Suppose that y varies inversely with x, and y= 3 when x = 10.
(a) Write an inverse variation equation that relates x and y.
Equation:
(b) Find y when x = 5
y =
Answer:
y=6
Step-by-step explanation:
the equation that relates x and y is y=30(1÷x)
Rationalise
[tex]{ \frac{1 + \sqrt{3} }{ \sqrt{12} } } [/tex]
Answer:
Step-by-step explanation:
Answer:
[tex]\frac{2\sqrt{3} + 6}{12}[/tex]
Step-by-step explanation:
Simplify the denominator of [tex]\frac{1 + \sqrt{3} }{\sqrt{12} }[/tex] completely.
[tex]=> \frac{1 + \sqrt{3} }{ \sqrt{(4 \times 3)} } = \frac{1 + \sqrt{3} }{\sqrt{4} \times \sqrt{3} } = \frac{1 + \sqrt{3} }{2\sqrt{3} }[/tex]
Now, to rationalise it you need to make the denominator rational.
Multiply & divide [tex]\frac{1 + \sqrt{3} }{2\sqrt{3} }[/tex] by [tex]2\sqrt{3}[/tex].[tex]=> \frac{1 + \sqrt{3} }{2\sqrt{3} } \times \frac{2\sqrt{3} }{2\sqrt{3} }[/tex]
[tex]=> \frac{(1 + \sqrt{3})\times 2\sqrt{3} }{2\sqrt{3} \times 2\sqrt{3} }[/tex]
[tex]=> \frac{2\sqrt{3} + 6 }{12}[/tex]
PLEASE HELP GUYS I’m being timed
The question is the base of the triangle, so we use the formula : b²=c²–a²
——————————————————————
[tex] {b}^{2} = \sqrt{c^{2} - {a}^{2} }[/tex]
[tex] {b}^{2} = \sqrt{ {16}^{2} - {8}^{2} } [/tex]
[tex] {b}^{2} = \sqrt{256 - 64} = \sqrt{192} [/tex]
[tex] \sqrt{192} =8 \sqrt{3} [/tex]
The 7th grade class is going on a trip to Disneyland there are 162 learners and 24 LF's attending the trip one bus can hold 65 people how many buses do they need to order to take everyone to Disneyland
Answer: about 3 buses
Step-by-step explanation: 162+24=186 and 65*3=195 so 3 buses is enough
Hope this helps:)
what is the probability of seeing a sample mean for 21 observations less or equal to the sample mean that we observed
Answer:
[tex]P(x \le 21) = 0.69146[/tex]
Step-by-step explanation:
The missing parameters are:
[tex]n = 64[/tex] --- population
[tex]\mu = 20[/tex] --- population mean
[tex]\sigma = 16[/tex] -- population standard deviation
Required
[tex]P(x \le 21)[/tex]
First, calculate the sample standard deviation
[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]
[tex]\sigma_x = \frac{16}{\sqrt {64}}[/tex]
[tex]\sigma_x = \frac{16}{8}[/tex]
[tex]\sigma_x = 2[/tex]
Next, calculate the sample mean [tex]\bar_x[/tex]
[tex]\bar x = \mu[/tex]
So:
[tex]\bar x = 20[/tex]
So, we have:
[tex]\sigma_x = 2[/tex]
[tex]\bar x = 20[/tex]
[tex]x = 21[/tex]
Calculate the z score
[tex]x = \frac{x - \mu}{\sigma}[/tex]
[tex]x = \frac{21 - 20}{2}[/tex]
[tex]x = \frac{1}{2}[/tex]
[tex]x = 0.50[/tex]
So, we have:
[tex]P(x \le 21) = P(z \le 0.50)[/tex]
From the z table
[tex]P(z \le 0.50) = 0.69146[/tex]
So:
[tex]P(x \le 21) = 0.69146[/tex]
Find the graph of the inequality y+2>-3(x+1)
Answer:
Below.
Step-by-step explanation:
y + 2 > -3(x + 1)
y + 2 > -3x - 3
y > -3x - 5
The graph will be the graph of the line y = -3x - 5 (dotted line), with the area above the line shaded.
Reflect (1,‐4) across the x‐axis what is the reflected ordered pair?
Answer:
(1,4)
Step-by-step explanation:
(1,-4) is over 1 and down negative 4 so reflected over the x-axis(the horizontal one) it would be four up so the answer is (1,4)
Answer: (1,4)
Step-by-step explanation:
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when point P with coordinates (1,-4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (1,4)
1 out of 5 pairs of Henry's shoes no longer fit him. what fraction of his shoe collection still fit ?
Answer:
4/5
Step-by-step explanation:
here ya are. I hope this helps, it's just 1 pair out of the 5 that don't fit. Meaning the 4 out of 5 fit. therefore 4/5
y is directly proportional to the positive square root of x when x = 9, y= 12 find y when x =1/2
Y =k√x
12 = 3k
k = 4
now X = 1\2
y = 4√1/2
y = 2√2
Answer:
y = 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given y is directly proportional to [tex]\sqrt{x}[/tex] then the equation relating them is
y = k[tex]\sqrt{x}[/tex] ← k is the constant of variation
To find k use the condition when x = 9, y = 12
12 = k[tex]\sqrt{9}[/tex] = 3k ( divide both sides by 3 )
4 = k
y = 4[tex]\sqrt{x}[/tex] ← equation of variation
When x = [tex]\frac{1}{2}[/tex] , then
y = 4[tex]\sqrt{\frac{1}{2} }[/tex] = 4 × [tex]\frac{1}{\sqrt{2} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]
y = [tex]\frac{4}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = [tex]\frac{4\sqrt{2} }{2}[/tex] = 2[tex]\sqrt{2}[/tex]
Type the correct answer in the box.
Consider the system of linear equations below.
-3x+4y=24
6x+2y=-18
Answer:
[tex] - 3x + 4y = 24 \\ 3x - 4y = - 24 - - - (a) \\ 6x + 2y = - 18 - - - (b) \\ 2 \times (a) - (b) : \\ = > 0x - 10y = - 30 \\ 10y = 30 \\ y = 3 \\ \\ 3x = - 12 \\ x = - 4 \\ { \boxed{x = - 4}} \: \: \\ { \boxed{y \: = \: 3}}[/tex]
Juan family hang their clothes outside to dry, if they use the dryer, there $400 monthly bill will increase by % wich means it will cost $700
Precision is a measure of how close an answer is to the actual or expected
value.
True or false ?
Answer:
False
Step-by-step explanation:
Precision describes repeatability.
Accuracy describes the closeness of a measurement to the actual value.
So your measurements may be precise but not accurate; for example if you used a faulty measurement system. And of course, you could get accurate results SOME of the time (which describes the exprerience of most researchers).
Errors in precision are usually detected.........eventually, invariably after you have shot your mouth off to your professor.
What is the measure of remote angle, ∠A?
Answer:
40
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
<A = 1/2 (80)
<A = 40
What is the product?
2 3 4
5 9 -1 -7
11 5 -3
Answer:
-1247400
Step-by-step explanation:
See the Image below:) I believe this is what you are looking for.
Pls help me on this due today plssss!!!
Answer:
Step-by-step explanation:
A+B+C+D=360 degree (being one complete turn)
360 degrees
Step-by-step explanation:
because it a venticular angle you one side(180) and the other side (180) given you 360 degrees
Write the following geometric sequence recursively: 10, 100, 1000, 10000.*
Answer:
i think the * is 100000, each number times 10
A man-made lake is stocked with 10,000 fish. This population is expected to decline by an annual rate of 12%
Predict the fish population 5 years after the lake is stocked
Answer:
4000 fish left in lake after 5 years
Step-by-step explanation:
12 x 5 = 60 (60%)
10000 - 60% = 4000
2 Which of the following is true about rhombus LMNO?
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent.
Angle MLO measures 112°. What is the measure of angle MLP?
45°
56°
68°
90°
Step-by-step explanation:
B
Help me PLEASEEEEEEEEEEEEE
Answer:
D. 144
Step-by-step explanation:
Find volume of shipping container:
2 2/3 = 8/3
2 x 1 = 2
8/3 x 2/1 = 16/3
Find volume of cube:
1/3 x 1/3 = 1/9 x 1/3 = 1/27
Find how many boxes fit in container:
16/3 ÷ 1/27
16/3 x 27/1
Simplify:
16/1 x 9/1 = 144/1
Answer: 144
HELP TIMED----AND NO BOTS WITH /BIT
A segment which goes through two points of a circle is a …
Arc
Chord
Diagonal
Radius
Secant
Find the equation of the linear relationship.
Answer:
y = -3x + 150
Step-by-step explanation:
2 points on the graph:
(30, 60) and (40, 30)
Slope:
m=(y2-y1)/(x2-x1)
m=(30 - 60)/(40 - 30)
m= (-30)/10
m= -3
Slope-intercept:
y - y1 = m(x - x1)
y - 60 = -3(x - 30)
y - 60 = -3x + 90
y = -3x + 150
Which answers describe the shape below
Answer:
B. parallelogramStep-by-step explanation:
stay safe, stay healthy and blessed.
thank u
Answer:
a b c d e
Step-by-step explanation:
Plz help me well mark brainliest if correct....??????????????...
Answer:
D). 100
Step-by-step explanation:
The range is the highest number-lowest number in data. 150 is the highest, 50 is the lowest. Therefore, 150-50=100
A company's daily cost c, in hundreds of r dollars, to manufacture n items of a certain product can be modeled by the function c^-1(5)=80, Lording to the model, which of the following is the best interpretation of c ^1(5) = 80, where c^1 is the inverse function of c ?
a) The company's daily cost to manufacture 5 items of the product is $80.
b) The company's daily cost to manufacture 5 items of the product is $8,000.
c) The company's daily cost to manufacture 500 items of the product is $80.
d) The company's daily cost to manufacture 80 items of the product is $5.
e) The company's daily cost to manufacture 80 items of the product is $500.
Answer:
e) The company's daily cost to manufacture 80 items of the product is $500.
Step-by-step explanation:
We have that:
c is the cost in hundreds of dollars to manufacture n items. The input is the number of items, and the output is the cost, in hundreds of dollars.
Inverse function:
In the inverse function, the input and the output are exchanged from the original function, that is, in this situation, the input in the cost, in hundreds of dollars, and the output is the number of manufactured items.
c^-1(5)=80
Input of the inverse function is 5, which is the cost, in hundreds of dollars, that is, $500, to manufacture 800 itens. This means that the correct answer is given by option e.
There is a population of millions of computer chips produced at a factory. The production process is so precious that it is known that the population standard deviation for their mass is 2 milligrams. We want to get a 95% confidence interval for the mass of a single microchip produced here. So we randomly sample 100 microchips. The sample average mass turns out to be 1972 milligrams. They found this by placing them all on a scale at once and finding a mass of 197.2 grams, and then dividing by 100. You don't think they would actually weigh each one individually, do you? That would be super annoying.
Required:
Find a 95% confidence interval for the mass of a microchip produced at this factory.
Answer:
The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{2}{\sqrt{100}} = 0.392[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1972 - 0.392 = 1971.608 milligrams
The upper end of the interval is the sample mean added to M. So it is 1972 + 0.392 = 1972.392 milligrams
The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.
If the surface area of the cone below is 628.32 m², find its volume.
I WILL MARK BRAINLEIST IF CORRECT AND 20 POINTS
Answer:
1586.91 m³
Step-by-step explanation:
From the diagram attached,
Applying,
A = πrl.................. Equation 1
Where A = surface area of the cone, l = slight heigth of the cone, π = pie.
make l the subject of the equation,
l = A/πr.............. Equation 2
From the question,
Given: A = 628.32 m², π = 3.14, r = 8 m
Substitite these values into equation 2
l = 628.32/(3.14×8)
l = 25 m
But,
l² = h²+r².................... Equation 3
Where h = height of the cone.
h = √(l²-r²)
h = √(25²-8²)
h = √(625-64)
h = √(561)
h = 23.69 m
Also Applying,
V = 1/3πr²h
Where V = volume of the cone.
Therefore,
V = (3.14×8²×23.69)/3
V = 1586.91 m³
RUNNING OUT OF POINTS PLEASE!! Find the perimeter and area for the triangle. Be sure to write the formula, and use correct measure.
Answer:
Area = 77ft²
Perimeter = 44 9/20 feets
Step-by-step explanation:
Area of a triangle = 1/2 * base * height
Base = 19 1/4 feets = 77/4 feets
Height = 8 feets
Area = 1/2 * 77/4 * 8
Area = (77 * 8) / 8
Area = 77 feet²
Perimeter of a triangle :
Sum of the sides
Perimeter = a + b + c
Perimeter = 19 1/4 + 10 + 15 1/5
Perimeter = 44 + (1/4 + 1/5)
Perimeter = 44 9/20
Suck please help thanks
Ecuaciones
A: 7=5-×
B: ×-2=-16
C: -8=4.×
D: ×.2=-6
Step-by-step explanation:
A:x=5-7
x=-2
B:x=-16+2
x=-14
l have answered only A and B
Jon Deposits $14,500 into an account paying 5% annual interest compounded quarterly and Sara deposits $16,250 into an account paying 4% annual interest compounded daily who will have more money after 1 year? How much more will that person have? Show and explain all work.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Jon:
Initial investment (PV)= $14,500
Interest rate (i)= 0.05/4= 0.0125
Number of periods (n)= 4 quarters
Sara:
Initial investment (PV)= $16,250
Interest rate (i)= 0.04/365= 0.00011
Number of periods (n)= 365 days
To calculate the Future Value, we need to use the following formula:
FV= PV*(1+ i)^n
Jon:
FV= 14,500*(1.0125^4)
FV= $15,238.71
Sara:
FV= 16,250*(1.00011^365)
FV= $16,915.67
Sara will have $1,676.96 more than Jon.