Which number line represents the solution set for the inequality -1/2x >= 4
Answers
Answer:
x≤-8
Step-by-step explanation:
-1/2x ≥ 4
Multiply each side by -2, remembering to flip the inequality
-2*-1/2x≤ 4*-2
x≤-8
Answer:
Step-by-step explanation:
Note: by the rule of order of operations, -1/2x == -1/2*x = -x/2
-x/2 >= 4
-x >= 4*2 = 8
x <= -8
The number line looks like this:
<============================O--------------------------------------
where the circle should be filled and at x= -8
The valid part of the number line is to the left of the circle but INCLUDING the circle (solid dot).
Related Questions
The picture has the question
Answers
Consider a two-station production line in which no inventory is allowed between stations (i.e., the stations are tightly coupled). Station 1 consists of a single machine that has potential daily production of one, two, three, four, five, or six units, each outcome being equally likely (i.e., potential production is determined by the roll of a single die). Station 2 consists of a single machine that has a potentialdaily production of eitther three or four units both which are equally likely (i.e. it produces three units if a fair coin comes up heads and four units if ir comes up tails).
Required:
a. Compute the capacity of each station (units per day). Is the line balanced (do both stations have the same capacity)?
b. Compute the expected throughput of the line. Does this diifer from a.?
c. Suppose a second identical machine is added to station 1 and station 2. What is the expected throughput of the line. How does this compare to previous throughput.
Answers
Answer:
a) Capacities : station 1 = 3.5 , station 2 = 3.5
Both stations have the same capacity
b) 3.5 ( it does not differ from a )
c) The value will double i.e. 3.5 * 2 = 7
Step-by-step explanation:
a) compute the capacity of each station and show if the line is balanced
for station 1
Units : 1 ,2 ,3, 4 ,5, 6
probabilities : 1/6 ( same value for all units )
for station 2
units : 3, 4
probabilities : 1/2 1/2
Capacity of station 1= ( 1/6 * 1 ) + ( 1/6 *2 ) + ( 1/6 *3) + (1/6 *4) + (1/6*5) + (1/6*6 )
= 3.5
Capacity of station 2 = ( 1/2 * 3 ) + ( 1/2 * 4 )
= 3.5
∴ both stations have the same capacity
B) Expected throughput of the line
= Min( capacity of station 1 , capacity of station 2 )
= 3.5 ( It does not differ from a )
C) When an additional identical machine is added to both stations the expected throughput of the line will be doubled
i.e. expected throughput = ( 3.5 ) * 2 = 7
Simplify the following expression
7-5/6 × 7-7/6
Answers
[tex]\longrightarrow{\blue{ 0 }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex]7 - ( \frac{5}{6} \times 7) - \frac{7}{6} [/tex]
[tex] = 7 - \frac{35}{6} - \frac{7}{6} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for the denominators.
The L. C. M is 6.
Now, multiply the L.C.M. with both numerator & denominator.
[tex] = \frac{7 \times 6}{1 \times 6} - \frac{35}{6} - \frac{7}{6} [/tex]
Now that the denominators are equal, we can add/subtract them.
[tex] = \frac{42- 35 - 7}{6} [/tex]
[tex] = \frac{42 - 42}{6} [/tex]
[tex] = \frac{ 0}{6} [/tex]
[tex] = 0[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Please help me with #26-28
Answers
Answers:
26) probability = 1/427) probability = 0.058828) probability = 0.157=================================================
Work Shown:
26)
1/2 = probability of an odd number, since half of the numbers are odd
1/2 = probability of tails
(1/2)*(1/2) = 1/4 is the probability of both events happening at the same time
----------------------------
27)
13/52 = probability of pulling out one club
12/51 = probability of pulling out a second club, assuming the first one is not put back
(13/52)*(12/51) = 156/2652 = 1/17 = 0.0588 is the probability of pulling two clubs in a row (without replacement).
----------------------------
28)
11/27 = probability first person has blonde hair
10/26 = probability second person has blonde hair (cannot reselect the first person again)
(11/27)*(10/26) = 110/702 = 55/351 = 0.157 is the probability of selecting two people with blonde hair
help pls
Draw a line segment AB=8cm. Construct angle BAC=angle ABC=60 DEGREE.
Now draw the angular bisector of each angle of angle ABC.
pls help
Answers
Answer:
Step-by-step explanation:
Bisection implies dividing a given segment into equal haves by construction. So that in the given question, angle ABC would be divided into equal parts.
After drawing segment AB to given length, use a compass to construct the required angle ABC. Then use the ends of the arc for the angle to bisect the angle.
The construction to this question is herewith attached to this answer for more clarifications.
if f(×) = [tex] \frac{1}{ \sqrt{x - 1} } [/tex]
then find [tex] \frac{f(x) - f(2)}{x - 2} [/tex]
Answers
9514 1404 393
Answer:
(1 -x +√(x -1))/(x² -3x +2)
Step-by-step explanation:
Fill in the given function definition and simplify.
[tex]\dfrac{f(x)-f(2)}{x-2}=\dfrac{\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{2-1}}}{x-2}=\dfrac{1-\sqrt{x-1}}{(x-2)\sqrt{x-1}}\\\\=\dfrac{\sqrt{x-1}-x+1}{(x-2)(x-1)}=\boxed{\dfrac{\sqrt{x-1}-x+1}{x^2-3x+2}}[/tex]
what will the time be after 1 hour 5 minutes from 8:15 am
Answers
Answer:
9:20 am
Step-by-step explanation:
So, lets go over two things.
Minutes and hours.
Minutes changes the second number.
You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.
Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.
In this case. we are moving the minutes place up by 5:
15+5=20
So the minutes place is 20, and does not change the hours place since it is below 60.
Next we have a increase in hours by 2:
8+1=9
So the hours place is 9, and does not reset or change the pm/am since its below 12.
Answer:
9:20am
Hope thias helps!
Answer:
9:20 am
Step-by-step explanation:
Add 1 hour
8:15 to 9:15
Add 5 minutes
9:15 to 9:20
To estimate the benefits of an SAT prep course, a random sample of 10 students enrolled in the course is selected.
For each of these students, their entrance score on the exam taken at the beginning of the course is recorded. Their
exit score on the exam they take at the end of the course is recorded as well. The table displays the scores.
Answers
Answer: 57%
Step-by-step explanation:
An aerodynamic 1,000 kg car takes about 270 newtons of force to maintain a speed of 25 m/s. how much horsepower is required from the engine to maintain this speed?
Answers
Answer:
9.05 horse power
Step-by-step explanation:
Given:
Force = 270 Newton
Speed = 25 m/s
Power = Force * velocity
Power = 270 Newton * 25 m/s
Power = 6750 watt
Recall:
1 horse power = 746 watts
Hence, required horsepower is :
6750 watt / 746 watt
9.048 hp
9.05 horse power
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When
the length is 12 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm/s)? Write an equation for A in terms of l and w.
Answers
Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
[tex]A=w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to t, where w and l are both functions of t:
[tex]\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell][/tex]
By the Product Rule:
[tex]\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w[/tex]
Since we know that dl/dt = 6 and that dw/dt = 5:
[tex]\displaystyle \frac{dA}{dt}=5\ell + 6w[/tex]
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
[tex]\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}[/tex]
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
If f(x) = x2 – 2x, find:
f(-3) = [?]
Answers
9514 1404 393
Answer:
15
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
f(-3) = (-3)² -2(-3) = 9 +6
f(-3) = 15
15
Step-by-step explanation:
f(-3)=(-3)^2 - 2(-3)
= 9 + 6 = 15
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
Answers
Answer:
Step-by-step explanation:
We first need to find the slope of the line that is graphed. We can wither use the slope formula or you can use the slope triangle. From the upper point on the line (-1, 1) count down til you're on the same horizontal as the lower point on the line (0, -3). You have to count down 4 (which is -4) and over to the right 1 (which is +1). So -4/+1 = -4 and the slope is -4. That means that the perpendicular slope, the opposite reciprocal of that, is 1/4. Using that slope and the point (-4, -3), the point-slope form of the line is
[tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex] which we can simplify a bit to
[tex]y+3=\frac{1}{4}(x+4)[/tex]. That's the line in point-slope form.
The two way table shows information about preferred drinks of some people how many males drank only coffee
Answers
Answer:
73% The two-way table shows information about the preferred drinks of some people. b a How many males drank only coffee? b What is the probability that any person is male and only drinks coffee? 73% The two-way table shows information about the preferred drinks of some people
Select the correct answer.
What is the solution to this equation?
g^x-1=2
A. -1/2
B. 1/2
C. 2
D. 1
Answers
9514 1404 393
Answer:
B. 1/2
Step-by-step explanation:
Maybe you want the solution to ...
[tex]9^x-1=2[/tex]
You can use logarithms, or your knowledge of powers of 3 to solve this.
[tex]9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}[/tex]
Using logarithms, the solution looks like ...
[tex]x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}[/tex]
Write the equation of the line that passes through the points (6,-6)
and (7,-4) Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
9514 1404 393
Answer:
y +6 = 2(x -6)
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -(-6))/(7 -6) = 2/1 = 2
The point-slope equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Using the slope we found and the first point, the equation is ...
y +6 = 2(x -6)
A box of golf balls contains 10 balls. Each golf ball has a diameter of 3.6 centimeters. What is the total
volume of golf balls in 3 boxes?
about 1465.74 cm
c. about 1221.45 cm
b. about 732.87 cm
d. about 81.43 cm
Answers
Answer:
C
Step-by-step explanation:
f(x)=x^2+2x-4 and g(x)=3x+1 find
Answers
Answer:
Step-by-step explanation:
[tex]f(x)=x^2+2x-4\\g(x)=3x+1\\\\g\circ f(x)=g(f(x)=3(x^2+2x-4)+1=3x^2+6x-11[/tex]
Answer:
g(f(x)) = 3x^2 + 6x - 11.
Step-by-step explanation:
Replace the x in g(x) by f(x):
g(f(x)) = 3(x^2 + 2x - 4) + 1
= 3x^2 + 6x - 12 + 1
= 3x^2 + 6x - 11.
At a local concert, the cost for 3 adults and 2 children was $32.00. The cost for 8 adults and 5 children
was $84.00. Find how much it costs for an individual adult and how much it costs for an individual
child.
Adult ticket price = $
Child ticket price = $
Answers
Answer:
Hence the cost of adult tickets is $8
and the cost of child ticket is $4
Step-by-step explanation:
Given data
Let the cost per adult be x
and the cost per child be y
So
3x+2y= 32------------1
8x+5y= 84------------2
Now solving 1 and 2 simultaneously, we have
3x+2y= 32------------1X 5
8x+5y= 84------------2 X 2
15x+ 10y= 160
16x+ 10y= 168
-x+0)=-8
-x= -8
x= 8
Put x= 8 in 1 to find y
3*8+2y= 32
24+2y= 32
2y= 32-24
2y= 8
y= 4
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
How many classes would Gina need to take for the total cost to be the same at both dance studios?
Answers
Answer:
Gina would need to take 10 classes.
Step-by-step explanation:
Cost of x classes at dance studio:
[tex]y_d(x) = 15x[/tex]
Cost of x classes at toe tappers:
[tex]y_t(x) = 25 + 12.5x[/tex]
How many classes would Gina need to take for the total cost to be the same at both dance studios?
This is x for which:
[tex]y_d(x) = y_t(x)[/tex]
So
[tex]15x = 25 + 12.5x[/tex]
[tex]2.5x = 25[/tex]
[tex]x = \frac{25}{2.5}[/tex]
[tex]x = 10[/tex]
Gina would need to take 10 classes.
Answer:
10 just took it on edge
you spin each spinner and find the sum how many different sums are possible
Answers
Answer:
let's use a sample set.
8+8, 8+4, 8+5, 8+6, 8+7
4+8, 4+4, 4+5, 4+6, 4+7
5+8, 5+4, 5+5, 5+6, 5+7
6+8, 6+4, 6+5, 6+6, 6+7
7+8, 7+4, 7+5, 7+6, 7+7
There is 25 sums.
In the coming year, a vehicle manufacturer has decided to manufacture 150 vehicles per day. The function v = 150d represents the company’s production for the coming year, v, with respect to the number of days, d.
The rate of change of the function representing the number of vehicles manufactured for the coming year is , and its graph is a . So, the function is a function.
Answers
Given:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.
I hope this helps!
Answer:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
4x - 3(2x - y) if x = and y = 4.
Help me pls
Answers
Answer:
[tex]=0[/tex]
Step-by-step explanation:
Given:
[tex]4x-3(2x-y)[/tex]
Let's substitute for y
[tex]4x-3(2x-4)=0[/tex]
Let's distribute the parenthesis
[tex]4x-6x+12=0[/tex]
Combine like terms
[tex]-2x+12=0[/tex]
Subtract 12 from both sides
[tex]-2x=-12[/tex]
divide both sides by -2
[tex]x=6[/tex]
Now let's insert 6 for the [tex]x[/tex] and 4 for the [tex]y\\[/tex]
[tex]24-3(12-4)=[/tex]
[tex]24-3(8)=[/tex]
[tex]24-24=0[/tex]
Hope this helps
Answer: The x = -1
Step-by-step explanation: I just looked it up on line.
What’s the volume of the rectangular prism in cubic meters
Answers
Answer:
Volume of the prism=60m3
Step-by-step explanation:
Volume of any prism=height*width*length
Volume of the prism=3m*5m*4m=60m3
Volume of the prism=60m3
please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answers
Answer:
A
Step-by-step explanation:
Because the angles must add to 180 we can see the misssing angle is 69
This means that answer is either A or C
Using SOH we can solve for side CD
sin(21)=x/18
18sin(21)=x
x=6.45
If CD= 6.45 this means that the answer is A
if f(y)=y^6/6lny-y^6/36, find f'(y)
Answers
It looks like you have
[tex]f(y)=\dfrac{y^6}{6\ln(y)}-\dfrac{y^6}{36}[/tex]
Differentating gives
[tex]f'(y)=\dfrac{6y^5\times6\ln(y)-6y^6\times\frac1y}{(6\ln(y))^2}-\dfrac{6y^5}{36}= -\dfrac{y^5\left(\ln^2(y)-6\ln(y)+1\right)}{6\ln^2(y)}[/tex]
please answer the question first
Answers
Answer:
Yes, 2.4
Step-by-step explanation:
Y is directly dependant on x, and the constant we multiply x by to get y is 2.4.
Answer:
Yes, 2,4
Step-by-step explanation:
This explains direct proportion because it shows that y equals the 2.4x which is the direct proportion
Hopes this helps
(I+ tan square theta)(1-sin square theta)
Answers
Answer:
1
Step-by-step explanation:
Formulas used:
[tex]sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta[/tex]
[tex]Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1[/tex]
Answer:
[tex](1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1[/tex]
A formula is given as J = 10V/11 + 143
make V the subject of the formula
answer asap please.
Answers
Answer:
11j - 1573/10
Step-by-step explanation:
J = 10v /11 +143
collect terms
J - 143 =10v /11
11 (J -143) = 10v
Divide both sides by 10
11(J - 143)/10 = v
v = 11J - 1573/10
Hope this helps!
b. If you take one spin, what is your expected value?
Answers
Answer:
3/7
Step-by-step explanation:
Expected Value:
3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7
Expected value when we take one spin = 3/7
What is the expected value?It is the sum of values multiplied by their respective probabilities.
How do we calculate the expected value after one spin?We have 2 red, 2 purple, 2 yellow, and 1 blue sector.
Total number of Sectors = 7
∴Probability of landing on red sector = 2/7
∴Probability of landing on purple sector = 2/7
∴Probability of landing on yellow sector = 2/7
∴Probability of landing on blue sector = 1/7
Points on blue sector = 3, on yellow sector = 1, on purple sector = 0, and on red sector = -1.
X 3 1 0 -1
P(X) 1/7 2/7 2/7 2/7
Expected Value = ∑X.P(X)
=3.(1/7) + 1(2/7) + 0(2/7) - 1(2/7)
= 3/7
Learn more about Expected Values on
https://brainly.com/question/15858152
#SPJ2
what is the volume of the triangular prism 13 m x 6 m x 5 m
Answers
Answer:
U R ANSWER
Step-by-step explanation:
177.26657
Answer:
[tex]V=195m^2[/tex]
Step-by-step explanation:
Volume formula of a triangular prism is [tex]V=\frac{1}{2} (b)(h)(l)[/tex]
[tex]V=\frac{1}{2}(13)(6)(5)[/tex]
[tex]V=\frac{1}{2} (390)[/tex]
[tex]V=195[/tex]
Hope this helps