The volume of metal is the difference of the overall volume of the cylinder and the volume of the hole in it. The formula for the volume of a cylinder is ...
... V = π·r^2·h . . . . . radius r and height h
For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm, so the volume in mm³ will be ...
... V_overall -V_hole = π(10)^2(21) -π(6)^2(21)
... = 21π·10^2 -21π·6^2 . . . . . . . matches the first selection
... = 2100π -756π . . . . . . . . . . . matches the third selection
... = 1344π . . . . . . . . . . . . . . . . doesnt' match any selection
The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters.
And, A cylindrical hole cut out of the center has a radius of 6 millimeters.
Hence, The formula for the volume of a cylinder is,
V = π·r²·h
Where, radius r and height h.
Now, For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm,
so the volume in mm³ will be;
V (overall) -V (hole) = π(10)²(21) -π(6)²(21)
= 21π·10² -21π·6²
= 2100π -756π
= 1344π
Thus, The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ5
a) Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: 18
b) Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: 0
Answer:
a) [tex]-5x^{2}+3x+27[/tex]
b) [tex]-5x^{2}+3x+9[/tex]
Step-by-step explanation:
a) Let the required polynomial be p(x).
We have the relation, [tex]5x^{2}-3x-9[/tex] + p(x) = 18
i.e. p(x) = 18 [tex]-5x^{2}+3x+9[/tex]
i.e. p(x) = [tex]-5x^{2}+3x+27[/tex]
b) Let the required polynomial be q(x).
We have the relation, [tex]5x^{2}-3x-9[/tex] + q(x) = 0
i.e. q(x) = 0 [tex]-5x^{2}+3x+9[/tex]
i.e. q(x) = [tex]-5x^{2}+3x+9[/tex]
Answer:
(a) [tex]-5x^2+3x+27[/tex]
(b) [tex]-5x^2+3x+9[/tex]
Step-by-step explanation:
(a)
Let the polynomial be Q(x).
Given polynomial P(x) = [tex]5x^2-3x-9[/tex]
As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 18.
[tex]P(x)+Q(x) = 18[/tex]
[tex]5x^2-3x-9 +Q(x) = 18[/tex]
⇒[tex]Q(x) = 18 -(5x^2-3x-9)[/tex]
or
[tex]Q(x) = 18 -5x^2+3x+9[/tex]
Simplify:
[tex]Q(x) =-5x^2+3x+27[/tex]
Therefore, the polynomial is, [tex]-5x^2+3x+27[/tex]
Check:
[tex]P(x)+Q(x)[/tex] = [tex]5x^2-3x-9 +(-5x^2+3x+27)[/tex]
= [tex]5x^2-3x-9 -5x^2 +3x+27[/tex]
= 18
(b)
Let the polynomial be Q(x).
Given polynomial P(x) = [tex]5x^2-3x-9[/tex]
As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 0.
[tex]P(x)+Q(x) = 0[/tex]
[tex]P(x) = -Q(x)[/tex]
⇒[tex]Q(x) = -(5x^2-3x-9)[/tex]
or
[tex]Q(x) = -5x^2+3x+9[/tex]
Therefore, the polynomial is, [tex]-5x^2+3x+9[/tex]
Check:
[tex]P(x)+Q(x)[/tex]=[tex]5x^2-3x-9 +(-5x^2+3x+9)[/tex]
= [tex]5x^2-3x-9-5x^2 +3x+9[/tex]
= 0
The ratio of students that ride the bus as compared to those that walk is 10:1. Does this school have more students that ride the bus or walk? how so you know?
Answer:
more that ride the bus10:1 is more than 1:1Step-by-step explanation:
riders : walkers = 10 : 1
The ratio tells you that 10 students ride the bus for every 1 student that walks. Since 10 is more than 1, more students ride the bus.
We know more students are riders, because we know that 10 is more than 1.
Pvc pipe is manufactured with a mean diameter of 1.01 inch and a standard deviation of 0.003 inch. the diameters are known to be normally distributed. find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.
Answer:
about 82%
Step-by-step explanation:
The distribution of sample means has a standard deviation that is the pipe standard deviation divided by the square root of the sample size. Thus, the standard deviation of the sample mean is 0.003/√9 = 0.001.
Then the limits on sample mean are 1.010 - 1×0.001 = 1.009 and 1.010 +2×0.001 = 1.012. The proportion of the normal distribution that lies between -1 and +2 standard deviations is about 81.9%.
The problem involves statistical calculation involving mean, standard deviation, and Z-scores of a normal distribution. We first calculate sample standard deviation, then the Z-scores for the given range. After finding probabilities for the Z-scores, we subtract to get the final probability of 0.8185.
Explanation:The problem at hand involves the field of statistics, specifically, the normal distribution, sample mean, and standard deviation. We can use the following steps to solve the problem:
Determine the standard deviation of the sample. Given the standard deviation of the population (σ population) is 0.003 inch and the sample size (n) is 9, we use the formula σ sample = σ population/sqrt(n), which gives 0.003/sqrt(9) = 0.001.Calculate the Z-scores for 1.009 and 1.012. The Z-score is determined by the formula: Z = (X - μ) / σ. For X=1.009, Z1 = (1.009-1.01)/0.001 = -1. For X=1.012, Z2 = (1.012-1.01)/0.001 = 2.Using a Z-table or appropriate statistical software, find the probability corresponding to these Z-scores. The probability for Z1=-1 is 0.1587, and for Z2=2, it is 0.9772.Lastly, subtract the smaller probability from the larger one to get the probability that a sample mean is greater than 1.009 but less than 1.012. So, the answer is 0.9772 - 0.1587 = 0.8185.Learn more about Normal Distribution here:https://brainly.com/question/34741155
#SPJ3
Find the missing side. Round to the nearest tenth.
Answer:
[tex]x=7.2\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle of the figure
The tangent of angle of 67 degrees is equal to divide the opposite side to the angle of 67 degrees (17 units) by the adjacent side to angle of 67 degrees (x units)
[tex]tan(67\°)=17/x[/tex]
Solve for x
[tex]x=17/tan(67\°)[/tex]
[tex]x=7.2\ units[/tex]
Find the quantity represented by each percent.
5.) 48% of 725 kg
6.) 15% of 138 lb.
Find the missing value.
7.) 45% of _____is 108.
Answer:
5.) 348 kg
6.) 20.7 lb
7.) 240
Step-by-step explanation:
5.) 48% of 725 kg
48 × 725 ÷ 100 = 348 kg
6.) 15% of 138 lb
15 × 138 ÷ 100 = 20.7 lb
7.) 45% of _____is 108.
100 × 108 ÷ 45 = 240
Thus, 5.) 348 kg; 6.) 20.7 lb; 7.) 240
-TheUnknownScientist
someone pls me out with this problem. Divide m2n2/p3 by mp/n2
Answer:
[tex]\dfrac{mn^5}{p^4}[/tex]
Step-by-step explanation:
As with dividing any fractions, invert the denominator and multiply. Use the rules of exponents to combine factors.
[tex]\dfrac{\dfrac{m^2n^3}{p^3}}{\dfrac{mp}{n^2}}=\dfrac{m^2n^3}{p^3}\cdot\dfrac{n^2}{mp}\\\\=\dfrac{m^2n^3n^2}{p^3mp}=\dfrac{m^{2-1}n^{3+2}}{p^{3+1}}=\dfrac{mn^5}{p^4}[/tex]
_____
The applicable rules are ...
[tex]a^ba^c=a^{b+c}\\\\\dfrac{a^b}{a^c}=a^{b-c}[/tex]
triangles abc and def are similar. The length of each side of triangle abc is 8 times the length of each corresponding side of triangle def. How many times greater is the area of triangle abc than the area of triangle def
64
Step-by-step explanation:If each side length is multiplied by 8, the product of two side lengths will be multiplied by 8×8 = 64.
Area is proportional to the product of two side lengths, so will be multiplied by 64.
What is -2 1/2 divided by 6?
A. -2 1/6
B. 5/12
C. 2 1/6
D. -5/12
Answer:
D -5/12
Step-by-step explanation:
2 1/2 = 2·(2/2) + 1/2 = 5/2
Dividing by 6 is the same as multiplying by 1/6.
... (-5/2)×(1/6) = -5·1/(2·6) = -5/12
PLEASE HELP
A laptop computer is purchased for $2500. After each year, the resale value decreases by 25%. What will the resale value be after 5 years?
Use the calculator provided and round your answer to the nearest dollar.
After 5 years, the resale value of the laptop will be approximately $592.
The resale value of the laptop after each year can be calculated by multiplying the previous year's value by 0.75. Starting with the initial value of $2500, the resale value after 5 years can be found by multiplying $2500 by 0.75 five times. Let's calculate:
Year 1: $2500 x 0.75 = $1875Year 2: $1875 x 0.75 = $1406.25Year 3: $1406.25 x 0.75 = $1054.69Year 4: $1054.69 x 0.75 = $790.02Year 5: $790.02 x 0.75 ≈ $592.52Therefore, the resale value of the laptop after 5 years will be approximately $592.
Learn more about Resale value of a laptop here:https://brainly.com/question/31869667
#SPJ3
There are 18 gallons of water in the tank. The tank is 3/4 full. How many gallons of water g can the tank hold
Answer:
24 gallons
Step-by-step explanation:
18 divided by 3 is 6
6 x 4 = 24
so there are 24 gallons as a whole
You said . . . . . 18 = 3/4 g
Multiply each side by 4 . . . 72 = 3g
Divide each side by 3 . . . 24 = g
The logistic growth function Upper P left parenthesis x right parenthesis equals StartFraction 90 Over 1 plus 271 e Superscript negative 0.122 x EndFraction P(x)= 90 1+271e−0.122x models the percentage, P(x), of Americans who are x years old and have some coronary heart disease. Use this function to find the the percentage of 66 66-year olds who have some coronary heart disease.
about 83%
Step-by-step explanation:Put the given value in the formula and do the arithmetic.
... P(66) = 90/(1 +271·e^(-0.122·66))
... = 90/(1 +271·e^-8.052)
... = 90/(1 +271·0.00031846)
... = 90/(1 +0.0863)
... = 90/1.0863
... = 82.8 . . . . percentage with some coronary heart disease
What are the solutions to the equation?
x2 + 6x = 40
x = −10 and x = 4
x = −8 and x = 5
x = −5 and x = 8
x = −4 and x = 10
Answer:
x = −10 and x = 4
Step-by-step explanation:
x2 + 6x = 40
Subtract 40 from each side
x^2 + 6x -40 =0
Factor, what 2 numbers multiply to -40 and add to 6
10 * -4 = -40 10+-4 = 6
(x+10) (x-4) = 0
Using the zero product property
x+10 =0 x-4=0
x=-10 x=4
Answer:
x = −10 and x = 4
Step-by-step explanation:
We are given the following quadratic equation and we are to solve it to find the two solution for the variable x:
[tex]x^2+6x=40[/tex]
Rearranging the equation by putting the constant on the same side as the variables to get:
[tex]x^{2} +6x-40=0[/tex]
Now factorizing it to get:
[tex]x^{2} -4x+10x-40=0\\\\x(x-4)+10(x-4)=0\\\\(x+10)(x-4)=0\\\\x= -10, x= 4[/tex]
Therefore, the solution to the given quadratic equation [tex]x^2+6x=40[/tex] are x = −10 and x = 4.
In the figure angle B is a right angle, side AB is 4 units long, and side BC is 6 units long. How many units long is side AC?
We know that , According to Pythagorean Theorem :
In a Right Angled Triangle :
✿ (Hypotenuse)² = (First Leg)² + (Second Leg)²
In the Figure : AC is the Hypotenuse and AB and BC are Two Legs
Given : Length of AB = 4 and Length of BC = 6
⇒ (AC)² = (AB)² + (BC)²
⇒ (AC)² = 4² + 6²
⇒ (AC)² = 16 + 36
⇒ (AC)² = 52
[tex]\mathsf{\implies AC = \sqrt{52}}[/tex]
[tex]\mathsf{\implies AC = 2\sqrt{13}}[/tex]
3rd Option is the Answer
A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost, 2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.For what number of $0.50 increases in the cost of a loaf of bread will the grocer's generated revenue be greater than zero?
A. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 20.
B. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 20.
C. The grocer's generated revenue will be greater than zero for any number of $0.50 increases greater than 15
.
D. The grocer's generated revenue will be greater than zero for any number of $0.50 increases less than 15.
Answer:
none of the above
Step-by-step explanation:
The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).
Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...
... 30 -2x = 0
... 15 -x = 0 . . . . . divide by 2
... x = 15 . . . . . . . add x
The price of each loaf will be zero when ...
... 2.50 +0.50x = 0
... 5 + x = 0 . . . . . . . multiply by 2
... x = -5 . . . . . . . . . . subtract 5
Revenue will be positive for any number of increases greater than -5 and less than 15.
_____
D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.
A graph has a constant of proportionality of 2.54. Let y represent centimeters and x represent inches.
What is the unit rate of the relationship?
Enter your answer, as a decimal, in the box
______cm/in.
2.54 cm/in
Step-by-step explanation:In this context, "constant of proportionality" and "unit rate" mean the same thing.
(X+5) to the power 6 use binomial theorem to expand the power of a binomial
Answer:
x⁶ +30x⁵ +375x⁴ +2500x³ +9375x² +18750x +15625
Step-by-step explanation:
The expansion is the sum of C(6, k)·x^(6-k)·5^k for k=0–6, where ...
... C(6, k) = 6!/(k!(6-k)!)
For k = 0–6, C(6, k) = {1, 6, 15, 20, 15, 6, 1}
Then the expansion is ...
... x⁶ +6·5¹·x⁵ +15·5²·x⁴ +20·5³·x³ +15·5⁴·x² +6·5⁵·x +5⁶
Using binomial theorem to expand the power of a binomial (X+5) to the power 6 and the result is [tex]X^6 + 30 \times X^5 + 300 \times X^4 + 1500 \times X^3 + 3750 \times X^2 + 4500 \times X + 3125[/tex].
To expand the expression (X+5) to the power 6 using the binomial theorem, we can use the formula [tex](a + b)^n = nC_0 \times a^n + nC_1 \times a^{(n-1)} \times b^1 + nC_2 \times a^{(n-2)} \times b^2 + ... + nC_n * b^n[/tex].
In this case, a = X, b = 5, and n = 6.
Using the binomial coefficients, the expanded expression becomes:
[tex]X^6 + 6 \times X^5 \times 5 + 15 \timesX^4 \times 5^2 + 20 \times X^3 \times 5^3 + 15 \times X^2 \times 5^4 + 6 \times X \times 5^5 + 5^6[/tex]
Simplifying this expression gives
[tex]X^6 + 30 \times X^5 + 300 \times X^4 + 1500 \times X^3 + 3750 \times X^2 + 4500 \times X + 3125[/tex].
please answer quickly thank you
For this case, we have that by definition:
Let "x" be an angle of any vertex of a right triangle.
[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]
So, if we want to find the angle x of the triangle shown we have:
[tex]tangent (x) = \frac {13} {6}\\x = arc \ tangent (\frac {13} {6})\\x = 65.23[/tex]
Rounding:
[tex]x = 65\ degrees[/tex]
Answer:
65 degrees
Option d
Consider the system of equations:
2x - 3y = 7
x + 4y = 9
What is the solution to the system?
( use elimination or substitution )
Answer:
(x, y) = (5, 1)
Step-by-step explanation:
To eliminate x, you can double the second equation and subtract the first.
... 2(x +4y) -(2x -3y) = 2(9) -(7)
...11y = 11 . . . . . simplify
... y = 1 . . . . . . divide by 11
Using the second equation to find x, we have ...
... x + 4·1 = 9
... x = 5 . . . . . subtract 4
_____
Check
2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation
(Since we used the second equation to find x, we know it will check.)
Noel has 5/6 of a yard of purple ribbon and 9/10 of a yard of pink ribbon. How much ribbon does she have altogether?
Translate the difference of five squared and n into symbols.
5^2- n
5^2+ n
5^2x n
5^2 ÷ n
Answer:
5² - n
Step-by-step explanation:
Five squared = 5²
n = n Subtract n from 5²
Diff. = 5² - n
We indicate "taking the difference" by a "minus" sign, so all the other options are wrong.
Answer:
5² - n
Step-by-step explanation:
Five squared is written as = 5²
The symbol of n is n.
The term difference is subtraction.
The difference of five squared and n ⇒ 5² - n
What is the simplified value of the expression below?
A. 18.25
B. 21.38
C. 27.56
D. 42.75
Answer:
A. 18.25
Step-by-step explanation:
After you do the multiplications, the problem is
... (56 +90)/8 = 146/8 = 18.25
_____
The division bar is a grouping symbol, equivalent to parentheses around both numerator and denominator. You must evaluate the numerator before you can divide by the denominator, which also must be evaluated before that division.
Modeling Circular Motion, Picture attached to the question.
The boat is traveling at a rate of 1 meter per second.
How long does it take the barnacle to get back to its starting point?
Answer:
2π secondsStep-by-step explanation:
The circumference of a circle of radius r is given by
... C = 2πr
When r = 1 m, then
... C = 2π(1 m) = 2π m
The relation between time, distance, and speed is ...
... time = distance/speed
... time = (2π m)/(1 m/s) = 2π s
_____
Comment on the scenario
We have a hard time imagining what sort of scenario this is modeling, as it appears the "boat" is rotating in such a way as to place the barnacle above and below the water level. This problem may be nonsensical, but at least it is workable. (Some aren't.)
Answer:2 pi
Step-by-step explanation:
URGENT !! What is the value of Y?
Answer:
B. 68°Step-by-step explanation:
We know:
The sum of the measures of the angles of the triangle is equal to 180 °.
Therefore we have the equation:
[tex]y+(y-12)+56=180[/tex] combine like terms
[tex]2y+44=180[/tex] subtract 44 from both sides
[tex]2y=136[/tex] divide both sides by 2
[tex]y=68[/tex]
The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm^2 less than the area of the rectangle.
36 cm
Step-by-step explanation:Let s represent the side of the square in cm. Then s+3 and s-2 are the sides of the rectangle of interest.
The area of the rectangle is the product of its side lengths:
... rectange area = (s+3)(s-2) = s² +s -6
The area of the square is the product of its side lengths, both of which are s.
... square area = s²
The difference of these areas is 30 cm², so ...
... rectangle area - square area = 30
... (s² +s -6) -(s²) = 30
... s = 36 . . . . . . . . . . . . simplify, add 6
The side of the square is 36 cm.
_____
Check
The rectangle dimensions are 39 cm by 34 cm, so its area is
... (39 × 34) cm² = 1326 cm²
The area of the square is (36 cm)² = 1296 cm²
The difference in areas is (1326 -1296) cm² = 30 cm², as required.
Solve the logarithmic equation.
y = log4 0.25
What does y equal?
[tex]\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=\log_4(0.25) ~\hfill 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{1}{4}\implies 4^{-1} \\\\\\ y=\log_4\left( 4^{-1} \right)\implies 4^y=4^{-1}\implies y=-1[/tex]
PLEASE ANSWER QUICKLY I WILL GIVE BRAINIEST
Answer:
[tex]<\:3[/tex] is the angle of elevation from the boat to the lighthouse.
Step-by-step explanation:
From the boat, the angle through which you will raise your head to see the light house is the angle of elevation, which is [tex]<\:3[/tex].
See graph for the illustration.
The correct answer is A
Answer:
The angle of elevation from the boat to the lighthouse is:
First option: <3
Step-by-step explanation:
The angle of elevation from the boat to the lighthouse is the angle of the visual since the boat to the lighthouse with the horizontal, according with the graph this angle is <3 (First option)
A town's population is 53,075. About 100 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 55,825. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
If we let m represent the number of months, then the population increase of the first town is 100m and its decrease is 200m. The population decrease of the second town is 175 m.
We want to find m such that the increases and decreases make the towns' populations equal. We add the increases and subtract the decreases to the base population in each case.
... first town population = second town population
... 53075 -100m +200m = 55825 -175m . . . . . the model equation
Solution
... 100m = 2750 -175m . . . . . collect terms, subtract 53075
... 275m = 2750 . . . . . . . . . . add 175m
... m = 10 . . . . . . . . . . . . . . . . . divide by 275
The populations will be equal in 10 months.
Answer:
175m-125m+38,200=40,600-150m
Step-by-step explanation:
I just completed it on imagine math
I need help fast please!!!!!!!!!!!!!!!!!
Answer:
HL
Step-by-step explanation:
The two hypotenuses of these right triangles are marked congruent, and the leg QS is shared, hence congruent.
The HL theorem applies.
If your car gets 26 miles per gallon, how much does it cost to drive 430 miles when gasoline costs $3.00 per gallon?
Answer:
$51
Step-by-step explanation:
To solve this, we must divide the total amount of miles by the miles per gallon, and multiply that by the cost per gallon.
430 / 26 = 16.53
Because this is talking about gallons, we should round up to 17.
17 * 3 = 51
It costs $51 to drive 430 miles when gasoline costs $3 per gallon.
Answer:
$49.62
Step-by-step explanation:
We know that the car travels for 26 miles in 1 gallon. So we will find out the number of gallons it requires to travel for 430 miles by simple ratio method.
[tex]\frac{1 gallon}{x} =\frac{26 miles}{430}[/tex]
[tex]x=\frac{430}{26}[/tex]
[tex]x=16.54[/tex]
Now that we know that the car needs 16.54 gallons of gasoline to drive for 430 miles, we can simply multiply the number of gallons by the cost per gallon to find its total cost.
Total cost of gasoline to drive 430 miles = 16.54 x 3 = $49.62
Which angle has a positive measure?
Answer:
The measure of angle B is positive
Step-by-step explanation:
we know that
Positive angles are those measured counterclockwise.
therefore
in this problem
The measure of angle B is positive