The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].
We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].
[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:
[tex]x^{2} +y^{2} -2x+1-9=0[/tex]
[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]
[tex](x-1)^{2}+y^{2}[/tex]-9=0
[tex](x-1)^{2} +y^{2} =9[/tex]
[tex](x-1)^{2}+y^{2} =3^{2}[/tex]
Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.
From the comparison of both the equations we get that radius is 3 units.
From the equation point will be (1,0). It is on the x axis.
Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].
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Answer: 1,2,5 on edge
Step-by-step explanation:
see above ans for work
Line JM intersects line GK at point N.
Horizontal line G K intersects vertical line J M at point N, forming a right angle. A line extends from point N to L, down and to the right.
Which statements are true about the figure? Select two options.
Angle GNJ is complementary to Angle JNK.
Angle MNL is complementary to Angle KNL.
Angle MNG is complementary to Angle GNJ.
Angle KNJ is supplementary to Angle MNL.
Angle GNM is supplementary to Angle JNK.
The statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK. Option B and E
How to determine the statements
Ray NL creates two angles in the lower right quadrant.
The two angles created form a total of 90°, so the two angles formed are complementary. The relation is given as;
∠MNL + ∠KNL = ∠MNK = 90°
Hence ∠MNL and ∠KNL are complementary
∠GNM and ∠JNK are both right angles (and also vertical angles). They sum up to180°. They can be said to be supplementary.
∠GNM and ∠JNK are supplementary
Thus, the statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK
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Find the value of x.
Round to the nearest tenth.
A
X
29
B
50
26
C
x = [?]°
Answer:
Below
Step-by-step explanation:
Using the given law of cosines c = 26 a = 50 b = 29
and cos c is cos x
26^2 = 50^2 + 29^2 - 2(50)(29) cos x
-2665 = -2900 cos x
cos x = 2665/2900
x = arc cos ( 2665/2900) = 23.2°
plesee help me do I need it under 25min and don't answer if you don't know or else u will be reported thank you (◔‿◔)
Answer:
l = 2.25 cm
Step-by-step explanation:
given l is inversely proportional to w² then the equation relating them is
l = [tex]\frac{k}{w^2}[/tex] ← k is the constant of proportion
(i)
to find k use the condition w = 1.5 , l = 16 , then
16 = [tex]\frac{k}{1.5^2}[/tex] = [tex]\frac{k}{2.25}[/tex] ( multiply both sides by 2.25 )
36 = k
l = [tex]\frac{36}{w^2}[/tex] ← equation of proportion
(ii)
when w = 4 , then
l = [tex]\frac{36}{4^2}[/tex] = [tex]\frac{36}{16}[/tex] = 2.25 cm
Need help with this!!
Answer:
below
Step-by-step explanation:
1) slope = rise / run
2 coordinates are (-4, 0), (0, 2).
2 - 0 = 2
0 -- 4 = 4
2 / 4 = 1/2 so the slope is 0.5 or ½
2) it crosses the y axis at the average of the origin and 4.
4 + 0 = 4 / 2 = 2 so y intercept is 2.
3) in y= mx + b form
f(x) = ½x + 2, or, f(x) = 0.5x + 2
Answer part ABCDE
B options is Z , T , chi-square, F
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the test statistic?The test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the number of hours.For this clinical trial (study), we should use a t-test and the null and alternative hypotheses would be given by:
H₀: μ = 7
H₀: μ ≠ 7
Next, we would calculate the t-test as follows:
[tex]t=\frac{7.08\;-\;7}{\frac{0.25}{\sqrt{14} } }\\\\t=\frac{0.08}{\frac{0.25}{3.7417 } }[/tex]
t = 0.08/0.0668
t = 1.198.
For the p-value, we have:
P-value = P(t < 1.198)
P-value = 0.1262.
Therefore, the p-value (0.1262) is greater than α = 0.10. Based on this, we should fail to reject the null hypothesis.
In conclusion, yes the mean discharge differs from 7 fluid ounces.
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Two discs are randomly taken without replacement from a bag containing 3 red discs and 2 blue discs. What is the probability of taking 2 red discs ?
Answer:
3/10
Step-by-step explanation:
There are totally 5 disks. On the first pick, there are 3 red discs. So
P(red disc on first pick ) = 3/5
Assuming that a red disc has been picked the first time, there will be 2 red discs and 2 blue discs so
(P red disc on second pick given red disc on first pick) = 2/4
P(red disc on both picks) = 3/5 x 2/4 = 3/10
Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is a
college graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)
(A) 32.6%
B 67.4%
64.0%
36.0%
The correct option is B) 67.4%
What is the z- score table?A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.
Given here, P(probability that a worker is a college graduate) = 32%
= 0.32
q (probability that a worker is not a college graduate) is 1-0.32 = 0.68
now μ(mean) = n×p
= 50×0.32
= 16
Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]
σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]
σ = 3.2985
now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)
= P(z<0.45)
= 0.674 [using z table]
= 67.4%
Hence option 2 is the correct answer
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The net of a pyramid is shown below. 4in 4in 4in 4in 8in. The surface area of the solid is __ square inches.
Answer:
80 in.²
Step-by-step explanation:
The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.
Square: area = s²
Square: side = 4 in.
Triangular side: area = bh/2
Triangular side: base = 4 in.; height = 8 in.
Area of the base: s² = (4 in.)² = 16 in.²
Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²
Surface area = 16 in.² + 64 in.² = 80 in.²
Find x(will give brainlest)
The data given to the right includes data from candies, and of them are red. The company that makes the candy claims that % of its candies are red. Use the sample data to construct a % confidence interval estimate of the percentage of red candies. What do you conclude about the claim of %?
Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:
[tex]n = 39, \pi = \frac{8}{39} = 0.2051[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.3318[/tex]As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
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2.) A shop sells oranges at 6 for N100. A trader sells the same kind of oranges at 8 for N120.
Which price is cheaper, by how much per orange?
The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.
How is the cheaper price determined?The cheaper price can be computed by finding out the price per unit.
Data and Calculations:Price of Set Unit Price
Sale of 6 oranges N100 N16.67 (N100/6)
Sale of 8 oranges N120 N15.00 (N120/8)
Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.
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Form a polynomial
Degree: 4
Zeros: -1, 2, & 1-2i
Answer:
(x+1)(x-2)(x-1)(x-1+2¡) multiply all together
Step-by-step explanation:
(x+1)(x-2)(x-1)(x-1+2¡)
multiply all together u have your answer
Target Costing
Instant Image Inc. manufactures color laser printers. Model J20 presently sells for $460 and has a product cost of $230, as follows:
Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
It is estimated that the competitive selling price for color laser printers of this type will drop to $400 next year. Instant Image has established a target cost to maintain its historical markup percentage on product cost. Engineers have provided the following cost-reduction ideas:
Purchase a plastic printer cover with snap-on assembly, rather than with screws. This will reduce the amount of direct labor by 15 minutes per unit.
Add an inspection step that will add six minutes per unit of direct labor but reduce the materials cost by $20 per unit.
Decrease the cycle time of the injection molding machine from four minutes to three minutes per part. Forty percent of the direct labor and 48% of the factory overhead are related to running injection molding machines.
The direct labor rate is $30 per hour.
a. Determine the target cost for Model J20, assuming that the historical markup on product cost and selling price are maintained.
$fill in the blank 1
per unit
b. Determine the required cost reduction.
$fill in the blank 2
per unit
c. Evaluate the three engineering improvements together to determine if the required cost reduction (drift) can be achieved. Do not round interim calculations but round your final answers to two decimal places.
1. Direct labor reduction $fill in the blank 3
per unit
2. Additional inspection $fill in the blank 4
per unit
3. Injection molding productivity improvement $fill in the blank 5
per unit
Total savings $fill in the blank 6
per unit
a) The target cost for Model J20, assuming that the historical markup on product cost and selling price is maintained, is $200 per unit.
b) The required cost reduction per unit is $30 per unit ($230 - $200).
c) An evaluation of the three engineering improvements together to determine if the required cost reduction (drift) can be achieved as follows:
While the calculated cost reduction, including direct materials, is $25, the required reduction to achieve the target markup cost is $30.
Thus, the expected target cost reduction does not add up with the calculated cost reduction, envisaged by the engineers.
Data and Calculations:Model J20 Selling price per unit = $460
Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
Direct labor rate = $30 per hour
Direct labor rate per minute = $0.50 ($30/60)
Direct labor hours per unit = 1¹/₃ hours ($40/$30) or 80 minutes
Direct labor hours per unit reduction:Normal direct labor time = 80 minutes
Plastic printer cover = -15 minutes
Total new direct labor time = 65 minutes
Direct labor rate per unit = $32.50 ($0.5 x 65)
Additional inspection time = 6 minutes
Injection molding machine = 1 minute
Direct materials cost = $155 ($175 - $20)
Historical markup = 200% ($460/$230 x 100)
Target cost based on historical markup = $200 ($400 x 100/200)
Required cost reduction per unit is $30 per unit ($230 - $200)
1. Direct labor reduction of $7.50 per unit ($40 - $32.50)
2. Additional inspection $3 per unit (6 x $0.50)
3. Injection molding productivity improvement $0.50 per unit
4. Material cost reduction = $20
Total savings are $25 per unit ($7.50 - $3 + $0.50 + $20).
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cual es el valor de v-15=-2
please help! just need answers for a and b, please!!!!
The answers are :
a)
A = (0, 1)B = (-1, 0)C = (1, 0)D = (-0.5, 0)b)
E = (-2, -3)Let's find point A by using g(x). A is clearly the y-intercept so take x = 0.
g(0) = 2(0) + 1g(0) = 1A = (0, 1)Points B and C can be found using f(x). As they are the x-intercepts, take y = 0.
0 = 1 - x²x² = 1x = ±1As B lies to the left of the y-axis, its x-coordinate is negative.
B = (-1, 0)As C lies to the right of the y-axis, its x-coordinate is positive.
C = (1, 0)Point D can be found using g(x). D is clearly the x-intercept so take y = 0.
0 = 2x + 12x = -1x = -1/2 = -0.5D = (-0.5, 0)Point E lies at the intersection of f(x) and g(x). So they have to be equated.
f(x) = g(x)1 - x² = 2x + 1x² + 2x = 0x (x + 2) = 0x = -2g(-2) = 2(-2) + 1g(-2) = -4 + 1g(-2) = -3E = (-2, -3)Answer:
see explanation
Step-by-step explanation:
(a)
A lies on the y- axis with x- coordinate of zero
substitute x = 0 into either of f(x) or g(x) for y- coordinate
g(0) = 2(0) + 1 = 0 + 1 = 1
then A (0, 1 )
---------------------
B and C lie on the x- axis with y- coordinate of zero
let f(x) = 0 and solve for x , that is
1 - x² = 0 , then
x² = 1 ( take square root of both sides )
x = ± [tex]\sqrt{1}[/tex] = ± 1
then B (- 1, 0 ) and C (1, 0 )
--------------------------------------
D is the point on the x- axis where g(x) crosses
let g(x) = 0 and solve for x
2x + 1 = 0 ( subtract 1 from both sides )
2x = - 1 ( divide both sides by 2 )
x = - [tex]\frac{1}{2}[/tex]
then D (- [tex]\frac{1}{2}[/tex] , 0 )
-----------------------------
(b)
E is the point of intersection of f(x) and g(x) so equate them, that is
2x + 1 = 1 - x² ( subtract 1 - x² from both sides )
x² + 2x = 0 ← factor out x from each term
x(x + 2) = 0
equate each factor to zero and solve for x
x = 0 ← x- coordinate of A
x + 2 = 0 ⇒ x = - 2 ← x- coordinate of E
substitute x = - 2 into g(x) for corresponding y- coordinate
g(- 2) = 2(- 2) + 1 = - 4 + 1 = - 3
then E (- 2, - 3 )
La dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once. Find the following probability. The number on the upward face is not 7
Answer:
11/12
Step-by-step explanation:
no of sample space=12
number of 7 to occur is 1/12
number of not 7:
since the total probability is 1
so 1-1/12=11/12
Consider the following figure:
Answer:
angle <B = 76
Step-by-step explanation:
The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.
We can write the following equation with this information to find the value of angle <B
<B + 71 = 147 subtract 71 from both sides
<B = 76
3. Jessie has 25 small
boxes to put his rock
collection in. He sorts 20
rocks into each box.
How many rocks does
he have in his collection?
Answer:
500 rocks
Step-by-step explanation:
25*20 = 500
9) If m/1 = 45° and 21 and 22 are complementary angles. Find m22.
❄ Hi there,
keeping in mind that the sum of complementary angles is 90°,
set up an equation, letting [tex]\angle2[/tex] be x –
[tex]\triangleright \ \sf{\angle1+x=90}[/tex] {and we know that [tex]\boxed{\angle1=45}[/tex]}
[tex]\triangleright \ \sf{45+x=90}[/tex]
[tex]\triangleright \ \sf{x=90-45}[/tex]
[tex]\triangleright \ \sf{x=45}[/tex]
[tex]\triangleright \ \sf{\angle2=45\textdegree}[/tex]
__________
Keeping in mind that a right angle is 90°,
set up an equation, letting [tex]\angle1[/tex] be x:
[tex]\triangleright \ \sf{x+\angle2=90}[/tex] {and we know that [tex]\boxed{\angle2=63}[/tex]}
[tex]\triangleright \ \sf{x+63=90}[/tex]
[tex]\triangleright \ \sf{x=27}[/tex]
[tex]\triangleright \ \sf{\angle1=47\textdegree}[/tex]
❄
HELP ME ,HELP ME ,HELP ME PLEASE.IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
a) 88 degrees
The measure of the central angle is the same as the measure of the arc it intercepts.b) 44 degrees
Angle FEG is inscribed in arc FG, and thus has half the measure of arc FG.area of regular polygon?
[tex]\huge\purple{Hi!}[/tex]
The area of a regular polygon is one-half the product of its apothem and its perimeter.
find the square (4x-6y^3)^2
|x - 1| > 4 is equivalent to which of the following?
a. -3 < x < 5
b. x > 5
c. x > 5 or x < −3
d. x < 5
*show your work*
Answer:
C. x > 5 or x < - 3
Step-by-step explanation:
|x - 1| > 4Step 1:
x - 1 > 4
x > 4 + 1
x > 5
Step 2:
x - 1 < -4
x < -4 + 1
x < -3
HP: {x > 5 or x < -3} (c)
on a unit circle, the terminal point of 0 is (1/2, square root 3/2). what is sin 0?
A. square root 3/2
B. 1/2
C. square root 3/3
D. square root 3
Answer: A
Step-by-step explanation:
[tex]\sin \theta[/tex] is equal to the y-coordinate.
Answer: square root 3/2
Step-by-step explanation:
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1
Tthe inequality that describes this graph is y ≤ 1/3x - 4/3
How to determine the linear inequality represented by the graph?The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(0, -1.3) and (3, -0.3)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-0.3 + 1.3)/(3 - 0)
Evaluate
m = 1/3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1/3(x - 0) - 1.3
Evaluate
y = 1/3x - 4/3
From the graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≤
Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3
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If the average score is 122 with a standard deviation of 35,
what percentage of students scored below 67? Answers are
rounded to the nearest whole percent.
O a.) 90%
O b.) 6%
O c.) 10%
O d.) 94%
Answer:
6%
Step-by-step explanation:
Got it right on the test.
Describe how to translate the graph of g(x) = in x into the graph of f(x) = in (-x) +5
we just need to reflect the graph of g(x) around the y-axis, and then shift the whole graph 5 units upwards.
How to translate the graph?Here we have two functions:
[tex]g(x) = ln(x)\\\\f(x) = ln(-x) + 5[/tex]
Ok, let's start with g(x), which graph we know. If we reflect it around the y-axis, then the new function will be:
f(x) = g(-x)
If now we shift it up 5 units, then we get:
f(x) = g(-x) + 5
Replacing g(x):
f(x) = ln(-x) + 5
Which is our function
So we just need to reflect the graph of g(x) around the y-axis, and then move the whole graph 5 units upwards.
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phoebe needs to use 3/4 cups of sugar to make one batch of cookies. how many batches can she make with 12 cups of sugar?
Answer:
16 batches
Step-by-step explanation:
we can divide 12 by 3/4 or 0.75: 12/0.75 = 16
7x+28=7(x+4) how many solutions
The equation 7x + 28 = 7(x + 4) has infinite many solutions
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the number of solutions?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
7x + 28 = 7(x + 4)
Open the bracket
7x + 28 = 7x + 28
Subtract 7x from both sides of the equation
28 = 28
Subtract 28 from both sides of the equation
0 = 0
The above equation is true, because both sides of the equation are the same
This means that the equation has infinite many solutions
Hence, the equation 7x + 28 = 7(x + 4) has infinite many solutions
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HELPPPP PLSSSSSSSS !?!?????
Answer:
(9/3) * 4 * 2
Step-by-step explanation:
:DDDD
Answer:
2(9 / 3) * 4
Step-by-step explanation:
this is one of the many ways to solve this
9/3 is 3
2 times 3 is 6
6 times 4 is 24
therefore 2(9 / 3) * 4 is 24