Answer:
1241
Step-by-step explanation:
∴
L.C.M. of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260
∴
the required number is 1260 - 19 = 1241
Hence, if we add 19 to 1241 we will get 1260 which is exactly divisible by 28, 36 and 45.
How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members?
Answer:
3024
Step-by-step explanation:
Each chosen member (out of 9 members) will occupy a different position
out of these four (president , vice-president , secretary , treasurer).
So, here we have to calculate the Number of Permutations of 9 members Taken 4 at a Time :
= 9P4
= 9 × 8 × 7 × 6
= 3024
A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. a regular hexagon has an apothem with length 14 centimeters and a perimeter of 96 centimeters. what is the approximate area of the hexagon?
The approximate area of the hexagon = 672 cm²
What is hexagon ?
In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.apothem of the hexagon = 14 cm
perimeter of the hexagon = 96 cm
Area of the hexagon = [(3√3) / 2] a² ; where a is the measure of the side
hexagon has 6 sides.
Perimeter = 6a
96 cm = 6a
96 cm / 6 = a
16 = a
There are 6 triangles in the hexagon .
Area of a triangle = (height * base) / 2
A = (14 cm * 16 cm) / 2
A = 224 / 2
A = 112 cm²
The approximate area of the hexagon = 112 cm² * 6 triangles = 672 cm²
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Answer: D). 672 cm2
Step-by-step explanation:
Simplify 7 + (−3)
A: -10
B: -4
C: 4
D: 10
Answer: 4
Step-by-step explanation:
[tex]7+(-3)\\=7-3\\=\boxed{4}[/tex]
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
The volume of the figure is 1, 005. 4 mi³
Volume of a cylinderNote that the figure is a cylinder
The formula for volume of a cylinder is given as;
Volume = πr²h
Where
h = height = 5 mi
r = radius = 8mi
Substitute into the volume
Volume = 3. 142 × 8 × 8 × 5
Volume = 1,005. 4 mi³
Thus, the volume of the figure is 1, 005. 4 mi³
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Kwame must earn more than 16 1616 stars per day to get a prize from the classroom treasure box. Write an inequality that describes S SS, the number of stars Kwame must earn per day to get a prize from the classroom treasure box.
The inequality that describes the number of stars S that Kwame must earn per day to get a prize from the classroom treasure box is: S > 16.
What is the inequality that models this situation?The number of stars that he earns is represented by the variable S. He must earn more than 16 stars to earn a prize from the classroom treasure box, hence the inequality that represents the desired amount is given as follows:
S > 16.
Which is read as:
S is greater than 16, which is derived from the Fact that Kwame must earn more than 16 stars per day to get a prize, as stated in the problem.
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Select the correct answer.
Consider this expression.
x-4
2(x+4)
For which product or quotient is this expression the simplest form?
O A.
B.
O C.
O D.
2x+8
x²16
x²16
2x+8
2x+8
x²16
x²16
2x+8
÷
÷
.
.
x² + 8x + 16
x +4
x +4
x² + 8x + 16
x² + 8x + 16
x + 4
x+4
x² + 8x + 16
The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Multiplying rational expressionsRational expressions are written in the form a/b where a and b are integers.
According to the question, we need to determine the expression that is equal to x-4/2(x+4)
From the fourth option;
x²-16/2x+8 * x+4/x²+8x+16
Factorize the quadratic part to have;
x²-16/2x+8 * x²+8x+16/x+4
(x+4)(x-4)/2(x+4) * x+4/(x+4)^2
Cancel out the common expression to have;
x-4 * 1/2(x+4)
x-4/2(x+4)
Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
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You decide that you want to purchase a Tesla SUV. You borrow \$95,000 for the purchase. You agree to repay the loan by paying equal monthly payments of \$1,200 until the balance is paid off. If you're being charged 6\% per year, compounded monthly, how long will it take you to pay off the loan?
Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.For this problem, the parameters are given as follows:
A(0) = 95000, r = 0.06, n = 12.
Hence the value of the loan after t years is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}[/tex]
[tex]A(t) = 95000(1.005)^{12t}[/tex]
You have monthly payments of $1,200, hence the amount paid after t years is:
P(t) = 12 x 1,200t = 14400t
Then we have to solve for:
A(t) = P(t)
[tex]14400t = 95000(1.005)^{12t}[/tex]
Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.
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What is the volume of this rectangular prism? 1cm,6cm,2cm
Step-by-step explanation:
The result is 12 cm³ because to get the volume of a figure you have to multiply all the characters
A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.
A solid right pyramid has a square base. The base edge length is 2 centimeters longer than the height of the pyramid. The height of the pyramid is 6 centimeters.
If the height is 6 cm, what is the volume of the pyramid?
24 cm3
48 cm3
128 cm3
144 cm3
Answer: it’s 128 (also what you did on my question was not cool, do better)
Step-by-step explanation:
We know the height is 6 and the length is 2 more than the height then the length is 8 (6+2=8) and then you solve for volume and get 128
The correct answer for the volume of the pyramid is [tex]128[/tex] cm³.
Given:
Square base edge lenght 2 cm than the height of the pyramid.
Height of the pyramid is 6 cm.
Square base edge length = Height of pyramid + 2cm
= 8 cm.
Base area:
Area of the square is calculated as side².
Area of square = 8*8
= 64 cm²
Volume of pyramid is calculated as [tex]\dfrac{1}{3} *basearea*height[/tex]
[tex]\dfrac{1}{3}*64*6\\\\ =128[/tex]
The volume of the pyramid is [tex]128[/tex] cm³.
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What number is represented by the question mark?
111= 0, 3213=0, 7756= 1,7662= 2, 6855= 3, 8096= 5,6666=4 . 8193= 3,9313= 1,8639= 4,1234=0, 2581 = 2,7186= 3, 2679=?
Based on the sequence of numbers given, the number that is represented by the question mark is 2679 = 2.
What is the sequence given?The sequence requires that you count the number of circles that a group of number has. For instance 9 has one circle and 8 has two circles because of the way they are drawn.
The numbers 111, 3213, and 1234 will therefore be equal to 0 because there is no number that has a circle in it.
The number 8096 however, will be equal to 5 because there are 5 circles. Two in 8. 1 in 0. 1 in 9. 1 in 6.
This means that the last number of 2679 will therefore be equal to 2 because there are two circles. One circle is in 6, and the other circle is in 9.
In conclusion, the number represented by the question mark is 2.
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How does the mean absolute deviation (mad) of the data in set 1 compare to the mean absolute deviation of the data in set 2? set 1: 12, 8, 10, 50 set 2: 13, 9, 8 the mad of set 1 is 13 less than the mad of set 2. the mad of set 1 is 13 more than the mad of set 2. the mad of set 1 is 2 more than the mad of set 2. the mad of set 1 is 2 less than the mad of set 2.
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
How to estimate the Mean Absolute Deviation from the given data?Set 1: 12, 8, 10, 50
Set 2: 13, 9,8
To determine the mean for each set
Mean = totality of elements/number of elements
Mean of Set 1:
[tex]$=\frac{12+8+10+50}{4}[/tex]
[tex]$=\frac{80}{4}=20$[/tex]
Mean of Set 2:
[tex]$=\frac{13+9+8}{3}[/tex]
[tex]$=\frac{30}{3}=10$[/tex]
To determine the mean absolute deviation (MAD) of the data in each set.
M.A.D of Set 1:
[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]
[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]
M.A.D of Set 2:
[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]
[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
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Simplify the expression. h4(h3)–6
Answer:
[tex]h^7-6[/tex]
Step-by-step explanation:
1) Regroup terms.
[tex]h^4h^3-6[/tex]
2) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]h^{4+3}-6[/tex]
3) Simplify 4 + 3 to 7.
[tex]h^7-6[/tex]
The angle between the generator and the central axis of a double-napped cone is 60°. a plane intersecting the cone makes an angle of 50° with the central axis. which conic section is formed?
The right option is (c).
As a result of the plane intersecting the cone here at an angle of 50° being less than the angle between the generator and central axis at an angle of 50°, a conic section is created.
What is Hyperbola?A smooth curve in a plane known as a hyperbola is one whose geometric characteristics or equations for which it is the solution set characterize it. Two parts of a hyperbola, known as connected components or branches, are mirror reflections of one another and resemble two infinite bows.
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I understand that the question you are looking for is:
"The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?"
(a)circle
(b)ellipse
(c)hyperbola
(d)parabola
The marked price of an article is rs 10000 . If he discounted rate and VAT rate are equal and the price with VAT is 9900 find the vat rate .
The rate of VAT is 10%.
In the question, we are asked to find the VAT rate, given that the market price of an article is Rs. 10000, the rate of discount and the rate of VAT are equal, and the price after VAT is Rs. 9900.
We assume the rate of discount and the rate of VAT to be r%.
Thus, discount = r% of Rs. 10000 = Rs. r/100 * 10000 = Rs. 100r.
Thus, the price after discount = Rs. 10000 - 100r = Rs. 100(100 - r)
Then, VAT = r% of (Rs. 100(100 - r)) = Rs. r/100 * 100(100 - r) = Rs. r(100 - r).
Thus, the price after VAT = Rs. 100(100 - r) + Rs. r(100 - r) = Rs. (100 + r)(100 - r).
The price after VAT is given to be Rs. 9900.
Thus, (100 + r)(100 - r) = 9900,
or, 100² - r² = 9900,
or, r² = 100² - 9900,
or, r² = 10000 - 9900 = 100,
or, r = ±√100 = ±10.
Since r is the rate of VAT, it cannot be negative, making r = 10.
Thus, the rate of VAT is 10%.
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PLS HELP PLS
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
The scale factor from Figure A to Figure B is 4
How to determine the scale factor from Figure A to Figure B?From the question, we have the following statement:
Figure B is a scaled copy of Figure A.
The corresponding side lengths of figure A and figure B are:
Figure A = 10
Figure B = 40
The scale factor from Figure A to Figure B is then calculated as:
Scale factor = Figure B/Figure A
Substitute the known values in the above equation
Scale factor = 40/10
Evaluate the quotient
Scale factor = 4
Hence, the scale factor from Figure A to Figure B is 4
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Using addition rules, show how to add the two real numbers. 7 + (-14)
Answer:
- 7
Step-by-step explanation:
note that
+ (- ) = - ( adding a negative is equivalent to subtraction )
- (- ) = + ( subtracting a negative is equivalent to addition )
then
7 + (- 14) = 7 - 14 = - 7
Using the online tool, find two different combinations of radius and height that produce two cylinders with nearly the same volume. Record the
dimensions and volumes of the two cylinders below.
The radii and the heights of the two cylinders are
Cylinder 1: Height = 6 and Radius = 5Cylinder 2: Height = 10 and Radius = 3.87How to determine the combinations of radius and height?The volume of a cylinder is
V = πr²h
When the volumes of two cylinders are almost equal, then it means that:
V1 ≈ V2
This gives
πr²h ≈ πR²H
Divide both sides by π
r²h ≈ R²H
Assume that r = 5 and h = 6
So, we have:
5² * 6 ≈ R²H
Evaluate the product
150 ≈ R²H
Assume H = 10
So, we have:
150 ≈ R² * 10
Divide by 10
R² ≈ 15
Take the square root of both sides
R ≈ 3.87
Hence, the radii and the heights of the two cylinders are
Cylinder 1
Height = 6 and Radius = 5
Cylinder 2
Height = 10 and Radius = 3.87
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Answer:
These radius and height values will produce the same volume:
radius = 6 units and height = 18 units
radius = 9 units and height = 8 units
Find the slope when y2=9, y1=13, x2=4, and x1=0.
Answer:
Formula=√(x2-x1)²+(y2-y1)² =√(4-0)²+(9-13)2 =√16+16 =√32
Answer: slope=-1
Step-by-step explanation:
9-13 -4
------ --------- -4/4=-1
4-0 4
Which of the following are possible measures of the interior angles of a regular polygon? If possible, how many sides does the polygon have: 90°, 100°, 110° 125°,
150°, 175°.
Step-by-step explanation:
180(n-2)/n=90 ( this is the solution for the 90)
cross multiplying
180n-360=90n
180n-90n=360
90n=360
90n/90=360/90
n=4, the number of sides for the polygon with 90° is 4 sides
Solution for 100°
180(n-2)/n=100
180n-360=100n
180n-100n=360
80n=360
80n/80=360/80
n=4.5
Same applies to the rest 110°,125° ,150°,175°
Solve the following question
Considering that a fraction is not defined when the denominator is zero, the equation is not defined for an angle of 90º.
When is a fraction not defined?A fraction is not defined when the denominator is zero.
In this problem, the expression is given by:
cos(θ)/(1 - sin(θ)) + cos(θ)/(1 + sin(θ)) = 4.
The denominators are zero in two cases:
1 - sin(θ) = 0 -> sin(θ) = 1 -> θ = 90º.1 + sin(θ) = 0 -> sin(θ) = -1 -> θ = 270º.Hence the equation is not defined for an angle of 90º.
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M angle JKL=
Help me please thank u so much
Answer:
22°
Step-by-step explanation:
Since IJ is a diameter, arc LJ measures 68 degrees.
Therefore, the measure of angle JKL is (112-68)/2=22°
The area of the regular octagon is approximately 54 cm2.
A regular octagon has an apothem with length 4 centimeters and an area of 54 centimeters squared. Line segment A B is a side of the octagon.
What is the length of line segment AB, rounded to the nearest tenth?
3.4 cm
4.8 cm
24 cm
27 cm
The length of the line segment of octagon which is AB equal to 3.4 cm.
Given that the area of the regular octagon is 54 [tex]cm^{2}[/tex], apothem of regular octagon is 4 cm. Line segment AB is side of the octagon.
We are required to find the length of the line segment AB.
A regular octagon has eight equal sides.
Area of regular octagon=Perimeter*apothem/2-----------1
We have to put the value of area and apothem in equation 1.
54=perimeter*4/2
Perimeter=(54*2)/4
=27 cm
Perimeter=27 cm.
Now we know that the perimeter is equal to the sum of the lengths of all sides of figure. So,
Perimeter=8*side
27=8*AB
AB=27/8
=3.375 cm
After rounding off it will be equal to 3.4 cm.
Hence the length of line segment is equal to 3.4 cm.
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Answer:
A
Step-by-step explanation:
A lampshade made from a piece of sheet plastic has a radius of the inner circle to be 7cm and that of the outer circle is 28cm. if its arc subtends an angle of 315 degree at the center, what is the area of the plastic used to form the lampshade
The area of the plastic used to form the lampshade is 2021.25 square centimeters
How to determine the area of the plastic used to form the lampshade?The given parameters in the question are:
Outer radius, R = 28 cm
Inner radius, r = 7 cm
Angle, ∅ = 315
The area of the plastic used to form the lampshade is calculated using the following area of sector formula
A = ∅/360 * π(R² - r²)
Substitute the known values in the above equation
A = 315/360 * 22/7 * (28² - 7²)
Evaluate the exponents
A = 315/360 * 22/7 * (784 - 49)
Evaluate the difference
A = 315/360 * 22/7 * 735
Evaluate the product
A = 2021.25
Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters
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Rearrange the formula to highlight the radius
[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{3V}{\pi h} } .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\V=\frac{1}{3} \pi r^2h.\\[/tex]
Multiply both sides of the equation by 3:
[tex]3V=\pi r^2h.[/tex]
Divide both sides of the equation by πh:
[tex]\displaystyle\\\frac{3V}{\pi h} =\frac{\pi r^2h}{\pi h} \\\frac{3V}{\pi h}=r^2\\ r^2=\frac{3V}{\pi h} .\\r*r=\sqrt\frac{3V}{\pi h} *\sqrt{\frac{3V}{\pi h} } \\r=\sqrt{\frac{3V}{\pi h} } .\\[/tex]
5. Mr. Griffin asked the students to form the number eighty-four million, five
hundred thirty thousand, two hundred sixteen. Ben still had the number card
with the 3. In what place was Ben standing? Show your work in the space
below. Remember to check your solution
Answer:
Ben was standing in the
Step-by-step explanation:
84 000 000
+ 00 530 000
+ 00 000 216
_________________
84 530 216
From this u can see that the 3 is in the ten thousands place
Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?
688,747,536 ways in which the people can take the seats.
How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.
When the whistle blows, each person needs to change to an orthogonally adjacent seat.
(This means that the person can go to the seat in front, or the seats in the sides).
This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.
Now, if we take the options that each seat has, and we take the product, we will get:
P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.
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Which best describes the relationship between the lines with equations 4x−8y=9 and 8x−7y=9?
Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
What was the relationship between the lines with equations 4x − 8y = 9 and 8x − 7y = 9?Given: 4x - 8y = 9 ............(1)
8x - 7y = 9 ............(2)
To be the same line, the equations have to be multiples of each other.
Multiplying (1) by 2, we get
2(4x - 8y = 9) = 8x - 16y = 18
From (1) solve the value of y, we get
4x - 8y = 9 ............(1)
-8y = -4x + 9
The value of y = (1/2)x - 9/8
From (2),
8x - 7y = 9
solve the value of y, we get
-7y = -8x + 9
The value of y = (8/7)x - 9/7
To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.
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Find the value of x if a, b, and c are collinear points and b is between a and c. ab=x 6,bc=3x−5,ac=36−x
The value of x if a, b, and c are collinear points and b is between a and c : 7
What is collinear points?Collinear points are those that are situated on the same line of sight or within a single line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either close to or far from one another.
According to the given information:
if A, B, and C are col-linear points and B is between A and C
then
AB+BC=AC
AB=x+6
BC=3x-5
AC=36-x
substituting value:(x+6)+(3x-5)=36-x
(x+3x)+(6-5)=36-x
4x+1=36-x
4x+x=36-1
5x=35
x=35/5
x=7
The value of x is 7
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2. If P = √2+1 √2-1 and Q = √2-1 √2+1 Find P2 + Q2 + PQ 1
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
How to find the value of a expression including elimination of radical in denominators
Herein we have two irrational terms whose denominators are radical expressions, which can be treated by algebraic handling and properties for radical expressions:
P = (√2 + 1) / (√2 - 1)
P = [(√2 + 1) / (√2 - 1)] · [(√2 + 1) / (√2 + 1)]
P = (√2 + 1)² / (2 - 1)
P = (√2 + 1)²
P = 2 + 2√2 + 1
P = 3 + 2√2
Q = (√2 - 1) / (√2 + 1)
Q = [(√2 - 1) / (√2 + 1)] · [(√2 - 1) / (√2 - 1)]
Q = (√2 - 1)²
Q = 2 - 2√2 + 1
Q = 3 - 2√2
Then, the value of P² + Q² + P · Q is:
M = (3 + 2√2)² + (3 - 2√2)² + (3 + 2√2) · (3 - 2√2)
M = 9 + 12√2 + 8 + 9 - 12√2 - 8 + 3 - 8
M = 9 + 8 + 9 - 8 + 3 - 8
M = 21 - 8
M = 13
The value of P² + Q² + P · Q including elimination of radical denominators is equal to 13.
RemarkThe statement is poorly formatted and reports typing mistakes, correct form is presented below:
If P = (√2 + 1) / (√2 - 1) and Q = (√2 - 1) / (√2 + 1), then find P² + Q² + P · Q.
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The rate of inflation in the fictional land of sardonia is such that the price of a car costing 24000 dollars in u.s. currency will double in eleven years. what is the annual rate of inflation? what will be the price of this car in five years?
The annual rate of inflation is 35560.86%.
What is inflation?Inflation is defined as an increase in the overall price of goods and services in an economy.When the general price level rises, each unit of currency purchases fewer products and services; hence, inflation equates to a loss of money's purchasing power. Deflation, or a sustained reduction in the general price level of goods and services, is the inverse of inflation. The inflation rate, which is the annualized percentage change in a general price index, is the most commonly used metric of inflation.To find the annual rate of inflation:
48,000=24,000e^k(7)24,000 24,0002=e^k(7)ln2=lne^k7ln2=k77 7k=0.099 --> k=9.9%Now, sub in 4 and 0.099
=24,000e^(0.099)(4)=35560.86Therefore, the annual rate of inflation is 35560.86%.
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The correct question is given below:
The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?
