Answer:
20 in
Step-by-step explanation:
The radius is half the diameter.
You are given the diamter is 40 in.
So the radius is half of 40 in.
Half of 40 in means what is 40 in divided by 2.
Half of 40 in or 40 in ÷ 2 is 20 in.
The radius is 20 in.
Answer: 20 inches
Step-by-step explanation: A radius is half of the circle, and a diameter is a whole circle. 2 radius are equal to one diameter. So divide the diameter by 2 to get the radius.
40/2 = 20
The radius of the circle is 20 inches.
Describe an example of an augmented matrix.
Answer:
Step-by-step explanation:
When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.
Let A= [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right][/tex]
B= [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
Then the augmented matrix is(A|B)
Note that a vertical line is used to separate te columns of A from the columns of B
(A|B) [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
This is a simple example of augmented matrix....
Answer:
An augmented matrix refers to a matrix formed by appending the columns of two matrices.
The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.
If we have the system
[tex]2x+3y=5\\x-4y=9[/tex]
The two maxtrix involved here are
[tex]\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right][/tex]
However, to solve the system using matrices, we have to formed an augmented matrix
[tex]\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right][/tex]
So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.
I need the answer to a parts I-iii and the answer to b
Answer:
a)
i) Mean = 72
ii) Median = 72
iii) Mode = 72
b)
69, 70, 71, 72, 72, 72, 73, 74, 75
Step-by-step explanation:
a. To find mean, median and mode
It is given that all the 9 students get 72 marks.
Therefore the data set be,
72, 72, 72, 72, 72, 72, 72, 72 72
i) mean = (sum of data)/(total number of data)
= (9 * 72)/9 = 9
ii) Median - Central data in the data set when arranging ascending or descending order
72, 72, 72, 72, 72, 72, 72, 72 72
Median = 72
iii) Mode - Most repeating data in the data set
Here mode = 72
b). To find a data set
69, 70, 71, 72, 72, 72, 73, 74, 75
Here Mean, mode and median are all 72
The drama club you are part of is hosting a pancake breakfast. You are in charge of buying the sausage, which costs $5 per pound, and bacon, which costs $4 per
pound. The meat budget you are given totals $500 dollars. The inequality 5x + 4y < 500 represents the possible combinations of pounds of sausage (x) and bacon
(y) you can buy
A. 20 pounds of sausage and 90 pound of bacon
B. 40 pound of sausage and 40 pound of bacon
C. 60 pound of sausage and 80 pound of bacon
D. 80 pound of sausage and 20 pound of bacon
Answer:
C.Step-by-step explanation:
Look at the pictures.
x - sausage
y - bacon
A. 20 pounds of sausage and 90 pound of bacon
x = 20 → y = 100 > 90
B. 40 pound of sausage and 40 pound of bacon
x = 40 → y = 75 > 40
C. 60 pound of sausage and 80 pound of bacon
x = 60 → y = 50 < 80
D. 80 pound of sausage and 20 pound of bacon
x = 80 → y = 25 > 20
Option A (20 pounds of sausage and 90 pounds of bacon) and Option B (40 pounds of sausage and 40 pounds of bacon) are the possible combinations of pounds of sausage and bacon that you can buy.
Explanation:The inequality 5x + 4y < 500 represents the possible combinations of pounds of sausage (x) and bacon(y) you can buy.
Let's check each option to see if it satisfies the inequality:
Option A: 20 pounds of sausage and 90 pounds of baconTherefore, options A and B are the possible combinations of pounds of sausage and bacon that you can buy.
For a sequence an=3/n(n+1) what is the value of a 10
Answer:
[tex]\large\boxed{a_{10}=\dfrac{3}{110}}[/tex]
Step-by-step explanation:
Put n = 10 to the equation [tex]a_n=\dfrac{3}{n(n+1)}[/tex]
[tex]a_{10}=\dfrac{3}{10(10+1)}=\dfrac{3}{10(11)}=\dfrac{3}{110}[/tex]
For this case we have the following sequence:
[tex]a_ {n} = \frac {3} {n (n + 1)}[/tex]
We must find the value of[tex]a_ {10}[/tex], then, substituting [tex]n = 10[/tex] in the formula we have:
[tex]a_ {10} = \frac {3} {10 (10 + 1)}\\a_ {10} = \frac {3} {10 * 11}\\a_ {10} = \frac {3} {110}[/tex]
ANswer:
[tex]a_ {10} = \frac {3} {110}[/tex]
A 4cm cube is cut into 1 CM cubes. what is the percentage increase in the surface area after such cutting?
Answer:
400%.
Step-by-step explanation:
The surface area of a 4 cm cube = 6 * 4^2
= 96 cm^2.
The number of 1 cm cubes that can be cut from the larger cube is :
16 * 4 = 64.
The surface area of each of these smaller cubes is 6*1 = 6 cm^2.
The increase in surface area is a factor of (6*64) / 96
= 4 = 400%.
Find an ordered pair to represent t in the equation t=1/2u+v if u=(-1,4) and v=(3,-2)
Answer:
t=(2.5,0)
Step-by-step explanation:
Given that
[tex]t=\frac{1}{2} u+v[/tex]
and
u=(-1,4)
v=(3,-2)
Then,substitute value of u and v in the equation
[tex]t=\frac{1}{2} (-1)+3=-\frac{1}{2}+ (3)=2.5\\\\\\\\t=\frac{1}{2} (4)+-2=2+-2=0\\\\\\t=(2.5,0)[/tex]
Answer:
The answer on edge is C
Step-by-step explanation:
Does the quadratic function have a maximum or minimum? Give the value
Answer:
Max is 4.
Step-by-step explanation:
Maximum means it has a highest point and what is the highest point.
Minimum means it has a lowest point and what is the lowest point.
It doesn't have a minimum because it keeps going down forever and ever.
It does have a maximum because it does stop at the top. The y-value that is stops at is 4 so the max is 4.
Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n 2 1?
2.5, 6.25, 15.625, 39.0625, ..
2.5, 5, 10, 20
-10,-7.5, -5, -2.5, ...
-10, -25, 62.5, 156.25
Answer:
Sequence 3
-10,-7.5,-5,-2.5,...
Step-by-step explanation:
So f(n+1)=f(n)+2.5 means a term can be found by adding it's previous term to 2.5. That means this is an arithmetic sequence with a common difference of 2.5.
f(n+1)=f(n)+d is the recursive form for an arithmetic sequence with common difference d.
So you are looking for a sequence of numbers that is going up by 2.5 each time.
Let's check sequence 1:
2.5+2.5=5 so not this one because we didn't get 6.25 next.
Let's check sequence 2:
2.5+2.5=5 is what we have for the 2nd term.
5+2.5=7.5 so not this one because we didn't get 10 next.
Let's check sequence 3:
-10+2.5=-7.5 is the 2nd term
-7.5+2.5=-5 is the 3rd term
-5+2.5=-2.5 is the 4th term
Sequence 3 is arithmetic with common difference 2.5 assuming the pattern continues.
Let's check sequence 4 for fun:
-10+2.5=-7.5 is not -25
So we are done. Sequence 3 is the only one that fits term=previous term+2.5 or f(n+1)=f(n)+2.5.
If the factors of a polynomial are x5 and x + 2, what values of x make that
polynomial O?
Answer:
x = 5, x=-2
Step-by-step explanation:
The factors are x-5 and x+2:
Set each factor equal to zero and then solve each of them for x to find out what values of x make the polynomial equal to zero.
x-5 = 0 , x+2 = 0
x=0+5 , x=0-2
x=5 , x= -2....
The values of x that make the polynomial 0, given its factors are x⁵ and x + 2, are x = 0 and x = -2.
If the factors of a polynomial are x⁵ and x + 2, to find the values of x that make the polynomial equal to zero, we set each factor equal to zero and solve for x.
For the factor x⁵ = 0, the only solution is x = 0.
For the factor x + 2 = 0, solving for x gives us x = -2.
Therefore, the values of x that make the polynomial 0 are x = 0 and x = -2.
What is the inequality in sentence form?
n/4.2 ≤ 21?
thanks!
Answer:
n ≤ 88.2
Step-by-step explanation:
Answer:
"n divided by four-point-two is greater-than or equal to twenty-one".
~
Evaluate the expression.
a3b2c-1d
Evaluate a2b2c1d
If a = 2, b = 4, C = 10, d = 15
Express your answer
as a reduced fraction.
Please help
Step-by-step explanation:
for a³b²c-1d
given
a=2
b=4
c=10
d=15
a³b²c-¹d
=(2³4²10^-1*15
=2³4²15/10
=8*16*15/10
=8*8*3
=64*3
=192
now
a³b²c¹d
=(2³4²10 15)
=(8*16*10*15)
=120*16*10
=1200*16
=19200
Answer:
3/4 if meant [tex]a=2,b=4,c=10,d=15[/tex]
is [tex]a^3b^{-2}c^{-1}d[/tex]
Step-by-step explanation:
So the expression we want to evaluate for [tex]a=2,b=4,c=10,d=15[/tex]
is [tex]a^3b^{-2}c^{-1}d[/tex]
Please make sure I typed the expression and the values for the letters right.
[tex]a^3b^{-2}c^{-1}d[/tex]
Plug in the given values:
[tex](2)^3(4)^{-2}(10)^{-1}(15)[/tex]
In the following step I said 2^3 equals 8 because 2^3 means 2*2*2. I also got rid of the negative exponents by taking reciprocal.
[tex]8 \cdot \frac{1}{4^2} \cdot \frac{1}{10^1} (15)[/tex]
In the following step I said 4^2=16 because 4^2 means 4*4. I also wrote 10^1 as 10.
[tex]8 \cdot \frac{1}{16} \cdot \frac{1}{10} (15)[/tex]
In the following step, I'm going to rewrite everything as a fraction if it isn't already a fraction. 8=8/1 and 15=15/1.
[tex]\frac{8}{1} \cdot \frac{1}{16} \cdot \frac{1}{10} \cdot \frac{15}{1}[/tex]
To multiply fractions, you just multiply straight across on top and straight across on bottom.
[tex]\frac{8(1)(1)(15)}{1(16)(10)(1)}[/tex]
Actually performing the multiplication:
[tex]\frac{120}{160}[/tex]
Time to reduce:
[tex]\frac{12}{16}[/tex] I divided top and bottom by 10 to get this.
One more time for reducing:
[tex]\frac{3}{4}[/tex] I divided top and bottom by 4 to get this.
An ant can travel 2 feet in 30 seconds and a beetle can travel 5 feet in 90 seconds. Which bug travels farther per second?
Answer:
The beetle does
Answer:
The Ant travels farther per second
Step-by-step explanation:
To Find how far the ant and beetle travels we have to find out how many feet per second the Ant and Beetle travel.
To find that out for the Ant I divided 30 by 2 and got 15 which means the ant travels 1 foot in 15 second.
To find that out for the beetle I divided 90 by 5 and got 18 which means the beetle travels 1 foot in 18 seconds.
Therefore the Ant travels faster.
What fraction of an hour is 33 minuets in the simplest form
Ok.
So an hour contains 60 minutes.
The fraction is therefore,
[tex]\dfrac{33}{60}=\boxed{\dfrac{11}{20}}[/tex]
Hope this helps.
r3t40
Answer:
33 minutes is 11/20 of an hour.
Explanation:
So we know that 30 minutes is equal to half an hour. 30÷60 = 0.5
0.5 as a fraction is equal to 1/2.
Now let's use that same method for 33.
33÷60= 0.55.
0.55×100== 55.
55 as a fraction would be 55/100.
Let's convert that to its simplest form.
55÷5 = 11
100÷5 = 20
33 minutes is 11/20 of an hour.
What is the ratio for the sine of Z ?
Answer:
55/73
Step-by-step explanation:
Soh Cah Toa gives us our definitions for the trigonometric ratios: sine, cosine, and tangent.
That is the first part means sine is opposite / hypotenuse.
The second part means cosine is adjacent / hypotenuse.
The last part means tangent is opposite / adjacent.
No matter what angle you are looking to label the right triangle from, the hypotenuse will always be the same. The hypotenuse is the side opposite the 90 angle. Opposite meaning not touching; across from.
The other two terms are adjacent and opposite and depending on what angle you are looking from these change.
Adjacent means touching (exclude the hypotenuse from this).
Opposite means across from; not touching.
So from Z:
The side that has measurement 55 is opposite to Z.
The side that has measurement 48 is adjacent to Z.
The hypotenuse is the side that has measurement 73.
So from Y:
The side that has measurement 48 is opposite to Y.
The side that has measurement 55 is adjacent to Y.
The hypotenuse is the side that has measurement 73.
We don't label are triangle with respect to the 90 degree, X.
Anyways we asked to find sin(Z).
[tex]\sin(Z)=\frac{\text{opposite to }Z}{\text{ hypotenuse}}=\frac{55}{73}[/tex]
1/2x+3 2/3x+1
What is the solution to the equation
Answer:
12
Step-by-step explanation:
Start by multiplying both sides by 2.
[tex]\frac{1}{2} x+3=\frac{2}{3} x+1\\x+6=\frac{4}{3} x+2[/tex]
Next, multiply both sides by 3.
[tex]x+6=\frac{4}{3} x+2\\3x+18=4x+6[/tex]
Combine like terms.
[tex]3x+18=4x+6\\18=x+6\\12=x[/tex]
??help me how to do this
Answer:
x = sqrt( 4^2 + 7^2)
Step-by-step explanation:
They want the equation to solve the triangle
We can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and be are the legs and c is the hypotenuse
4^2 + 7^2 = x^2
Take the square root of each side
sqrt(4^2 + 7^2) = sqrt(x^2)
sqrt( 4^2 + 7^2) = x
Answer:
[tex]\large\boxed{x=\sqrt{7^2+4^2}=\sqrt{65}}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=7,\ leg=4,\ hypotenuse=x[/tex]
Substitute:
[tex]x^2=7^2+4^2\to x=\sqrt{7^2+4^2}[/tex]
[tex]x=\sqrt{49+16}\\\\x=\sqrt{65}[/tex]
The value of -8/-15 · 29/64 is _____. -1/-6 1/6 -2/-3 2/3
Answer:
29/120
Step-by-step explanation:
-8/-15 · 29/64
Lets rewrite the problem
-8/64 *29/-15
We can simplify the first fraction
-1/8 * 29/-15
Multiply the numerators
-1*28 = -29
Multiply the denominators
8*-15 =-120
Put the numerator over the denominator
-29/-120
A negative over a negative is a positive
29/120
Are you sure you have the factions correct
[tex]\text{Hey there!}[/tex]
[tex]\dfrac{-8}{-15}\times\dfrac{29}{64}[/tex]
[tex]\dfrac{8\times29}{15\times64}[/tex]
[tex]{8 \times 29 = 232}\\\\\ 15\times 64 = 960[/tex]
[tex]\text{Both numbers goes into 8 (or the GCF is 8.)}\text{ So divide both numbers by 8.}[/tex]
[tex]231\div8 = 29\leftarrow \text{numerator (top number)}\\\\ 960\div8=120\leftarrow\text{denominator (bottom number)}[/tex]
[tex]\boxed{\boxed{\text{Answer: }\bf{\dfrac{29}{120}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
I don’t which one it is?
Answer:
7.4
Step-by-step explanation:
The information given is in from SAS.
This is a job for law of cosines.
This is the law of cosines [tex]a^2=b^2+c^2-2bc cos(A)[/tex]
The angle A is opposite side a and b,c are the other sides.
So 13 degrees is opposite the y there.
[tex]y^2=16^2+22^2-2(16)(22)\cos(13)[/tex]
Now I'm going to put 16^2+22^2-2*16*22*cos(13) in my calculator:
[tex]y^2=54.04347439[/tex]
Now one more step. To get rid of the square, you need to square root both sides:
[tex]y=\sqrt{54.04347439}=7.351426691[/tex]
Sp the answer is approximately 7.4
Answer:
7.351
I don't know how they have rounded; the closest answer is A
Step-by-step explanation:
The only way I know to do this is with the cos law
y^2 = x^2 + z^2 - 2*x*z cos(Y)
x = 22
z = 16
y = ?
I have serious doubts that this will make a triangle. I ran it though a calculator and it does work -- surprise for me. Substitute the givens.
y^2 = 256 + 484 - 2*10*22*cos(13)
y^2 = 740 - 704*cos(13)
y^2 = 740 - 704*0.9744
y^2 = 740 - 685.95
y^2 = 54.05 Take the square root of both sides
y = √54.05
y = 7.351
Instructions:Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The native bird population in a city is decreasing at a rate of 10% per year due to industrialization of the area by humans. The population of native birds was 14,000 before the decrease began. Complete the recursively-defined function to describe this situation. f(1) = f(n) = f(n - 1) · , for n ≥ 2 After 3 years, birds will remain.
Answer:
The recursive function is;
f(n)=f(n-1)×0.9 for n≥2
After 3 years, 11340 birds will remain.
Step-by-step explanation:
First the native population was 14,000 before decreasing started, hence this is your f(1)
f(1)=14000
⇒A decrease of 10% is similar to multiplying the native value of birds with 90%
New number of birds = native value × 90% ⇒f(1)×0.9
For second year , you multiply the value you get after the first decrease by 0.9 to get the new number of birds;
f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600
For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%
f(3)=f(2)×0.9=12600×0.9=11340
Apply the same for the 4th year and above, hence for nth year;
f(n)=f(n-1)×0.9 for n≥2
there are 480000 books in two public libraries if each cupboard in the library hold 80 books then how many cupboard are required to keep all of the books if one library has 267112 books then how many books are there in the other library
Answer:
there would be 212,888 books in the 2nd library, and 6,000 cupboards needed to hold all the books.
Step-by-step explanation:
simple division is all you need to answer. 480,000 divided by 80 is 6,000. for the second part, if the total amount of books between both libraries is 480,000 and one library has 267,112 books, 480,00 - 267,112 is 212,888
Hope this helps :)
feel free to ask if you have any questions
meaningful use was created to help improve quality safety and efficiency true or false
Answer:
TRUE
Step-by-step explanation:
Meaningful use is used to define the minimum standards of the American government for electronic health records and it has five main objectives:
Provide privacy and security for personal health informationExpand public healthImprove care coordinationIncrease patient engagementImprove quality, safety, efficiency and reduce health disparities.Therefore, the statement is true.
Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3) y = -2x + 1/3 y = -2/3x + 1 y = -2x + 1 y = -2/3x + 1/3
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===============================================
We have the points (2, -1) and (5, -3). Substitute:
[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
We have the equation:
[tex]y=-\dfrac{2}{3}x+b[/tex]
Put the coordinates of the point (2, -1):
[tex]-1=-\dfrac{2}{3}(2)+b[/tex]
[tex]-1=-\dfrac{4}{3}+b[/tex] add 4/3 to both sides
[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]
solve the equation 169x^2+36=0
If 50% of days are sunny and 50% of days are rainy, what is the ratio of sunny days to rainy
days? (4 points)
Answer:
1:1
Step-by-step explanation:
Since both equal up to 100% and both are 50%, it's 1:1.
1 stands for 50% and the other 1 stands for 50% too.
in triange ABC, AB=5 and AC=14. Find The measure of angle c to the nearest degree
Answer:
The answer is ∠C= 20 degree
Step-by-step explanation:
The answer is ∠C= 20 degree
We have given:
AB= 5
AC = 14
and we have to find ∠c to the nearest degree.
So,
We know that:
tan(C)= AB/AC
tan(C)= 5/14
tan(C)= 0.3571
C=20 degree
Thus the answer is ∠C = 20 degree ....
Use the elimination method to solve the system of equations. Choose the
correct ordered pair,
2y = x + 2
x - 3y = -5
Answer:
x = 4, y = 3 → (4, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2y=x+2&\text{subtract x from both sides}\\x-3y=-5\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=2\\x-3y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-y=-3\qquad\text{change the signs}\\.\qquad\boxed{y=3}\\\\\text{put the value of y to the second equation:}\\\\x-3(3)=-5\\x-9=-5\qquad\text{add 9 to both sides}\\\boxed{x=4}[/tex]
f(x) = x3 – 2x + 6
g(x) = 2x3 + 3x2 - 4x + 2
Find (f – g)(x).
Answer:
-x^3-3x^2+2x+4
Step-by-step explanation:
Just calculate each coefficient of the polynomial separately.
x^3-2x+6-(2x^3+3x^2-4x+2) = (1-2)x^3+(0-3)x^2+(-2-(-4))x+(6-2) = -x^3-3x^2+2x+4.
Answer:
- x³ - 3x² + 2x + 4
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute by - 1
= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms
= - x³ - 3x² + 2x + 4 ← in standard form
Which point represent the location of the vertex of the
given function? *
f(x) = -2(x – 4)2 – 7?
Answer:
(4,-7) is the vertex
Step-by-step explanation:
The equation of the parabola is of the form
y= a(x-h)^2 +k
where (h,k) is the vertex
f(x) = -2(x – 4)^2 – 7
(4,-7) is the vertex
Answer:
The vertex point is (4, -7)
Step-by-step explanation:
Compare withe the general form of the vertex form:
f(x) = a(x - h)^2 + k where (h, k) is the vertex.
f(x) = -2(x - 4)^2 - 7.
- so the vertex is (4, -7).
one line segment is 5 cm more than four times the length of another the difference in their lengths is 35cm how long are they
Answer:
Length of the segments will be 10 cm and 45 cm.
Step-by-step explanation:
Let the length of one segment is x.
Then by the statement of this question,
"one segment is 5 cm more than four times the length of another".
Length of other segment = 4x + 5
(4x + 5) - x = 35
4x + 5 - x = 35
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 10 cm
Length of other segment = 4(10) + 5 = 45 cm
Therefore, two segments are of length 10 cm and 45 cm.
simplify this expression 6g 11g
Answer:
[tex](6g)(11g)=\bigg((6)(11)\bigg)(gg)=66g^2[/tex]