The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Given data;
z be the unknown number
Given conditions;
1. The difference between a number and −23.
2.−23 is equal to the product of the number and 13.
The mathematical form of the given phrase is;
⇒ z - (-23) = z × 13
⇒z+23 = 13z
⇒12z -23
The English phrase of the obtained equation is 12 times z subtracted by 3.
Hence the simplification of the given expressions is 12z -23.
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The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is
An opportunity cost of 9 percent, is $42.
We have given that,
The present value of $100 is to be received 10 years from today,
assuming an opportunity cost of 9 percent,
present value =$100
N=10 years
I/y=9
What is the formula for the present value?PV= FV/(1+r)^n
Where FV is the future value.
Use the given values in the formula we get,
Therefore the correct answer is 42.
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If f(x)= 3x +2 and g(x)=x^2+1, which expression is expression is equivalent to (fog) (x)
Composite functions occur when we take two functions and input one into the other as x.
Example:
[tex]f(x) = 2x[/tex]
[tex]g(x) = 3x^2[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x) = 2(3x^2)[/tex]
Solving the QuestionWe're given:
[tex]f(x)= 3x +2[/tex][tex]g(x)=x^2+1[/tex]To find [tex](f\circ g)(x)[/tex], input g into f as x:
[tex]f(x)= 3x +2[/tex]
[tex](f\circ g)(x)=3(x^2+1) +2\\(f\circ g)(x)=3x^2+3 +2\\(f\circ g)(x)=3x^2+5[/tex]
Answer[tex](f\circ g)(x)=3x^2+5[/tex]
Solve: 8 + x/3 = 1/6 (x-6) -1
A. x = 60
B. x = -60
C. x = -36
D. There are infinitely many solutions
Answer: B -60
Step-by-step explanation: When you plug in -60 into the equation it all equals out into -12 = -12, which is true. All of the other solutions don't work.
Answer:
B. x = -60
Step-by-step explanation:
8 + x/3 = 1/6 (x-6) - 1
Multiply both sides by 6.
48 + 2x = x - 6 - 6
x = -12 - 48
x = -60
Use the graph of the function provided to find the indicated values.
a) When x = -2, g(x) = 5.
b) When x = -4, g(x) = 7.
c) When g(x) = 6, x = -3
d) When g(x) = -1, x = 4
what is the constant proportionality in the equation y = 5/4x?
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of ten automobile insurance liability claims is under study.
The mean will be 10.08 and the standard deviation will be 1.27.
The complete question is given below:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.
Find the mean and standard deviation of this probability distribution.
For samples of size 12, what is the expected number of claims made by people under 25 years of age?
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
Given that:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age.We need to find For samples of size 12, what is the expected number of claims made by people under 25 years of age?The mean will be calculated by the formula below:-
Mean = [tex]\mu[/tex] = np = 12 x 0.84 = 10.08
The standard deviation will be calculated as:-
Standard deviation = [tex]\sqrt{npq}[/tex] = [tex]\sqrt{12\times 0.84\times 0.16}[/tex] = 1.27
Therefore the mean will be 10.08 and the standard deviation will be 1.27.
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What are the solutions to the following system of equations?
2x − y = 6
y = x2 − 9
(3, 0) and (−1, −8)
(3, 0) and (4, 2)
(−3, 0) and (−1, −8)
(−3, 0) and (4, 2)
Answer:
(3, 0) and (−1, −8)
Equation's:
2x − y = 6y = x² − 9Substitute equation 2 into 12x − (x² − 9) = 6
2x - x² + 9 = 6
-x² + 2x + 9 - 6 = 0
-x² + 2x + 3 = 0
x² - 2x - 3 = 0
x² - 3x + x - 3 = 0
x(x - 3) + 1(x - 3) = 0
(x + 1)(x - 3) = 0
x = -1, x = 3
Find values for yIf x = -1, then y = (-1)² - 9 = -8
If x = 3, then y = (3)² - 9 = 0
Solution Set:(x, y) = (-1, -8), (3, 0)
My friend has $672 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $17/yard on one side, and cheaper metal fencing which costs $7/yard for the other three sides.
What are the dimensions of the garden with the largest area she can enclose?
The dimensions of the garden with the largest area she can enclose are given by 24*14 square yards.
The area (A) of the rectangle with length L and Width W is given by,
A=L*W
The maximum of [tex]y=ax^2+bx[/tex] occurs at x = -b/2a
Let the length and width of the garden be L and W respectively.
Now let my friend use cedar fencing for one width and cheaper metal fencing for rest sides.
Rate of cedar fencing is $17/yard
Then she has to pay for cedar fencing = 17W
rate of cheaper metal fencing is $7/yard
Then she has to pay for metal fencing = 7W+7*2L = 7W+14L
Then according to condition,
17W+7W+14L = 672
24W+14L = 672
12W+7L = 336
7L = 336-12W
L = (336-12W)/7
Then the area of the rectangular garden is given by,
A = L*W
[tex]A=\frac{336-12W}{7}\times W\\A=-\frac{12}{7}W^2+48W[/tex]
So here a = -12/7 and b = 48
Then maximum of W occurs at,
W = -48/(2*(-12/7)) = (48*7)/(2*12) = 336/24 = 14
Then maximum width = 14 yards
then length (L) = (336-12*14)/7 = 168/7 = 24 yards
Hence the dimensions with the leargest area she can enclose is given by = 24 * 14 square yards.
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What is the initial value of the sequence? Please help
The initial value of the sequence is 1
How to determine the initial value?From the graph, we have the following ordered pairs
(x, y) = (1, 1), (2, 4) and (3, 8)
Remove the x values
y = 1, 4, 8
The first value in the above sequence is 1
Hence, the initial value of the sequence is 1
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Hello,
I need help with this exercise.
A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform. The equation for the ball’s height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60. How long before the ball hits the ground? What is the maximum height of the ball?
Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Answer: I HOPE THAT MY ANSWER WILL HELP U
Step-by-step explanation:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
David rolls a fair dice 30 times. How many times would David expect to roll a number greater than 3?
Answer:
15
Step-by-step explanation:
so if its a 6 faced dice then there is a 3/6 numbers greater than 3. which simplifies to 1/2. 30(1/2)= 15
What is the length of each leg of the triangle below?
45°
90⁰
22
OA. 15
B. √22
C. 11
45°
D. 11/2
E. VIT
F. 1
Answer:
A. 15
Step-by-step explanation:
Hypotenuse = 22
Since the two angles other than the 90° are both
45° , it means that the two legs of the right triangle are of equal length.
So, (x)²+ (x)² = 22²
2x² = 22²
x² = 484/2
x² = 242
x = √242
x = 15.55
x ≈ 15
Suppose the only measuring cup you own is a one-third measuring cup. Using this measuring cup how many scoops will you need to have 3 2/3 cups of sugar
Answer:
11
Step-by-step explanation:
for each full cup of sugar, you need 3 one-third measuring cups.
we have 3 full cups so 3×3=9
and another 2 for the 2/3, 9+2=11
so a total of 11 scoops
6. 0, 16, 32, 48, 64, ______, ______, ______
what is the next 3 numbers.
Answer:
Step-by-step explanation:
Remark. Since 6 has a decimal after it, I take it that is the question number.
y = 16x is the basic formula. x starts at 0. Then you add 16 to each number to get the next number in the sequence. Or you could do it the way I propose it.
x 0 1 2 3 4 5 6 7
y 0 16 32 48 64 80 96 112
Is 9.3 X 100^9 in scientific notation
Answer:
No.
Step-by-step explanation:
This problem in scientific notation would be 9.3 * 10^10.
pleeeeeeeeeeeease hellllllllp meeeeeee the circle has a center of 0.its raduis is 3 cm,and the central angle A measures 100.what is the area of the shaded region? give exact anwsers in term of pi .please hurry dont worry I have permission to post this for anybody who decides to report me again
Answer:
2.5 pi
Step-by-step explanation:
Comment
If you were trying to get the area of a whole circle, you would use
Area = pi r^2
You have to modify the formula to show that just part of the circle has an area that you are interested in.
The new formula is
Area = (theta/360) pi r^2
Givens
r = 30 cm
theta = 100
Solution
Area = (100 / 360) * pi * r^2 Substitute the givens into this formula
Area = (5 / 18) * pi * 3^2 Expand
Area = (5 / 18) * pi * 9 Cancel 9 into 18
Area = 5/2 * pi
Area = 2.5 * pi
Adriana can ride her bicycle
6 miles in one hour. How long will it
take her to ride 15 miles?
A. 0 m/s
B. -0.17 m/s
C. 12 m/s
D. 0.17 m/s
Answer:
0 m/s
Step-by-step explanation:
What is the solution to t - 3 < 12
Answer:
[tex]\boxed {t < 15}[/tex]
Step-by-step explanation:
Given :
⇒ t - 3 < 12
Add 3 to each side :
⇒ t - 3 + 3 < 12 + 3
⇒ t < 15
Answer: t < 15
Step-by-step explanation:
rearrange the terms t - 3 < 12
calculate the sum or difference t < 12 + 3
answer t < 15
Huilan is 8 years older than Thomas. The sum of their ages is 80. What is Thomas's age?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\texttt {\:Thomas's age = 44 years } [/tex]
[tex]\texttt {\:Hulian's age = 36 years } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Assume Thomas's age be ' x ' } [/tex]
[tex] \textsf{and that of Huilan's age be y } [/tex]
[tex] \texttt{we have two conditions :} [/tex]
[tex]\qquad \tt \rightarrow \:y = x + 8[/tex]
it can be simplified as : -
[tex]\qquad \tt \rightarrow \:y - x= 8 \: \: \: \: \: \: \: \: \: - (1)[/tex]
[tex] \texttt{Next condition } [/tex]
[tex]\qquad \tt \rightarrow \:x + y = 80 \: \: \: \: \: \: \: - (2)[/tex]
`` Add both equations ``
[tex]\qquad \tt \rightarrow \:y - x + x + y = 8 + 80[/tex]
[tex]\qquad \tt \rightarrow \:2y = 88[/tex]
[tex]\qquad \tt \rightarrow \:y = 44[/tex]
[tex] \large \textsf{For x :} [/tex]
[tex]\qquad \tt \rightarrow \:y - x = 8[/tex]
[tex]\qquad \tt \rightarrow \:44 - x = 8[/tex]
[tex]\qquad \tt \rightarrow \:x = 44 - 8[/tex]
[tex]\qquad \tt \rightarrow \:x = 36[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]\fbox {36 years old}[/tex]
Step-by-step explanation:
Let :
⇒ Age of Huilan = x
⇒ Age of Thomas = x - 8
Then :
⇒ x + x - 8 = 80
⇒ 2x = 88
⇒ x = 44
Thomas's age :
⇒ x - 8
⇒ 44 - 8
⇒ 36 years old
The statement “a > 2 and a < 5” is true when a is equal to
A. 5
B. 3
C. 10
D. 2
Answer:
B
Step-by-step explanation:
because > means greater than or more than
and < means less than
the answer is B because 3 is more than 2 and the same time less than 5
2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
The graph is attached with the answer.
What is an Inequality ?When two algebraic expressions are equated using an inequality operator , The statement formed is called In equality.
The given Inequality is 2x + y ≤ 2
in slope intercept form can be written as
y ≤ -2x +2 , here slope is -2 and intercept is 2
As an equation it will be
y = -2x +2
x y
0 , 2
1 , 0
2 -2
The graph is plotted
The area is shaded and the test for the origin is applied , and it lies in the shaded region.
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Enter the amplitude of the function. f(x)=2sin x
Answer:
2
Step-by-step explanation:
In asin(bx - c) + d, a is the amplitude. In this case, it's 2.
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What are the zeros of the quadratic function f(x)=6x^2+12x-7
Answer:
[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]
Step-by-step explanation:
if to solve the given equation, then
D=6²+42=78;
[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]
Choose the correct range , mean and standard deviation for participant age written in correct APA format . A. Participants ranged in age from 4 to 90 ( M = 26.24 , SD = 23.00 ) . B. Participants ranged in age from 18 to 54 ( M = 26.24 , SD = 8.04 ) . C. Participants ranged in age from 18 to 54 ( M = 23.00 , SD = 26.24 ) . D. Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ) . E. Participants ranged in age from 18 to 58 ( M = 23.00 , SD = 8.04 ) .
The range, the mean, and standard deviation are mathematically given as
Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ). Option D.
What are the range, the mean, and standard deviation?Given the data presented below the given
A look at the result shows that the lowest and highest values are between 1s and 58, with a mean and standard deviation of 26.10 and 8.90, respectively.
Participants' ages varied from 18 to 58 (m-26.14, std dev = 8.01), hence option (d) is accurate.
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The function f(x) is shown in this graph.
The function g(x) = -7x-1.
Compare the slopes.
f(x)
(0.3)
A. The slope of f(x) is greater than the slope of g(x).
B. The slope of f(x) is less than the slope of g(x)..
C. The slope of f(x) is the same as the slope of g(x).
I need help
Answer:
A maybe?
Step-by-step explanation:
by looking at the graph you can see there are two points with one being at (0, 3) (given) and the other being at (1, 1) (by looking at the graph). You can use the slope formula (y2 - y1) / (x2 - x1) which gives you the slope.
Plug Values In:
(1-3) / (1-0) = -2/1 = -2
slope of f(x) = -2
slope of g(x) = -7 (slope-intercept form y=mx+b where m is the slope and b is the y-intercept)
I'm honestly not quite sure what it means by greater than since technically the slope of f(x) is greater than the slope of g(x) but does it mean how much it's changing by in which case the sign doesn't matter. Although I'm just going to assume it purely means the value in which case A is true.
Which graph represents y= sqrt x-4
Based on the characteristics of the function and the image generated by the graphing tool, we conclude that the first choice represents the function [tex]y = \sqrt{x} - 4[/tex].
How to find the right graph of a given function
In this question we have a radical function ([tex]f(x) = \sqrt{x}[/tex]) translated vertically 4 units in the -y direction. The domain of the function is [0, + ∞). A quick and efficient approach consists in graphing the function and comparing with each image to determine the right choice.
We present the graph description in the image attached below and we conclude that the first choice represents the graph of the function.
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A restaurant offers 7 appetizers and 8 main courses. In how many ways can a person order a two-course meal?
There are ways a person can order a two-course meal.
Answer:
56
Step-by-step explanation:
so 7 appetizers times 8 main courses
I do a easy trick where I multiple so
7×8=56
Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression.
Answer:
k(magnitude of vector a).vector a
Step-by-step explanation:
Given question is based on vectors so,
vectors :- Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Various operations can be applied to vectors such as addition, subtraction, and multiplication.
To produce an another vector form a given vector we increase its magnitude only not its direction as we have to produce another vector from a given vector.
as its clear from the graph given in the question that only the magnitude of vector a is increased to produce another vector b
hence we multiply any constant ('k') with the magnitude of vector a to increase its magnitude.
and finally multiply the increased magnitude with the vector 'a' itself.
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Choose the function that includes the given points.
(0,−2),(5,13),(−2,−8),(4,10)
The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
What is the function about?Note that all function of (0,−2),(5,13),(−2,−8),(4,10) can be seen as all the brackets are placed in the form (X, Y), Y=P(x)
In the case above, how we arrived at the answer, you have to fill up the X's in the brackets using the X's in the Options.
Then since P(x) is the number one see in place of Y in the brackets, then that the top Right option is correct as it has −2.
Therefore, The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
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