Which logarithmic equation is equivalent to the exponential below? e^a= 35

Answer:

$53,700

Step-by-step explanation:

If we have 537 people coming and paying $100 each, we multiply 537  and $100

537 * $100

$53,700

Answer:

B

Step-by-step explanation:

using the cofunction identity

• sin (90 - x) = cosx / cos(90 - x) = sinx, hence

cos 19° = sin(90 - 19)° = sin 71°

Answer:

B

Step-by-step explanation:

using the cofunction identity

• sin (90 - x) = cosx / cos(90 - x) = sinx, hence

cos 19° = sin(90 - 19)° = sin 71°

Answer:

$150   PLEASE GIVE BRAINLIEST

Step-by-step explanation:

The minimum you can earn would be $150.  This would be your base salary and you selling 0 cell phones.

Answer:

see explanation

Step-by-step explanation:

(a)

1.2² = 1.2 × 1.2 = 1.44

(b)

2³ + 17 - 3 × 4 ← evaluate exponent and multiplication before adding/subtracting

= 8 + 17 - 12 = 25 - 12 = 13

(c)

9² ÷ 3³ ← evaluate exponents before dividing

= 81 ÷ 27 = 3

Answer:

a = 1.44

b = 21.6

c = 3

Step-by-step explanation:

a is 1.44 because 1.2 × 1.2 = 1.44

b is 21.6 because 2 × 2 × 2 = 8 so it is 8 + 17 - 3.4 which is 21.6

c is 3 because 9 × 9 = 81 and 3 × 3 × 3 = 27 so 81 ÷ 27 = 3

Answer:

J. $638.14

Step-by-step explanation:

We will use compound interest formula to solve our given problem.

[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,

A=Final amount after T years.

P= Principal amount.

r= Interest rate in decimal form.

n= Period of compounding.

T= Time in years.

Let us convert our given interest rate in decimal form.

[tex]5\%=\frac{5}{100}=0.05[/tex]

Let us substitute our given values in above formula.

[tex]A=500*(1+\frac{0.05}{1})^{1*5}[/tex]

[tex]A=500*(1+0.05)^{5}[/tex]

[tex]A=500*(1.05)^{5}[/tex]

[tex]A=500*1.2762815625[/tex]

[tex]A=638.14078125\approx 638.14[/tex]

Therefore, we will have an amount of $638.14 after 5 years and option J is the correct choice.

The balance in your account after depositing $500 with an annual compound interest rate of 5% for 5 years would be $638.14, according to the formula for compound interest.

To calculate the balance in an account after a certain period of time, we would use the formula for compound interest. This formula is

, where 'A' is the amount of money accumulated after n years, taking into account interest. 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal), 'n' is the number of times that interest is compounded per year, and 't' is the time the money is invested for in years.

Here, P = $500, r = 5/100 = 0.05 (because the rate was given in percentage), n = 1 (because the interest is compounded annually), and t = 5 years. Inserting these values into the formula gives us

which simplifies to A = $638.14. So, the balance in your account after 5 years would be $638.14, rounded to the nearest cent.

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Answer:

option B

Step-by-step explanation:

9/10 + 6/5 + 3/2...........

We find the difference between the terms

[tex]\frac{6}{5} - \frac{9}{10}[/tex]

[tex]\frac{12}{10} - \frac{9}{10} = \frac{3}{10}[/tex]

We will get the same difference when we subtract consecutive terms.

so , d= 3/10, a= 9/10

we find the formula for nth term

a_n = a+(n-1) d

[tex]a_n = \frac{9}{10} + (n-1)\frac{3}{10}[/tex]

[tex]a_n = \frac{9}{10} +\frac{3}{10}n-\frac{3}{10}[/tex]

[tex]a_n = \frac{6}{10} +\frac{3}{10}n[/tex]

[tex]a_n = \frac{3}{5} +\frac{3}{10}n[/tex]

we need to find eighth partial sum so we  take n=1 to 8

sum of 8 terms ([tex]\frac{3}{5} +\frac{3}{10}n[/tex])

So option B is correct

The eighth partial sum of a series, denoted as S8, sums up the first 8 terms in the series. In summation notation, it can be expressed as S8 = Σ_[k=1]^8 a_k.

In mathematics, specifically in series and sequences, the notation for the eighth partial sum of a series is denoted by S8. Here the numeral 8 indicates the number of terms in that partial sum which is 8 in this case. The general formula for the sum of an arithmetic series is S_n = n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term.

If the terms of the series are denoted by a_k where k=1,2,3,... is the index of the term, the eighth partial sum of a series can be written in summation notation as:

 S8 = Σ_[k=1]^8 a_k

This means that the eighth partial sum is the sum of the first 8 terms of the series.

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Answer:-70

Step-by-step explanation:

Answer:-70

Step-by-step explanation:

−3.5

0.05

=−70

Answer:The answer is 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The population density is the ration between the population and the area covered. So, the population density of Marble City

[tex]M=\frac{52348}{125}\approx418.78[/tex]

If both cities have the same population density, this can be used to find the dimension of Pebble City:

[tex]P=\frac{85312}{A}\\ 418.78=\frac{85312}{A}\\A=\frac{85312}{418.78}\approx 203.72[/tex]

Now, knowing the area of Pebble City, we can find its length

[tex]A=(length)(width)\\203.72=l(11.8)\\l=\frac{203.72}{11.8}\approx 17[/tex]

Therefore, the length of Pebble City has a length of 17 miles, approximately.

Answer:

(0, - 4 )

Step-by-step explanation:

under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y ), hence

C(2, 4) → (- 2, - 4)

A translation of 2 units to the right means add 2 to the original x- coordinate while the y-coordinate remains unchanged.

(- 2, - 4 ) → (- 2 + 2, - 4 ) → (0, - 4 )

Answer:

(0, - 4 )

Step-by-step explanation:

Answer:

$3.75

Step-by-step explanation:

To find the price after discount subtract this from $25.00

25.00 - 21.25 = 3.75

21.25 + 3.75 = 25

Hope this helped!

Answer:

25/2

Step-by-step explanation:

Answer:

a= 1/2m+25

Step-by-step explanation:

As the statement says that Sophie pays for one half of the cost of the car rental (m) and that she spent $25 on gasoline, the expression that could be used to determine the amount that she spent would be equal to the sum of one half of the cost of the car rental plus 25:

a= 1/2m+25

a= amount Sophie spent

m= cost of the car rental

Answer:

I'mma be honest someone else asked the same question and this is the answer they gotten They gotten 4 and 5 and 4.1 but in my opinion I say the answer should be 4

Step-by-step explanation:

Best estimate would be B, because the answer is 4.1067 and you would round down

Answer:

D

Step-by-step explanation:

5+7(8r-2)

5+56r-14

-9+56r=56r-9

d

Answer:

D) 56r - 9

Step by Step Explanation:

Answer:

Annalisa uses 7/6 cups altogether.

Step-by-step explanation:

First you find common denominators for both fractions, which is 6, then convert the fractions to the denominator 6.

You get 3/6+4/6.

The answer is 7/6!

Answer: Yes, they have equivalent volumes.

Step-by-step explanation:

For the volumes to be equal, a would have to be equal to b. We'll assume x=x

1. Set the volumes equal to each other

x +a +2b =x +2a +b

2. Simplify

[x +a +2b =x +2a +b] -x

[a +2b =2a +b] -a

[2b =a +b] -b

b =a

Therefore, 2a=2b, a=b, and x=x

Since the two prisms have the same measurements, they have the same volumes.

Answer:

See below. The result using the binomial theorem  is 1049.8560 compared with 1049.8573 using a calculator.

Step-by-step explanation:

Binomial theorem:-

( a + x)^n  =   a^n + nC1 a^(n-1) x + nC2 a^(n - 2)x^2 +  .......

(4 + 0.02)^5 = 4^5  + 5C1* 4^4 *0.02 + 5C2* 4^3* 0.02^2 +  5C3*4^2*0.02^3

+ 5C4 * 4 * 0.02^4 + 0.02^5

= 1024 +  5*4^4*0.02 + 10*4^3*0.02^2 + 10*4^2*0.02^3 + 5*4*0.02^4 + 0.02^5

= 1024 + 25.6 + 0.256 + 0.0000032

Answer:

Keisha's Response: The 4th term is almost 0, so the 5th and 6th terms are also close to 0. Add the terms shown to approximate 4.025:  1024 + 25.6 + 0.256 + 0.001 = 1049.857.

Step-by-step explanation:

EDGINUITY

Answer:

15

Step-by-step explanation:

Via the law of exponents power of a power property we have:

[tex](a^b)^c=a^{bc}[/tex]

Therefore:

[tex](15^{1/5})^5=15^{\frac{1}{5} \times 5}=15^{\frac{5}{5}}=15^1=15[/tex]

~~~Brainliest Appreciated~~~

The number of decimal places that the quotient has will be 3.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The numbers are given below.

7.7 and 700

The quotient of the numbers 7.7 and 700 will be

⇒ 7.7 ÷ 700

⇒ 0.011

Then the number of decimal places that the quotient has will be 3.

More about the Algebra link is given below.

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Answer: The number of pounds each camel have to carry=44 pounds

The pounds of goods left=3 pounds

Step-by-step explanation:

The total pounds of goods the merchant have=[tex]269+167+51[/tex]

=487 pounds

The total number of camels the merchant have = 11

If each camel carry same weight of goods, then we divide total weight by 11, we get

487÷11=44.27

The number of pounds each camel have to carry=44 pounds

The pounds of goods left=487-44×11=487-484=3 pounds

Answer: y = 2x^4

The graph represents a parabolic-looking shape so it's either a quadratic or some even degree polynomial. This rules out y = -2x^3 and y = 2x^3 as they are cubics with odd degrees

The degree of a polynomial is the largest exponent. It determines the end behavior. In this case, both ends are rising upward together. Because they are rising up in the positive y direction, this means that we cannot have y = -2x^4 as the answer. For example, if x = 2 then y = -2*x^4 = -2*2^4 = -32, but the point (x,y) = (2,-32) isn't on the blue curve. So we can rule y = -2x^4 out.

The fact that y = 2x^4 has a positive leading coefficient tells us that the endpoints point upward.  

Answer:

slope = -1/2

Step-by-step explanation:

To find the slope, we can use the formula

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

   = (4-3)/(-2-0)

   = 1 /-2

   = -1/2

The slope is -1/2

Answer:

Let charge per day be $x  and charge per mile be $y  

then:

as per the given condition we have;

3x + 300y =159          .....[1]

5x + 600y = 289       .....[2]

Multiply equation [1] both sides by 5 we get;

[tex]5(3x+300y) = 5 \cdot 159[/tex]

Using distributive property: [tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]

15x+1500y = 795                 .....[3]

Multiply equation [2] by 3 both sides we get;

[tex]3(5x+600y) = 3 \cdot 289[/tex]

Using distributive property: [tex]a \cdot(b+c) = a\cdot b+ a\cdot c[/tex]

15x+1800y = 867                    .....[4]

Subtract equation [3] from [4] to eliminate x and solve for y;

15x+1800y-15x-1500y = 867 -795

Combined like terms;

300y = 72

Divide both sides by 300 we get;

[tex]y = \frac{72}{300}=0.24[/tex]

⇒  y =$0.24 per mile.

Now substitute this value y in equation [1] to solve for x;

3x + 300(0.24) =159

3x + 72 =159

Subtract 72 both sides we get;

3x + 72 -72 = 159 -72

Simplify:

3x = 87

Divide both sides by 3 we get;

[tex]x = \frac{87}{3} = 29[/tex]

Therefore, the best rental charges per day is, $ 29 and the charges per mile is, $0.24

The problem can be solved by setting up a system of linear equations from the given information. Then, solving these equations will yield the daily fee and mileage fee that Best Rental charges.

To solve this problem, we can create a system of linear equations. Let's denote the daily fee as 'd' and the mileage fee as 'm'

From Barney's rental, we know that 3d + 300m = 159.

From Mary's rental, we know that 5d + 600m = 289.

We solve these two equations to find the values of 'd' and 'm'. This is an application of algebra in solving real-world problems

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Answer:

[tex](x-1)^2+(y+5)^2=100[/tex]

Step-by-step explanation:

The equation of a circle has the following form:

[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.

Our equation center is (1.-5) and radius is 10.

[tex](x-1)^2+(y--5)^2=10^2[/tex]

[tex](x-1)^2+(y+5)^2=100[/tex]

Answer:

x = 387

Step-by-step explanation:

The wind acts in the opposite direction to the plane when the time is longer.

The wind acts in the same direction as the plane when the time is shorter.

Equation

d = r*t

Givens

Substitution

Since the two distances are the same, you can equate the right hand sides.

Now use one of the given equations with the distance

Answer: g(x) is the image of f(x)

Step-by-step explanation:

multiplying the x value by -1 means you reflect that point across y-axis, therefore, g(x) is the reflection of f(x) across y-axis.

Multiplying the x value by -1 means you reflect that point across y-axis,

therefore, g(x) is the reflection of f(x) across y-axis.

You are basically assigning the same y-value to the opposite x-values to make g(x). So, for the point (x, 31), on f(x), x is -2, but on g(x), x is 2. Thinking about this visually, you can imagine that this represents a reflection of f across the y-axis.

Here is the general rule for reflection across the y-axis: Given an equation y=f(x) y = f ( x ) , the new reflection equation of the reflected graph will be y=f(−x) y = f ( − x ).

The relationship between the graphs is Option 3 . they are reflection of each other across the y axis.

The reflection vector is generated by applying the equation R = U − 2NT(U · N), where N is the vertex normal transformed into eye space. The reflection equation used is the standard for computing the reflection vector given a surface normal and incident vector.

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.

Learn more about reflection equation, refer

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Answer:

Yes, there is a similarity transformation that maps triangle ABC to Triangle DEF.

Step-by-step explanation:

Similarity transformation;

Triangle DEF has been transformed(dilated) by a factor of 2.

Since each dimension is twice that of the triangle ABC.

Two triangles are similar if their corresponding sides are congruent and corresponding angles are congruent.

Similarity statement:

ΔABC [tex]\sim[/tex] ΔDEF

these two triangles are similar because;

[tex]\frac{AB}{DE}= \frac{4}{8} = \frac{1}{2}[/tex]

[tex]\frac{AC}{DF}= \frac{4}{8} = \frac{1}{2}[/tex]

[tex]\frac{BC}{EF}= \frac{3}{6} = \frac{1}{2}[/tex]

⇒ [tex]\frac{AB}{DE}=\frac{AC}{DF} =\frac{BC}{EF}[/tex]

Yes, there is a similarity transformation that maps Triangle ABC to Triangle DEF.

To determine if two triangles are similar, one must check if they have the same shape, which means their corresponding angles are equal and their corresponding sides are in proportion.

Let's denote the angles of Triangle ABC  [tex]\(A\), \(B\), and \(C\),[/tex] and the angles of Triangle DEF as [tex]\(D\), \(E\), and \(F\),[/tex] respectively. Similarly, let's denote the sides opposite these angles as [tex]\(a\), \(b\), and \(c\)[/tex] for Triangle ABC, and [tex]\(d\), \(e\), and \(f\)[/tex] Triangle DEF.

For Triangle ABC and Triangle DEF to be similar, the following conditions must be met:

1. [tex]\(A = D\), \(B = E\), and \(C = F\)[/tex] (AA postulate for similarity).

2. [tex]\(\frac{a}{d} = \frac{b}{e} = \frac{c}{f}\)[/tex] (corresponding sides are in proportion).

If these conditions are satisfied, then there exists a similarity transformation that maps one triangle to the other. This transformation can be broken down into the following steps:

1. Dilation: To make the sides of Triangle ABC proportional to the sides of Triangle DEF, we perform a dilation. The scale factor k can be determined by the ratio of any pair of corresponding sides. For example, [tex]\(k = \frac{d}{a} = \frac{e}{b} = \frac{f}{c}\)[/tex]. This single scale factor should work for all three sides if the triangles are similar.

2. Rotation/Reflection (optional): If Triangle DEF is not oriented in the same direction as Triangle ABC, we may need to rotate or reflect Triangle ABC to align it with Triangle DEF. This does not affect the similarity.

3. Translation (optional): Finally, if Triangle DEF is not in the same position as Triangle ABC (but has the same orientation and size after the dilation), we perform a translation to move Triangle ABC to the position of Triangle DEF.

Since the angles are preserved under dilation, rotation, and translation, and the sides are made proportional by the dilation, the similarity transformation is complete.

If the corresponding angles are equal and the corresponding sides are in proportion, then the two triangles are similar, and a similarity transformation exists that maps one to the other. The similarity statement captures this relationship, indicating that the triangles are similar to the AA postulate and the sides are in proportion.

Hello from MrBillDoesMath!

Answer:

Choice B (176)

Discussion:

Volume of a box = (area of base) * height.    

In our case this  becomes

"2 of the boxes have a height of 3"      + "and one box has a height of 5"

16 * 3  + 16 * 3                                         + 16 * 5 =

48 + 48 + 80  =

96 + 80 =

176

which is choice B

Thank you,

MrB

Answer:

C. 12

Step-by-step explanation:

The last vertical line in a Box-and-Whisker plot is the upper quartile value, also know as 75% into the data. Since 75% is the same as three quarters and the last vertical line is on 12, C is the answer

Answer: C

Step-by-step explanation: I am a pro

4 rectangles are 3 in x 2 in = 6 square inches each.

4 * 6 = 24 square inches.

2 squares are 3 in x 3 in = 9 square inches each

2 * 9 = 18 square inches.

Total area = 24 + 18 = 42 square inches.