What is the base of the following natural logarithm?
In(x)
O 1
O 10
O e

9514 1404 393

Answer:

  te, tm, (m-e), t

Step-by-step explanation:

The problem statement tells you how to interpret the expressions and their parts.

Swap the top two expressions on the right and the list will be in the appropriate order:

Answer:

Answer:

Step-by-step explanation:

x - 12 ≤ 3 - 2x

3x ≤ 15

x ≤ 5

To graph this, just draw a VERTICAL line passing through x = 5, then shade the area to the LEFT

Answer:

0.04

Step-by-step explanation:

We are given that

The probability  that the alumnus did not provide response=5%

The probability  that the alumnus did not provide response=\(\frac{5}{100}=0.05\)

The probability that the alumnus would say their experience  fell short of expectations=26%=0.26

The probability that the alumnus would say their experience met expectations=65%=0.65

We have to find the  probability that the alumnus would say their experience surpassed expectations.

We know that

Sum of all probabilities =1

Using the property

The  probability that the alumnus would say their experience surpassed expectations=1-(0.05+0.26+0.65)

The  probability that the alumnus would say their experience surpassed expectation=0.04

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y-intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y-intercept is of function -

f(x) = 2x + 4

and the least y-intercept is of the function shown in graph [4] or function [4].

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Answer:

Carlos puts $3 into his bank account and it grows by 50% each year

f(x)=4^x+1

(The Table)

(The Graph)

Answer:

  g(x) = (1/6)(x +7)^2 -8

Step-by-step explanation:

The transformation ...

  g(x) = a·f(x -h) +k

represents vertical scaling by a factor of 'a', right shift by h units, and up shift by k units. You want the function g(x) for f(x) = x^2, a = 1/6, h = -7, and k = -8. Those transformations give you ...

  g(x) = (1/6)(x +7)^2 -8

Answer:

x = 150 miles

Cost = $100

Step-by-step explanation:

Company A = 50 + 20 + 0.20x

= 70 + 0.20x

Company B = 55 + 0.30x

Where,

x =number of miles

find the number of miles for which the companies charge will be the same

Equate the charges of both companies

70 + 0.20x = 55 + 0.30x

70 - 55 = 0.30x - 0.20x

15 = 0.10x

Divide both sides by 0.10

x = 15 / 0.10

= 150

x = 150 miles

The number of miles for which the companies charge will be the same is 150 miles

Substitute 150 miles into any of the companies charges to find the charge

Company B = 55 + 0.30x

= 55 + 0.30(150)

= 55 + 45

= $100

We want to find the number of miles for which both companies charge the same amount.

We will see that the number of miles such that the costs are equal is 150 miles, and both companies charge $100 for that number of miles.

Adobe charges $50 for rental, $20 for gas and $0.20 per mile drive, so if you drive for x miles, the cost is:

A(x) = $50 + $20 + $0.20*x = $70 + $0.20*x

While we know that Vamos card charges $55 for rental and gas (together) and $0.30 per mile, so if you drive for x miles the cost is:

V(x) = $55 + $0.30*x

We want to find the value of x such that the cost equations are equal, so we must solve:

A(x) = V(x)

$70 + $0.20*x = $55 + $0.30*x

$70 - $55 = $0.30*x - $0.20*x

$15 = $0.10*x

$15/$0.10 = x = 150

So for 150 miles, both companies charge the same amount.

The cost is:

V(150) = A(150) = $70 + $0.20*150 = $100

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The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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Answer:

  3

Step-by-step explanation:

5(9/12 -1/4) +0.5

= 5(9/12 -3/12) +1/2 . . . . . . express the fractions using a common denominator

= 5(6/12) +1/2 . . . . . . . add the fractions

= 5(1/2) +1/2 . . . . . . reduce the result

= (5 +1)(1/2) . . . . factor out 1/2 (easier than adding mixed numbers)

= 6/2 = 3

_____

A calculator can be a useful tool for evaluating numerical expressions.

Answer:

-3/2

Step-by-step explanation:

6=|x|+3-x

move the terms

-|x|+x=3-6

-|x|+x=-3

-x+x=-3 , x > 0 (put a line under >)

-(-x)+x=-3 , x < 0

-3/2 , x < 0 find the intersection

x= -3/2

if you dont want it as a fraction you can do -1.5 in decimal form

The weekly gross pay will be $2732.80.

Based on the information, the extra hours that was spent will be:

= 48 - 40 = 8 hours

Therefore, the gross pay will be;

= ($17.08 × 40) + (8 × $17.08 × 1.5)

= $683.20 + $2049.6

= $2732.80

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Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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Answer:

4 more units

Step-by-step explanation:

1.25x + 12.00 > 15.75

1.25(4) =5

5 + 12 = 17

\( \frac{1}{3} \times 3 \times ({ \frac{14}{2} )}^{2} = 1 \times {7}^{2} = 49\)

Answer:

answer is 205.146666666666

Step-by-step explanation:

ur welcome

The sales tax rate that Blake pay on the clothes he buys is correctly given by: Option D: 5%

The sales tax rate is the rate at which the sales tax is applied.
Total payable amount = Original amount + sales tax on that amount.

We are given that:

He(Blake) works in Illinois, but he buys all of his clothes at a store in Wisconsin.

So, the sales tax rate will be applied according to the rate of Wisconsin.

From the table, we see that the sales tax rate of Wisconsin is 5%.

Thus, the sales tax rate that Blake pay on the clothes he buys is correctly given by: Option D: 5%

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Answer:

5%

Step-by-step explanation:

Answer:

25 liters

Step-by-step explanation:

15x + 45(5) = 20(x + 5)

15x + 225 = 20x + 100

Simplify

125 = 5x

Divide both sides by 5

25 = x

25 liters

Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²

The graphs of y = x + 1 and y = 2^x intersect at approximately (-0.3517, 0.6483) and (1.561, 3.561).

To find the points of intersection between the graphs of y = x + 1 and y = 2^x, we need to set the two equations equal to each other and solve for x.

Setting y = x + 1 equal to y = 2^x, we have:

x + 1 = 2^x

To solve this equation, we can use numerical methods or make observations to find the points of intersection. By observing the behavior of the two functions, we can see that they intersect at two points: one when x is negative, and another when x is positive.

For x < 0, the exponential function y = 2^x approaches 0 as x approaches negative infinity, while the linear function y = x + 1 continues to decrease as x becomes more negative. Thus, there is one point of intersection in this region.

For x > 0, the exponential function grows faster than the linear function, so there is another point of intersection in this region.

However, finding the exact values for the points of intersection requires numerical methods such as using a graphing calculator or solving the equation numerically. Approximate values for the points of intersection can be found as x ≈ -0.3517 and x ≈ 1.561.

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Answer:

100% B

Step-by-step explanation:

Answer:

The first choice: x^6y^5

Step-by-step explanation:

When you multiply exponential you add the exponents.

Answer:

b. 1.69

Step-by-step explanation:

So to solve this problem we need to simply find the percentage increase from 11.8 to 12 =>

to solve this we would do 12 - 11.8 = 0.2 --> 0.2 is our "difference in the increase" -->

now we divide this by our amt. which is 11.8 --> 0.2/11.8 = approx. 0.0169

--> finally multiply that by 100 which is simply moving the decimal places 2 places right giving us the final answer of 1.69

Hope this helps!

Answer:

B. 1.69%

Step-by-step explanation:

If Ross calculated the countertop for a laundry room to be 12 square feet but turns out to be actually 11.8 square feet, we need to find out how much percentage error Ross has made!

In order to solve this question,

1) We need to create proportions:

Ross' calculations              x

______________ =   _________

   actual area                   100

x represents the percentage error.

100 is the total percentage.

2) Now we plug in the numbers:

We plug in 12 for Ross' calculations. We plug in 11.8 for the actual area. So, it will look like this:

   12                x

______ = _______

   11.8           100

3) Time for cross multiplication:

12 times 100 is 1,200

11.8 times x is 11.8x

So,

1,200 = 11.8x

4) Now we divide:

1,200 divided by 11.8 equals to 101.69 %

5) We are not done! We still have to subtract:

101.69

-100.00

_______

    1.69

Finished!!

Our answer is 1.69%, which is B.

Hope this was helpful !!!

Answer:

1

Step-by-step explanation:

Hope this helpsss

Answer:

1

Step-by-step explanation:

The equation is 3/10 times 10/3, which is 30/30, which equals 1.

(hope this helps :P)

C, D, F

because i said so ok dumbies

Answer: 54 inch²

Step-by-step explanation:

The total surface area of the cube can simply be found by finding the area of one face and multiplying by 6 because the cube has 6 faces

Area of one face = 3 inch x 3 inch = 9 inch²

Total surface area of the cube = 9 inch² x 6 = 54 inch²

Answer:

\(\boxed{\sf \ \ \ 15a^5b^{15} \ \ \ }\)

Step-by-step explanation:

hello,

\((3a^2b^7) (5a^3b^8)=15a^{2+3}b^{7+8}=15a^5b^{15}\)

hope this helps

The additional gas it will take to fill the tank is 16 gallons

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

Capacity = 24 gallons

Current volume = 1/3 full

This means that

Remaning volume = 1 - 1/3

Evaluate

Remaning volume = 2/3

The additional gas it will take to fill the tank is

Additional = 2/3 * 24

Evaluate

Additional = 16

Hence, the additional gas it will take to fill the tank is 16 gallons

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Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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Explanation

Given that the rate of change is'

We can get the function of the population by integrating the above function