Can the range of a function be written like this {6,7,8,10} instead of like this [tex]6\leq x\leq 10[/tex]?
Answer:
No unless x is being used to define only elements of an integer set.
Step-by-step explanation:
No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....
Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.
{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.
People think that that babies are equally likely to be either boys or girls. Actually, about 51.3% of all babies are boys. If a family has two children (not twins), what is the chance both children are boys
Answer:
26.32%
Step-by-step explanation:
The probability that both children are boys would be a sequence of events. Therefore, in order to calculate this we need to multiply the probability of the first baby being a boy with the probability of the second baby being a boy. Since the probability of any baby being a boy is 51.3%, we simply multiply this value in decimal form by itself.
51.3 / 100 = 0.513
0.513 * 0.513 = 0.263169 or 26.32%
Write two pairs of integers (a, b) such that a / b = -4.
One such pair is (8, -2) because 8/ -2 = (-4).
Answer: a= 16 a=8
b=4 b=2
because, 2 when multiplied by 4 gives 8
4 when multiplied gives 16
Tory and Emilio's motorboats travel at the same speed Tory pilots her boat 60 km before docking Emilio continues for another 4 hr traveling a total of 120 km before docking How long did it take Tory to navigate the 60 km?
It took Tory hr to navigate the 60 km
(Simplify your answer. Type an integer, a mixed numeral or a fraction)
Answer:
2 hours
Step-by-step explanation:
Since Tory and Emilio's motorboats travel at the same speed, they are traveling at the speed of 30 km/h. Therefore, it should take Tory two hours to travel 60 km.
Tory took 2 hours to navigate the 60 kilometers.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given:
Tory pilots her boat 60 km before docking.
Emilio continues for another 4 hours traveling, a total of 120 km before docking.
The speed of Emilio's boat = 120 / 4 = 30 kilometers per hour.
Tory and Emilio's motorboats travel at the same speed.
Tory's boat speed,
= 60/30 = 2 hours.
Therefore, Tory takes 2 hours.
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Question 9 of 10
What is the area of the polygon given below?
3
3
19
14
2
12
Answer:
Please could you add an image, maybe I could answer then
Step-by-step explanation:
271 unit² is the area of the polygon. The correct option is option B among all the given options.
What is area?The size of a patch on a surface is determined by its area. Surface area is defined as the circumference of an open surface or indeed the boundaries of a three-dimensional object, whereas the area of a plane region and plane area relates to the area of a form or planar lamina.
Area can be interpreted as the quantity of material with such a specific thickness required to create a replica of the shape or as the quantity of paint required to completely cover a surface in a single coat. This is the two-dimensional equivalent of the volume of a solid or the length of a curve.
The area is the sum of 3 rectangles are:
First 12 × 19 = 228
Second 3 × 3 = 9
Third 2 × 17 = 34
total area = 228 + 34 + 9 = 271 unit²
Therefore, 271 unit² is the area of the polygon. The correct option is option B.
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Your question is incomplete but most probably your full question was,
What is the area of the polygon given below
Y=-4x-2 and intersects at the points (4,-1)
Answer:
It doesn't intersect at that point
[tex]{ \bf{y = - 4x - 2}} \\ y = - (4 \times 4) - 2 \\ y = - 18[/tex]
Answer: N/A
Step-by-step explanation:
The line y = -4x - 2 does not go through the point (4, -1); it only passes through the point (4, -4(4) - 2) = (4, -18)
hello can anyone help with this?
Answer:
<2 and <13 are alternate exterior angles.
In simple form, alternate exterior angles are the opposite angle on the opposing parallel line. So, to make you understand better, <4 and <15 are alternate exterior angles.
Hope this helps :D
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
10-
If(x)
1
х
10
-5
5
10
g(x)
-10
A. g(x) = (– x)2 - 3
B. g(x) = – x2 + 3
c. g(x) = (-x)2 + 3
D. g(x) = -X2 - 3
Answer:
[tex]g(x) = -x^2 + 3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex]
Required
Determine g(x)
First, shift f(x) down by 3 units
The rule is:
[tex]f'(x) = f(x) - 3[/tex]
So:
[tex]f'(x) = x^2 - 3[/tex]
Next, reflect f'(x) across the x-axis to get g(x)
The rule is:
[tex]g(x) = -f(x)[/tex]
So, we have:
[tex]g(x) = -(x^2 - 3)[/tex]
Open bracket
[tex]g(x) = -x^2 + 3[/tex]
Answer:
D
Step-by-step explanation:
I figured out the hard way
accoridng to byu idaho entorllemtn statistic there are 12000 femailes student here on camputes during any given semster of those 3500 have served a mission what is the probalbity that a rodnlby sleclted femal student on cmapus will have served a mission
Answer:
so this as a fraction is 3500/12000 which is equivalent to
0.29166666666 we multiply this by 100
29.166666666
so about 29.1% or the students are female and have served a mission
Hope This Helps!!!
Please explain absolute values?
Answer:
the magnitude of a real number without regard to its sign.
Step-by-step explanation:
For example, |-3| would just be a 3 in general, no negative sign in the front.
hope this answers your confusion.
Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linearly independent solutions to the corresponding homogeneous equation for t > 0.
ty'' + (2t - 1)y' - 2y = 7t2 e-2t y1 = 2t - 1, y2 = e-2t
Recall that variation of parameters is used to solve second-order ODEs of the form
y''(t) + p(t) y'(t) + q(t) y(t) = f(t)
so the first thing you need to do is divide both sides of your equation by t :
y'' + (2t - 1)/t y' - 2/t y = 7t
You're looking for a solution of the form
[tex]y=y_1u_1+y_2u_2[/tex]
where
[tex]u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt[/tex]
[tex]u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt[/tex]
and W denotes the Wronskian determinant.
Compute the Wronskian:
[tex]W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}[/tex]
Then
[tex]u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t[/tex]
[tex]u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}[/tex]
The general solution to the ODE is
[tex]y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}[/tex]
which simplifies somewhat to
[tex]\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}[/tex]
In order to test for the significance of a regression model involving 4 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are Select one: a. 3 and 43 b. 4 and 43 c. 4 and 42 d. 3 and 42
Answer:
c. 4 and 42
Step-by-step explanation:
Given
[tex]p = 4[/tex] -- independent variables
[tex]n = 47[/tex] ---- observations
Required
The numerator and denominator degrees of freedom
The denominator degrees of freedom is:
[tex]df =n - p - 1[/tex]
[tex]df =47 - 4 - 1[/tex]
[tex]df =42[/tex]
For the numerator, we have:
[tex]df = p[/tex]
[tex]df = 4[/tex]
a garden has more roses than daisies, and it has 9 daisies.furthermore, each flower in the garden has more then 3 petals.Let r represent the number of roses and let P represent the total number of petals in the garden. let’s compare the expressions P and 3(r+9). which statement is correct
Answer:
There is not enough info to tell
Step-by-step explanation:
Khan acadamey
Mary is 3 years older than Sarah. Winifred is twice as old as Mary. Altogether their ages total 89. How old is Sarah?
24 years old
22 years old
18 years old
None of these choices are correct.
Answer:
Step-by-step explanation:
M = S+3
W = 2M = 2(S+3) = 2S+6
M+S+W = 89
(S+3)+S+(2S+6) = 89
S = 20
Answer:
20
Step-by-step explanation:
Sarah: 21
Mary: 24
Winifred: 48
No
Sarah: 20
Mary: 23
Winifred: 46
Yes
Solve by using matrices. 2x – y +2 + w = -3 x + 2y – 3z + w = 12 3x - y - + 2w = 3 -2x + 3y + 2 – 3w = -3
Some symbols and numbers are missing. I assume the system is supposed to read
2x - y + 2z + w = -3
x + 2y - 3z + w = 12
3x - y - z + 2w = 3
-2x + 3y + 2z - 3w = -3
In matrix form, this is
[tex]\begin{bmatrix}2&-1&2&1\\1&2&-3&1\\3&-1&-1&2\\-2&3&2&-3\end{bmatrix}\begin{bmatrix}x\\y\\z\\w\end{bmatrix}=\begin{bmatrix}-3\\12\\3\-3\end{bmatrix}[/tex]
which we can strip down to the augmented matrix,
[tex]\left[\begin{array}{cccc|c}2&-1&2&1&-3\\1&2&-3&1&12\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
Now for the row operations:
• swap rows 1 and 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\2&-1&2&1&-3\\3&-1&-1&2&3\\-2&3&2&-3&-3\end{array}\right][/tex]
• add -2 (row 1) to row 2, -3 (row 1) to row 3, and 2 (row 1) to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&-7&8&-1&-33\\0&7&-4&-1&21\end{array}\right][/tex]
• add 7 (row 2) to -5 (row 3), and row 3 to row 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&16&-2&-24\\0&0&4&-2&-12\end{array}\right][/tex]
• multiply through rows 3 and 4 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&8&-1&-12\\0&0&2&-1&-6\end{array}\right][/tex]
• add -4 (row 4) to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&0&3&12\\0&0&2&-1&-6\end{array}\right][/tex]
• swap rows 3 and 4
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&3&12\end{array}\right][/tex]
• multiply through row 4 by 1/3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&-1&-6\\0&0&0&1&4\end{array}\right][/tex]
• add row 4 to row 3
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&2&0&-2\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 3 by 1/2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&8&-1&-27\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -8 (row 3) and row 4 to row 2
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&-5&0&0&-15\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• multiply through row 2 by -1/5
[tex]\left[\begin{array}{cccc|c}1&2&-3&1&12\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
• add -2 (row 2) and 3 (row 3) and -1 (row 4) to row 1
[tex]\left[\begin{array}{cccc|c}1&0&0&0&-1\\0&1&0&0&3\\0&0&1&0&-1\\0&0&0&1&4\end{array}\right][/tex]
Then the solution to the system is (x, y, z, w) = (-1, 3, -1, 4).
Is f(x)=4x^2 linear,quadratic,or exponential
Answer:
Step-by-step explanation:
it is a quadratic function.
Combine as indicated by the signs. Write answer In descending powers of x.
X+6/x^28x+15+3x/x+5-x-3/x+3
= ?
Answer:
Step-by-step explanation:
How many people have at least 1?
Answer:
15
Step-by-step explanation:
3+7+5
PLEASE BRAINLIESTTTTTTTTT
PLSHELPASAPDFFFFFFFFFFFFFFFFFFFFFFFFFF
im struggling with the same one
A ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the function h = –16t2 + 24t + 7. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. b. What is the ball’s maximum height?
Answer:
Step-by-step explanation:
Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.
If the position function is
[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is
v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:
0 = -32t + 24 and
-24 = -32t so
t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:
s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so
s(.75) = 16 feet
11 Emilio makes metal fences.
He is making a fence using this design.
1.44 m
DO NOT WRITE IN THIS AREA
1.8 m
.
The fence will need
3 horizontal metal pieces of length 1.8m
2 tall metal pieces of length 1.44 m
5 medium metal pieces
6 short metal pieces as shown on the diagram.
The heights of the tall, medium and short metal pieces are in the ratio 9:8:7
.
How many metres of metal in total does Emilio need to make the fence?
Answer:
21.4 m
Step-by-step explanation:
Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:
(9/24) * x = 1.44
x = 3.84 m
For the medium metal pieces:
(8/24) * 3.84 = medium metal height
medium metal height = 1.28 m
For the short metal pieces:
(7/24) * 3.84 = short metal height
short metal height = 1.12 m
Total horizontal metal piece length = 3 * 1.8 m = 5.4 m
Total tall metal piece length = 2 * 1.44 m = 2.88 m
Total medium metal piece length = 5 * 1.28 m = 6.4 m
Total short metal piece length = 6 * 1.12 m = 6.72 m
Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m
Use Cramer's Rule to solve (if possible) the system of linear equations.
x1 + 2x2 =8
- x1 + x2 = 1
Required:
Find the coefficient matrix.
Answer:
x1 = 2
x2 = 3
Step-by-step explanation:
[tex]x_1=\frac{D_{x1}}{D}\\\\x_2=\frac{D_{x2}}{D}[/tex]
Here D is the coefficient matrix.
Hence
[tex]x_1=\frac{6}{3}\\x_1=2[/tex]
&
[tex]x_2=\frac{9}{3}\\x_2=3[/tex]
please help me now I need it please this is calculuse
Answer:
none of these
Step-by-step explanation:
the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths
Answer:
Length of the rectangle:
[tex]x = \frac{4800}{106} = \frac{2400}{53} [/tex]
Breadth of the rectangle:
[tex]60\%(x) = \frac{60}{100} \times \frac{4800}{106} \: \: \: \: \: \: \: \: \: \: \: \\ =60 \times \frac{48}{106} \\ = \frac{2880}{106} [/tex]
Step-by-step explanation:
Longer side of the rectangle(length) = x
Shorter side of the rectangle(breadth) = (60%)x
Perimeter of the rectangle = 2(l+b) = 96 inches
Hence,
[tex]96 = 2(x + 60\%(x))[/tex]
[tex]96 = 2(x + \frac{6}{100 } x)[/tex]
[tex]96 = 2( \frac{100}{1 00} x + \frac{6}{100} x)[/tex]
[tex]96 = 2( \frac{106}{100} x)[/tex]
[tex]96 = \frac{106}{50} x[/tex]
[tex]96 \div \frac{106}{50} = x[/tex]
[tex]96 \times \frac{50}{106} = x[/tex]
[tex] \frac{4800}{106} = x[/tex]
Rahim is constructing a proof to show that the opposite angles of a
quadrilateral inscribed in a circle are supplementary. Which step would be the
first in his proof?
Given: Quadrilateral QRST is inscribed in circle X.
Prove: R is supplementary to T
9514 1404 393
Answer:
Given: Quadrilateral QRST ...
Step-by-step explanation:
The first statement of a proof is always a restatement of the facts that are Given. The "prove" statement is a goal, never stated in the proof. The statement to be proven is the last statement (conclusion) of a proof.
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Answer:
4
Problem:
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Step-by-step explanation:
One approach would be to plug in the choices and see.
If n=1, then we have m^2-1=9.
This would give m^2=10 after adding 1 on both sides. There is no integer m when squared would give us 10. ( Square root of 9 is a decimal )
If n=16, then we would have m^2-256=9.
This would give m^2=265 after adding 256 on both sides. There is no integer m when squared would give us 265. ( Square root of 265 is a decimal )
If n=9, then we would have m^2-81=9.
This would give m^2=90 after adding 81 on both sides. There is no integer m when squared would give us 90. ( Square root of 90 is a decimal )
If n=4, then we would have m^2-16=9.
This would give m^2=25 after adding 16 on both sides. There is an integer m when squared would give us 25. ( Square root of 25 is a 5)
would someone help me out with this question? I got it wrong the first time but I don't understand how.
Answers:
Choice 2) Angle ABC is bisected by ray BD.
Choice 3) BC = 1/2 AC
Choice 5) 2*(angle DBC) = angle ABC
================================================
Explanation:
Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC
We can then say
AB+BC = AC
BC+BC = AC
2BC = AC
BC = (1/2)*AC
which shows why choice 3 is one of the answers
----------------------
Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x
(angle ABD) + (angle DBC) = 180
90 + x = 180
x = 180 - 90
x = 90
So angle DBC is also 90.
We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.
------------------------
Using the angle addition postulate, we know that,
(angle ABD) + (angle DBC) = angle ABC
(angle DBC) + (angle DBC) = angle ABC
2*(angle DBC) = angle ABC
Showing why choice 5 is the third answer.
------------------------
Choice 1 isn't true since ray BD helps form angle DBC.
Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.
6v^2x^3y^7 and 20v^8x^5
Answer:
LCD????
[tex]2v^2x^3[/tex]
Step-by-step explanation:
What are all the values of w such that|-W | = 5?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]w = 5, -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
Absolute value is simply how far a digit is from zero.The digits '-5' and '5' are 5 away from zero.Therefore:
[tex]w =\pm5[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is the true solution to the equation below?
l n e Superscript l n x Baseline + l n e Superscript l n x squared Baseline = 2 l n 8
x = 2
Given:
The equation is:
[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]
It can be written as:
[tex]\ln x+\ln x^2=2\ln 8[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\ln (x\cdot x^2)=2\ln 8[/tex] [tex][\because \ln a+\ln b=\ln (ab)][/tex]
[tex]\ln (x^3)=\ln 8^2[/tex] [tex][\because \ln x^n=n\ln x ][/tex]
On comparing both sides, we get
[tex]x^3=8^2[/tex]
[tex]x^3=64[/tex]
Taking cube root, we get
[tex]x=\sqrt[3]{64}[/tex]
[tex]x=4[/tex]
Therefore, the required solution is [tex]x=4[/tex].
Answer:
x=4
Step-by-step explanation:
What is the true solution to the equation below?
ln e Superscript ln x Baseline + ln e Superscript ln x squared Baseline = 2 ln 8
x = 2
x = 4
x = 8