The value of the expression Z² + Q² is 4321
How to evaluate the expression?The radius of the chocolate spheres is given as:
r = 2
The maximum number of chocolates that can fit in a spherical capsule is calculated as:
Max = R³/r³
Where:
R represents the radius of the sphere.
For the spherical capsule whose radius is 8 inches, we have:
Z = 8³/2³
Evaluate
Z = 64
For the spherical capsule whose radius is 5 inches, we have:
Q = 5³/2³
Evaluate
Q = 15.625
Remove decimal
Q = 15
So, we have:
Z² + Q² = 64² + 15²
Evaluate the exponent
Z² + Q² = 4096 + 225
Evaluate the sum
Z² + Q² = 4321
Hence, the value of Z² + Q² is 4321
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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
4y^4
Step-by-step explanation:
This polynomial is supposed to be ordered:
-3x^4+4y^4+5x^2y^2-10xy^3+9x^3y
I dont totally understand the question but I hope the ordered polynomial helps
Explain what the result of your proof tells you about angles a and b. Specifically, if you measured one angle, what would you know about the other? (2 points)
If the measure of one of the angles ∠a or ∠b is known, then the other angle is given by subtracting the known angle from 180°
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line.
The required two-column proof is presented as follows;
Statement Reason
∠1 and ∠a are linear pair angles Given
∠1 + ∠a = 180° Linear pair ∠s are supplementary
∠2 and ∠b are linear pair angles Given
∠2 + ∠b = 180° Linear pair ∠s are supplementary
∠a and ∠b are consecutive interior ∠s Definition
x║y Given
∠1 and ∠b are corresponding angles Definition
∠1 ≅ ∠b Corr. ∠s formed between║ lines
∠1 = ∠b Definition of congruency
∠a + ∠b = 180° Substitution property
∠a and ∠b are supplementary Definition
We can conclude from the proof that given ∠1 and ∠b are located in corresponding locations relative to the common transversal of the parallel lines, they (∠1 and ∠b) are equal.
Therefore, the sum of ∠a and ∠b is 180°, given that the sum of ∠1 and ∠a is 180° by substitution property of equality. So, ∠a and ∠b are supplementary angles.
Therefore, If the measure of one of the angles ∠a or ∠b is known, then the other angle is given by subtracting the known angle from 180°
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The price of a computer at an electronics store is $1200. If the store gives an "End of the year Sale"
discount of 20%, how much Mark needs to pay to buy the computer?
Answer:
$960
Step-by-step explanation:
The discount is 20%, so we need to find 80% of the original price:
[tex].80 \times 1200 = 960[/tex]
3.5 decimals to mixed numbers
Explain how to find the average rage of change for a function over a given interval.
The average rate of change for a function over an interval is the slope
How to explain the steps?Take for instance, we have the function to be
Function f(x)
And the interval is (a,b)
The average rate of change for the function over the interval is
Rate = (f(b) - f(a))/(b - a)
The above represents the slope
Take for instance, we have:
f(x) = x^2 [2, 4]
We have:
f(2) = 2^2 = 4
f(4) = 4^2 = 16
So, we have:
Rate = (16 - 4)/(4 - 2)
Rate = 6
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The World Health Organization lists the following overall literacy rates per 100 people for countries. Which answer choice includes all countries with literacy rates above 90%?
Answer:
The answer is D
Cuba, Poland, U.S., Argentina, Turkey, and Spain
Step-by-step explanation:
Basically, what it was asking, is what countries are over 90%? So, all you have to do - to put it simply - is just look at the countries that's numbers are greater than 90%
Help with Pre Calculus
What is the area of the shaded sector of the circle? 9pi units squared 27pi units squared 81pi units squared 162pi units squared
Answer:
27
Step-by-step explanation:
i promise :)
Answer:
27π units^2
Step-by-step explanation:
what is an equivalent expression
Answer:
1st option
Step-by-step explanation:
using the rules of logarithms
• log x + log y = log xy
• n logx ⇔[tex]x^{n}[/tex]
given
2[tex]log_{2}[/tex] 3 + [tex]log_{2}[/tex] 3
= [tex]log_{2}[/tex] 3² + [tex]log_{2}[/tex] 3
= [tex]log_{2}[/tex] 9 + [tex]log_{2}[/tex] 3
= [tex]log_{2}[/tex] (9 × 3)
= [tex]log_{2}[/tex] 27
Here is a list of numbers: 3.9 , 7 , 3.3 , 1 , 1.4 , 1.7 , 2.1 , 3.3 , 5.2 State the median. Give your answer as a decimal.
The "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number.
When there are two middle numbers we average them.
We have:
3.9, 7, 3.3, 1, 1.4, 1.7, 2.1, 3.3, 5.2
Let's sort the numbers from the smallest to the largest
1, 1.4, 1.7, 2.1, 3.3, 3.3, 3.9, 5.2, 7
The median is 3.3Answer:
3.3
Step-by-step explanation:
The first thing you have to do is put them in order from least to greatest.
1, 1.4, 1.7, 2.1, 3.3, 3.3, 3.9, 5.2, 7
Check off one from the left side and one from the right side until you are left with the one in the middle.
When you do that, you are left with 3.3
p=f/a, where f=70 and a=20 f is increased by 10 a is increased to by 10
Answer:
P=3.5
P=2.667
Step-by-step explanation:
p=f/a
P=70/20
P=3.5
then f is increased by 10
f=70+10=80
and a is increased by 10
a=20+10
a=30
therefore; P=f/a
P=80/30
P=2.667
Please help me with this thanks!!
Answer:
x° = 47°
Step-by-step explanation:
The sum of the measurements of three interior Angles in a triangle is 180°.This is known as angle sum property.Same case is here.
78°,55° and x° are interior angles here.
So,
[tex] 78{}^{ \circ} + 55 {}^{ \circ} + x {}^{ \circ} = 180 {}^{ \circ} [/tex]Solving for x°,
[tex]133 {}^{ \circ} + x {}^{ \circ} = 180 {}^{ \circ} [/tex][tex]x {}^{ \circ} = 180 {}^{ \circ} - 133 {}^{ \circ} [/tex][tex]x {}^{ \circ} = \boxed{47 {}^{ \circ} }[/tex]Hence,the value of x° is 47°.
whenx=2y=50 and whenx=4y=100 Which direct variation equation can be used to model this function?
The equation which is used to model this function is y = 25x.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
Given:
x=2 , y=50
x=4, y=100
As, corresponding to x =2 , y =50
For x=1 , y=25
Hence, the equation which is used to model this function is y = 25x.
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at what height will the air pressure equal 50%
Answer:
Im pretty sure its C which is 5776.2m
Step-by-step explanation:
How do you find what exponents of i are? like I know i^2 is -1, but how are you supposed to figure out i^26? do you have to write it all out?
THANK YOU
Answer:
-1
Step-by-step explanation:
so "i" is the square root of -1 (√-1). We know that i² = (√-1)², and that when we square a square root we end back up with whatever is inside of the square root.
This is why i² = -1
We can find a pattern from writing out a few exponents:
i¹ = i
i² = -1
i³ = -i [(-1)(i)]
i⁴ = 1 [-1 · -1]
------
i⁵ = i [(1)(i)]
i⁶ = -1 [(i)(i)]
i⁷ = -i [(-1)(i)]
i⁸ = 1 [(-i)(i)= -(i²)= -(-1) = 1]
------
i⁹ = i [1 · i]
we can see that the pattern of i repeats every 4 numbers, so by dividing 26 by 4 (and finding the remainder), we can figure out which step of the pattern we are on
26 / 4 = 6 [remainder of 2]
we know that there is a remainder of 2, meaning that we are on the "second step" in the pattern: -1
you can do the same thing for any number
hope this helps!!
Answer:
-1
Step-by-step explanation:
4 goes into 26 6 times, and then there's 2 remainder, so it's the same thing as i², which is -1
hope this is helpful :)
If f (x) = one-ninth x minus 2, what is ?
A.
B.
f - 1 Baseline (x) = one-ninth x + 2
f - 1 Baseline (x) = -2 x + one-ninth
Please see picture: helpppppp
Answer:
1st option
Step-by-step explanation:
let y = f(x) and rearrange making x the subject , that is
y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply both sides by 9 to clear the fraction )
9(y + 2) = x
9y + 18 = x
change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = 9x + 18
Answer: A
Step-by-step explanation:
GOT IT RIGHT ON EDG TEST
Which equation is the inverse of y = 9x² - 4?
Answer:
y = ± [ √(x+4) ] / 3
Step-by-step explanation:
1) To find the inverse of the function y = 9x2 – 4, exchange the variables x and y, and then solve for the new y.
2) Exchange of the variables: y = 9x^2 – 4 → x = 9y^2 – 4
3) Solve for y:
=> 9y^2 = x + 4
=> y^2=> y = ± [ √(x + 4) ] / 9
= > y = ± [ √(x + 4) ] / 3
Suppose a deposit of $ 2 , 000 in a savings account that paid an annual interest rate r (compounded yearly) is worth $ 2 , 209 after 2 years. using the formula a = p ( 1 + r ) t , we have 2 , 209 = 2 , 000 ( 1 + r ) 2 solve for r to find the annual interest rate (to the nearest tenth).
Answer:
5.1% (nearest tenth)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
A = $2,209P = $2,000t = 2 yearsSubstitute the given values into the formula and solve for r:
[tex]\implies \sf 2209=2000\left(1+r\right)^{2}[/tex]
[tex]\implies \sf \dfrac{2209}{2000}=(1+r)^2[/tex]
[tex]\implies \sf 1.1045=(1+r)^2[/tex]
[tex]\implies \sf \sqrt{1.1045}=1+r[/tex]
[tex]\implies \sf r = \sqrt{1.1045}-1[/tex]
[tex]\implies \sf r = 0.05095194942...[/tex]
[tex]\implies \sf r = 5.095194942...\%[/tex]
Therefore, the annual interest rate is 5.1% (nearest tenth)
Select the correct answer.
Which graph best models the inequality?
y ≤ -2/5x + 2
Answer:
it would look like this
Step-by-step explanation:
15.95 to the nearest cent
Step-by-step explanation:
95 95 branded to the nearest 10 with the number line
deter determine the two constructive multiples of 10 that bracket 95
9 is between 90 and 100
asteroid on the number line 95 is the midpoint between the 90 and 100
therefore 95 rounding to the nearest 10 is equal to 100
Please help meeeeeeeeee???
The answer for the exponential expressions 1,2,3 and 4 will be [tex]4.5,\frac{1}{2},2,1[/tex] respectively.
What exactly is an exponent?Exponential notation is a type of mathematical shorthand that allows us to write complex formulas in a more concise manner.
The basis of an exponent is a number or letter. It means that the base will be raised to a given level of power. The base is X, and the power is n.
The properties of the exponent used;
[tex]\rm m^a \times m^b = m^{a+b} \\\\ m^a \times n^a = {mn}^a \\\\ m^a \times m^b = m^{a-b} \\\\ m^0 = 1[/tex]
Expression 1;
[tex]\frac{(2.3^{-2})^2(5.3^2.2)^2}{(3)^-2(5.2)^2} \\\\ \frac{2^3.3^{-6}.5^2.3^6}{3^{-2}.5^2.2^2} \\\\ 4.5[/tex]
Expression 2;
[tex](3^3)(4^0)(3.2)^{-3}(2)^2 \\\\ 3^3.1.3^{-3}.2^{-3}.2^2 \\\\ \frac{1}{2}[/tex]
Expression 3;
[tex]\frac{(3^7.4^7)(2.5)^{-3}(5)^2}{12^7.5^{-1}.2^{-4}} \\\\ \frac{3^7.4^7.25^{-3}.5^{-3}.5^2}{12^7.5^{-1}2^{-4}} \\\\ 2[/tex]
Expression 4;
[tex]\frac{(2.3)^{-1}.2^0}{(2.3)^{-1}}\\\\ \frac{2^{-1}.3^{-1}.1}{2.3}\\\\ 1[/tex]
Hence, the answer for the exponential expressions 1,2,3, and 4 will be [tex]4.5,\frac{1}{2},2,1[/tex] respectively.
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In the figure below, segment HK and segment IJ intersect at P, and segment HI is parallel to segment Jk. Which of the following angles must be congruent to angle PKJ?
Answer:
angle PHI
Step-by-step explanation:
Using the alternate interior angle theorem, we can figure out that PHI is congruent to PKJ
Which table can be created using the equation below?
-2 + 4x = y
X
y
-5-22
0
3
X
y
-22 -5
-2 0
10
3
X
-5
0
-2
10
03
y
-18
-2
10
Answer:
h
Step-by-step explanation:
h
This is the last question PLSSSSS HELP
Answer:
D
Step-by-step explanation:
The volume of a cylinder is pi * r^2 * h
A) V = 3.14 * (0.7/2)^2 * 6.2 = 2.4 m^2
B) V = 3.14 * (0.9/2)^2 * 3.4 = 2.2 m^2
C) V = 3.14 * (1.2/2)^2 * 6.8 = 7.7 m^2
D) V = 3.14 * (1.4/2)^2 * 6.2 = 9.5 m^2
what is the answr to -5(b + 1) = 8
[tex] - 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5} [/tex]
PLEASE GIVE BRAINLIEST
\\\///\\\///\\\///\\\///\\\///\\\///\\///\\\///\\\///\\\///\\\///\\\//\\//\\//\\//\\\///\\//\\\///\\\///\\\///\
[tex]\Rsh[/tex] Hey! [tex]\Lsh[/tex][tex]\Rsh[/tex]Let's solve this! We can do this! [tex]\Lsh[/tex]
>>> First, let's multiply -5 by b and 1. Then we obtain
[tex]\pmb{-5b-5=8}[/tex].
>>> Now we add 5 to both sides.
[tex]\pmb{-5b=13}[/tex]
>>> And then, divide both sides by -5.
[tex]\pmb{b=-\dfrac{13}{5}}[/tex]
>>> That is the value of b.
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Hope the answer - and explanation - assisted you!
Happy studies! :)
A local mechanic on average services 14 cars a week. How many cars does he service in 4 years
What is the absolute value of -6 ?
Answer:
the answer is just 6
Step-by-step explanation:
Answer:
Step-by-step explanation:
An absolute value of a number is written like this | x |, where x could be any number that you want.
The absolute value is a math function that counts from your given number to 0.
Example: If you put the number 3, the function will count from 3 to 0, and the number will be 3.
| 3 | = 3
If you input the number 8, from 8 to 0 are 8 numbers. So, the output's function will be 8.
| 8 | = 8
If you input a negative number, for example, -6, the function will do the same thing. It will count from -6 to 0. From -6 to 0, are 6 numbers.
| -6 | = 6
Any number that you input in this function, will always output the same number, but positive
| -10 | = 10
| -46348 | = 46348
Hope I helped !
A company manufactures school desks. The table shows the number of units that the company sold each month over a nine-month period
beginning in January.
Month, x
Units, y
Which equation best models the situation?
1
800
2
500
3
400
4
300
5
200
6
300
7
450
8
600
9
800
Based on the values of x and y for the company and its school desks, the equation that best models the situation is D. y = 34x² - 334x + 1,075.
How does this equation model the situation?The best equation would be the one that gives the closest value of y to the value of the actual value of y on the table.
The first two equations can be ruled out because the table shows that this is not a linear model as there is no constant rate of change.
Test the other two equations:
x=1:
y = -34(1)² + 334(1) + 1,075
= 1,075
This is too high.
Other equation:
y = 34(1)² - 334(1) + 1,075
= 775
This is close to 800 so this is the best equation.
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Points Z, L, and S are:
Points Z, L, and S are collinear points
How to determine the relationship?When 2 or more points are on a line, the points are said to be collinear.
From the figure, we have:
Points Z, L and S on the same line
This means that they are collinear points
Hence, points Z, L, and S are collinear points
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How many sulotions does this system have? 6x-y=-1 6x+y=-1
Answer:
6/6
Step-by-step explanation:
6/6 not equal -1/1 so these lines intersect each other at only one point hence these have only one solution.
Answer:
I can give you the answer if you can answer a question
Step-by-step explanation: