To evaluate the expression (6^7)(3^3)/(6^6)(3^4), simplify each term, resulting in 6^10 / 6^10, which equals 1.
Explanation:To evaluate the expression (6^7)(3^3)/(6^6)(3^4), we can simplify each term first. The numerator can be simplified as (6^7)(3^3) = 6^(7+3) = 6^10. The denominator can be simplified as (6^6)(3^4) = 6^(6+4) = 6^10. Therefore, the expression simplifies to 6^10 / 6^10, which is equal to 1. So the value of the expression is 1.
Learn more about Simplifying Exponentials here:https://brainly.com/question/28199759
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Find the area of the shaded sector. Leave your answer in terms of pi.
Answer options:
18pi ft2
24pi ft2
32pi ft2
3pi ft2
Answer:
18π ft^2
Step-by-step explanation:
Area of Sector = [tex]\frac{\theta}{360}*\pi r^2[/tex]
Where
[tex]\theta[/tex] is the angle of the sector (in our case it is 45°), and
r is the radius (which is 12 ft)
So we plug these into the formula and get our answer to be:
[tex]A=\frac{\theta}{360}*\pi r^2\\A=\frac{45}{360}*\pi (12)^2\\A=\frac{1}{8}\pi*144\\A=18\pi[/tex]
This is our answer: 18π
Answer:
= 18 ft²
Step-by-step explanation:
The area of a sector is given by the formula;
Area = θ/360 × πr² ; where θ is the angle subtended by the arc to the center, r is the radius.
Therefore;
Area = 45/360 × π ×12²
= 18 ft²
Please help ASAP
this table shows how many students from high schools attended a foot ball game.
A student is randomly selected.
what is the probability that a student attended the game, given that the student is from North Beach? Round your answer to two decimal places.
Answer:
The probability that a student attended the game, given that the student is from North Beach will be: 0.55
Step-by-step explanation:
Given data,
Number of North Beach students who attended the game = n1 = 110
Number of North Beach students who did not attend the game = n2 = 90
Total number of students = n1 + n2
=> 110 + 90
=> 200
The probability that a student attended the game, given that the student is from North Beach will be:
probability of students attended the game of North Beach/ probability of total students attended
=> n1/n
= 110 / 200
= 0.55
Therefore, the probability that a student attended the game, given that the student is from North Beach will be: 0.55
Answer:
0.55
Step-by-step explanation:
PLEASE HELP, I’LL GIVE BRAINLIST!!
For a ratio make a fraction using the quantities of the colors.
You want the ratio of red to purple.
There are 16 red and 2 purple, so the ratio would be 16/2, which can be reduced to 8/1
Jeremiah is shopping for sunflower seeds and is looking for the best deal. He had three choices. What package of sunflower seeds is the best deal? Rank the packages in order from best to worst deal. Please show your work!!
Answer:
Step-by-step explanation:
A=$4.49/5 =$0.90 per LB
B=$0.64 per LB
C=$1.35/2.3 =$0.59 per LB
D=$0.98/1.75 =$0.56 per LB
E=$0.25/3 =$0.08 per oz
The best deal is E because he is only paying 8cents.
Best deals to worst deals= E,D,C,B,A.
put me as branilist answer.
a cone and a sphere have the same volume. the height of the cone is 96 units. what would be the values for the radius of the cone and the sphere?
Answer:
The radius = 24 units.
Step-by-step explanation:
I am assuming that the 2 radii are equal then:
1/3 pi r^2 * 96 = 4/3 pi r^3
then:
4/3 pi r^3 / 32 pi r^2 = 1
4/3r^3 / 32 r^2 = 1
4/3 r * 1/ 32 = 1
r = 32 * 3/4
= 24.
If x and y vary inversely, as y increase as, what happens to the value of x
inverse proportionality between 2 variables follows this .
y = k/x
where k is proportional constant
as value of one variable increases/decreases , value of other variable decreases/increases
so
if x increases, y will decrease
if x decreases , y will increase
The Perpendicular to Parallels Theorem proves that _____.
A. alternate interior angles are congruent
B. congruent angles are equal
C. two lines are perpendicular
D. two lines are parallel
C. two lines are perpendicular
hope this helps :)
PLEASE HELP ASAP! WILL GIVE BRAINLIEST! I don’t really understand how to do this?
Silas is going to use 5 ounces of glue and 2 ounces of detergent. What percent of his slime is detergent?
Can you explain to me how to do this problem please?
A. 5%
B. 40%
C. 71.4%
D. 28.6%
E. 42.9%
F. 60%
G. 250%
so we're trying to figure what portion of silas' slime is detergent. we know that his slime is a combo of 5 oz glue and 2 oz detergent for a total of 7 oz of slime.
what we want to find is how much of those 7 oz of slime is detergent.
quite simply 2 oz of the 7 is detergent.
to make that into a percent just divide 2 by 7.
2/7 = 0.2857
then move the decimal over two spots to get
28.57 or
D. 28.6%
just remember that percents are just how much makes up the whole.
HEP FAST PLZ!!!! THANK YOU!
Chandresh has several fishing rods that she would like to pack in boxes. One box is shown below.
Which fishing rod will fit in the box shown?
A) 17-inch fishing rod B) 24-inch fishing rod C) 27-inch fishing rod D) 32-inch fishing rod
A is the answer to this question
Answer:
Your answer is A.)
Plz help me with this !
Answer: x³
Step-by-step explanation:
[tex]\sqrt[n]{x^{3n}}=x^{\frac{3n}{n}}=x^3[/tex]
Note: There is no radical expression, only an exponential expression.
Can I get step by step help on numbers 52,54,60, and 64 please
Answer:
52: 8-Z
54: 18+X
60: 12.3
64: 2.5
52: 8 subtracted from z, the equation will only be 8-z because we do not know what z is.
54: 18 more than a number, we do not know what the number is so we will name it X, more than is adding, so the equation will look like this, 18+X
60: Since y is 6.7, all you have to do is subtract 19-6.7.
64: Since n is 7.5 just divide 7.5 from 3 and you will get 2.5.
Hailey and Kacie are selling candles to raise money. • Hailey is selling candles for $4 each and has already raised $160. • Kacie is selling candles for $7 each and has already raised $70. Which equation can be used to find c, the number of candles each girl needs to sell so that the total amount raised is the same for both Hailey and Kacie?
Answer:
The number of candles each girl needs to sell so that the total amount raised is the same for both is
Hailey 70 candles
Kacie 40 candles
Step-by-step explanation:
Let
x------> the number of candles sold
y----> total amount raised
we know that
Hailey's equation
[tex]y=4x+160[/tex] -----> equation A
Please note that Hailey has already raised $160, so he has sold 40 candles.
Kacie's equation
[tex]y=7x+70[/tex] -----> equation B
Please note that Kacie has already raised $70, so he has sold 10 candles.
equate equation A and equation B solve for x
[tex]4x+160=7x+70[/tex]
[tex]7x-4x=160-70[/tex]
[tex]3x=90[/tex]
[tex]x=30\ candles [/tex]
The number of candles each girl needs to sell so that the total amount raised is the same for both is
Hailey
40+30=70 candles
Kacie
10+30=40 candles
Answer: C. 4c+160=7c+70
Step-by-step explanation:
If I were you I would also put the answer choices
Please help me with this ! ! ! ! !
Answer:
First choice: m = -4
Step-by-step explanation:
The second equation is already solved for n, so lets's use the substitution method and substitute m - 2 for n in the first equation.
m - 2n = 8
m - 2(m - 2) = 8
m - 2m + 4 = 8
-m + 4 = 8
-m = 4
m = -4
The second equation tells you what 'n' is. It's "m-2" .
So you can simply write "m-2" in place of 'n' in the first equation.
Then the first equation says [ m - 2(m-2) = 8 ], and you should have no trouble solving that.
Round to the given place: 340,413 (hundred thousands)
Answer:
The answer is 300,000.
Step-by-step explanation:
Hundred thousand would be one hundred (100) and a thousand, which is three zeroes. So we put three zeroes after 100 and we get 100,000. So in this case we're rounding to 300,000.
The answer is: 300,000
Step-by-step explanation:Hundred thousand is the natural number which follows 99,999 and 100,001.
Hence, the number is given by: 100,000.
Hence, when we round any number to the hundred thousand then there must be 5 zeros in the number.
i.e. the number 340,413 rounding to the nearest hundred thousand is given by: 300000
( Since the first digit i.e. 3 is at the hundred thousand place and all the number that precedes this place is converted to 0 )
the vertices of a rectangle are R(-5, -5), S(-1,-5), T(-1,1) and U(-5,1). A translation maps R to the point (2,-7). find the translation rule and the image of U.
a. T <-7,-2> (RSTU); (-12,-1)
b. T <7,-2> (RSTU); (2,-1)
c. T <7,2> (RSTU); (2,3)
d. T <-7,2> (RSTU); (-12,3)
Answer:
b. T <7,-2> (RSTU); (2,-1)
Step-by-step explanation:
The given triangle has vertices R(-5, -5), S(-1,-5), T(-1,1) and U(-5,1).
Let the translation rule be T(a,b).
Then the mapping for the translation will be;
[tex](x,y)\to (x+a,y+b)[/tex]
Then the point R(-5,-5) has the image;
[tex]R(-5,-5)\to R'(-5+a,-5+b)=R'(2,-7)[/tex]
This implies that;
[tex]-5+a=2[/tex]
[tex]\Rightarrowa=2+5=7[/tex]
and
[tex]-5+b=-7[/tex]
[tex]\Rightarrow b=-7+5[/tex]
[tex]\Rightarrow b=-2[/tex]
Therefore the translation rule is T(7,-2)
Hence;
[tex]U(-5,1)\to U'(-5+7,1-2)=U'(2,-1)[/tex]
the correct choice is B.
find the value x
[tex]3x + 16 + 8x + 3 - 10x - 28[/tex]
Answer: x - 9
Step-by-step explanation: Collect like terms.
(3x + 8x - 10x) + (16 + 3 - 28)
Answer:
[tex]\boxed{\bold{x-9}}[/tex]
Step-by-step explanation:
[ Step One ] Group Like Terms
[tex]\bold{3x+8x-10x+16+3-28}[/tex]
[ Step Two ] Combine Similar Elements: [tex]\bold{3x+8x-10x=x}[/tex]
[tex]\bold{x+16+3-28}[/tex]
[ Step Three ] Add / Subtract: [tex]\bold{16+3-28=-9}[/tex]
[tex]\bold{x-9}[/tex]
➤ [tex]\boxed{\bold{Mordancy}}[/tex]
Shondra wants to find the measure of angle JKL. Her work is started. What is the measure of angle JKL? 1. m
Answer:
[tex]m<JKL=38\°[/tex]
Step-by-step explanation:
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
In this problem
[tex]m<JKL=\frac{1}{2}(arc\ ML-arc\ MN)[/tex]
substitute the values
[tex]m<JKL=\frac{1}{2}(138\°-62\°)[/tex]
[tex]m<JKL=\frac{1}{2}(76\°)[/tex]
[tex]m<JKL=38\°[/tex]
Answer: jkl=38°
Step-by-step explanation:
Which best describes the graphs of the line that passes through (0,2) and (6,4) and the line that passes through (2,1) and (5,7)?
Answer:
The line which has slope 1/3 is a shallow line.
The line which has slope 2 is a steep line.
Both are increasing.
Step-by-step explanation:
Compare the lines by finding the slope between each pair of points.
Using the slope formula, substitute the points.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]
The line which has slope 1/3 is a shallow line.
The line which has slope 2 is a steep line.
Plz help !!!!!!!!!!!
Answer: [tex]\large{\bold{x^\frac{2}{3}}}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{x^2} \\\\\text{The exponent is the numerator and the root is the denominator:}\\\\\huge{\boxed{x^{\frac{2}{3}}}}[/tex]
The math teacher asked Edith, “How old are you?” “Sixty years less than five times my brother’s age,” she answered. “That doesn’t help me,” replied the teacher. “Yes, it does,” said Edith, “He and I are twins!” How old is Edith?
Answer:
15 years
Step-by-step explanation:
Let e represent Edith's age. Then e also represents her brother's age.
Then:
e = 5e - 60.
Consolidating the e terms, we get 60 = 4e. Thus, e = 15.
Edith is 15 years old. So is her brother.
Edith is 15 years old and so is her twin brother. Hope this helps!
Brainly for correct answer and explanation for the right answer <3
the correct answer is b, think of it as a mirror, if x and y are positive and you flip them, it will soon be -x and -y :)
Answer:
The answer wold be B the reason for this is because at first the student started in the positive area of the x and y axis but when reflected over the x axis it cause it to go into the negative part know as quadrant 4 in a graph
Step-by-step explanation:
read and write the number in two other forms 70,000,000 + 8,000,000+20,000+8
Answer:
Standard form:
78,020,008
Word form:
seventy-eight million, twenty thousand, eight
points that lie on the function h(x) = 3x 2
Answer:
To see all the points that lie on the equation
h(x) = 3*x^2
We use a graphing calculator, to plot the function h(x)
Please see attached image for more information.
We can see in red all the points that lie on the function. There are an infinite number of points in it.
Which of the following values are zeros for the function below g(x)=(x2+4x-12)(x-3)
Answer:
-6, 2 and 3Step-by-step explanation:
[tex]g(x)=(x^2+4x-12)(x-3)=(x^2+6x-2x-12)(x-3)\\\\=[x(x+6)-2(x+6)](x-3)=(x+6)(x-2)(x-3)\\\\\text{The zeros for}\ g(x)=0:\\\\(x+6)(x-2)(x-3)=0\iff x+6=0\ \vee\ x-2=0\ \vee\ x-3=0\\\\x=-6\ \vee\ x=2\ \vee\ x=3[/tex]
Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. What is the total amount of your emergency fund? How much is in the CD and savings account? How much is the total interest earned between both accounts in 60 days?
The emergency fund total amount is [tex]$\boxed{\$11,413.78}$[/tex]. The amount in CD is [tex]$\boxed{\$8,557.334}$[/tex]. The amount in savings account: [tex]$\boxed{\$2,853.445}$[/tex]. Total interest earned: [tex]$\boxed{\$94.896695}$[/tex].
To solve this problem, we will follow these steps:
1. Calculate the total deductions from the gross income.
2. Determine the realized income after deductions.
3. Calculate the fixed expenses based on the realized income.
4. Compute the amount saved in the emergency fund.
5. Divide the emergency fund into the portions for the CD and the savings account.
6. Calculate the interest earned on both the CD and the savings account over 60 days.
7. Sum the interest earned from both accounts to find the total interest.
Let's begin:
1. Calculate Total Deductions:
Gross income = $4,520.00/month
FICA = 7.65% of gross income
Federal tax withholding = 11.75% of gross income
State tax withholding = 8.5% of gross income
Total deductions = FICA + Federal tax withholding + State tax withholding
Total deductions = 0.0765 × $4,520 + 0.1175 × $4,520 + 0.085 × $4,520
2. Determine Realized Income:
Realized income = Gross income - Total deductions
3. Calculate Fixed Expenses:
Fixed expenses = 30% of realized income
4. Compute the Amount Saved in the Emergency Fund:
Emergency fund = 5 months' worth of realized income after fixed expenses
Emergency fund = 5 × (Realized income - Fixed expenses)
5. Divide the Emergency Fund:
75% in a CD and 25% in a savings account
CD amount = 0.75 × Emergency fund
Savings account amount = 0.25 × Emergency fund
6. Calculate Interest Earned:
Interest on CD = CD amount × (5.25% APR / 12) × (60 / 30)
Interest on savings = Savings account amount × (3.8% APR / 12) × (60 / 30)
7. Calculate Total Interest Earned:
Total interest = Interest on CD + Interest on savings
Now, let's perform the calculations:
1. Total deductions = 0.0765 × $4,520 + 0.1175 × $4,520 + 0.085 × $4,520
Total deductions = $344.28 + $530.44 + $384.20
Total deductions = $1,258.92
2. Realized income = $4,520 - $1,258.92
Realized income = $3,261.08
3. Fixed expenses = 0.30 × $3,261.08
Fixed expenses = $978.324
4. Emergency fund = 5 × ($3,261.08 - $978.324)
Emergency fund = 5 × $2,282.756
Emergency fund = $11,413.78
5. CD amount = 0.75 × $11,413.78
CD amount = $8,557.334
Savings account amount = 0.25 × $11,413.78
Savings account amount = $2,853.445
6. Interest on CD = $8,557.334 × (0.0525 / 12) × 2
Interest on CD = $8,557.334 × 0.004375 × 2
Interest on CD = $76.640625
Interest on savings = $2,853.445 × (0.038 / 12) × 2
Interest on savings = $2,853.445 × 0.0031667 × 2
Interest on savings = $18.25607
7. Total interest = $76.640625 + $18.25607
Total interest = $94.896695
Can someone please help me ??
C, the higher a negative is, the lower its value gets
It is C because -2.05 is really -2.050 which is less then -2.047
Find the value of x to the nearest tenth.
Answer options: 8.9, 7.5, 8.1, 7.9
Answer:
8.9
Step-by-step explanation:
apply pythagorean relationship
a²+b²=c²
where a=? b=4 and c=6
hence c²-b²=a²
6²-4²=a²
36-16=a²
√20=a
a=√20
but x= 2a
x=2 × √20
x=8.944 ⇒8.9 to the nearest tenth
Find the cost of one item to the nearest cent. Round if necessary.
12 lbs. of potatoes for $4.92
41 cents per pound
12/4.92=0.41
For this case we have to:
12 pounds of potatoes equals $ 4.92. You want to know the unit cost, that is, the cost per pound of potatoes.
For this, we make a rule of three:
12lb -----------------> $ 4.92
1lb --------------------> x
Where the varibale "x" determines the cost per pound of potatoe
[tex]x = \frac {1 * 4.92} {12}\\x = 0.41[/tex]
Thus, each pound of potatoe costs $ 0.41
Answer:
Each pound of potatoe costs $ 0.41
A sphere has a volume of V=324 in^3. Find it's surface area
To find the surface area of the sphere, we can use the formula Surface Area = 4πr². By substituting the given volume value into the volume formula and solving for r, we find that the radius of the sphere is 3 inches. Substituting this radius value into the surface area formula, we find that the surface area is 36π square inches.
Explanation:To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr2
Given that the volume of the sphere is 324 in3, we can use the volume formula to find the radius:
Volume = (4/3)πr3
By substituting the volume value (324) into the volume formula and solving for r, we find that the radius of the sphere is 3 inches. Now, we can substitute this radius value into the surface area formula to find the surface area:
Surface Area = 4π(3)2
Calculating this expression, we get a surface area of 36π square inches.
I need help please ..
Answer:
just add all the side which equals 27 feet
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
Because the perimiter is just the outside, we are only adding to find the answer.
hope this helps