The revised bank statement of Pina is $919.11 if ending balance from statement $1,115.5 and Deposits outstanding is $409.03.
What is meant by deposit outstanding?Unpaid deposits are receipts that appear in your accounting records but not on your bank statement. Money that you have received, such as cash and checks, is included in receipts. A receipt may occasionally be entered in your books before it shows up on your bank statement. Your books' line item corresponds to the unpaid deposit.
An outstanding deposit is a term used to describe a business's receipts (cash, customer checks, etc.) that have been entered into the general ledger accounts but have not yet been shown on the bank statement. Deposits in transit are another name for outstanding deposits.
Revised statement=End balance+ deposits-check outstand
=1115.5+409.03-605.42
=919.11
Therefore, the revised bank statement of Pina is $919.11
To know more about deposit outstanding, visit:
https://brainly.com/question/3719189
#SPJ1
find the distance between points (4,2) and (-3,2)
The answer is in the form [tex]\sqrt{A}[/tex]. Determine A
Distance between points is 7 units.
What are co-ordinate system?
In pure mathematics, a co-ordinate system could be a system that uses one or a lot of numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space.
Main body;
points given = (4,2) and(-3,2).
Distance formula = √(x₁-x₂)² +(y₁ -y₂)²
so,
distance between points = √(4-(-3))² + (2-2)²
=√ 7² +0²
distance between points = 7 units
Hence ,distance between points is 7 units.
to know more about co-ordinate system , visit:
https://brainly.com/question/4726772
#SPJ1
Are the slopes to the equations
y=2x+5 and y=3x+5 parallel,
perpendicular, or neither
Answer: Neither
Step-by-step explanation:
Given that f (x) = 2x + 1 and g(x) = 6 - x, find the following. If necessary, use a 0 in the denominator!
a. ( f + g) (2) = ____________
b. ( f - g) (-5) = ___________
c. ( g - f) (4) = ____________
d. ( f ⋅ g) ( 1/2) = ___________
e. ( f/g) (-1) = _____________
The results of operations between the two functions f(x) = 2 · x + 1 and g(x) = 6 - x are listed below:
(f + g)(2) = 9 (f - g)(- 5) = - 20 (g - f)(4) = - 7 (f · g)(1 / 2) = 11 (f / g)(- 1) = - 1 / 7How to derive and evaluate a composite function
In this problem we have the definitions of two functions, linear equations on both cases. The procedure consists in using the definitions of operations between two functions and evaluate the resulting expression at a given value of x:
Addition
(f + g)(x) = f(x) + g(x)
Subtraction
(f - g)(x) = f(x) - g(x)
Multiplication
(f · g)(x) = f(x) · g(x)
Division
(f / g)(x) = f(x) / g(x)
Now we proceed to derive each expression and evaluate the resulting expression:
(f + g)(x) = (2 · x + 1) + (6 - x)
(f + g)(x) = x + 7
(f + g)(2) = 2 + 7
(f + g)(2) = 9
(f - g)(x) = (2 · x + 1) - (6 - x)
(f - g)(x) = 3 · x - 5
(f - g)(- 5) = 3 · (- 5) - 5
(f - g)(- 5) = - 20
(g - f)(x) = (6 - x) - (2 · x + 1)
(g - f)(x) = - 3 · x + 5
(g - f)(4) = - 3 · 4 + 5
(g - f)(4) = - 7
(f · g) (x) = (2 · x + 1) · (6 - x)
(f · g) (x) = 2 · x · (6 - x) + 6 - x
(f · g) (x) = 12 · x - 2 · x² + 6 - x
(f · g) (x) = - 2 · x² + 11 · x + 6
(f · g)(1 / 2) = - 2 · (1 / 2)² + 11 · (1 / 2) + 6
(f · g)(1 / 2) = 11
(f / g) (x) = (2 · x + 1) / (6 - x)
(f / g)(- 1) = [2 · (- 1) + 1] / [6 - (- 1)]
(f / g)(- 1) = - 1 / 7
To learn more on operations between functions: https://brainly.com/question/27915566
#SPJ1
the perimeter of the rectangle is 26inches and the length is 8 inches what is the width?
Answer:
5 inches
Step-by-step explanation:
P=2(l+w)
Solving for w
w = p / 2 - l = 26 /2 - 8 = 5
Question 16 (1 point)
What is the correct reason for Step 2?
Angles forming linear pairs sum to 180
Corresponding Angle Theorem
Substitution
Vertical Angle Theorem
The correct reason for Step 2 is the Vertical Angle Theorem
Vertical Angles Theorem:There are four angles created when two straight lines cross or intersect at a point, in which two sets of angles are not contiguous. These pair of non-adjacent angles are known as Vertical angles or Vertically opposite angles.
According to The theorem of vertical angles, two opposing vertical angles that are created when two straight lines intersect at a point, are always equal to one another.
Here we have
3 three straight lines named SZ, TV, WY
Where Line SZ and TV intersected at U,
Thus the formed pairs of Vertical angles are ∠SUV, ∠TUX; ∠SUT, ∠VUX
As we know according to Vertical Angles Theorem the vertical angles are equal
=> ∠SUV = ∠TUX
Therefore,
The correct reason for Step 2 is the Vertical Angle Theorem
Learn more about Angle theorems at
https://brainly.com/question/29597631
#SPJ4
"Solve for Input of Function Given Output
Given } h(x)=-3 x-5 solve for x when } h(x)=-2 "
Answer: " x = [tex]-\frac{7}{3}[/tex] " ; or, write as: " x = [tex]-2\frac{1}{3}[/tex] " .
Step-by-step explanation:
" Given h(x) = -3x − 5 ; solve for x when h(x) = 2 " .
_________________
So, substitute 2 for h(x) ; and rewrite:
2 = -3x − 5 ;
Add 5 to Each Side of the equation;
2 + 5 = -3x − 5 + 5 ;
To get:
7 = -3x ;
Now divide Each Side of the equation by -3 ;
to isolate x on one side of the equation;
& to solve for x ;
7 / -3 = -3x / -3 ;
to get:
- 7/3 = x ;
↔ x = - [tex]\frac{7}{3}[/tex] ;
Or; to write as a mixed number:
_____________
Note: -7/3 = - (7/3) = - (7 ÷ 3) ;
We can use long division to obtain the mixed number ;
→ which is the "opposite value of the following: " [7 ÷ 3]" ;
First: We shall solve for the value of [7 ÷ 3] ;
_____
2
3⟌ 7 ⇒ So we have " 2 R 1 " , or, "2 remainder 1" ;
- 6 ⇒ or: 2 and 1/3 ;
1
⇒ Note: The remainder; 1 , is the numerator ; and:
The divisor; 3, is the denominator ; and:
The number; 2, is the "whole number portion" of this mixed number.
[which we shall make, "- 2 "; as explained later.
_____
Second: We shall write out the mixed number" by:
A] writing the value from the information above' ; with our obtained values; as: " [tex]2\frac{1}{3}[/tex] " ; and by:
B] writing the correct 'mixed number' by writing the 'oppositive value'
of that said number. In our case, we take " [tex]2\frac{1}{3}[/tex] " ; and make the value "negative". In our case, we write the correct value by adding a
'negative sign'—as follows: " [tex]-2\frac{1}{3}[/tex] " .
_____
The answer is: " x = [tex]-\frac{7}{3}[/tex] " ; or, write as: " x = [tex]-2\frac{1}{3}[/tex] " .
_____
Hope this is helpful to you! Best wishes!
_____
Mrs. Perky bought 2 3/4 gallons of blue paint. Each gallon of blue paint cost $19.50. Mrs. Perky also bought 1 1/3 gallons of orange paint. Each gallon of orange paint cost $16
Answer:
$74.96 if rounding to hundredths place.
Step-by-step explanation:
If you are looking for the total amount spent, first we will convert 2 3/4 into a decimal, which is 2.75. 2.75 X 19.50 = 53.625. She bought 53.525 dollars worth of blue paint, now we solve for orange. 1 1/3 X 16 = 64/3, which is simplified to 21 1/3. If we add the two togetherwe get 74.9583, but the 3 is repeated. If you are asked to rount to the 100th place, the asnwer is $74.96. If you are rounding to nearest dollar, it is about $75.
Hope this helped :)
Micha is getting a fountain drink. He can pick from four cup sizes, eight different drink flavors and two different straw colors. How many drink outcomes are possible?
Micha can choose her drink is 64 different ways.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, She can pick from four cup sizes, eight different drink flavors, and two different straw colors.
∴ The no. of ways in which she can choose from is [tex]^4C_1 \times ^8C_1 \times ^2C_1[/tex] ways.
= 4!/(4-1)!1! + 8!/(8-1)!1! + 2!/(2-1)!1!.
= 4!/3! × 8!/7! × 2!/1!.
= 4 × 8 × 2.
= 64 ways.
learn more about permutation and combination here :
https://brainly.com/question/28720645
#SPJ1
To help open up a jewelry store, Ann borrowed money from a bank.
She took out a personal, amortized loan for , at an interest rate of , with monthly payments for a term of years.
For each part, do not round any intermediate computations and round your final answers to the nearest cent.
If necessary, refer to the list of financial formulas.
(a) Find Ann's monthly payment.
(b) If Ann pays the monthly payment each month for the full term, find her total amount to repay the loan.
(c) If Ann pays the monthly payment each month for the full term, find the total amount of interest she will pay.
(a) Ann's monthly payment: $133.33
(b) Ann's total amount to repay the loan:$8000
(c) The total amount of interest Ann will pay:-$12000
What is amortized loan?
A loan that has planned, monthly payments that are applied to both the principle and interest accrued is known as an amortized loan.
To solve this problem, we need to use the following formula for an amortized loan:
[tex]Monthly\ payment = (Interest rate / 12) * Loan\ amount / (1 - (1 + (Interest \ rate / 12))^(-Term * 12))[/tex]
(a) Find Ann's monthly payment:
Substituting the given values into the formula, we get:
[tex]Monthly\ payment = (0.08 / 12) * 20000 / (1 - (1 + (0.08 / 12))^(-5 * 12))\\\\Monthly\ payment = 133.33[/tex]
Therefore, Ann's monthly payment is $133.33.
(b) Find Ann's total amount to repay the loan:
The total amount to repay the loan is equal to the sum of the monthly payments over the term of the loan. Since Ann's monthly payment is $133.33 and the term of the loan is 5 years, the total amount to repay the loan is equal to $133.33 * 5 * 12 = $8000.
(c) Find the total amount of interest Ann will pay:
The total amount of interest Ann will pay is equal to the total amount to repay the loan minus the loan amount. Since Ann's total amount to repay the loan is $8000 and the loan amount is $20000, the total amount of interest Ann will pay is equal to $8000 - $20000 = -$12000.
Note that the total amount of interest Ann will pay is a negative number because the loan amount is greater than the total amount to repay the loan. This means that Ann will end up paying less than the loan amount due to the amortization of the loan.
To know more about amortized loan visit,
https://brainly.com/question/17960115
#SPJ1
You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent the price of the shirt and y represent the price of the pants. Write an equation that can be used to find the price of the shirts and pants. Directions: Write the equation in both slope-intercept and standard form for each of the scenarios below. a. Standard Form: b. Slope-Intercept Form: c. If the shirts cost $20 each how much were each of the pants? d. Using the Standard Form, identify the x-intercept of the graph and explain how the x-intercept relates to the price of the pants and shirts. e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the price of the pants and shirts
Answer:
see the explanation
Step-by-step explanation:
Let
x ----> the price of the shirt
y ---> he price of the pants
we have that
The price of three shirts plus the price of two paints must be equal to $300
so
This is the equation of the line in standard form
Convert to slope intercept form
Isolate the variable y
subtract 3x both sides
Divide by 2 both sides
----> equation of the line in slope intercept form
Find out the x-intercept
Remember that the x-intercept is the value of x when the value of y is equal to zero
In this problem, the x-intercept is the price of the shirt when the price of the paints is equal to zero
Using the Standard Form, identify the x-intercept of the graph
The standard form is
The x-intercept is C/A
we have
so
The x-intercept is the point (100,0)
That means---> The price of the shirt is $100 when the price of the paints is equal to $0
Alternative method to find out the x-intercept (equation in slope intercept form)
For y=0
solve for x
The x-intercept is the point (100,0)
For more answers, Contact:
https://brainly.com/app/profile/63103549/answers
Please Help Me With This Question!!!
Answer:
B. 11/12
Step-by-step explanation:
Answer: B. 11/12
Step-by-step explanation:
.
imagine an experiment where you measure the width, length and height of a box, in centimeters. additionally, you estimate an uncertainty (error) in each measurement. the goal is to calculate the box's volume and the propagated error in the volume. suppose you measure the box's width, w
The volume of a box with dimensions a, b, and c is given by
V(a,b,c)=abc.
It follows that
dV(a,b,c)/V(a,b,c)=da/a + db/b + dc/c .
Therefore, "in first approximation", the relative error in volume is the sum of the relative errors in the side lengths.
In the given example the relative errors in the side lengths are 1%. As the case may be these add up, and we obtain a relative volume error of 3% or 1.5 cubic inches as a "first estimate".
The actual minimal volume of the box under the given constraints is
4.95*4.95*1.98=48.51495 cubic inches, which is <1.5 cubic inches off; and the maximal volume is 5.05*5.05*2.02=51.51505 cubic inches, which is 1.51505>1.5 off the intended value of 50 cubic inches. It follows that the worst-case analysis gives a larger error than the "first estimate".
To know more about volume visit: brainly.com/question/13338592
#SPJ4
Find the requested measurement. Use 3.14 and round your answer to the nearest hundredth
Answer:
C) 20.72 (Question 1: Solve for Circumference)
Step-by-step explanation:
Question 1:
Using the formula:
[tex]C=2\pi r[/tex]
- C = circumference- π = the constant pi- r = radius of the circleGiven radius:⇒ r = 3.3
[tex]C=2\pi r[/tex]
[tex]2\times\pi\times3.3[/tex]
≈ [tex]20.73451[/tex]
Rounding, 20.72.
Thanks.
Mariam runs 7.5 miles in one hour How much distance will she cover in 3 hours
Which fraction is equivalent to a whole number?
Select all that apply.
Answer:
The answers are A B and C
they could be whole numbers
Step-by-step explanation:
need brainliest
Use the formula A=P (1+ r/n)ⁿ⁺ to solve the compound interest problem.
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately ___ years. (Round to the nearest tenth.)
The answer to the given problem can be stated as, "$ 500 interest will be earned in approximately 0.14 years."
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
The formula to calculate the amount is as follows,
A = P(1 + r)^(nt)
The, the interest is given as P[(1 + r)^(nt) - 1]
Substitute all the corresponding values in the above expression to obtain,
500 = 1700[(1 + 2/100)^(nt) - 1]
=> 500 + 1700 = 1700(1 + 2/100)^(nt)
=> (1 + 2/100)^(nt) = 2200/1700
=> 1.02^(nt) = 22/17
Since, there are 4 quarters in one year, n = 4.
1.02^(4t) = 1.294
=> 4t = log(1.294) ÷ log(1.02)
=> 4t = 0.562
=> t = 0.14
Hence, it will take 0.14 years to earn the interest of $500.
To know more about compound interest click on,
https://brainly.com/question/14295570
#SPJ1
The graph shows the proportional relationship between the number of gems collected and the number of levels that h been completed in a video game.
Determine the constant of proportionality for the relationship.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The constant of proportionality for the relationship is 70.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
We have,
The number of gems collected at different levels is:
At 2 levels, 140 gems are collected.
At 4 levels, 280 gems are collected.
At 6 levels, 420 gems are collected.
This means.
y ∝ x
y is the number of gems collected.
x is the level.
Now,
y = kx
140 = k x 2
k = 140/2
k = 70
Thus,
The constant of proportionality for the relationship is 70.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Takeuru only uses eggs for souffles in his restaurant. He uses 3 eggs per souffle. Last week he bought 4 times as many eggs as he baked souffles. Takeuru has 18 eggs left over.
How many eggs did Takeuru buy and how many souffles did he bake?
Takeuru made 18 souffles with the 72 eggs he purchased.
What is meant by ratio?A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7).
The quantities in a ratio can be of any kind, such as counts of people or things, measures of lengths, weights, or times, etc. Both numbers must be positive in the majority of situations.
Let e = the quantity of eggs Takeuru purchased.
Takeuru purchased s souffles total.
Then, as Takeuru purchased 4 times as many eggs as he used to make soufflés, e=4s.
Since Takeuru uses 3 eggs for each souffle he bakes and has 18 eggs remaining after backing, the equation is: e-3s=18.
This states that after Takeuru utilized three eggs for each souffle, there are still 18 eggs available.
There are now two equations:
e=4s
e-3s=18
When we solve for s using equation (2) and the value of e from equation (1), we get the following results: s=18
e=4s
e=4×18
e=72
Therefore, Takeuru purchased 72 eggs.
There were 18 soufflés that Takeuru purchased.
To know more about ratio, visit
https://brainly.com/question/13419413
#SPJ1
Find the value of Za:
Z 0.47=
Round to 2 decimals
The value of za is 80.47.
What is value?Value is the regard that something is held to deserve,the important, worth or usefullness of something.
let us find the value of zero Alpha, Given that alpha is .32. So the value of Z the it is 0.32. Well, we need to begin to considering that we need to the find actually the differentiate one minus alpha. Thus it is going to be in this case one of the (-) 10.32. This is going to be the 0.68. So actually Z of .32, we're going to need to find 0.68 inside the Z table. So let's look at it at it. Look at that at 0.68 oh eight.Let give us the Z score of 80.47. So we can tell that the Z score of zero of alpha, given that the Alpha is 00.32 is going to be 0.47.
To know more about value click-
https://brainly.com/question/843074
#SPJ1
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
y = x5, y =
square root of x
; about the x-axis
Rotating the area bounded by the given curves around the designated line yields the solid's volume as [tex]V = \frac{9}{22}\pi[/tex]
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Different forms have various volumes.
The amount
of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. The capacity of an object to hold matter is generally thought of as its volume in three dimensions.
The functions provided are,
[tex]`y = f(x) = \sqrt{x}``y = g(x) = x^5`[/tex]
By rotating the area around the x-axis, the solid's volume is given by (using washer method)
[tex]V = \pi int_a^b [f^2(x)-g^2(x)]dx[/tex]
evaluate the integral, limit the plugins, and
[tex]V = \pi int_0^1 [(\sqrt{x})^2-(x^5)^2]dx\\\\V= \pi int_0^1 [x-x^10]dx V = \pi [\frac{x^2}{2}-\frac{x^11}{11}]_0^1 V = \pi [\frac{1^2}{2}-\frac{1^11}{11}]. V = \pi [\frac{1}{2}-\frac{1}{11}] = \frac{9}{22}\pi[/tex]
To know more about Volumes, refer to this link:
https://brainly.com/question/1578538
#SPJ4
what is 1/2 times 3
Answer:
1.5
Step-by-step explanation:
Answer:
1.5
Step-by-step explanation:
3 times 1/2=1/5
Which expression has a term with a base of 8?
3xy +8
8m
28
84
Answer: 8^4
Step-by-step explanation: A 'base' is a number with an exponent.
please help me
A 91/198
B 459/1000
C 17/37
D 51/110
past records show that the average number of accidents drowning at a beach resort is 3 per year for every 100000 of tourists visiting the resort. if in a year 200000 tourists visited this resort, find the probability that;
a. there will be no drowning this year
b. there will be at least 6 accidents this year
The probability that there will be no drowning this year is 0%
and the probability that there will be at least 6 accidents this year is 0.003%
What is the probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We have,
3 per year for every 100000 of tourists
if in a year 200000 tourists visited this resort,
Probability formula:
P(A) = f / N
P(A) = Probability of an event (event A) occurring.
f = Number of ways an event can occur (frequency)
N = Total number of outcomes possible.
so f = 3,
N = 100000
P(A) = f / N = 3/100000 = 0.00003 = 0.003%
so, the probability of the previous year is 0.003%.
0.003% = f / 200000
f = 200000 * 0.003% = 6
a) The probability that there will be no drowning this year:
P(A) = 0 / 200000 = 0
b) The probability that there will be at least 6 accidents this year:
P(A) = 6 / 200000
P(A) = 0.003%
Hence, the probability that there will be no drowning this year is 0%
and the probability that there will be at least 6 accidents this year is 0.003%
To learn more about the probability visit,
https://brainly.com/question/25870256
#SPJ1
12 15 18 A' B V C Identify the reflection rule to map AABC onto AA'B'C' in the given figure. A) Reflection across the origin. B) Reflection across the line y = x. C) Reflection across the line y = -X. D) Reflection across the x-axis.
The reflection rule for the given graph is Option A.
What is reflection?
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Given the graph of triangle ABC under reflection, we analyse each answer choice one by one
For Option A) Reflection across the origin, the y-coordinate is negated, as well as the x-coordinate (their signs are changed). The image of the point (x,y) is the point in a point reflected in the origin (-x,-y).
So, A(-3,-1) becomes A'(3,1) which is correct for the given coordinates of the reflected graph of the figure.
Hence, Option A is the correct choice and the remaining choices are eliminated.
To learn more about the reflection
https://brainly.com/question/28910569
#SPJ1
20 point question! Please help!
1. Identify all pairs of congruent corresponding parts, then write a congruency statement.
∠A ≅ ___ AB≅___
∠B≅ __ BC≅___
∠C≅ ___ AC≅__
Congruency statement
The congruent pairs for the angles and sides of the given two congruent triangles are
∠A ≅ ∠D
∠B ≅ ∠ E
∠C ≅ ∠F and
AB ≅ DE
BC ≅ EF
AC ≅ FD
What is congruent triangles?
If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.
Let the given two triangles, ΔABC and ΔDEF are congruent.
We have to find the congruent pairs from the given two congruent triangles.
First to find the congruent pairs for angles.
∠A ≅ ∠D
∠B ≅ ∠ E
∠C ≅ ∠F
Now to find the congruent pairs for sides,
AB ≅ DE
BC ≅ EF
AC ≅ FD
These are the congruent pairs for the angles and sides of the given two congruent triangles.
To know more about congruent triangles, click on the link
https://brainly.com/question/2938476
#SPJ4
z>0
z
>
0
?
Responses
10p2z4
10
p
2
z
4
10 p 2 z 4
10p2z6
10
p
2
z
6
10 p 2 z 6
20p2z4
20
p
2
z
4
20 p 2 z 4
20p2z6
The equivalent of the radical expression √(100p⁴z⁸) is
10p²z⁴
How to find the equivalence of the radical expressionThe given expression √(100p⁴z⁸) is first rewritten in exponents form
Writing in exponents form
= √(100p⁴z⁸)
= (100p⁴z⁸)^1/2
multiplying through
= 100^1/2 * p^(4 * 1/2) * z^(8 * 1/2)
noting that √100 = 100^1/2 = 10
= 10 * p^(2) * z^(4)
= 10p²z⁴
Learn more on exponents here:
https://brainly.com/question/28939682
#SPJ1
The formula A=18.5 e⁰.¹⁷⁰⁸⁺ models the population of a US state, A, in millions,
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 26.6 million?
The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The equation is given below.
[tex]\rm A = 18.5 \times e^{0.1708\times t}[/tex]
The population of the state in 2,000 is calculated as,
[tex]\rm A = 18.5 \times e^{0.1708\times 0}[/tex]
A = 18.5 × e⁰
A = 18.5 Million
The time at which the population of the state reaches 26.6 million will be given as,
[tex]\rm 26.6 = 18.5 \times e^{0.1708\times t}\\\\1.4378 = e^{0.1708\times t}[/tex]
Take natural log on both sides, then we have
0.1708 × t = ln 1.4378
t = 2.126 years
The population of the state 2,000 is 18.5 Million. And the time at which the population of the state reaches 26.6 million will be 2.126 years.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ1
The price of a cake plus 11% delivery charge comes to a total cost of $19.98. What was the price of the cake?
Step 1 of 2 : Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity. Enter the equation in the box below:
Answer:
x + 0.11x = 19.98
Step 2 of 2 : Solve the equation for the unknown quantity.
x = 18.18