Select the correct answer. What is this equation rewritten in logarithmic form? 9x = 3
A. log9 3 = x
B. logx 3 = 9
C. log3 9 = x
D. log3 x = 9

The ending balance after 3 years is $1508.34

What is compound interest?

The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.

The compound amount and compound interest are calculated by:

  Compound amount,   [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

  Compound interest, [tex]I = A - P[/tex]

where, P is the principal amount

           r is the rate of interest(in decimal)

           n is the number of  times the interest is compounded annually

           t is the time.

Given, Principal amount, P = $1400

           rate of interest, r = 2.5% = 0.025

           n = 2 (compounded semi-annually)

           t = 3 years

Then, the compound amount is calculated by:

                 [tex]A=1400(1+\frac{0.025}{2} )^{2*3}\\[/tex]

          or,       [tex]A=1400(1+0.0125 )^{6}\\[/tex]

          or,       [tex]A=1400(1.0125 )^{6}\\[/tex]

          or,       [tex]A=1508.34[/tex]

Therefore, the ending balance is $1508.34

To learn more about compound interest

https://brainly.com/question/3989769

#SPJ13

The probability that the student will pass the test, using the binomial distribution, is of:

0.172 = 17.2%.

The formula that gives the probability of x successes is presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the formula are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

The probability of passing is given by:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{10,7}.(0.5)^{7}.(0.5)^{3} = 0.1172[/tex]

[tex]P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0440[/tex]

[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]

[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.0010[/tex]

Then:

P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.1172 + 0.0440 + 0.0098 + 0.0010 = 0.172 = 17.2%.

More can be learned about the binomial distribution at https://brainly.com/question/24756209

#SPJ1

Answer: mode is 94

Step-by-step explanation:

Answer:

he read 9 chapters

Step-by-step explanation:

4:30 pm to 6:00 pm is 1:30 hours, which is 90 minutes

90/10=9

⇒[tex]\frac{d}{dx} (e^{x} )= e^{x} *\frac{d}{dx} (x)\\\frac{d}{dx} (e^{x} )=e^{x}*1\\\frac{d}{dx} (e^{x} )=e^{x}[/tex]

⇒Note this is all applied due to chain rule.

The Perimeter of triangle CED  is 57 in.

What is a parallelogram?

A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.

Rhombus: An equal-length parallelogram with four sides.

The diagonals of a parallelogram bisect each other AC = 2 CE

Substitute AC= 34 into AC = 2CE =34 = 2CE

Calculate 34 = 2 CE=>  CE = 17

The diagonals of a parallelogram bisect each other BD = 2DE

Substitute BD= 28 into BD = 2DE =>  28 = 2DE

Calculate 28 = 2DE  => DE = 14

Opposite sides of parallelogram are congruent AB = CD

Substitute AB = 26 into AB = CD =>  CD = 26

Perimeter of a triangle PΔCDE = CE + CD + DE

Substitute  CE = 17, DE = 14, CD = 26.

PΔCDE = CE + CD + DE

PΔCDE = 17+ 26 + 14

PΔCDE = 57 in

To learn more about parallelogram from the link:

brainly.com/question/970600

#SPJ1

Given polynomial with descending degrees of x would be,

x^4z^4 + x^3 - x^2z + z^3

In this question we have been given a polynomial x^3 + z^3 - x^2z + x^4z^4

We need to write given polynomial by descending degrees of x.

The highest degree of x in above polynomial is 4

x^3 + z^3 - x^2z + x^4z^4

then the second term would be x with degree 3.

x^3 + z^3 - x^2z + x^4z^4

the third term would be x with degree 2

x^3 + z^3 - x^2z + x^4z^4

and the last term is the term x with degree 0:

x^3 + z^3 - x^2z + x^4z^4

Therefore, given polynomial with descending degrees of x would be, x^4z^4 + x^3 - x^2z + z^3

Learn more about the polynomial here:

https://brainly.com/question/14344049

#SPJ1

Answer:

A

B

Step-by-step explanation:

that's it

The value of y is,  [tex]y = \frac{tan^-^1(-x) + \pi n}{x}[/tex].

What is tangent function?

One of the primary six trigonometric functions, the tangent function is typically expressed as tan x. When considering the angle in a right-angled triangle, it is the ratio of the opposite side to the adjacent side.

Consider, the given function

x + tan(xy) = 0

Subtract x from both sides,

x + tan(xy) - x = -x

          tan(xy) = -x

Apply tan inverse on both sides,

[tex]xy = tan^-^1(-x) + n\pi[/tex]                      (Tangent function is a periodic function)

Divide both sides by x,

[tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex],         x ≠ 0

Hence, the value of y is, y = [tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex].

To know more about the tangent function, click on the link

https://brainly.com/question/1533811

#SPJ13

The first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.

From given question, the cost per set of markers = $3

The teacher had a $2-off coupon to use toward the total cost of the markers bought.

It is given that the number of sets of markers bought by the teacher is x, and y is the total cost of the markers.

so, we get a linear equation as:

3x - 2 = y

From table A we can see that the data satisfied the given equation,

3x - 2 = y

when x = 3, y = 3(3) - 2 = $7

when x = 9, y = 3(9) - 2 = $25

when x = 12, y = 3(12) - 2 = $34

when x = 24, y = 3(24) - 2 = $70

Therefore, the first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.

Learn about linear equations here:

brainly.com/question/11897796

#SPJ1

4500 is the Cost price.

What do you mean by price at cost?

SP = 5625

Profit = 25%

CP = ?

 CP =    5625/125 * 100

       = 45 * 100

       = 4500

Learn more about Cost price

brainly.com/question/17716968

#SPJ13

Answer:

3.2 pages per minute

Step-by-step explanation:

Unit Rate: 64 / 20 = 3.2 pages per minute

A unit rate is just a measure of either how fast you can do one of something, or how fast you can do something in one unit of time :)

Answer:

Step-by-step explanation

64 pages ÷ 20 =

20 minutes ÷ 20 =

3.2 pages

1 minute

so she read 3.2 pages per minute

Step-by-step explanation:

To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.

(a) What was the total amount Linda ended up paying for the equipment

(including the down payment and monthly payments)?

How much on loan:

12,200 - 1,600 = $10,600 loan amount

How much paid on loan:

$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan

Total paid:

= loan amount + amount paid on loan

$10,600 + $$11,608.28

= $22,208.28 paid overall

________________________________________

(b) How much interest did Linda pay on the loan?

= loan amount - amount  paid on loan

= $11,608.28 - $10,600

= $1,009.28 paid in interest

a) Length of Fence = 50 meters

b) Weight of Grass Seeds = 20 kg

c) Area of Carriageway = 516 sq. meters

d) Time taken by the Striping Car = 7.6 minutes

What is a Circle?

A circular plane figure with a circumference made up of points equidistant from a given point (the center).

Solution:

a) To calculate the length of fence we need to find the circumference of the inner circle

Circumference of Circle = 2*22/7 *Radius

Circumference of Circle = 2 * 22/7 * (16)/2

Circumference of Circle = 50.24

So, the length of fence is 50 meters approx

b) To calculate the the total weight of grass we need to first find the area of the inner circle

Area of Circle = 22/7 * (Radius)^2

Area of Circle = 22/7 * (16)^2

Area of Circle = 22/7 * 256

Area of Circle = 803.84 meter sq.

For 1 meter sq. = 25 grms of grass seeeds are required

So, for 804 meters = 25*804 = 20100 grams

20100 grams = 20.1 kg = 20 kg (approx)

c) The are of Inner Carriageway will be calculated by substracting the area of inner circle from outer circle

Area of Outer Circle = 3.14 * (16+4.5)^2

Area of Outer Circle = 1320 sq. meters (approx)

Area of Inner Circle = 804 sq. meters (approx) #we have calculated it above

Area of Carriageway = 1320 - 804 = 516 sq. meters (approx)

d) Speed of Stripping Car = 25 cm/sec

Circumference of the part to be stripped = 2*3.14*(16+2.25)

Circumference = 115 meters approx. = 11500 cm

Time = Distance / Speed

Time = 11500/25 = 460 seconds

460 seconds in minutes = 7.6  minutes

To learn more about Circles from the given link

https://brainly.com/question/25938130

#SPJ9

Answer:

1000

Step-by-step explanation:

n x 5 = 5000

n = 5000/5

n = 1000

Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.

An equation is an algebraic equality in which letters appear with unknown value.

In an equation appears:

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:

Being "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:

y + (-3)= -8

Solving:

y -3= -8

y= -8 +3

y= -5

Finally, the number "y" is -5.

Learn more about equations:

brainly.com/question/4983716

brainly.com/question/13314678

#SPJ1

Step-by-step explanation:

=6a^3+7a^2-5a^3-9a^2-a

=a^3-2a^2-a this is the final answer.

The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Length = y

Width = y - 5

Area = 750

The area of a rectangle is written as,

Length x Width = Area

y x (y - 5) = 750

y² - 5y = 750

y² - 5y - 750 = 0

(y + 25)(y – 30) = 0

The equations that can be used are y(y - 5) = 750, y² - 5y = 750, and (y + 25)(y – 30) = 0.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1

The zeroes of the parabola is -1, -5.

What is parabola and zeroes of parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:

f(x) = y= ax2 + bx + c

To find zeroes of parabola

x = -b ±[tex]\sqrt{b^{2}-4ac } /2[/tex]

Given equation is

f(x) = [tex]x^{2} +6x+5[/tex]

a = 1, b = 6, c = 5

x = -6 ±[tex]\sqrt{36-4(5)}[/tex]/2

x = -6 ±[tex]\sqrt{16} /2[/tex]

x = -6 ± 4 /2

hence,

x = -6-4/2 and x = -6 +4/2

x = -5 or x = -1

To know more about parabola, visit:

https://brainly.com/question/18054637

#SPJ1

Answer:

Step-by-step explanation:

a

The answers to the worksheet are in the included picture! :p

-------------------------------------------------------------------------------

This is just an example on how to simplify fractions: Write the simplified form of the fraction 12/24.

The given fraction is 12/24.

Step 1: Let us write the factors of 12 and 24.

Factors of 12 are: 1, 2, 3, 4, 6, 12

Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Step 2: Let us identify the common factors of 12 and 24.

Common factors are: 1, 2, 3, 4, 6, 12

Step 3: Keep dividing the numerator and denominator by the common factors.

(12 ÷ 2)/(24 ÷ 2) = 6/12

And

(6 ÷ 2)/(12 ÷ 2) = 3/6

Now divide by 3,

(3 ÷ 3)/(6 ÷ 3) = 1/2

Thus, 1/2 is the simplified fraction of 12/24.

-------------------------------------------------------

Have a great day and God bless! :D

According to the given statement the correct option is A.

The researcher did not assign individuals to treatment groups.

Typically, researchers are employed by either university or commercial organizations. To support future research, enlarge the body of academic literature, and enhance decision-making, researchers collect data over the course of a project, evaluate the data, and publish the results.

Researchers have an obligation to share their findings, collaborate with others when needed, and transmit and use information for the good of their employer, the economy, and society at large. In the process of their research, researchers have an obligation to conduct themselves honestly and ethically.

To know more about Researchers visit:

https://brainly.com/question/11685682

#SPJ1

Answer:

Rector, Pine, Taylor

Step-by-step explanation:

The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!

Answer:

  (d)  Jamar's ending account balance is higher than Beth's ending balance.

Step-by-step explanation:

You want to know the best description of the relationship between final balances of two ordinary annuities:

The attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.

Jamar's balance: $274,083.57

Beth's balance: $167,247.33

The best description is ...

Jamar's ending account balance is higher than Beth's ending balance.

__

Additional comment

Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.

The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.”

A simple random sample of 50 adult Americans is collected.

n(p) = 50(0.22)

n(1 - p) = 50(1 - 0.22)

The CLT would hold here.

n = 50

p = 0.22

p cap = 0.25

The test statistic, z = (p cap - p) / (√p (1 - p) / n)

z = (0.25 - 0.22)/(√0.22(1-0.22)/50)

z = 0.51

The p-value is 0.3043.

Hence, The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.

To know more about the probability, click on the link

https://brainly.com/question/24756209

#SPJ1

The probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3% is 0.9968

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 9% = 0.09

sample size, n = 789

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.09(1 - 0.09)) / 789}

= √{(0.09 * 0.91) / 789}

= 0.0102

The probability

differ from the population proportion by less than 3%

|X - 0.09| < 0.03

X < 0.12 OR X > 0.06

0.06 < X < 0.12

P(z < 0.12) - P(z < 0.06 )

z score for z < 0.06

z = (0.06 - 0.09) / 0.0102

= -2.9412

p value for z < -2.9412 = 0.0016

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9984

The probability required = 0.9984 - 0.0016 = 0.9968

Learn more about p - values at:

https://brainly.com/question/28940355

#SPJ1