The volume of the cylinder is 301.593 cubic centimeter.
What is the volume of the given cylinder ?Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.
The dimensions of the cylinder is given as - 8 cm and 12 cm .
The formula of the volume of the cylinder is given as -
V = π * (8) * (12)
Thus the volume is = 96π ≈ 301.593 cubic centimeter.
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Calculate the total amount in an investment account if $2800 was invested at a simple interest rate of
5.5% for 18 months.
a. $3034.15
b. $3031.00
Trinh invected $2400.st.0866
c. $7340.11
d.
$5544.00
The total amount in the investment account is $3031.00
How to determine the total amount?The given parameters are
Principal, P = $2800
Rate, r = 5.5%
Time = 18 months i.e. 1.5 years
The amount is then calculated as:
A = P + PRT
This gives
A = 2800 + 2800 * 5.5% * 1.5
Evaluate
A = 3031
Hence, the total amount in the investment account is $3031.00
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There are 4 books on a shelf. books are added to the shelf at a rate of 2 books per minute. the total number of books on the shelf, y, is a function of the number of minutes, x, that the books have been added to the shelf. write an algebraic equation for the function.
The algebraic equation to represent the given situation is as follows,
y = 4 + 2x
What is an algebraic equation?
The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).
Forming the Algebraic Equation
Number of book present on the shelf initially = 4
It is given that 2 books are added per minute to the shelf.
If x is the number of minutes, then the books added will be 2x.
If y is the total number of books present on the shelf, then the algebraic equation is given as,
y = Number of books initially present on the shelf + 2x
⇒ y = 4 + 2x
Thus, y = 4 + 2x is the required algebraic equation.
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According to the graph, for which values of x is y always negative?
Answer:
3rd option
Step-by-step explanation:
y is negative below the x- axis , that is for values of x in the interval
x > - 6 and x < 6
A pizza company is building a rectangular solid box to be able to deliver personal pan pizzas. The pizza company wants the volume of the delivery box to be 756 cubic inches. The length of the delivery box is 6 inches less than twice the width, and the height is 2 inches less than the width. Determine the width of the delivery box.
The width of the delivery box is 9 inches.
Given that volume of delivery box is 756 cubic inches,length is 6 inches less than twice the width, height is 2 inches less than width.
let width be x
Length = 2x- 6
Height = x - 2
Width = x
We can find the value of x by putting values one by one and then we will be able to get the value of x which is width.
Because the delivery box is cuboid in shape so the volume is equal to product of length,breadth and height.
When x=7: Volume=7 x (7 - 2) x (2x7 - 6) = 7 x 5 x 8 = 280
When x=9,Volume will be 9 x (9 - 2) x (2x9 - 6) = 9 x 7 x 12 = 756
Therefore, the width of the delivery box is 9 inches.
Hence the width of the delivery box is 9 inches.
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The ratio of the number of galleons to the number of galleys in the spanish armada is 5 : 1 . what missing information could be used to find the total number of galleons to galleys in the spanish armada ?
The amount of the galleys or the number of galleys.
If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.
If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.
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What is the type? f(x)=-1/5x³-5+10x²
URGENT, PLEASE ANSWER THESE QUESTIONS
Can send helicopter 3 but not helicopter 1 and 2.
What is distance formula?
Consider two points (x1, y1) and (x2, y2) in the two-dimension, then the distance between these two points is given by,
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
We will solve given problem as shown below:
Let fire have coordinate F (-3,-5)
Let Helicopter 1 have coordinate H1(1,4)
Let Helicopter 2 have coordinate H2(-2,3)
Let Helicopter 1 have coordinate H3(4, -2)
A. Distance between helicopter 1 and fire
[tex]=\sqrt{(1-(-3))^2+(4-(-5))^2}[/tex]
[tex]=\sqrt{16+81}[/tex]
[tex]=\sqrt{97}=9.8[/tex]
No, cannot send helicopter 1
B. Distance between helicopter 2 and fire
[tex]=\sqrt{(-3-(-2))^2+(-5-3)^2}[/tex]
[tex]=\sqrt{1+64}[/tex]
[tex]=\sqrt{65}=8.06[/tex]
No, cannot send helicopter 2
Distance between helicopter 3 and fire
[tex]=\sqrt{(4-(-3))^2+(-2-(-5))^2}[/tex]
[tex]=\sqrt{49+9}[/tex]
[tex]=\sqrt{58}=7.6[/tex]
Yes, can send helicopter 3
Hence, can send helicopter 3 but not helicopter 1 and 2.
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100 POINTS PLEASE HELP!!!
The coordinate plane below represents a community. Points A through F are houses in the community.
graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.
Part A: Using the graph above, create a system of inequalities that only contains points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (7 points)
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A. (5 points)
Part C: Erica wants to live in the area defined by y < 7x − 4. Explain how you can identify the houses in which Erica is interested in living. (2 points)
Answer:
[tex]\sf A) \quad \begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}[/tex]
B) see below
C) points C, E and F
Step-by-step explanation:
Given points:
A = (-5, 5)B = (-4, -2)C = (2, 1)D = (-2, 4)E = (2, 4)F = (3, -4)Part AA system of inequalities is a set of two or more inequalities in one or more variables.
To create a system of inequalities that only contains C and F in the overlapping shaded region, create a linear equation where points C, F and E are to the right of the line and a linear equation where points C, F, A, B and D are to the left of the line.
The easiest way to do this is to find the slope of the line that passes through points C and F, then add values to move the lines either side of the points.
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{y_F-y_C}{x_F-x_C}=\dfrac{-4-1}{3-2}=-5[/tex]
Therefore:
[tex]\sf y = -5x + 5[/tex] → points C, F and E are to the right of the line.
[tex]\sf y=-5x+12[/tex] → points C, F, A, B and D are the left of the line.
Therefore, the system of inequalities that only contains points C and F in the overlapping shaded regions is:
[tex]\begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}[/tex]
To graph the system of inequalities:
Plot 2 points on each of the lines.Draw a dashed line through each pairs of points.Shade the intersected region that is above the line y > -5x + 5 and below the line y < -5x + 12.Part BTo verify that the points C and F are solutions to the system of inequalities created in Part A, substitute the x-values of both points into the system of inequalities. If the y-values satisfy both inequalities, then the points are solutions to the system.
Point C (2, 1)
[tex]\implies \sf x=2 \implies 1 > -5(2)+5 \implies 1 > -5\quad verified[/tex]
[tex]\implies \sf x=2 \implies 1 < -5(2)+12\implies 1 < 2 \quad verified[/tex]
Point F (3, -4)
[tex]\implies \sf x=3 \implies -4 > -5(3)+5 \implies -4 > -10\quad verified[/tex]
[tex]\implies \sf x=3 \implies -4 < -5(3)+12\implies -4 < -3 \quad verified[/tex]
Part CMethod 1
Graph the line y = 7x - 4 (making the line dashed since it is y < 7x - 4).
Shade below the dashed line.
Points that are contained in the shaded region are the houses in which Erica is interested in living: points C, E and F.
Method 2
Substitute the x-value of each point into the given inequality y < 7x - 4.
Any point where the y-value satisfies the inequality is a house that Erica is interested in living.
[tex]\sf Point\: A: \quad x=-5 \implies 5 < 7(-5)-4 \implies -5 < -39 \implies no[/tex]
[tex]\sf Point\: B: \quad x=-4 \implies -2 < 7(-4)-4 \implies -2 < -32 \implies no[/tex]
[tex]\sf Point\: C: \quad x=2 \implies 1 < 7(2)-4 \implies 1 < 10 \implies yes[/tex]
[tex]\sf Point\: D: \quad x=-2 \implies 4 < 7(-2)-4 \implies 4 < -18 \implies no[/tex]
[tex]\sf Point\: E: \quad x=2 \implies 4 < 7(2)-4 \implies 4 < 10 \implies yes[/tex]
[tex]\sf Point\: F: \quad x=3 \implies -4 < 7(3)-4 \implies -4 < 17 \implies yes[/tex]
Sheila has a plan to save $45 a month for 18 months so that she has $810 to remodel her bathroom. After 13 months Sheila has saved $510. If the most Sheila can possibly save is $70 per month, which of the following statements is true?
a.
Sheila will meet her goal and does not need to adjust her plan.
b.
Sheila must save $50 per month to achieve her goal.
c.
Sheila must save $60 per month to achieve her goal.
d.
Sheila will not be able to achieve her goal.
The statement that is true about Sheila's savings plan is that; C.
Sheila must save $60 per month to achieve her goal.
What is true about the savings plan?
The price of bathroom remodeling is $ 810.
After 13 months , she has saved $ 510
This means that she has a $300 shortage to cover in 5 months.
This means that she need to save :
$300/5 = $60 / month in order to achieve her goal
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Answer: C
Step-by-step explanation: edge
PLEASE HELP I HAVE AN HOUR LEFT!!
Which statement correctly identifies an asymptote of g (x) = StartFraction 42 x cubed minus 15 Over 7 x cubed minus 4 x squared minus 3 EndFraction using limits?
Limit of g (x) as x approaches plus-or-minus infinity= 5, so g(x) has an asymptote at x = 5.
Limit of g (x) as x approaches plus-or-minus infinity= 6, so g(x) has an asymptote at x = 6.
Limit of g (x) as x approaches plus-or-minus infinity= 5, so g(x) has an asymptote at y = 5.
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
The statement that correctly describes the horizontal asymptote of g(x) is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the limit of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]g(x) = \frac{42x^3 - 15}{7x^3 - 4x^2 - 3}[/tex]
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{42x^3 - 15}{7x^3 - 4x^2 - 3} = \lim_{x \rightarrow \infty} \frac{42x^3}{7x^3} = \lim_{x \rightarrow \infty} 6 = 6[/tex]
Hence the correct statement is:
Limit of g (x) as x approaches plus-or-minus infinity = 6, so g(x) has an asymptote at y = 6.
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what is the solution to the equation 35-2x=23
Answer:
x = 6
Step-by-step explanation:
35 - 2x = 23
35 - 23 - 2x = 0
35 - 23 = 2x
12 = 2x
x = 6
35- 2x = 23
Subtract 35 from both sides.
-2x = 23 - 35Subtract 35 from 23 to get −12.
-2x = -12Divide both sides by −2.
x = -12 / - 2Divide −12 by −2 to get 6.
x = 6 ===> AnswerQuestion 6 of 25
A high school teacher grades a math test. She wants to see the numerical
grade of each student. Which item should she use so she can quickly see
how many students got each score?
A. None of these
B. Frequency table
OC. Line plot
OD. Pie chart
Jeri finds a pile of money with at least $200. If she puts $80 of the pile in her left pocket, gives away 1/3 of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $200 of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
The possible values of the number of dollars in the original pile of money is on the interval (200, 440)
How to solve Inequality Word Problems?We are told that Jeri finds a pile of money with at least $200.
Now, let x be the additional amount over the original amount of $200.
The greater side of the inequality will be expressed as;
Original pile = (200 + x)
After she gives away $80 and as such she has; (120 + x)
And she gives (1/3) of this away which means she will have;
= (1/3) (120 + x)
Thus, she must have (2/3) of this left
= (2/3)(120 + x) = amount in her right pocket
The lesser side of the inequality is expressed as;
(x + 200) - 200 = x
Thus, we now have that;
2[120 + x ]/3 > x
240 + 2x > 3x
240 > 3x - 2x
240 > x
x < 240
Thus, we can conclude that the original amount could be on the interval (200, 440)
The possible values of the number of dollars in the original pile of money is on the interval (200, 440)
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Find all solutions to 2w^4 - 5w^2 + 2 = 0
asap please
Answer:
w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]
Step-by-step explanation:
if we say some variable y = w^2, we can rewrite the equation to:
2y^2 - 5y + 2 = 0
this can be factored into (2y-1)(y-2) = 0
putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0
The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.
If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots
the four solutions are ±√1/2 and ±√2
(because the positive counts as one solution and the negative another solution)
Marge conducted a survey by asking 350 citizens whether they frequent the city public parks. of the citizens surveyed, 240 responded favorably. what is the approximate margin of error for each confidence level in this situation?
Using the z-distribution, considering the standard 95% confidence level, the margin of error is of 0.0486 = 4.86%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate are given by:
[tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]
Hence the margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.6857(0.3143)}{350}}[/tex]
M = 0.0486 = 4.86%.
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Answer:
99% - 0.06
95% - 0.05
90% - 0.04
Step-by-step explanation: i got it right
can someone please help me
solve for the balloon volume using the equation below
The volume of the balloon is 1441.64cm³.
How to calculate the volume?The radius of the balloon is given as 7cm. Also, the equation to calculate the volume is given as c³/6π²
The circumference c will be:
= 2πr = 2 × 22/7 × 7
= 44
The volume will be:
= c³/6π²
= 44³/(6 × 3.14²)
= 85284/(59.1576)
= 1441.64
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Rearrange the equation so a is the independent variable.
−3a+6b=a+4b
Answer:
6b-4b=a+3a
2b=4a
4a=2b
a=2b/4
a=b/2
rewrite the exponential expression to have the indi cated base.
(1/8)2*, base 2
Answer:
2^-6
Step-by-step explanation:
(1/8)^2 = (2^-3)^2 = 2^-6
Area=
Help me please asap thanks
Answer:
10 unit^2.
Step-by-step explanation:
The base of the triangle (CE)
= 6 - 2 = 4 units
The height = 5
Area = 1/2 * 4 * 5
= 10 unit^2.
Answer:
10
Step-by-step explanation:
area = hight ×base÷2
hight = 5-0
= 5
base = 6-2
= 4
area = 4×5÷2
=10
The number of bicycles parked in the parking area on 11 days are listed
below:
27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99
Find the 50th percentile, 25th percentile, and 75th percentile.
Answer:
the 50th percentile = 66
The 25th percentile = 35
The 75th percentile = 85
Step-by-step explanation:
We have 11 numbers ,so we are dealing with an odd set of values.
Also ,we notice that the numbers are already in order.
then
the 50th percentile of the set 27, 34, 35, 48, 48, 66, 75, 85, 85, 96, 99
is the 6 number in the list [ 6 = (11+1)/2 ]
Which is 66.
The 25th percentile (the median) of the set 27, 34, 35, 48, 48
is the 3rd number [ 3 = (5+1/)2 ]
Which is 35.
The 75th percentile (the median) of the set 75, 85, 85, 96, 99
is the 3rd number [ 3 = (5+1/)2 ]
Which is 85.
Which sequence of transformations produces A’B’C’ from ABC?
On a coordinate plane, triangle A B C has points (3, negative 1), (4, negative 4), (1, negative 2). Triangle A prime B prime C prime has points (negative 2, 3), (1, 4), (negative 1, 1).
a translation up 3 and then a 90º counterclockwise rotation about the origin
a 90º counterclockwise rotation about the origin and then a translation up 3
a reflection over the x-axis and then a translation left 2 and down 1
a translation left 5 and down 2 and then a reflection over the x-axis
Answer:
The first chose is correct
Step-by-step explanation:
You can see in the first picture that graphed both of the triangles and then I followed the directions. It is very, very helpful if you have tracing paper. You can trace the original and then translate it three up. For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign. That would be 90 degrees.
What is the total probability of rolling a single die twice, and having it land on 3 the
first roll, and a number greater than 3 the second roll?
er:
Answer:
0,5*0,5=0,25
Step-by-step explanation:
assuming a die of 6 faces
25
0,5 for < 4; 0,5 for < 3
Which function could be a stretch of the exponential decay function shown on the graph?
f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x
We find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)
What function represents a stretch of a exponential decay function?
Exponential functions are trascedent functions whose form is described below:
[tex]y = a\cdot r^{x}[/tex] (1)
Where:
a - Stretch factorr - Growth rateThere are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)
RemarkThe picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.
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Y is inversely proportional to the square of x. If Y = 2 when x = 8, then Y = , when x is_______.
The value of x when y =2 is 8
How to solve for x?The inverse proportion to the square of x represented as:
k = yx^2
Where
k represents the constant of proportion
When y = 2, x = 8.
So, we have:
k =2 * 8^2
k =128
Substitute k = 128 in k = yx^2
So, we have:
yx^2 = 128
When y = 2, we have:
2x^2 = 128
Divide by 2
x^2 = 64
Take the square roots
x = 8
Hence, the value of x when y =2 is 8
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Use a model to solve six multiplied by seven eighths. Leave your answer as an improper fraction.
A. forty two forty eighths
B. thirteen eighths
C. thirteen fourteenths
D. forty two eighths
Let's see
seven eighths means 7/8
So
6(7/8)42/821/4Forty two eighths
in quadrilateral ABCD, AB || CD. which additional piece of information is needed to determine the ABCD is a parallelogram?
The additional information needed to determine that ABCD is a parallelogram is: A. AB ≅ CD.
How to Identify a Parallelogram?One of the criteria for proving that a quadrilateral is a parallelogram is that one of the pairs of opposite sides are congruent and also parallel to each.
We are already given that side AB is parallel to side CD, therefore, the additional information we would need to prove that quadrilateral ABCD is a parallelogram is: A. AB ≅ CD.
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A sequence consists of the positive odd integers 1, 3, 5,. What's the sum of the first 12 terms of the
sequence?
hi
we have an aroithmetic serie of first term 1 and pace 2
so sum of 12 first terms, namming 1 as S1 and 12th term as S12
S12 = 1 + 2*11 = 23
formula of summ : number of term * ( final term + first term) / 2
So sum of terms from S1 +S12 = 12 ( S12 +S1 ) / 2 = 12 * ( 23+1) /2
12* 12= 144
-
The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°.
A) Use the Law of Cosines to find the length of the diagonal.
A) Use the Law of Sines to find the length of the shorter base.
Round your answers to the nearest hundredth.
You must show all of your work to receive credit.
The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
How to determine the lengthThe cosine rule is given as;
[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]
c = length of the diagonal
a = base length = 22 feet
b = 7 feet
[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]
[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]
[tex]c = \sqrt{533 - 235. 93}[/tex]
[tex]c = \sqrt{297. 072}[/tex]
[tex]c = 17. 24[/tex] feet
Using sine rule
[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]
Cross multiply
[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]
[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]
[tex]a = \frac{16. 20}{0. 8660}[/tex]
a = 18. 7 feet long
Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
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Determine the equation of a line that passes through (-2,5) and is parallel to the line whose equation is 5y +2x = 10.
Answer:
Step-by-step explanation:
Givens
line: 5y + 2x = 10
point (-2 , 5)
Discussion and Solution
You have to rearrange the given line to get the slope. It isn't nice, but it's not impossible.
5y + 2x = 10 Subtract 2x from both sides
5y + 2x - 2x = -2x + 10 Simplify
5y = - 2x + 10 Divide by 5
5y/5 = -2x/5 + 10/5 Simplify
y = -0.4x + 2
So the new equation is going to have a slope of - 0.4
So far what you have is
y = - 0.4x + b
Now use the point to find the y intercept. What you should be thinking about the point is that when x = -2 then y = 5. Substitute that into the new equation.
5 = -0.4*-2 + b
5 = 0.8 + b Subtract 0.8 from both sides
5 - 0.8 = 0.8 - 0.8 + b Simplify
4.2 = b
Answer
y = -0.4x + 4.2