Exponential Logarithmic Equations
7^3x+5=7^x+1

The length of the base edge of the square pyramid is 6 feet.

The surface area of a square pyramid is 96 square feet. The height is two thirds of the length of the base edge.

The length of the base edge can be found as follows:

Hence,

surface area of square pyramid = a² + 2al

where

Therefore,

using Pythagoras's theorem, let find the slant height of the pyramid.

c² = a² + b²

where

Hence,

height = 2 / 3 a

Therefore,

l² = (2 / 3 a)² + (1 / 2a )²

l² = 4 / 9 a² + 1 / 4 a²

l² = 25 / 36 a²

square root both sides

l = 5 / 6 a

Hence,

surface area of square pyramid = a² + 2a(5 / 6 a)

surface area of square pyramid = a² + 10 / 6 a²

surface area of square pyramid = 16 / 6 a²

96 = 16 / 6 a²

96 = 8 / 3 a²

cross multiply

96 × 3 = 8a²

288 / 8 = a²

a² = 36

a = √36

a = 6 feet

Therefore, the base length is 6 feet.

learn more on square pyramid here: https://brainly.com/question/29330401

#SPJ1

Answer: because it has the same numbers

Step-by-step explanation:

Answer:

abc = 18.5

cbx = 28

Step-by-step explanation:

Answer:

7ygfce

Step-by-step explanation:

Answer:

tpuedoec dir ee haas cog qmoa  untarampu

Solo haavmae srame ipunater iad

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

for more question on probabilities visiT:

https://brainly.com/question/25839839

#SPJ8

Answer:

g(f(x)) = 2x - 6

f(g(x)) = 2x - 4

Step-by-step explanation:

g(f(x)) = 2x - 8 + 2

g(f(x)) = 2x - 6

f(g(x)) = 2(x + 2) - 8

f(g(x)) = 2x - 4

Answer: g ( 2 x − 8 ) = 2 x− 6

Step-by-step explanation: MAKE ME BRAINLIEST!!!!!

The intercept is 3 and 5

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

To find x- intercept, y=0

x² + 2x -15=0

x² -5x + 3x -15=0

x(x-5) - 3(x-5) = 0

(x-5)(x-3)=0

Hence, the x- intercept is 3 and 5.

Learn more about this concept here:

https://brainly.com/question/27819804

#SPJ1

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

Learn More About marginal utility from the below link:

https://brainly.com/question/15050855

#SPJ11

Total length  = Amount cut off +  amount remaining.

Total length = 12 + 18 = 30 inches

Step-by-step explanation:

x−7(x−2)=10x+9−x

Step 1: Simplify both sides of the equation.

x−7(x−2)=10x+9−x

x+(−7)(x)+(−7)(−2)=10x+9+−x(Distribute)

x+−7x+14=10x+9+−x

(x+−7x)+(14)=(10x+−x)+(9)(Combine Like Terms)

−6x+14=9x+9

−6x+14=9x+9

Step 2: Subtract 9x from both sides.

−6x+14−9x=9x+9−9x

−15x+14=9

Step 3: Subtract 14 from both sides.

−15x+14−14=9−14

−15x=−5

Step 4: Divide both sides by -15.

−15x−15=−5−15

x=13

Answer:

x=13

Answer:6777

Step-by-step explanation: 1+6776=6777

Question i: To express mlog_(z)n+5=q in exponential form, we need to rewrite it using exponentiation. In logarithmic form, the base (z), exponent (n+5), and result (q) are given. The exponential form will have the base (z), exponent (unknown), and result (m). Therefore, the exponential form would be:

z^(n+5) = m

Question ii: To solve the equation 2^(3x+1) = (1/4)^(x-5), we can rewrite both sides with the same base and equate the exponents:

2^(3x+1) = (2^(-2))^(x-5)

Using the property of exponentiation (a^(bc) = (a^b)^c), we simplify the equation to:

2^(3x+1) = 2^(-2(x-5))

Since the bases are the same, we can equate the exponents:

3x + 1 = -2(x-5)

Solving for x:

3x + 1 = -2x + 10
5x = 9
x = 9/5

Therefore, the solution to the equation is x = 9/5.

 To  To  learn  more about exponential form click here:brainly.com/question/29166310

#SPJ11

Answer:

Please check my interpretation of your written equation.

Step-by-step explanation:

f(x) = (-x^2 - 2x - 2)/(x-2)

Wild.  See attached graph.

Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

Let's calculate the z-score:

Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.

Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).

Therefore, approximately 87.1% of people have an IQ score less than 117.

Answer:

b

Step-by-step explanation:

Answer:

-7.25

Step-by-step explanation:

because the dolphin is going down, its negative so you add -4.5+-2.75

The option that is true based on the equation is that B. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

This is the degree of the hotness and the coldness that's in a body.

In this case, based on the information, the conversion of Celcius to Fahrenheit is simply by multiplying by 1.8.

Therefore, 1°C to F will be:.

= 1 × 1.8

= 1.8°F

Learn more about temperature on:

brainly.com/question/24746268

#SPJ1

Yup! I would just get rid of the plus sign after the 1.5x^2 because you don't really need it

yh but it must be y=1.5x^-7.5x+3

The estimated forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future is approximately 7.495%.

To estimate the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future, given the 3-month Eurodollar futures price of 95.20 and a standard deviation of the change in the short-term interest rate in 1 year of 1.1%, follow these steps:

1. Convert the Eurodollar futures price to an implied interest rate:
 Implied Interest Rate = (100 - Eurodollar Futures Price) = (100 - 95.20) = 4.80%

2. Calculate the number of standard deviations for the 6-year period:
  Number of Standard Deviations = √(6 years) = √6 ≈ 2.45

3. Multiply the number of standard deviations by the annual standard deviation of the change in the short-term interest rate:
  Change in Interest Rate = Number of Standard Deviations × Annual Standard Deviation = 2.45 × 1.1% = 2.695%

4. Add the change in the interest rate to the current implied interest rate to get the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future:
  Forward LIBOR Interest Rate = Implied Interest Rate + Change in Interest Rate = 4.80% + 2.695% = 7.495%

So, the estimated forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future is approximately 7.495%.

for such more question on interest rate

https://brainly.com/question/25720319

#SPJ11

Answer: 1000

Step-by-step explanation:

\(\frac{5}{5000} =\frac{1}{1000}\)

Answer:

1,890

Step-by-step explanation:

Alice will be paid the amount of $868.7 interest in the loan at the end of one year.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

Here Principal (P) = $24,820, Rate of Interest (R) = 3.5%, and Time (T) = 1 year

simple interest = P × R × T

Substitute the values of P, R, and T in the above formula, and we get

simple interest = 24,820 × 3.5/100 × 1

simple interest = $868.7

Therefore, he will be paid the amount of $868.7 interest in the loan at the end of one year.

Learn more about the simple interest here:

brainly.com/question/22621039

#SPJ1

Answer:

Step-by-step explanation:

onor code

Brainly Tutor

brourgay

10/03/2022

Mathematics

High School

answered • expert verified

alice has a loan of $24,820. This loan has a simple interest rate if 3.5% per year. No payments will be kade on the loan until the end if the year. how much interest will alice pay in this loan at the end of one year?

How did you get that answer 868.70

brourgay is waiting for your help.

Add your answer and earn points.

Expert-Verified Answer

No one rated this answer yet — why not be the first?

JaneWright and many other Tutors are verifying Brainly answers

Tutors in math & science270 000 students helped

Want MORE expert-verified answers like this one? Try Brainly Tutor and get personalized help from a pro in minutes!

saimaparvezVT

Expert

6.7K answers

7.4M people helped

Alice will be paid the amount of $868.7 interest in the loan at the end of one year.

2(5x + 9) = 48

10x + 18 = 48

10x = 48 - 18

10x = 30

x = 30/10

x = 3

Answer:

Perimeter of one triangle is 65 dm

Perimeter of other triangle is 52 dm

Step-by-step explanation:

Please remember the concept

If sides are in the ratio of a:b

Then the area in the ratio of \(a^{2} :b^{2}\)

It is given sum of their perimeter is 117.

Let the small triangle has perimeter as x.

So, perimeter of big triangle is 117-x.

So, we can set up equation as

\(\frac{50}{32} =\frac{x^{2} }{(117-x)^{2} }\)

Cross multiply

50(117-x)^2 =32x^2

Expand the left side

50\((13689 -234x+x^{2} )\)=\(32x^{2}\)

Distribute the left side

684450-11700x+\(50x^{2}\)=\(32x^{2}\)

Subtract both sides \(32x^{2}\) and rewrite it \(18x^{2} -11700x+684450=0\)

Solve this quadratic for x.

Divide both sides of the equation by 18 to simplify.

\(x^{2}\)-650 x+38025=0

Now, if possible let's factor

Find two integers whose multiplication is 38025 but adds to -650.

-65 and -585 works.

So, we can rewrite it as

(x -65)(x-585) =0

Solve them using zero product property

x=65, x=585

So, x=65 works here.

So, perimeter of one triangle is 65 dm

Perimeter of other triangle is 117-65= 52 dm

Answer:x= -1367284

over     170975

Step-by-step explanation:

-173.38=1368.35- 1.066

subtract the numbers

17.975x=1367.284

divide both sides

alternate form

x=7 170459

170975 x=7.999698

Answer:

the same! 30

Step-by-step explanation:

similar shapes will always have the same angle degrees

Answer: it 2790

Step-by-step explanation:

The value of 5,860÷2.1 is 2790.

In easy phrases, the division may be described because of the splitting of a massive institution into smaller companies such that every institution may have the same number of items. it's far an operation used for identical grouping and the same sharing in math.

Learn more about division here: https://brainly.com/question/25289437

#SPJ2

The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

To know more about banker here

https://brainly.com/question/14328094

#SPJ4