About 3 full cones of water are needed to be added to the cylinder to completely fill it.
The radius of the right circular cone is 3cm and the slant height is 5 cm.
The height of the cone can be found as,
H = √(5)²- (3)²
H = 4cm
The volume of the cone is given by,
V = πR²H/3
R is the radius and H is the height of the cone,
Putting values,
v = π x 5 x 5 x 4/3
v = 104.71 cm³
Now, the height h of cylinder is given to be 6 cm and the radius r of the cylinder is 4cm.
The volume of the cylinder is given as,
V = πr²h
V = π x 4 x 4 x 6
V = 301.59
Let us assume that we have to add n full cones of water to completely fill the cylinder, so, we can write,
nv = V
Putting values,
n104.71 = 301.59
n = 2.85
So, we have to add roughly three full cones of water to completely fill the cylinder.
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Simplify each expression. Select the correct answer from the drop-down menu.
−6(3i)(−2i) =
2(3 − i)(−2 + 4i)
16+14i will the required simplified value as the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number having imaginary and real part.
What is complex number?A complex number is one with the formula a + bi, where a and b are real numbers and I is an imaginary number. Complex numbers are those that are expressed as a+ib, where a,b are real numbers and I is an imaginary number known as "iota." (√-1) is the value of i. 2+3i is a complex number, for example, where 2 is a real number (Re) and 3i is an imaginary number (Im). A complex number is one that can be expressed as a + bi, where a and b are real numbers and I is an imaginary unit, and which solves the equation i² =-1. In this expression, a represents the complex's real part and b represents its imaginary part.
Here,
-6(3i)(-2i)=2(3-i)(4i-2)
-6(-6i²)
=36i²
=-36
2(3-i)(4i-2)
=2(12i-4i²-6+2i)
=2(14i+4-6)
2(14i-2)=-36
14i-2=-18
on simplifying,
16+14i will the required simplified value.
As the expression is -6(3i)(-2i)=2(3-i)(4i-2) which is a complex number with imaginary and real parts, the required simplified value is 16+14i.
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Answer:
−6(3i)(−2i) =
✔ –36
2(3 − i)(−2 + 4i) =
✔ –4 + 28i
Step-by-step explanation:
i need help with the question where I wrote +1 and +2. to find the slope do I just do 2/1
To find out the slope we need two points
from the table
we take
(0,1) and (1,3)
so
m=(3-1)/(1-0)
m=2/1
m=2need help with error analysis assingment, im in high school and ive always struggled with math alot pls help
Given
A) The angles A and B are supplementary.
If,
[tex]\begin{gathered} \angle A=x+6 \\ \angle B=7x+30 \end{gathered}[/tex]B) The figure,
To find
A) The value of x.
B) The value of x.
Explanation:
A) It is given that,
Angle A and angle B are supplementary.
Then,
[tex]\angle A+\angle B=180\degree[/tex]Hence, the error is in the statement,
Since the angles are supplementary, when added together they equal 90.
As, the correct answer is when added together they equal 180.
That implies,
[tex]\begin{gathered} x+6+7x+30=180 \\ 8x+36=180 \\ 8x=180-36 \\ 8x=144 \\ x=\frac{144}{8} \\ x=18\degree \end{gathered}[/tex]Hence, the value of x is 18 degrees.
B) It is given that,
From, the figure the given angles are interior angles.
Also, the interior angles on the same side of the transversal is supplementary.
Which means when you add them they equal 180.
Hence, the error is in the statement,
Since the angles are adjacent, they are complementary angles.
Which means when you add them they equal 180.
As, the angles are interior angles on the same side of the transversal.
Also,
[tex]\begin{gathered} 64+x=180 \\ x=180-64 \\ x=116\degree \end{gathered}[/tex]Hence, the value of x is 116 degrees.
i 45° 1030 909 600 9. Is the pentagon a regular pentagon?
internal angles of the polygon
angle a = 180 - 45 = 135°
angle b = 180 - 90 = 90°
angle c = 180 - 60 = 120°
angle d = 540 - 135 - 90 - 120 - 77 = 118°
angle e = 180 - 103 = 77 °
angle x = 180 - 118 = 62°
the polygon is not a regular polygon because the measure of its angles are different
Write the fraction 27/72 in simplest form
Therefore, 27/72 simplified to lowest terms is 3/8.
Priya practiced the violin for 152% as much time as Han practiced the piano hiw long did she practiced, if Han practiced for 74 minutes
To find the time that Priya spent practicing violin, calculate what is 152% of 74 minutes by multiplying 74 times 152/100:
[tex]\frac{152}{100}\times74=112.48[/tex]Therefore, Priya practiced for 112.48 minutes.
2 points
Question at position 5
Using the chart, which two students have the same unit rate? Explain how you know this.
Name Pages Read Number of Nights
Leah 45 3
Rose 48 4
Hannah 30 3
Philip 150 10
Leah and Philip have same unit rate.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The table is shown for the number of pages and number of nights.
Now,
The unit rate to read the number of pages for Leah;
⇒ 45 / 3 = 15
The unit rate to read the number of pages for Rose;
⇒ 48 / 4 = 12
The unit rate to read the number of pages for Hannah;
⇒ 30 / 3 = 10
The unit rate to read the number of pages for Philip;
⇒ 150 / 10 = 15
Thus, Leah and Philip have same unit rate.
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(2x+1)(x-2)(x+3)
please help
Answer: 2x^3 + 3x^2 - 11x - 6
Step-by-step explanation: simplified
Please help me! It is about proofs, SSS and SAS.
The two given triangles are congruent because of SAS.
What does congruency mean?In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other. Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.
The given triangles are RTP and STP
P is the midpoint of RS and TP is the altitude of triangle RTS.
In the triangles RTP and STP
TP = TP (common)
∠RPT = ∠ SPT (90°)
RP = SP (median divides the side equally)
So, both triangles are congruent using SAS property.
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A teacher buys packs of notebooks to give to their students. The tape diagram represents the ratio of brown notebooks to red notebooks. Brown notebooks Red notebooks Based on the ratio, if there are 24 red notebooks, what is the number of brown notebooks?
The number of brown notebooks is 40.
What is the ratio?
A ratio displays the multiplicity of two numbers. For example, if there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-fruit ratio is 8:14.
We have,
24 red notebooks,
∴ 5/3 = x/24.
Cross-multiply, and we now have
120 = 3x.
Divide both sides by 3,
x = 120/3
x = 40
x = 40 brown notebooks.
Hence, the number of brown notebooks is 40.
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A 2 liter bottle filled is filled with water the water leaks 80 milliliters of water every 3 minutes will the bottle be empty in 1 hour why or why not?
Answer:
the program I will get back to you on that date is approaching the
Step-by-step explanation:
the program I will get back to you on that date is approaching the
what is 1 1/2 divided by 1/6
Answer: 66/2 or in simplest form, 33/1
Step-by-step explanation:
11/2 divided by 1/6
*Keep the first fraction, flip the sign to multiplication, reciprocal or flip the fraction*
= 11/2 x 6/1
=66/2
=33/1
Which value of y makes this equation true?
Which value of y makes this equation true?
12y - 1/2 = 9y +8/5
A. 1/6
B. 1/2
C. 2
D. 6
On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "
What is solution to equation?A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.
Here,
12y - 1/2 = 9y +8/5
3y=8/5+1/2
3y=(16+5)/10
3y=21/10
y=7/10
According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.
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Brian drove from Houston to New York, then to Chicago, then back to Houston. How far did he drive altogether?
Houston to NY= 1608
NY to Chicago=802
Chicago to Houston=1067
Philip drove 66km from Liverpool to Sheffield at 80km/h.
How many minutes did this take him?
Answer:
49.5 minutes
Step-by-step explanation:
Amount of time that Philip took
= [tex]\frac{distance}{speed}[/tex]
= [tex]\frac{66km}{80km/h}[/tex]
= [tex]0.825h[/tex]
= [tex]49.5 min[/tex]
(6×10 to the ninth power)divided by (2.4×10 to the third power)
Answer:
2.5×10 to the sixth power
Step-by-step explanation:
6÷2.4=2.5
10^9÷10^3=6
(-5p+8)(-3p-5) pls help me solve this asappp
Step-by-step explanation:
(-5p + 8)(-3p - 5)
[tex]15p^2 +25p - 24p -40[/tex]
[tex]15p^2 +p -40[/tex]
2km:0.2m .....................
a. Complete the area model and the
equation.
23 x 62 =
Answer:
Step-by-step explanation:
for part B how do I find the coordinate for A double prime after the rotation
When we rotate a figure 90° around a point, we need to check the difference in x and y coordinates between the point and the center of rotation.
Then these differences will swap among themselves.
The difference in x-coordinate between A and B is 1, so now this difference will be the difference in y-coordinate.
The difference in y-coordinate between A and B is 7, so now this difference will be the difference in y-coordinate.
So the coordinates of A'' will be:
[tex]B(-2,-1)\to A^{\doubleprime}(-2+1,-1+7)=A^{\doubleprime}(-1,6)[/tex]Also, the point will be in the third quadrant, so all coordinates are negative:
[tex]A^{\doubleprime}(-1,6)\to A^{\doubleprime}(-1,-6)[/tex]Therefore the answer is C.
Write an equation in slope-intercept form that represents the data in the table.
The equation of the line that represents the data in the table is y = 30x + 30.
How to determine the equation of line from points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept
From the data;
Point 1( 0,30 )
x₁ = 0y₁ = 30Point 2( 2,90 )
x₂ = 2y₂ = 90First, we determine the slope.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 90 - 30 )/( 2 - 0 )
Slope m = ( 60 )/( 2 )
Slope m = 30
Next, we determine the y-intercept b by substituting the given values into the equation of line formula.
y = mx + b
30 = (30)0 + b
30 = b
b = 30
Now, plug these values into y = mx + b to determine the equation of the line.
y = mx + b
y = 30x + 30
Therefore, y = 30x + 30 is the equation of the line.
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Please answer this question!
Answer: 1/4
Step-by-step explanation: 1/2 turned into decimal form is 0.5 but halved equals 0.25 which in fraction form is 1/4
The area of this parallelogram is 49 square centimeters.y = ____ cm.
Answer:
7 cm
Explanation:
The area of a parallelogram:
[tex]A=\text{Base}\times Height[/tex]From the diagram:
• Base = y cm
,• Height = y cm
Thus:
[tex]\begin{gathered} y\times y=49 \\ y^2=49 \\ y=\sqrt{49} \\ y=7\operatorname{cm} \end{gathered}[/tex]The value of y is 7cm.
Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return. How much does she pay in fees for her actively managed fund?
As per the given interest rates, she have to pay $103.95 in fees for her actively managed fund.
Interest:
Interest means the amount to be paid on the borrowed money or the amount received on the money lent.
Given,
Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return.
Here we need to find the fees for her actively managed fund.
First we have to change rate of return percent to decimal form,
That is,
5% = 0.05
Now, we have to multiply the amount and decimal to get Alizeh 's profit,
=> 9000 x 0.05
=> 450
Therefore, the fund's total after 1 year, including initial investment and profit is
=>9000 + 450
=> 9450.
Now, we have to change fee percent that is the expense ratio into decimal form,
=> 1.1% = 0.011
Therefore, the fees for her fund is,
=> 9450 x 0.011
=> 103.95
Therefore, she have to pay $103.95 for her managed fund.
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Which exponential function matches the values in the table below?3521612967776y=21631y = 6xy=6(67y=(6
Verify each equation
option A
For x=3 ------> y=216(3^3)=
combine like terms algebra
Solve the equation 20 + 0.44x + 4 = 19 + 1.69x.
A. x = 4
B. x = 2.14
C. x = 5
D. x = 34.4
Answer: A
Step-by-step explanation: The starting equation is 24 + 0.44x = 19 + 1.69x,
First, combine the x's on the RHS, and the integers on the LHS.
1.69x - 0.44x = 1.25x
24 - 19 = 5
So the equation will be 1.25x = 5
Divide both sides by 1.25 to isolate the x.
x = 4
A number time 5 less that number has a product of -4. What are the two numbers?
Let the first number be x.
The second number is 5 times less than x => x - 5
Therefore, we can write the statement as
[tex]\begin{gathered} x\times(x-5)=-4 \\ x^2-5x=-4 \\ \therefore \\ x^2-5x+4=0 \end{gathered}[/tex]Solving the quadratic equation:
Let us replace -5x in the equation with -4x and -x to be able to factorize.
Hence,
[tex]\begin{gathered} x^2-4x-x+4=0 \\ x(x-4)-1(x-4)=0 \\ (x-4)(x-1)=0 \\ \text{Therefore} \\ x-4=0\text{ } \\ or \\ x-1=0 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x=1 \\ or \\ x=4 \end{gathered}[/tex]Therefore, the number can be 1 or 4.
The second number can be
[tex]\begin{gathered} 1-5=-4 \\ or \\ 4-5=-1 \end{gathered}[/tex]Therefore, the pair of numbers can be
[tex](1,-4)\text{ or (4, -1)}[/tex]
Two friends drive off in different directions from the same place. One heads North at 30 miles per
hour, while the other heads East at 40 miles per hour.
Distance =
Complete an equation for the distance between the friends after t hours. Hint: Assume the starting
point is the origin.
An equation for the distance between the two friends after time (t) in hours is given by: c = 50t
Given,
Two friends drive off in different directions from the same place. One heads North at 30 miles per hour, while the other heads East at 40 miles per hour.
We have to find the equation for the distance between the friends after t hours.
Here,
The distance covered by each friend should be calculated as follows:
For the first friend heading North, we have;
Distance, a = speed × time
Distance, a = 30t
For the second friend heading East, we have:
Distance, b = speed × time
Distance, b = 40t
By applying Pythagorean theorem, the distance between these two friends after an amount of time (t) is given by:
Distance, c² = a² + b²
Distance, c² = (30t)² + (40t)²
Distance, c² = 900t² + 1600t²
Distance, c² = 2500t²
Distance, c = √(25 × 100t²)
Distance, c = √25t² × √100
Distance, c = 5t x 10
Distance, c = 50t
Therefore,
The equation for the distance between the friends after t hours is c = 50t
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From the diagram below, if AC is a tangent line, and if PD = 8 and DC = 9, find the length of BC.
Given,
PD = 8 and DC = 9
Required
The length of line BC.
Here, PB and PD are the ardius of the circle. By the definition of circle, the measure of all radius is equal.
So, PB = PD = 8.
The tangent is always perpendicular to the radius at the point of tanjency.
By the pythagoras theorem,
[tex]\begin{gathered} PB^2+BC^2=PC^2 \\ 8^2+BC^2=(17)^2 \\ BC^2=289-64 \\ BC^2=225 \\ BC=15 \end{gathered}[/tex]Hence, the measure of BC is 15 units.
A building security code has 2 numeric digits, 0 through 9, followed by 2 letters. What is the probability that the first digit is nine and the last letter is a?.
The probability of the event that the first digit is nine and the last letter is a is 1/260.
The building security code has 2 numeric digits in between 0-9 and 2 letters.
The choices for letters is 26 each and the choices for digits is 10 each.
So, the total possible security code can be,
Total security codes possible = 10 × 10 × 26 × 26
Total security codes possible = 67600
Now, the number of codes that starts with 9 and end with a are,
= 1 × 10 × 26 × 1
= 260
The probability that the first digit is nine and the last letter is a is,
P(E) = 260/67600
P(E) = 1/260
So, the probability that the first digit is nine and the last letter is a is 1/260.
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