The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24
meters.
Х
8 m
Not drawn to scale
What is x, the width of the original rectangle on the left? Round to the nearest hundredth if necessary.
O 5 meters
O 8 meters
10 meters
12 meters

The solutions to each of the given exponential functions are;

1) g = 1.356

2) u = 1.725

3) x = 3

4) k = -5.288

5)  a = 4/3

6) z = 1.295

7) x = 13/2

8) v = -1.5286

9) y = 4.17

10) b = 1.2648

Exponential equations are usually in the form a^(x) = b^(y) . To solve exponential equations with same base, we normally make use of the property of equality of exponential functions .

1) 7^(g) = 14

gIn 7 = In 14

g = In 14/In 7

g = 1.356

2) 6^(u) = 22

u In 6 = In 22

u = In 22/In 6

u = 1.725

3) 7^(x - 2) = 7

7^(x - 2) = 7¹

Equating the exponents gives;

x - 2 = 1

x = 3

4) (0.66)^k = 9

k In 0.66 = In 9

k = In 9/In 0.66

k = -5.288

5) Exponential equation 8^a = 16

2^(3a) = 2⁴

Equating the exponents gives;

3a = 4

a = 4/3

6) The exponential equation 12^z = 25;

z In 12 = In 25

z = In 25/In 12

z = 1.295

7) The exponential equation 4^(x-5) = 8

2^(2(x - 5)) = 2^(3)

2x - 10 = 3

2x = 13

x = 13/2

8) (0.28)^v = 7

vIn 0.28 = In 7

v = In 7/In 0.28

v = -1.5286

9) 2^y = 18

y In 2 = In 18

y = In 18/In 2

y = 4.17

10) 17^b = 36

b In 17 = In 36

b = In 36/In 17

b = 1.2648

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Answer:

548 > 373

Step-by-step explanation:

548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.

The ">" symbol is used to represent "greater than" in mathematical comparisons.

Hope this helps!

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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The solution is,  2.5 miles per hour was her walking rate in miles per hour.

We know that,

Speed is measured as distance moved over time.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time.

In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, given that,

Bao walked 15 miles in 6 hours.

so, we get,

in 6 hours = 15 miles

so, in 1 hour = 15 / 6 miles

                    =2.5 miles

Hence, The solution is,  2.5 miles per hour was her walking rate in miles per hour.

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The property used to solve 7r + 2r is distributive property.

The distributive property states that an expression which is given in form of x (y + z) can be solved as x × (y + z) = xy + xz.

In other words,  the distributive property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers .

Therefore,

7r + 2r

Using distributive law,

7r + 2r = r(7 + 2) = 9r

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⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ B = Bracket

⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ O = Open

⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ D = Division

⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ M = Multiplication

⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ A = Addition

⠀⠀⠀⠀⠀⠀⠀⠀⠀➥ S = Subtraction

Answer:

B= Bracket

O= Open

D=Divide

M=Multiplication

A=Addition

S=Subtraction

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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Answer:

540

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

9 out of 10 is 90% of 10. Therefore, you have to calculate what's 90% of 600. Which is 540. Hope this helps!

9514 1404 393

Answer:

  a.  $134,880.24

Step-by-step explanation:

Put the numbers into the formula and do the arithmetic.

  A = $65,000×e^(0.073×10) ≈ $134,880.24

_____

Additional comment

The doubling time for continuously compounded interest is 69.3 years divided by the interest rate in %. Here, that is 69.3/7.3 = 9.49 years. That means an investment of 10 years will be slightly more than double the original amount. 2×65,000 = 130,000, so choice A is in the right ballpark. The other numerical choices are not.

Answer:

hello your question is incomplete attached below is the complete question

answer : The population mean LDL level after six months is same for all four treatments

Step-by-step explanation:

A null hypothesis represents a no difference in the question. therefore the correct option is The population mean LDL level after six months is same for all four treatments

Answer:

\(1.6456 * 10^{3}\)

Step-by-step explanation:

Step 1:  Convert to Scientific Notation

\(1645.6\) is in standard notation

\(1.6456 * 10^{3}\) is in scientific notation

Answer:  \(1.6456 * 10^{3}\)

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

check the attachment given belοw tο understand.

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Answer:

Step-by-step explanation:

Using a standard normal table or calculator, we can determine the probabilities as follows:

(a) P(z ≤ 2.37) = 0.9910

(b) P(1.14 < z < 3.35) = P(z < 3.35) - P(z < 1.14) = 0.9992 - 0.8708 = 0.1284

(c) P(-0.77 ≤ z ≤ -0.56) = P(z ≤ -0.56) - P(z < -0.77) = 0.2868 - 0.2224 = 0.0644

(d) P(z ≥ -3.28) = 1 - P(z < -3.28) = 1 - 0.0005 = 0.9995

Therefore,

P(z ≤ 2.37) = 0.9910,

P(1.14 < z < 3.35) = 0.1284,

P(-0.77≤ z ≤-0.56) = 0.0644,

P(z≥ -3.28) = 0.9995.

Answer:

P(z ≤ 2.37) = 0.9910,

P(1.14 < z < 3.35) = 0.1284,

P(-0.77≤ z ≤-0.56) = 0.0644,

P(z≥ -3.28) = 0.9995.

Step-by-step explanation:

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:

The length of the largest side of DEF is 40.

Step-by-step explanation:

Similar triangles' corresponding sides are proportional in length.

The smallest side of ABC is 12, and that is the corresponding side to the smallest side of DEF.

Calculate the proportional factor.

24 / 12 = 2.

Since similar triangles' sides are corresponding, the largest side of ABC will correspond with the largest side of DEF.

Calculate the largest side length.

20 * 2 = 40.

Answer: 9, -4

Step-by-step explanation:

We can write an equation:

xy=-36

x+y=5

Factors of -36 are: 1, -36, -1, 36, 2, -13, -2, 13, 4, -9, -9, 4, 6, -6

There are only 2 factors here that add up to -36: 9 and -4

Answer:

97

Step-by-step explanation:

Answer:

1. 2 -- x-axis represents time, each vertical line represents 2 hours. (8 lines, 16 hours total)

2. 10 --- y-axis represents number of customers. (5 lines, 52 customers total. points go just above 5th line)

hope this helps :)

Step-by-step explanation:

what is the criteria for success ? how many questions must be right ? and how many must be wrong for failure ?

if success means all answers right, then she has 4 choices on the first question to pick one right answer. and then for each of those again 4 choices on the second question and so on.

so, all possible outcomes are 4²⁰.

that means the probability to guess all 20 right is

1/4²⁰

a tiny, tiny number.

and the probabilty to have all wrong ?

she has 4 choices to pick 1 of 3 wrong answers.

so, the probability is 3/4 to answer the first question wrong.

for that she has again then the same chance to get the second question wrong too.

so, it is 3/4 × 3/4 = 9/16

and so on.

the probability to guess all 20 wrong is then

(3/4)²⁰ ≈ 0.0032

that is still a small number but much, much larger than the probability to get everything right.

still, even the goal to truly get everything wrong is highly unlikely.

The answer is in the picture. Click on it

The total amount that the person with base salary 42000; total sales 175000; commission 4% gets is $51000.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. In this case, the percentage of commission is given as 4%.

The commission will be:

= Percentage × Amount

= 4% × 175000

= 7000

Therefore, the total amount that the person gets will be:

= Salary + Commission

= 42000 + 7000

= $51000

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Answer:

y - 3 = -1/2(x - 1)

Step-by-step explanation:

Hey there!

Well point slope form is,

\(y - y_{1} = m(x - x_{1})\)

We can use the point (1,3)

y - 3 = m(x - 1)

Now we need to find slope with the following formula,

\(\frac{y^2-y^1}{x^2-x^1}\), we’ll use the points (1,3) and (5,1).

\(\frac{1-3}{5-1}\)

-2/4

Slope or m = -1/2

y - 3 = -1/2(x - 1)

Hope this helps :)

Answer:

K=8

Step-by-step explanation:

The triangles are similar so you can set up the porpotions: 3/6=4/k then you cross multiply and solve for k

Answer:

yes

Step-by-step explanation:

because it sells the best price

Answer:

No

Step-by-step explanation:

Stores D dose not have the best deal when you compare the unit prices. The best deal isn't from having more loaves. The best deal from store B because the unit price is the lowest.

Answer:

The expected value of X, E(X), for the given probability distribution is 1.2

Step-by-step explanation:

Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E(x).

Hope is the sum of the product of the probability of each event and the value of that event. That is, it is the sum of the probability of each possible event multiplied by the frequency of said process, this indicates that if you have a discrete quantitative variable X with "n" possible events x₁, x₂, x₃... xₙ and probabilities P (X = xi) = Pi the mathematical expectation is:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + ... + xₙ*Pₙ

In this case:

E(x)=x₁*P₁ + x₂*P₂ + x₃*P₃ + x₄*P₄

Being:

and replacing:

E(x)= 0* 0.5 + 1* 0.1 + 2*0.1 + 3*0.3

you get:

E(x)= 1.2

The expected value of X, E(X), for the given probability distribution is 1.2

The fraction of the remaining cars in the lot that are preowned is 7/15

In order to determine the fraction of the remaining cars in the lot that are preowned, we have to first determine the total number of new cars and preowned cars before the sale occurred.

Total number of preowned cars before the sales = (ratio of preowned cars / total ratio) x total number of cars

ratio of preowned cars = 5

total ratio = 6 + 5 = 11

total number of cars = 66

(5/11) x 66 = 30 cars

Total number of new cars before the sale = (ratio of new cars / total ratio) x total number of cars

ratio of new cars = 6

total ratio = 6 + 5 = 11

total number of cars = 66

(6/11) x 66 = 36 cars

Total number of new cars after the sale = total number of new cars before the sale - number of new cars sold

36 - 4 = 32

Total number of preowned cars after the sale = total number of preowned cars before the sale - number of preowned cars sold

30 - 2 = 28

The fraction of the remaining cars on the lot that are preowned = number of preowned cars after the sale / total number of cars on the lot after the sale

total number of cars on the lot after the sale = 28 + 32 = 60

28/60

to convert to the simplest term, divide the numerator and the denominator by 4

7/15

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