the greatest common factor will be (r + 3). Then the expression will be

⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)

⇒ [(5r - 6) - (2r - 1)](r + 3)

⇒ (3r - 5)(r + 3)

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Answer:

equation : 3x + 5y + 2 = 0

Step-by-step explanation:

y - y1 = m (x - x1)

y - (-1) = -3/5 ( x - 1 )

5(y + 1) = -3(x - 1)

5y + 5 = -3x + 3

3x + 5y + 2 = 0

The age of accountant is more variable than salary.

Standard deviation is the square of difference between the sets of data and mean.

Comparison for variation of data can be determined by coefficient of variation (C.V).

We know C.V = [tex]\frac{\sigma}{|\overline{x|}}[/tex] × 100.

First we are determining C.V for ages.

Where [tex]\sigma[/tex] = standard deviation and [tex]|\overline{x}|[/tex] = arithmetic mean or average.

∴ C.V for ages, where  [tex]\sigma[/tex] = 4 and [tex]|\overline{x}|[/tex] = 25 years is

C.V = [tex]\frac{4}{25}[/tex] × 100.

C.V = 16.

[tex]C.V_a_g_e[/tex] = 16%.

Now C.V for salary,

where [tex]\sigma[/tex] = 4500 and [tex]|\overline{x}|[/tex] = 30500.

C.V = [tex]\frac{4500}{30500}[/tex] × 100.

C.V = [tex]\frac{4500}{305}[/tex].

[tex]C.V_s_a_l_a_r_y =[/tex] 14.75 %.

So, the coefficient of variation of age is more than that of salary.

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Let the equation of the line perpendicular to line 3x+2y=16 is:-

2x - 3y = C. ………………(1)

Line (1) passes through the point (9,-2), therefore

2×9 - 3×(-2)= C

or, C = 24.

Thus, the required equation is:-

2x - 3y = 24.

or, 3y = 2y - 24.

or, y = (2/3).x + (-8). Answer.

Answer:

Step-by-step explanation:

The amplitude of the function is 1/3

The function is given as:

y = negative one-third sine x

Rewrite properly as

y = -1/3sin(x)

A sine function is represented as:

y = Asin(x)

And the amplitude is

Amplitude = |A|

In y = -1/3sin(x), we have

A = -1/3

So, we have

Amplitude = |-1/3|

Evaluate

Amplitude = 1/3

Hence, the amplitude of the function is 1/3

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The translation of the phrase The sum of -15y and 16y is −4 is

-15y + 16y = -4 and the value of y is -4.

An algebraic equation is written in the form of variables and constants and we combine these variables and constants with arithmetic operations.

In the given question there is a statement The sum of -15y and 16y is −4 and we have to express it in form of numerical and solve for y or find the value of y.

∴ The sum of -15y and 16y is −4 can be expressed numerically as,

-15y + 16y = -4.

y = -4.

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Answer: B.

Step-by-step explanation:

the goal of the question is to make <AZB ≈ (around) <AYB. Answer b is the only one that makes sense because in the first answer triangle AYB is obtuse and much wider than triangle AZB. While in answer c, triangle AYB is acute and way too small to be around triangle AZB. In answer b, the angles are around the same even though one triangle is slightly larger than the other.

Answer:

  (d)  9x² -12y² -11x

Step-by-step explanation:

The sum of polynomials (8x² -9y² -4x) and (x² -3y² -7x) is found by combining like terms.

When simplifying the sum of polynomials, the distributive property comes into play. It lets you add and remove parentheses, recognizing that factors outside parentheses multiply each term inside parentheses.

  (8x² -9y² -4x) + (x² -3y² -7x)

  = 8x² -9y² -4x + x² -3y² -7x . . . . . eliminate parentheses

  = (8 +1)x² +(-9 -3)y² +(-4 -7)x

  = 9x² -12y² -11x

The original price of the suit before markdowns will be $520.83.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Le's suppose the original price was x dollars.

Now, the first discount of 40%

40% of x = 0.40x

Retail price = x - 0.40x = 0.60x

The second discount is 60% on the first retail price

60% of 0.60x = 0.60×0.60x

⇒ 0.36x

Final retail price = 0.60x - 0.36x

0.24x = 125

x = 520.83

Hence "The original price of the suit before markdowns will be $520.83".

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Answer:

I believe it's 15.21x

Step-by-step explanation:

10.79 - 26 * x

10.79 - 26x =

15.21x

Let [tex]S[/tex] be the sum. Introduce a factor of [tex]\Gamma\left(\frac12\right)=\sqrt\pi[/tex] to rewrite the summand as a beta function integral. Then in the sum, interchange it with the integral, and [tex]S[/tex] reduces to a simple integral.

[tex]\displaystyle S = \sum_{n=0}^\infty \left(-\frac12\right)^n \frac{\Gamma\left(\frac{n+1}2\right)}{\Gamma\left(\frac n2+1\right)}[/tex]

[tex]\displaystyle . ~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \, \mathrm{B}\left(\frac n2+\frac12, \frac12\right) \\\\ ~~~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \int_0^1 \frac{t^{n/2}}{\sqrt t \sqrt{1-t}} \, dt \\\\ ~~~~ = \frac1{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t \sqrt{1-t}} \sum_{n=0}^\infty \left(-\frac{\sqrt t}2\right)^n \\\\ ~~~~ = \frac2{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t\sqrt{1-t}\left(\sqrt t+2\right)}[/tex]

Substitute [tex]u=\sqrt t+2[/tex] and [tex]du=\frac{dt}{2\sqrt t}[/tex].

[tex]\displaystyle S = \frac4{\sqrt\pi} \int_2^3 \frac{du}{u\sqrt{-(u-1)(u-3)}}[/tex]

Now substitute [tex]u=1+\frac2{1+t^2}[/tex] and [tex]du=-\frac{4t}{(1+t^2)^2}\,dt[/tex] - this comes from an Euler substitution of the form [tex]\sqrt{a(x-\alpha)(x-\beta)}=(x-\alpha)t[/tex]. [tex]S[/tex] reduces drastically to a trivial arctangent integral.

[tex]\displaystyle S = \frac8{\sqrt\pi} \int_0^1 \frac{dt}{t^2+3} \\\\ ~~~~ = \frac8{\sqrt\pi} \cdot \frac\pi{6\sqrt3} = \boxed{\frac43\sqrt{\frac\pi3}}[/tex]

Answer:

602,630

Step-by-step explanation:

The amount of fencing needed to enclose the secular pond is 72.22 feet

The perimeter of a shape is the sum of the side lengths of the shape

For all regular quadrilaterals, you add up the side lengths to determine the area

The given parameter is

Diameter, d = 23 feet

The radius is calculated as

r = d/2

So, we have

r = 23/2

This gives

r = 11.5 feet

The circumference of the circle is calculated as

C = 2pi r

So, we have

C = 2 * 3.14 * 11.5 feet

Evaluate the product

C = 72.22 feet

Hence, the amount of fencing needed to enclose the secular pond is 72.22 feet

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