From the characteristics of the given cylinder, we have that:
a) The equation is h = 15 - 2r.
b) The volume of the cylinder is of V = πr²(15 - 2r).
c) The values of r should be in the range of 0 < r < 7.5.
What is the volume of a cylinder?The volume of a cylinder of radius r and height h is given according to the following equation:
V = πr²h.
The sum of the height and the diameter is of 15 feet, hence:
h + d = 15.
The diameter is twice the radius, hence:
h + 2r = 15.
For item a, the solution of h in terms of r is:
h = 15 - 2r.
Hence, in item b, the equation is:
V = πr²h.
V = πr²(15 - 2r).
For item c, there are two constraints, as follows:
r > 0, as the radius of a cylinder cannot be negative nor zero.r < 7.5, as the height must be positive.More can be learned about the volume of a cylinder at https://brainly.com/question/9554871
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pls pls help whoever gets it right gets marked brainliest
Answer:
Step-by-step explanation:
B
Solve for x.
X-5=11
x = [?]
Answer: =16
Step-by-step explanation:
X-5=11
⇒X=11+5=16
⇒X=16
Find the distance from the point A(−2, 3) to the line y = 12x+1. Round your answer to the nearest tenth.
When adding and subtracting with significant digits, it's important to consider decimal places in the numbers being added.
TRUE or FALSE?
Answer:
false
Step-by-step explanation:
For the equation:
5 (2X +7) -15= 15
What might be the first step to solving the equation?
Answer:
Using inverse operations to isolate teh variable 'X'.
Step-by-step explanation:
THE FIRST STEP IS TO MULTIPLY EACH AND EVERY TERM IN THE BRACKETS BY 5
[tex]5(2x) + 5(7) - 15 = 15 \\ 10x + 35 - 15 = 15[/tex]
THEN GROUP THE LIKE TERMS TOGETHER. WHEN TERMS MOVE ACROSS THE EQUAL SIGN THEY CHANGE SIGNS.
[tex]10x = 15 - 35 + 15 \\ 10x = - 5[/tex]
[tex] \frac{10x}{10} = \frac{ - 5}{10} \\ x = \frac{ - 5}{10} \\ x = - \frac{1}{2} [/tex]
ATTACHED IS THE SOLUTION
Polly used 15/16 pounds of sugar to make 5 batches of cupcakes for a party. She uses the same amount of sugar to make each batch of cupcakes. How many pounds of sugar are in each batch? (I have my answer, but have no clue how to show it visually.
Based on the number of batches of cupcakes, the pounds of sugar in each batch can be found to be 3 / 16 pounds
Find out more below
How to find the pounds of sugar?The total number of pounds of sugar that Polly used was 15/16 pounds of sugar and she used these to make 5 batches of cupcakes.
Each of this batches of cookies used the same amount of sugar so the amount of sugar per batch of cookie is:
= Total number of pounds of sugar used / Number of batches of sugar
Solving for the pounds of sugar gives:
= 15/16 ÷ 5
= 15/16 x 1/5
= 15 / 80
= 3 / 16 pounds
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Please help! See attachment! Thank u
The missing statements in the given paragraph proof are:
1) corresponding angle postulate
2) angles 3 and 1
3) transitive property of parallel lines
In this question, we have been given a paragraph proof.
we need to complete this proof.
We have been given L || K and M || K
To prove: L || M
Since L || K, ∠2 ≅ ∠1 by the corresponding angle postulate
Since M || K, angles 3 and 1 are congruent for the same reason.
By the transitive property of congruence, ∠2 ≅ ∠3
By the transitive property of parallel lines, L || M
Therefore, the missing statements in the given paragraph proof are:
1) corresponding angle postulate
2) angles 3 and 1
3) transitive property of parallel lines
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CARD #9:
V (2,2) U(6,2) T(2,10)
Triangle TUV will be dilated by a
scale factor of 2.
Isaac says
that T will be
located at
(4, 20).
Isabelle says
that T' will be
located at (4, 12).
Isaac's statement that T will be located at (4, 20) is correct
How to determine the correct statement?The coordinates of the triangle are given as
V (2,2) U(6,2) T(2,10)
The transformation is given as
Scale factor of 2, across the origin
The transformation can be described by (x, y) --> (2x, 2y)
There are four types of transformation, and they are:
DilationRotationReflectionTranslationThe representation of the types of transformation are:
Dilation: k(x, y)Rotation: rotation by anglesReflection: reflection across linesTranslation: (x + h, y + k)By comparing the rules of the above types of transformation, we have
(x, y) --> (2x, 2y)
For point T, we have
(2, 10) --> (2 x 2, 2 x 10)
Evaluate
(2, 10) --> (4, 20)
When the above is compared to the student's result, we have
Isaac = (2, 10) --> (4, 20)
Hence, the correct statement about the transformation is Isaac's statement is correct
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#2 The number of bacteria in a refrigerated food is given by N(T)=20T2-20T+120 for -2T14 Tand where T is the temperature of the food in Celsius.
(a)Explain the meaning of -2T14 in this context
(b)Determine the temperature the number of bacteria will be minimal?
(c)Find number of bacteria in a above
(d) Sketch a graph
From the given quadratic function, it is found that:
a) The interval -2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.
b) The number of bacteria will be minimal for a temperature of 0.5 ºC.
c) The minimum number of bacteria is of 115.
d) The graph that models the situation is sketched at the end of the answer.
What does the quadratic function models in this problem?The quadratic function is given as follows:
N(T) = 20T² - 20T + 120, -2 ≤ T ≤ 14.
In which:
T is the temperature in Celsius of the food.N(T) is the number of bacteria in the food.The function has a domain of -2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.
For a concave up quadratic function, the minimum value happens when the input is of:
Tm = -b/2a.
For this problem, the coefficients of the quadratic function are as follows:
b = -20, a = 20.
Hence the temperature in which the number of bacteria will be minimal is of:
Tm = 20/40 = 0.5 ºC.
The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:
N(0.5) = 20(0.5)² - 20(0.5) + 120 = 115 bacteria.
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If the measure of 43 is 70 degrees, what is the measure of <6?
A. 20; ∠s 3 and 6 are complementary angles
B. 70; ∠ s 3 and 6 are alternate interior angles
C. 110; ∠ s 3 and 6 are supplementary angles
D. 180; ∠ s 3 and 6 are same-side interior angles
Answer:
b
Step-by-step explanation:
angle 3 and angle 6 are alternate interior angles which makes the congruent
PLS HELP QUICK!!!
help me solve 3<2p-3≤ 12 and graph the solution
The solution to the given inequalities is 3 < p and p ≤ 7.5. That is 3 < p ≤ 7.5.
The graph of the solution is shown below.
Solving Linear InequalitiesFrom the question, we are to solve the given inequalities
The given inequalities are
3 < 2p - 3 ≤ 12
We will solve the inequalities separately
That is
3 < 2p - 3 and 2p - 3 ≤ 12
Solve 3 < 2p - 3
3 < 2p - 3
3 + 3 < 2p
6 < 2p
6/2 < p
3 < p
Solve 2p - 3 ≤ 12
2p ≤ 12 + 3
2p ≤ 15
p ≤ 15/2
p ≤ 7.5
Hence,
Joining the two solutions together, the solution is 3 < p ≤ 7.5.
The graph is shown below.
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Liz has a recipe that uses 1 1/3 cups of sugar and 2 1/4 cups of flour to make 18 muffins. She has a total of 9 cups of flour. Liz wants to use all of her flour to make as many muffins as possible using this recipe.
Exactly how many cups of sugar will Liz use if she use all 9 cups of flour? & how many muffins will Liz make if she uses all 9 cups of flour?
well, first off let's convert the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} ~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}}[/tex]
now, let's use proportions to bind the sugar and flour that she'll be using, now if she were to use the 9 cups of flour, let's see how much will that be in sugar for this recipe
[tex]\begin{array}{ccll} \stackrel{cups}{sugar}&\stackrel{cups}{flour}\\ \cline{1-2} \frac{4}{3}&\frac{9}{4}\\[1em] S&9 \end{array}\implies \cfrac{~~ \frac{ 4}{3 } ~~}{S}~~ = ~~\cfrac{~~ \frac{ 9}{ 4} ~~}{9}\implies \cfrac{~~ \frac{ 4}{3 } ~~}{\frac{S}{1}}~~ = ~~\cfrac{~~ \frac{ 9}{ 4} ~~}{\frac{9}{1}}\implies \cfrac{4}{3S}=\cfrac{1}{4} \\\\\\ 16=3S\implies \cfrac{16}{3}=S\implies \boxed{ {\Large \begin{array}{llll} 5\frac{1}{3}=S \end{array}}}[/tex]
now, we know that 9/4 cups of flour gives Liz 18 muffins, well hell how many for 9 cups of flour then?
[tex]\begin{array}{ccll} \stackrel{cups}{flour}&muffins\\ \cline{1-2} \frac{9}{4} & 18\\[1em] 9& M \end{array} \implies \cfrac{~~ \frac{ 9}{4 } ~~}{9}~~=~~\cfrac{18}{M}\implies \cfrac{~~ \frac{ 9}{4 } ~~}{\frac{9}{1}}~~=~~\cfrac{18}{M} \\\\\\ \cfrac{1}{4}=\cfrac{18}{M}\implies \boxed{M=72}[/tex]
One of your friends is working on their math homework. They decide to translate the phrase "subtract 3 from 5" like this:
3-5
Which statements below give a reason why your friend's expression is incorrect?
Select ALL that apply.
A.The expression is written with the wrong operation.
B.in subtraction, order matters and the expression in the incorrect order.
C.the expression should be written as an addition expression with the 5 being added to the 3
D. The expression was written in the order from the phrase which is incorrect
Answer:
B
Step-by-step explanation:
When you are taking 3 away from 5 it would be 5-3, when you are taking 5 away from 3 it would be 3-5, but in this case it is not so the answer would be B as the order is incorrect.
On 1st January 2017, Samantha and Dyfan invested money into different
savings accounts.
They did not make any further payments into their accounts or withdraw any
money from their accounts.
Dyfan invested £3000 in a savings account that paid interest at a rate of
1.02% every 3 months.
Interest is paid on the last day of each 3-month period.
Calculate the date when Dyfan will first have over £3600 in his account.
Input note: give your answer in the form DD/MM/YY
(4 marks)
(8
The number of years when Dylan would have over £3,600 in his account is 18 June, 2021.
When would Dylan have over £3,600?The time that If the account earns interest every 3 months, it means that the value increases quarterly or 4 times a year. The account would increase at an exponential rate. This means that both the amount invested and the interest that has already been earned would increase in value 4 times a year.
The formula that can be used to determine the time is:
Time = In(FV / PV) / r
Where:
FV = future value
PV = present value
r = interest rate
t = In (£3,600 / £3,000) / 0.0102
t = In 1.2 / 0.0102 = 17.87 / 4 = 4.468 years
4 years = 2017 + 4 = 2021
0.468 x 12 = 5.616 months
January + 5 months = June
0.616 x 31 = 19 days
18 June, 2021
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if two dice are rolled one time, find the probability of getting these results. enter your answers as fractions or as decimals rounded to 3 decimal places. part: 0 / 40 of 4 parts complete part 1 of 4 (a)a sum of 11
When two dice are rolled one time, the probability of getting a sum of 11 is 1/18.
How to calculate the probability?From the information, two dice are rolled one time. There are 6 different possibilities and the outcomes of rolling the dice will be:
= 6 × 6 = 36
It should be noted that the sum of 11 can be gotten as (6, 5) and (5, 6). That's 2 out of 36.
Therefore, the probability will be:
= 2 / 36
= 1 / 18
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DOMAIN AND RANGE FOR BOTH OF TGOSE FUNCTIONS!!! PLEASE HELP IMMEDIATELY!!! WILL MARK BRAINLIEST AND GIVE EXTRA POINTS!! PLEASE HELP!!!
Answer: So think of x to y cordinents. You have reguler numbers and negitive numbers where would you but the regulear numbers? and where would you put the negitve numbers? So what is range? Range is yo subtracting the largeest number form the littlest number.
Step-by-step explanation:
Please Help I would really appreciate it!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:slope(m) = \dfrac{3}{4} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Slope (m) of a line can be calculated by using this formulae :
[tex]\qquad \tt \rightarrow \: m = \dfrac{rise}{run} [/tex]
Considering two points [ (10 , 10) and (50 , 40) ]
[tex]\qquad \tt \rightarrow \: m = \dfrac{y2 - y1}{x2 - x1} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{40 - 10}{50 - 10} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{30}{40} [/tex]
[tex]\qquad \tt \rightarrow \: m = \dfrac{3}{4} [/tex]
So, slope of given line is 3/4
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
To find the slope of a graph you need to look for 2 pairs of accurate xand y values
First value which is accurate is:
x = 10 and y= 10
Second pair which is accurate is :
x = 50 and y = 40
Gradient = rise/run = y2-y1/x2-x1
im taking y2 as 40, x2 as 50, y1 as 10 and x1 as 10
40-10/50-10
= 30/40
=3/4
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please help me on this i don’t know how to do it like help me my brother
The line segment NO of the triangle MNO, that is similar to the triangle QRS, has a length of 25 meters.
How to determine the missing length of geometric system formed by two similar triangles
In this problem we have a system of two similar triangles. Two triangles are proportional when the sides of a triangle are proportional to the corresponding sides of the other triangle. Herein we find the following relationship:
MN / QR = NO / RS = MO / QS
If we know that QR = 1 m, MN = 5 m and RS = 5 m, then the length of the line segment NO is:
NO = (MN / QR) · RS
NO = (5 m / 1 m) · 5 m
NO = 25 m
The line segment NO has a length of 25 meters.
RemarkThere is a typing mistake in the statement, correct form is introduced below:
Given ΔMNO and ΔQRS are similar triangles. If QR = 1 meters, MN = 5 meters and RS = 5 meters. What does line NO equal to?
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9. Describe and correct the error in performing the operation.
X 4x²(3x - 2x² + 7) = 12x³ - 8x + 28x²
Answer:
12[tex]x^{3}[/tex]-8[tex]x^{4}[/tex]+ 28[tex]x^{2}[/tex]
Step-by-step explanation:
the second term should not be -8x, it should be -8[tex]x^{4}[/tex]
The product of powers principle tells us that when we are multiplying powers with the same bases, we add the exponents. 4[tex]x^{2}[/tex](2[tex]x^{2}[/tex]) is 8 but then we add the exponents 2 + 2 = 4
What is the truth value for the following conditional statement?
p: false
q: true
~p~q
OTF F
OTF-T
OFF-T
OFT F
This is the right response: T F- F.
What is the explanation:
If the answer to the following question is p, then 2 + 2 = 4.
which is accurate, meaning that this statement has a truth value of True.
The following assertion q illustrates q: 7 + 1 Equals 7.
This is untrue, making the statement's truth value Untrue
As far as we are aware, "pq (p implication q)" means that the truth value of the implication is False only when the truth value of statement p is True.
The truth table reveals that the truth value of pq will be False
So T F → F
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When Riley left her house in the morning, her cell phone battery was partially
charged. The charge remaining in Riley's battery, as a percentage, can be modeled by
the equation B = 40 - 5t, where t is the number of hours since Riley left her
house. What is the x-intercept of the equation and what is its interpretation in the
context of the problem?
Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t. The x-intercept of the equation is (8,0). After 8 hours, Riley battery has no charge left in it ( since Riley left her house).
Given that,
Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t, where t is the number of hours since Riley left her residence, can be used to predict the percentage of charge still in Riley's battery.
We have to find what is the equation's x-intercept and how is it interpreted in the problem's context.
The equation B=40-5t can be used to model Lauren's battery charge remaining as a percentage when t is the number of hours since she left her home.
Put B = 0 to determine the x-intercept. (In this case, the independent variable is "t," as x signified the independent variable).
0=40-5t
5t=40
t=40/5
t=8
Therefore, the x-intercept of the equation is (8,0).
After 8 hours, Riley battery has no charge left in it ( since Riley left her house).
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Please answer the question in the photo
Answer: 8
Step-by-step explanation:
180 degrees in a triangle, so 180 - 92 - 48 = 40
So, the missing angle is 40, which is equal to 5t, so
40 = 5t
t = 8
can some one help i will give 100 points and brainliest can you show your work step by step?
I need help with number 11 - 16
Answer: Where is the question I can help if you put in the question.
Step-by-step explanation:
Is the function linear? (actual answers please, i know someone could easily say yes or no)
Answer:
Obviously yes...
Step-by-step explanation:
Because there is not a single curve, hence the fn is linear.
Had it been if there are some curves, it may result in having more than one zeroes...
Cuz there's no curve it has only one zero, which made the fn linear..
Thanks.
hello please help me on this question as soon as possible
10 POINTS
The number of groups of 5/7 that are in 1 is 1 2/5.
when 8 is divided by 5/7, the quotient is 11 1/5.
What are the required values?A proper fraction is a non-integer in which the numerator is less than the denominator. The numerator is the number above and the denominator is the number below. An example of a proper fraction is 5/7.
In order to determine the groups of 5/7 are in 1, divide 1 by 5/7. Division is the process of determining the quotient of two or more numbers. Division is the process of grouping a number into equal groups using another number. The sign that denotes division is ÷.
1 ÷ 5/7
1 x 7/5 = 7/5 = 1 2/5
8 ÷ 5/7
8 x 7/5 = 56 / 5 = 11 1/5
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suppose abc is a right triangle with sides a, b, and c and right angle at c. use the pythagorean theorem to find the unknown side length. then find the values of the six trigonometric functions for angle b. rationalize the denominators when applicable.
The unknown length is 28. the values of the six trigonometric functions for angle b that is tan B = 7/24
From the question,
we are given
a = 96 and c = 100, to get the unknown side 'b',
we will substitute the given values into the formula above;
c² = a²+b²
100² = 96² +b²
b² = 100² - 96²
b² = 10,000 - 9216b²
= 784b = √784b = 28
Hence, the unknown length is 28.
To get tanB, we will use the SOH, CAH, TOA trigonometry identity.
According to TOA,
tan B = opposite/adjacenttan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)
Given, b = 28 and a = 96tan B = 28/96tan B = 4*7/4*24
tan B = 7/24
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The question is incomplete. Here is the complete question.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.
Write the standard form of the line that contains a slope of -3/2
and y-intercept of 6. Include your work in your final answer. Type your answer in the box provided to submit your solution.
The standard form of the line that contains a slope of -3/2 and y-intercept of 6 is y = (-3/2)x + 6.
The slope intercept form of a line is:-
y = mx + c
Where,
m represents the slope of the line,
(x,y) represents the ordered pair of coordinates of each point on the line, and
c is the y-intercept
The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
Hence, we have,
m = -3/2
c = 6
Hence, the standard form of the line that contains a slope of -3/2 and y-intercept of 6 is given by:-
y = (-3/2)x + 6
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write and find the general solution of the differential equation that models the verbal statement. the rate of change of n is proportional to n. (use k for the proportionality constant.) evaluate the solution at the specified value of the independent variable. when t
the whole answer to the differential equation used to model the statement. The relationship between the rate of change of n and n is (dN/dt)=kN.
Differential equation definitionA differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
According to given data;
The derivative of N with respect to t, or (dN)/(dt), represents the rate of change of N.
dN/dt = kN, where k is the proportionality constant, if the rate of change of N is proportional to N. We must solve this differential equation.
To solve it, separate the variables:
(dN)/N = kdt
Integrating both sides results in
ln N = kt + C , where C is another constant.
This can be rewritten in exponential form as
N = e^(kt + C)
= N_0e^(kt) .
Here, N_0 = e^C
and it equals N(t) when t = 0.
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Estimate the quotient of 41 ÷ 7.94.
4
5
6
7