Answer:
[tex]2^2=4[/tex]
Step-by-step explanation:
[tex](3^8 \cdot 2^{-5} \cdot 9^0)^{-2} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}[/tex]
Using exponent rule [tex]a^0=1[/tex]
[tex]\implies (3^8 \cdot 2^{-5} )^{-2} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}[/tex]
Using exponent rule [tex](a^b \cdot a^c)^d=(a^{bd} \cdot a^{cd})[/tex]
[tex]\implies 3^{(8\times-2)} \cdot 2^{(-5\times-2)} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-2}}{3^3}\right)^4 \cdot3^{28}[/tex]
Using exponent rule [tex]\left(\dfrac{a^b}{a^c}\right)^d=\left(\dfrac{a^{bd}}{a^{cd}}\right)[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{(-2\times4)}}{3^{(3\times4)}}\right) \cdot3^{28}[/tex]
[tex]\implies 3^{-16} \cdot 2^{10} \cdot \left(\dfrac{2^{-8}}{3^{12}}\right) \cdot3^{28}[/tex]
Rewrite as one fraction:
[tex]\implies \dfrac{3^{-16} \cdot 2^{10} \cdot2^{-8}\cdot3^{28}}{3^{12}}[/tex]
Using exponent rule [tex]a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies \dfrac{3^{(-16+28)} \cdot 2^{(10-8)}}{3^{12}}[/tex]
[tex]\implies \dfrac{3^{12} \cdot 2^{2}}{3^{12}}[/tex]
Cancel the common factor [tex]3^{12}[/tex]
[tex]\implies 2^2[/tex]
[tex]\implies 4[/tex]
Penny buys 3 bouquets for $3 each and 4 bouquets for $2 each. Which expression gives the total cost of the bouquets that Penny buys?
A.
33 2+ 4
B.
33 4+ 2
C.
33 + 4 × 2
D.
32 + 4 × 2
you forget the last two digits of your cell phone number password. What is the probability that you choose the correct digits? Explain your reasoning
I will give BRAINLY and
FIVE STAR and a THANKS
Please help me
Answer:
120 security person
Step-by-step explanation:
the ratio is 1:170 so for every 170 people there is one security guard. So you take the number of people attending 20400 and divide by your ratio which is 170.
20400/170 = 120
what two numbers can be multiplied to get 16 but added to get -2?
Answer:
2 and 8
Step-by-step explanation:
A scoop of ice cream in the shape of a whole sphere sits in a right cone. The radius of the ice cream scoop is 3.0 cm and the radius of the cone is 3.0 cm. What is the volume of the scoop of ice cream? Show all your work. How tall must the height of the cone be to fit all the ice cream without spilling if it melts? Show all your work.
The volume of the scoop of ice cream is 113.14 cm³.
The height of the cone that would keep the ice cream from spilling is 12cm.
What is the volume of the scoop of ice cream?Volume of a sphere = 4/3 x pi x r^3
4/3 x (3^3) x 22/7 = 113.14 cm³
What must the height of the cone be?
Volume of the ice cream / 1/3(nr^2)
113.14 / (1/3 x 22/7 x 3^3) = 12 cm
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Which statements about the composite figure are true? Check all that apply. The composite figure consists of two rectangular pyramids. The composite figure can be broken down into rectangular prisms. The volume of the composite figure is 1. 5(9)(5) 1. 5(9)(5). The total volume is 45 units3. The total volume is 90 units3.
Total volume is 45 unit³
We have given that the composite figure consists of two rectangular pyramids.
Suppose they are joined together to form the given figure, stacked to each other on their base.
What is the volume of one pyramid?[tex]Volume of pyramid=\frac{L\times w\times h}{3}[/tex]
Bye using the formula we get
[tex]=\frac{9\times 1.5\times 5}{3}\\ =\frac{45}{2}[/tex]
now, Since there are two pyramids in the figure on same base and height,
their volume will be equal
So area of composite figure
[tex]=\frac{45}{2}\times2[/tex]
Therefore, the volume of the given figure = 45 units³
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PLEASE HELP!!: 600 raffle tickets were sold for $5 each. There is one $500 first prize and three $200 second prizes. The remainder of the tickets do not win anything. What is the expected value of this raffle?
Answer:
$4,100
Step-by-step explanation:
600 x $5 = $3000
$3000 + $500 = $3500
$3500 + $200 + $200 + $200 = $4100
Thanks to
27turekkm
Write an expression in factored form to represent the volume in the canister not occupied by the tennis balls.
Assume the canister is cylinder with volume V = π r2 h.
Answer:
[tex]\implies V=\pi r^2(h-4 r)[/tex]
Step-by-step explanation:
Volume of the canister LESS the volume of 3 tennis balls:
[tex]V=\pi r^2h-3\left(\dfrac43\pi r^3\right)[/tex]
Expand brackets:
[tex]\implies V=\pi r^2h-4\pi r^3[/tex]
Factor:
[tex]\implies V=\pi r^2(h-4 r)[/tex]
Canister is a cylinder
[tex]\\ \rm\rightarrowtail V=\pi r^2h-3(\dfrac{4}{3}\pi r^3)[/tex]
[tex]\\ \rm\rightarrowtail V=\pi r^2h-\dfrac{12}{3}\pi r^3[/tex]
[tex]\\ \rm\rightarrowtail V=\pi r^2h-4\pi r^3[/tex]
Take πr^2 common[tex]\\ \rm\rightarrowtail V=\pi r^2(h-4r)[/tex]
ABCD is a Rhombus with side length 10 cm. Angle ADC = 40. DAC is a sector of a circle with center D. BAC is a sector of a circle with center B. Calculate the shaded area.
The value of the shaded area is approximately 34.907 square centimeters.
How to calculate the area between a rhombus and a circle
According to the description in statement we prepared a representation of the figure in the image attached below. The shaded area is equal to the area of the circle sector ([tex]A[/tex]), in square centimeters:
[tex]A = \frac{\theta\cdot \pi \cdot R^{2}}{360}[/tex] (1)
Where:
[tex]R[/tex] - Length of the radius, in centimeters. [tex]\theta[/tex] - Angle of circle arc, in degrees.If we know that [tex]\theta = 40^{\circ}[/tex] and [tex]R = 10\,cm[/tex], then the area of the circle is:
[tex]A = \frac{(40)\cdot \pi\cdot (10\,cm)^{2}}{360}[/tex]
[tex]A\approx 34.907\,cm^{2}[/tex]
The value of the shaded area is approximately 34.907 square centimeters. [tex]\blacksquare[/tex]
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•
1. Michael deposits $120 into a new savings account.
The account earns 5.5% simple interest per year.
No money is added or removed from the savings account for 5 years.
What is the total amount of money in her savings account at the end of the 5 years.
A. $ 127.50
B. $ 85
C. $ 153
D. $ 330
Answer:
I53 $
Step-by-step explanation:
So, now we can set up the proportion:
5.5 x
-------- = ------
100 120
We need to find the value of x.
120 × 5.5 = 660
660 ÷ 100 = 6.6
So, now we know 6.6 is the amount Michael gets every year for interest.
Let's multiply that over 5 years.
5 × 6.6 = 33.
So, in total interest, Michael got 33$ in 5 years. Let's add that amount to the amount he originally added to into his savings account.
33 + 120 = 153.
Therefore, 153 will be the answer.
-kiniwih426
The magnitude of an earthquake, R, can be measured by the equation r=log(a/t)+d, where A is the amplitude in micrometers, T is measured in seconds, and D accounts for the weakening of the earthquake due to the distance from the epicenter. If an earthquake occurred for 4 seconds and D = 2, which graph would model the correct amount on the Richter scale?
Functions can be represented using equations and graphs
The function that represents the magnitude of an earthquake, R, is [tex]r = \log(0.25a) + 2[/tex]
How to determine the graph of the functionThe equation of the function is given as:
[tex]r = \log(a/t) + d[/tex]
From the question, we have the following parameters
t = 4 seconds
D =2
So, the function becomes
[tex]r = \log(a/4) + 2[/tex]
Divide a by 4
[tex]r = \log(0.25a) + 2[/tex]
Next, we plot the graph of the function (see attachment)
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Answer:
WAHAHAH It's the second graph
Step-by-step explanation:
(B) na im sayin
Tom and Jane decided to see who could collect more seashells. The relation is given by the
inequality j> 21+ 8. If Tom collected 24 seashells, what is the least number of seashells Jane
collected?
8 seashell
9 seashells
56 seashells
57 seashells
The least number of seashells Jane collected is 56 seashells.
What is an inequalityAn inequality is an expression used to show the relationship between two or more variables and numbers.
Let j represent the number of seashells collected by Jane and t represent that of Tom, hence:
j > 2t + 8
For 24 seashells collected by Tom:
j > 2(24) + 8
j > 56
The least number of seashells Jane collected is 56 seashells.
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Solve for the value of c
Answer:
C=15
Step-by-step explanation:
Equation: (7c-7)+(6c-8)=180
180 because a STRAIGHT LINE is 180degrees
Then you do 'math'
(7c+6c)-15=180
13c=195
c=15
would rather be a celebrity or related to whatever celebrity you choose? if you chose the second one who did you choose?
Have a great day! I hope this question makes your day!
so I don't lie what is 1+3?
Answer:
Id rather be related to a celebrity. I would choose prob Milly Bobby Brown (Eleven from Stranger Things) Lol
Step-by-step explanation:
Rlly made my day have a wonderful day too<33
(Its 4 lol)
What is the value of X
Answer:
x = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 6[tex]\sqrt{2}[/tex]
I WILL MARK AS BRAIN-LIST PLEASE HELP ME
Answer:X=12
Step-by-step explanation:
Natalie has 412 apples that she must package into bags. Each bag must hold 8 apples. Natalie divides 412 by 8 and gets an answer of 51 R 4.
What is the correct interpretation of R 4 for this situation? pls help here are the answers
Natalie can fill 4 more bags after filling 51 bags.
Natalie has 4 bags left after filling 51 bags.
Natalie has 4 apples left after filling 51 bags.
Natalie can fill at most 51 bags with 4 apples each
Answer:
Natalie has 4 apples left
Step-by-step explanation:
one bag is 8 apples and only has 4 left so it cant fill another bag let alone 4, so a is out. Natalie has 4 apples, not 4 bags, so there goes B. The only one left is C Natalie has apples left after filling 51 bags.
3) Write an equation in slope intercept form for each line of the right
Line
Help pls this is due today so i need a fast answer
In 1 through 3, use the following table to find the missing variables.
1. Rate of the vehicle in Trip A.
2. Time traveled in Trip B.
3. Distance traveled in Trip C.
Answer:
see below
Step-by-step explanation:
Formula: [tex]speed=\frac{distance}{time}[/tex]
In Problem 1, the question is asking the rate of the vehicle in Trip A. This can be interpreted as miles per hour; basically finding the speed.
Using the formula:
[tex]7,794[/tex] ÷ [tex]18[/tex] = [tex]433 mi/h[/tex]
Both values were plugged in and then divided, which narrowed it down to the final value/answer.
The rate of the vehicle was 433 miles per hour.
In Problem 2, the question is asking us the time traveled in Trip B. Basically the amount of time it took.
Once more using the formula, * This indicates DIVISION*
time = 7.2 hours
= 7.2 h
= 07:12:00
= 7 hours, 12 minutes, 0 seconds
The total time traveled in Trip B was 7 hours and 12 minutes.
In Problem 3, the question is asking the distance traveled in Trip C.
Using the formula one last time,
distance = 96 miles
= 96 mi
How I got this was through multiplication.
12 * 8 = 96.
Therefore, the distance traveled in Trip C was 96 miles.
Round to the nearest whole number 5.156
Answer:
5
Step-by-step explanation:
1 is lower than 5 so you take away the decimal and it's 5
The actual income for this month has been reduced by $200. How can this budget be modified so there will be a positive actual net income?
Monthly Budget
Budgeted Amount
Actual Amount
Income
Wages
$1250
$1050
Expenses
Rent
Utilities
Food
Clothes
Cell Phone
$450
$150
$220
$200
$75
$____
$____
$____
$____
$____
Net Income
$155
$____
a.
This budget can be modified by increasing the amount spent on food and utilities and decreasing the amount spent on clothes and rent, thereby maintaining a positive actual net income.
b.
This budget can be modified by reducing the amount spent on rent and utilities, thereby reducing overall expenses to have the maximum amount of money for all other expenses.
c.
This budget can be modified by reducing the amount spent on food and clothes, thereby reducing overall expenses to have the maximum amount of money for fixed expenses and maintaining a positive actual net income.
d.
This budget cannot be modified.
To give a positive actual net income, the budget can be modified by reducing the amount spent on food and clothes, thereby reducing overall expenses to have the maximum amount of money for fixed expenses.
Option C is correct.
What is an actual net income?In accounting, the actual net income is defined as an entity's income minus the costs of expenses on goods sold, depreciation, amortization, interest, and taxes.
To determine actual net income, start with gross income, which is the whole amount of money earned, and then deduct costs like taxes and interest payments.
To give a positive actual net income, the budget can be modified by reducing the amount spent on food and clothes, thereby reducing overall expenses to have the maximum amount of money for fixed expenses.
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Answer:
( C ) : This budget can be modified by reducing the amount spent on food and clothes, thereby reducing overall expenses to have the maximum amount of money for fixed expenses and maintaining a positive actual net income
Step-by-step explanation:
what is the slope of the line shown below? (-7, 2) (5, 8)
A) ½
B) 2
C) -2
D) -½
Answer:
A
Step-by-step explanation:
so we have to use the equation y2 - y1/ x2 - x1 to solve this
8 - 2/ 5 - (-7)
6/12
1/2
The slope of the line is 1/2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Coordinates:
(-7, 2) and (5, 8)
Now,
Slope.
= (8 - 2) / (5 + 7)
= 6 / 12
= 1/2
Thus,
The slope of the line is 1/2.
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Maya can run 18 miles in 3 hours, and she can bike 18 miles in 2 hours.
what distance did Maya travel if she ran for t hours and then biked for r hours?
The distance Maya traveled is (6t + 9r) miles
Speed, distance and timeFrom the question, we are to determine the distance Maya traveled
First, we will determine the speed at which she runs and the speed at which she bikes
Using the formula,
[tex]Speed = \frac{Distance}{Time}[/tex]
Running
Distance = 18 miles
Time = 3 hours
Then,
Speed = [tex]\frac{18}{3}[/tex]
Speed = 6 miles/hour
BikingDistance = 18 miles
Time = 2 hours
Then,
Speed = [tex]\frac{18}{2}[/tex]
Speed = 9 miles/hour
Now, for the distance she ran for t hours
From
Distance = Speed × Time
Distance = 6 × t
Distance = 6t miles
For the distance she bikes for r hours
Distance = 9 × r
Distance = 9r miles
Total distance traveled = 6t + 9r miles
Hence, the distance Maya traveled is (6t + 9r) miles
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Factor 20x2 25x – 12x – 15 by grouping. 1. Group terms with common factors. 2. Factor the GCF from each group. 3. Write the polynomial as a product of binomials. (20x2 – 12x) (25x– 15) 4x(5x – 3) 5(5x – 3) (5x – 3)( x ).
The factors of the specified polynomial by the grouping the polynomial and taking out GCF is,
[tex](4x+5)(5x-3)[/tex]
What is the factor of polynomial?Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The factor of a polynomial is the terms in linear form, which are when multiplied together, give the original polynomial equation as result.
The given polynomial expression in the problem is,
[tex]20x^2+25x-12x-15[/tex]
Factor the above polynomial by grouping as,
[tex](20x^2+25x)+(-12x-15)[/tex]
Factor the greatest common factor (GCF) from each group as,
[tex]5x(4x+5)-3(4x+5)\\[/tex]
Write the polynomial as a product of binomials as,
[tex]5x(4x+5)-3(4x+5)\\(4x+5)(5x-3)[/tex]
The above polynomial is written as a product of binomials.
Hence, the factors of the specified polynomial by the grouping the polynomial and taking out GCF is,
[tex](4x+5)(5x-3)[/tex]
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Answer:
its 4 and 5 in the blank spots :)
Step-by-step explanation:
20 POINTS!!! PLS HELP <3
Please write it in your own words.
Answer:
See below ↓↓↓
Step-by-step explanation:
(a)
The point (8, 28) represents the fact that in 8 minutes time, the water level of the horse trough is at 28 cm(b)
The unit rate will be equal to the slope of the graphy = 3.5x is given as the equationm = 3.5Therefore, rate is 3.5 cm/min(c)
On taking the slope of these two points it is equal to the slope of the lineTherefore, we can say that the rise in water level directly varies with timeWrite an equation. Then solve. Will mark the brainliest if correct!
Answer:
42 + 8m = 36 + 10m
-10m -10m
42 - 2m = 36
-42 -42
-2m = -6
/-2 /-2
m = 3, 3 months
Explain the mistake 13x+4 =17x
I need this question please I will give lots of points to whoever awnsers it
Answer:
-6
Step-by-step explanation:
21/7+3(-3)
=3-9
=-6
hope it helps!
have a great day/night ahead ┐( ˘_˘)┌
in the following diagrams ABD=y,DBC=x,EFH=y, EFG=x and PQS=SQR=x.write the following in terms of x and y ABC
Angles are the space between intersecting lines, and they are measured in degrees or radians
The measure of angle ABC is y + x
How to determine angle ABCThe given parameters are:
ABD=y,
DBC=x,
EFH=y,
EFG=x
PQS = SQR = x
To determine the measure of angle ABC, we make use of angle ABD and angle DBC
Note that angle ABD and angle DBC have common vertices at points B and D
So, we have:
ABC = ABD + DBC
Substitute known values
ABC = y + x
Hence, the measure of angle ABC is y + x
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help guys pls cmon im bad at math
Answer:
1. 942.48
Step-by-step explanation:
Input the numbers in the formula.
