Answer:
(-9, 9)
Step-by-step explanation:
Each coordinate is multiplied by the scale factor.
B' = 3B
B' = 3(-3, 3)
B' = (-9, 9)
Answer:
B'(-9,9)
Step-by-step explanation:
Given:
A(-6,8)
B(-3,3)
Dilation: factor = 3,
centre of dilation = (0,0)
Solution:
Image of B
B' = 3(-3,3) = (-9,9)
Mario and tabitha are calculating the probability of getting a 4 and a 2 if they roll a die twice. Who is correct?
Answer:
[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
4 = [tex]\frac{1}{12}[/tex]
2 = [tex]\frac{1}{12}[/tex]
[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]
A 20-kilogram mass is attached to a spring. If the frequency of simple harmonic motion is 2/p cycles/s, what is the spring constant k? What is the frequency of simple harmonic motion if the original mass is replaced with an 80-kilogram mass?
Step-by-step explanation:
Frequency of a mass-spring system is:
f = √(k/m) / (2π)
Given f = 2/π Hz and m = 20 kg:
2/π Hz = √(k / 20 kg) / (2π)
4 Hz = √(k / 20 kg)
16 s⁻² = k / 20 kg
k = 320 kg/s²
k = 320 N/m
If the 20 kg mass is replaced with an 80 kg mass, the frequency is:
f = √(320 kg/s² / 80 kg) / (2π)
f = √(4 s⁻²) / (2π)
f = 2 Hz / (2π)
f = 1/π Hz
The sprint constant is 320 N/m
And, the frequency is [tex]1\div \pi Hz[/tex]
Calculation of the spring constant & the frequency:Since A 20-kilogram mass is attached to a spring. And, the frequency of simple harmonic motion is 2/p cycles/s.
Now we know that
[tex]f = \sqrt (k\div m) \div (2\pi)[/tex]
Here
[tex]f = 2\div \pi Hz[/tex]
and m = 20 kg:
So,
[tex]2\div \pi Hz = \sqrt (k \div 20 kg) / (2\pi)\\\\4 Hz = \sqrt(k \div 20 kg)\\\\16 s^{-2} = k \div 20 kg[/tex]
k = 320 kg/s²
k = 320 N/m
Now the frequency is:
[tex]f = \sqrt(320 kg/s^2 \div 80 kg) \div (2\pi)\\\\f = √(4 s^{-2}) \div (2\pi )\\\\f = 2 Hz \div (2\pi)[/tex]
[tex]f = 1\div \pi Hz[/tex]
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Jason has bought a new pool and has already measured some of the sides. Using the figure below and your knowledge of quadrilaterals, solve for x and y.
Answer:
x = 12
y = 12
Step-by-step explanation:
Each triangle is a right angle triangle
5² + x² = 13²
x² = 169 - 25
x = √144
x = 12
The shape is a parallelogram
Therefore
x = y
y = 12
find the value of x if (1.1)^x=100
Answer:
x ≈ 48.3177
Step-by-step explanation:
This is what logarithms are for (among other things).
log(1.1^x) = log(100)
x·log(1.1) = 2
x = 2/log(1.1) ≈ 48.3177
PLSS GUYS I NEED HELP
Answer:
Option B. is the right choice.
Step-by-step explanation:
f(-3) = 3 and f(3) = 5 (First and the last column of table B)
Best Regards!
A function F parentheses X is graft what is the slope of the function what is the Y intercept of the function which equation represents the graph of the function
Answer:
5
Step-by-step explanation:
A food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 9.9 and the sample standard deviation is 0.30, find the 95% confidence interval for the true mean.
Answer:
[tex]9.9-2.14\frac{0.30}{\sqrt{15}}=9.734[/tex]
[tex]9.9+2.14\frac{0.30}{\sqrt{15}}=10.066[/tex]
Step-by-step explanation:
Information given
[tex]\bar X= 9.9[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=0.3 represent the sample standard deviation
n=15 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=15-1=14[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value wuld be [tex]t_{\alpha/2}=2.14[/tex]
Now we have everything in order to replace into formula (1):
[tex]9.9-2.14\frac{0.30}{\sqrt{15}}=9.734[/tex]
[tex]9.9+2.14\frac{0.30}{\sqrt{15}}=10.066[/tex]
There is a safety fence around a circular pool with a gate. The gate is 150 cm wide. What is the length of the fence not including the gate? m Use π = 3.14
Answer:
The length of the fence is 6.28x-150 cm.
Step-by-step explanation:
Let the circular pool has the radius (r ) = x cm.
Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.
Length of fence = Circumference of the pool – width of the gate.
Length of fence = 2 π r – 150
Length of fence = 2 × 3.14 × x – 150
Length of fence = 6.28x – 150 cm.
. A box contains four red, three yellow, and seven green balls. Three balls are randomly selected from the box without replacement. (a) What is the probability that all three balls are the same colo
Answer:
10/91
Step-by-step explanation:
Number of Red balls = 4
Number of Yellow balls = 3
Number of green balls=7
Total=4+3+7=14
If we pick three balls of the same color, there are three possibilities: (All Red, All Green Or all Yellow).
Therefore:
The probability that all three balls are the same color (note that the selections are without replacement)
=P(RRR)+P(GGG)+P(YYY)
[tex]=(\frac{4}{14} \times \frac{3}{13} \times \frac{2}{12})+(\frac{3}{14} \times \frac{2}{13} \times \frac{1}{12})+(\frac{7}{14} \times \frac{6}{13} \times \frac{5}{12})\\\\=\frac{1}{91} + \frac{1}{364}+ \frac{5}{52}\\\\=\frac{10}{91}[/tex]
The probability that all three balls are the same color is 10/91.
a canoe in still water travels at a rate of 12 miles per hour. the current today is traveling at a rate of 2 miles per hour. if it took an extra hour to travel upstream, how far was the trip one way?
Answer:
60 miles
Step-by-step explanation:
We assume the trip is "d" miles and that the "extra hour" refers to the additional time that a current of 2 mph would add. That is, we assume the reference time is for a current of 0 mph.
The time with no current is ...
time1 = distance/speed
time1 = d/12 . . . . hours
With a current of 2 mph in the opposite direction, the time is ...
time2 = d/(12 -2) = d/10
The second time is 1 hour longer than the first, so we have ...
time2 = 1 + time1
d/10 = 1 + d/12
6d = 60 + 5d . . . . multiply by 60
d = 60 . . . . . . . . . subtract 5d
The one-way distance is 60 miles.
Which of the following functions is graphed below?
Answer:
C
Step-by-step explanation:
C is the solution
Answer:
Option C
Step-by-step explanation:
The graph is a horizontal translation 4 units left and a vertical translation 2 units down ⇒ y= |x+4|-2
An electronics store is selling mp3 players for 30% off. A customer purchases an mp3 player for $42. What was the price of that mp3 player before the reduction?
Answer:
60
Step-by-step explanation:
If the price is 30% off, you pay 70% of the price
Let x be the original price
.70x = sale price
.70x = 42
Divide each side by .7
.70x/.7 = 42/.7
x =60
The original price is 60
Answer: $ 60
Step-by-step explanation:
42 = x (1 - .3)
42 = .7 x
42/.7 = x
X = 60
4x+6y= 10 -10x+2y= −8
Answer:
x=1, y=1
Step-by-step explanation:
To solve the equations, we first have to label them.
4x +6y= 10 -----(1)
-10x +2y= -8 -----(2)
From (1): 2x +3y= 5 -----(3)
From (2):
-5x +y= -4
y= 5x -4 -----(4)
Subst. (4) into (3):
2x +3(5x -4)= 5
2x +15x -12= 5 (expand)
17x= 12 +5 (simplify, +12 on both sides)
17x= 17 (simplify)
x= 17 ÷17
x= 1
subst. x=1 into (4):
y= 5(1) -4
y= 5 -4
y= 1
I NEED HELP PLEASE, THANKS! :)
While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis. Determine the magnitude of the torque about her elbow. (Show work)
Answer:
54.8 N·m
Step-by-step explanation:
The horizontal distance from the dumbbell to the elbow is ...
(0.366 m)cos(15°) ≈ 0.3535 m
Then the torque due to the vertical force is ...
(155 N)(0.3535 m) = 54.8 N·m
can anyone help me with this?
Answer: 16y² - x²
Step-by-step explanation: The - sign means a difference, so the choices with + signs are eliminated (though 64x² and 9 are squares)
10 is not a square so that one is eliminated (though the y² and the 4x² are squares)
16 is the square of 4, y² is the square of y, and x² is the square. That expression shows a difference of squares.
The ratio of the number of circles to the number of triangles in simplest form is ___. The number of circles that need to be added to make the ratio 1 : 1 is ___.
Answer:
its 3:4
Hope this helps! :)
The ratio is 3:4 and the number of circle need is 3.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, from the given picture, we get that,
No. of circles = 9
No. of triangles = 12
So, required ratio = 9:12
=3:4
Now, Let, x circles are needed to make ratio 1:1
i.e. 9+x:12=1:1
9+x=12
x=3
Hence, The ratio is 3:4 and the number of circle need is 3.
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3.
A passenger jet can fly 1,290 mil
in 3 hours with a tailwind bi
1,230 miles in 3 hours
headwind. Find the speed
the Jet in Still air and the
of the wind.
Answer:
Jet= 420 mph Wind = 10mph
Step-by-step explanation:
The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.
The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.
This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.
So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.
Andrea and Helen participated in a donut eating contest. Andrea ate six more than four times the number of donuts that Helen ate. Let d represents the number of donuts Helen ate. Write the expression that gives the number of donuts that Andrea ate.
Answer:
4d + 6
Step-by-step explanation:
Helen ate d donuts.
Andrea ate 6 more than 4 times d.
4d + 6
Which number is irrational??
Answer:
√6
Step-by-step explanation:
√6 = 2.44948974278...
The number never ends and the values don't repeat therefore, the correct answer is √6.
Hope this helps! :)
Answer:
B. The square root of 5
Step-by-step explanation:
You can only square root a number that can be the answer to an equation like x*x=5, which it is not.
Jeff worked 4 and 2/3 hours in the morning and 3 and 3/4 hours in the afternoon. How many total hours did he work
1. 8 and 1/2 hours
2.7 and 5/7 hours
3.7 and 5/12 hours
4.8 and 5/12 hours
Answer:
4. 8 5/12
Step-by-step explanation:
4 2/3 + 3 3/4 =
= 4 + 2/3 + 3 + 3/4
= 4 + 3 + 8/12 + 9/12
= 7 + 17/12
= 7 + 12/12 + 5/12
= 7 + 1 + 5/12
= 8 5/12
pls help me help me
Answer:
A
Step-by-step explanation:
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 2 + 0.6 + 0.18 + 0.054 + ...
Answer:
sum: 2 6/7
Step-by-step explanation:
The first term is 2, and the common ratio is 0.6/2 = 0.3. This value is less than 1, so the series converges.
The sum is ...
S = a0/(1 -r) = 2/(1 -0.3) = 2/0.7
S = 2 6/7
Toby cuts a pizza into 6 equal slices. He eats half a slice. What fraction of the pizza has he eaten?
The pizza is cut into 6 slices so each slice would be 1/6 of the pizza.
He at 1/2 of a slice:
1/6 x 1/2 = 1/12 of the pizza
How to find the sides and angle of these two problems
Answer:
See step-by-step explanation.
Step-by-step explanation:
Part 1: Use the law of cosines to find the measure of angle B:
Law of cosines: c^2 = a2 + b2 − 2ab cos(C)
In this case, you're finding b, so b is basically c.
b^2 = a2 + c2 − 2ab cos(b)
b=21 a=22 c=16 (just for now)
21^2 = 22^2+16^2- 2(22)(16) cos (b)
441= 484 + 256 - 704 cos(b)
Measure of angle B= 64.8673
Part 2: Use the law of sines to find the measure of angle C
[tex]\frac{a}{sin (A)}[/tex] =[tex]\frac{b}{sin (B)}[/tex]=[tex]\frac{c}{sin(C)}[/tex]
Using angle b and sides b and c: 43.6121
21/ sin ( 64.8673) = 16/ sin(C)
Measure of angle C = 43.6121
Part 3: Find the measure of angle A
1. The angles in a triangle add up 180.
m<A+m<B+m<C=180
m<A+64.8673 + 43.6121 =180
Measure of angle A=71.5206
Page 2
Part 1: Find the measure of angle B
The angles in a triangle add up 180.
m<A+m<B+m<C=180.
42+ m<B+83=180
Measure of angle B= 55 degrees
Part 2: Use the law of sines to find the length of side a
[tex]\frac{a}{sin (A)}[/tex] =[tex]\frac{b}{sin (B)}[/tex]=[tex]\frac{c}{sin(C)}[/tex]
Length of side a = [tex]\frac{b sin(A)}{sin (B)}[/tex] =[tex]\frac{175 sin(42)}{sin (55)}[/tex]
The length of side a: 142.95
Part 3: Use any method to find the length of side c.
Method= brainpower
aka law of sines:
[tex]c=\frac{a sin (C)}{sin A}[/tex] = [tex]\frac{142.95sin(83)}{sin(42)}[/tex]
c= 212.043
The length of side c: 212.043
Which of the following relations is a function?
a{(1, 3), (2, 3), (4,3), (9,3)}
b{(1, 2), (1, 3), (1, 4), (1,5)}
c{(5, 4), (-6, 5), (4, 5), (4, 0)}
d{(6,-1), (1,4), (2, 3), (6, 1)}
Answer:
a{(1, 3), (2, 3), (4,3), (9,3)}
Step-by-step explanation:
For the relation to be a function, each x can only go to 1 y
a{(1, 3), (2, 3), (4,3), (9,3)}
function
b{(1, 2), (1, 3), (1, 4), (1,5)}
x=1 goes to 4 different y's so not a function
c{(5, 4), (-6, 5), (4, 5), (4, 0)}
x=4 goes to 2 different y's so not a function
d{(6,-1), (1,4), (2, 3), (6, 1)}
x = 6 goes to 2 different y's so not a function
Kira looked through online census information to determine the average number of people living in the homes in her city. What is true about Kira’s data collection?
Kira used an observational study where the data is qualitative.
Kira used an observational study where the data is quantitative.
Kira used published data that is qualitative.
Kira used published data that is quantitative.
The published data refers to the government census info being published online. She did not do an observational study because she didn't go to each household herself (rather let the census workers do that task).
The data is quantitative because she is looking at the number of people living in homes in her city. Quantitative data is simply dealing with quantities or numbers. Contrast this with qualitative data that talks about something like color choice.
Answer:
D: Kira used published data that is quantitative.
Step-by-step explanation:
edg2020
Quantitative means regarding numbers and facts. How many people live in homes in her city is a factual number that is quantitative data. What color shirt they are all wearing is qualitative.. Its not an observational study at all either, so A and B are false
An auto parts shop carries an oil filter for trucks. The annual demand for the oil filter is roughly 1200 units. The ordering cost per order for the auto parts shop is $80; the holding cost of carrying 1 unit is $1.2 per year. The shop has 360 working days per year. The lead time is usually 12 working days. Determine the annual total relevant, including ordering and carrying, cost._______
a) 240
b) 80
c) 480
d) 300
e) None of the above.
Answer:
Total annual inventory cost = $480
c) 480
Step-by-step explanation:
given data
annual demand for the oil filter = 1200 units
ordering cost per order S = $80
holding cost of carrying 1 unit = $1.2 per year
lead time = 12 working days
number of working days = 360 days
solution
we get here economic order quantity that is express as
economic order quantity = [tex]\sqrt{\frac{2DS}{H}}[/tex] ...............1
here D is annual demand and S is ordering cost and H is per unit cost
so put here value and we get
EOQ = [tex]\sqrt{\frac{2\times 1200 \times 80}{1.2}}[/tex]
EOQ = 400 units
and
Annual ordering cost = annual demand × ordering cost ÷ order size .........2
and here
No orders (Q) = annual demand ÷ order size ...........3
Q = 1200 ÷ 400
Q = 3 orders
so
Annual ordering cost = ordering cost × number of order ................4
put here value
Annual ordering cost = 80 × 3
Annual ordering cost = $240
and
Annual carrying cost = average inventory × per unit cost ..........5
and
average inventory = EOQ ÷ 2 ...........6
Annual carrying cost = (EOQ × H) ÷ 2
put here value and we get
Annual carrying cost = 400 × 1.2 ÷ 2
Annual carrying cost = $240
and
so here Total annual inventory cost = Annual ordering cost + Annual carrying cost .........................7
Total annual inventory cost = $240 + $240)
Total annual inventory cost = $480
given that f(x)=x^-1, g(x)=2x+8 find (g-f)(10)
Hey there! :)
Answer:
(g-f)(10) = 279/10.
Step-by-step explanation:
Given:
[tex]f(x) = x^{-1}[/tex]
and
[tex]g(x) = 2x + 8[/tex]
Begin by solving for (g-f) by subtracting f(x) from g(x):
[tex](g-f)(x) = 2x + 8 - x^{-1}[/tex]
Substitute in 10 for x in the equation to solve this problem:
[tex](g-f)(10) = 2(10) + 8 - 10^{-1}[/tex]
Simplify:
[tex](g-f)(10) = 20 + 8 - \frac{1}{10}[/tex]
Create a common denominator to simplify further:
[tex](g-f)(10) = \frac{200}{10}+ \frac{80}{10} - \frac{1}{10}[/tex]
[tex](g-f)(10) = \frac{279}{10}[/tex]
Therefore:
(g-f)(10) = 279/10.
From a group of graduate students including 25 men and 22 women, 37 are chosen to participate in a presentation. What is the probability that exactly 19 men and 18 women are chosen
Answer:
25.02% probability that exactly 19 men and 18 women are chosen
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
19 men, from a set of 25
18 women, from a set of 22
[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]
Total outcomes:
37 people from a set of 25 + 22 = 47. So
[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]
25.02% probability that exactly 19 men and 18 women are chosen
The equation x2 − 6x − 27 = 0 when solved is:
Answer:
-3 , 9
Step-by-step explanation:
Sum = - 6
Product = -27
Factors = 3, -9
x² - 6x-27 = 0
x² + 3x - 9x - 9*3 = 0
x(x + 3) - 9(x + 3) = 0
(x + 3) (x - 9) = 0
x +3 = 0 ; x - 9 = 0
x = - 3 ; x = 9
Solution: x = -3 , 9