Answer:
Diameter is 10 units
Step-by-step explanation:
Convert standard form to general form by completing the square:
[tex]x^2+y^2-8x+2y-8=0[/tex]
[tex]x^2-8x+y^2+2y-8=0[/tex]
[tex]x^2-8x+y^2+2y=8[/tex]
[tex]x^2-8x+16+y^2+2y+1=8+16+1[/tex]
[tex](x-4)^2+(y+1)^2=25[/tex]
[tex](x-4)^2+(y+1)^2=5^2[/tex]
So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.
Answer:
50
Step-by-step explanation:
x2 + y2 - 8x + 2y - 8 = 0
first we find the radius with the equation.
write the equation in standard form.
x2 + y2 - 8x + 2y - 8 = 0
(x-4)^2 + (y+1)^2 = 25
(x-h)² + (y-k)² = r²
this means 25 is the radius and the diameter is two times the radius so,
25 x 2 = 50
Homework:Assignment 3 Question 20 Score: 0 of 1 point A vending machine dispenses coffee into -ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of ounce. You can allow the cup to overfill % of the time. What amount should you set as the mean amount of coffee to be dispensed?
Answer:
19.92
Step-by-step explanation:
To overfill 5% of the time ;
The Zscore (value) to the left of (1 - 0.05) = 0.95 is 1.645
Using this Zscore value with the Zscore formula :
Zscore = (x - μ) / σ
σ = 0.05 ; x = 20 ounce
Substituting into the Zscore formula :
1.645 = (20 - μ) / 0.05
1.645*0.05 = 20 - μ
0.08225 = 20 - μ
μ = 20 - 0.08225
μ = 19.91775
μ = 19.92
A supervisor records the repair cost for 22 randomly selected VCRs. A sample mean of $75.50 and standard deviation of $18.07 are subsequently computed. Determine the 99% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The t value for 99% CI for 21 df is 2.831.
The critical value that should be used in constructing the confidence interval is (64.593, 86.407).
Step-by-step explanation:
Now the sample size is less than 30 and also population standard deviation is not known.
Then we will use t distribution to find CI
t value for 99% CI for 21 df is TINV(0.01,21)=2.831
The margin of error is [tex]E=t\times\frac{s}{\sqrt{n}}\\\\=2.831\times\frac{18.07}{\sqrt{22}}\\\\=10.907[/tex]
Hence CI is[tex]CI=\overline{x} \pm E\\\\ =75.50 \pm 10.907\\\\=(64.593,86.407 )[/tex]
Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?
HELP PLS
Answer:
(x-4)^2=-8(y-3)
This is a parabola.
Step-by-step explanation:
Since the directrix is horizontal, the parabola faces up or down. Since the focus is below the directix it faces down. This means p will be negative in the equation (x-h)^2=4p(y-k).
p also tells us the half the distance between the focus and the directrix. The distance between 1 and 5 is 4, so p=-2.
The vertex is half way point between focus (4,1) and directrix y=5.
So the vertex is (4, [1+5]/2 )= (4 ,6/2)=(4,3). This is (h,k) in our equation.
(x-h)^2=4p(y-k)
(x-4)^2=4×-2(y-3)
(x-4)^2=-8(y-3)
Find y on this triangle
Answer:
5√3 / 2
Step-by-step explanation:
tan 30 = ( 5 / 2 ) / y
1 / √3 = 5 / 2y
2y = 5√3
y = 5√3 / 2
A party rental company has chairs and tables for rent. The total cost to rent 6 chairs and 5 tables is $63. The total cost to rent 2 chairs and 3 tables is $35. What is the cost to rent each chair and each table?
Answer:
1.75dollars - the value of each chair, 10.5 dollars - the value of each table
Step-by-step explanation:
The value of chair is x, the value of table is y. Then 6chairs cost 6x, 5 tables cost 5y. 6x+5y= 63
Then the value of 2 chairs is 2x, for 3 tables it is equal to 3y. 2x+3y=35
We have the system of equations6x+5y= 63 and 2x+3y=35
Multiply the second one by -3
-3(2x+3y)= -3*35
-6x-9y= -105.
Plus the first equation and the second one multiplied by -3 (the right side to the right side and the left side to the left side with sign= between them)
6x+5y-6x-9y= 63-105
-4y= -42
y=10.5 dollars - the value of a table
6x+5*10.5=63
6x= 63-52.5
6x=10.5
x=1.75dollars - the value of a chair
if 2 shirts cost 18.80, how much would 9 shirt cost.
Answer:
84.60
Step-by-step explanation:
We can write a ratio to solve
18.80 x
--------- = --------------
2 shirts 9 shirts
Using cross products
18.80 *9 = 2x
169.2 =2x
Divide each side by 2
169.2/2 =2x/2
84.60 =x
There are 8 midsize cars and 15 compact cars and 6 will be selected. What is the probability of selecting all midsize cars?
Answer:
Assuming order does not matter, the probability of selecting all midsize cars is 0.000277373, or [tex]\frac{4}{14421}[/tex].
Step-by-step explanation:
First, we must find the n(Total arrangements of selections)=(8+15)C6
n(Total arrangements of selections)=23C6
n(Total arrangements of selections)=100,947
Second, we must find the n(Arrangements where all are midsize cars)=8C6
n(Arrangements where all are midsize cars)=28
To find the probability of selecting all midsize cars, we divide the n(Arrangements where all are midsize cars) by the n(Total arrangements of selections):
P(All midsize cars)= [tex]\frac{28}{100,947}[/tex]
P(All midsize cars)= [tex]\frac{4}{14421}[/tex]=0.000277373.
Help with this Area question
Step 1: Find the area of the rectangle
A = base x height
A = 39 x 20
A = 780
Step 2: Find the area of the semi-circles
---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.
A = pi x r^2
A = pi x 10^2
A = 100pi = 314
Step 3: Find the area of the figure
Area = area of the rectangle - area of the semi-circles
A = 780 - 314
A = 466 cm^2
Hope this helps!
Answer:
466 cm^2
Step-by-step explanation:
This one is done basically the same as the other.
Rectangle = 20 x 39
Circle = (3.14) x 10^2
Rectangle = 780
Circle = 314
rectangle - circle
780 - 314 = 466
PLS HELP I DONT KNOW THIS ONE
Answer:
x+3
---------------
(x-3)(x-2)(x-4)
Step-by-step explanation:
x+4 x^2 -16
---------------÷ -------------
x^2 - 5x+6 x+3
Copy dot flip
x+4 x+3
--------------- * -------------
x^2 - 5x+6 x^2 -16
Factor
x+4 x+3
--------------- * -------------
(x-3)(x-2) (x-4)(x+4)
Cancel like terms
1 x+3
--------------- * -------------
(x-3)(x-2) (x-4)1
x+3
--------------- x cannot equal 3,2,4 -4
(x-3)(x-2)(x-4)
Find the missing side length in the image below
Answer:
87.5
Step-by-step explanation:
Let the missing side be x.
28 / 35 = x / 50
4 / 7 = x / 50
4 ( x ) = 7 ( 50 )
4x = 350
x = 350 / 4
x = 87.5
plz help and explain this :)
Answer:
y=3x+6
Step-by-step explanation:
in a line graph, y=mx+c
m refers to gradient, c refers to y-intercept.
since lines are parallel, both lines have the same gradient.
the line intersects (1,9)
x=1,y=9
9=3(1)+c
c=6
so y=3x+6
Answer:
y = 3x+6
Step-by-step explanation:
Parallel lines have the same slope
y = 3x+2 is in slope intercept form (y=mx+b where m is the slope and b is the y intercept)
So the slope is 3
Y = 3x+2
Using the point given substitute into the equation and solve for b
9 = 3(1)+b
9 =3+b
9-3 =b
6=b
y = 3x+6
A newsstand spends $600 a month on rent and electricity, and it spends $2
for each magazine that it sells. The newsstand charges $5 for each
magazine. If n is the number of magazines, which equation represents the
profit function of the newsstand?
O A. p = 2n + 600
B. p = 3n-600
O c. p = 600n + 3
O D. p = 5n-600
Answer: B. p = 3n-600
Step-by-step explanation:
Cost = 2n + 600Earned = 5nProfit(p) = Earned - Cost
p = 5n - (2n + 600) = 5n - 2n - 600 = 3n - 600
The equation representing the profit function of the newsstand is
p = 3n - 600
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The revenue generated by selling n magazines is 5n dollars.
The cost of selling n magazines is the sum of the cost of purchasing n magazines and the fixed cost of rent and electricity, which is $2n + $600.
Now,
The profit function can be represented by:
p = revenue - cost
= 5n - (2n + 600)
= 3n - 600
Thus,
The equation representing the profit function of the newsstand is
p = 3n - 600
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Assume 2 in every 3000 students at the local community college have to quit due to serious health issues. An insurance company offers them $12000 policy for $40a year. What is the amount the insurance company should expect to make on average on every student that pays?
The amount the insurance company should expect to make on average on every student that pays is $
Answer:
$32
Step-by-step explanation:
Multiply $40*3000 students. Subtract 2 students that might receive a $12000 policy each. Divide by 3000 students to find average payout.
Help ! Please and thanks
Choose the expression that represents “divide 0.04 by n.”
Answer:
.04/n=4/100n or 4÷100n
Solve x∕3 < 5 Question 5 options: A) x ≥ 15 B) x > 15 C) x < 15 D) x ≤ 15
Answer:
C
Step-by-step explanation:
Given
[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )
x < 15 → C
Please help explanation if possible
Answer:
10% gain
Step-by-step explanation:
[P2-P1]/P1
(33-30)/30=3/30=.1 or 10% gain.
Answer:
10%
Step-by-step explanation:
→ Minus the new share from the old one
33 - 30 = 3
→ Divide the answer by the original price
3 ÷ 30 = 0.1
→ Multiply the answer by 100
0.1 × 100 = 10%
true or false?
help me please
Answer:
False
Step-by-step explanation:
The point that is equidistant from the vertices of a triangle is called the circumcenter.
9514 1404 393
Answer:
False
Step-by-step explanation:
The incenter is the center of the inscribed circle, which is tangent to all of the sides of the triangle. The incenter is equidistant from the sides, not the vertices.
_____
Additional comment
The circumcenter is the center of the circumscribing circle. Each of the vertices of the triangle is on the circumcircle, so the circumcenter is equidistant from the vertices.
The incenter is located at the intersection point of the angle bisectors. The circumcenter is located at the intersection point of the perpendicular bisectors of the sides.
which fraction has a greater value than 0.4
Answer:
0.4 as a fraction is 2/5, so as long as the fraction is greater than 2/5 then you are good
5/9 || 0.55
Step-by-step explanation:
i need some help with this question. it says find x
Answer:
x = 9.8
Step-by-step explanation:
Please see attached photo for diagram.
We'll begin by calculating the value of y. This can be obtained as follow:
Angle θ = 45
Opposite = 6
Hypothenus = y
Sine θ = Opposite /Hypothenus
Sine 45 = 6/y
0.7071 = 6/y
Cross multiply
y × 0.7071 = 6
Divide both side by 0.7071
y = 6 / 0.7071
y = 8.5
Finally, we shall determine the value of x. This can be obtained as follow:
Angle θ = 60
Opposite = 8.5
Hypothenus = x
Sine θ = Opposite /Hypothenus
Sine 60 = 8.5 / x
Cross multiply
x Sine 60 = 8.5
Divide both side by sine 60
x = 8.5 / sine 60
x = 8.5 / 0.8660
x = 9.8
Which polynomial function is best represented by the graph?
ƒ(x) = –x(x – 1)4
ƒ(x) = x2(x + 1)3
ƒ(x) = x2(x – 1)3
ƒ(x) = x(x – 1)4
Answer: ƒ(x) = x2(x – 1)3
Aliana is supposed to get back to a customer with an answer about a refund by the end of the day, but she won't have all the approvals she needs to process the refund by that time. What should she do? O a) Call the customer only when she has processed the refund Ob Tell the customer that she should have called about the problem earlier Oc) Explain to the customer that her bosses are the ones that are taking forever O di Apologize to the customer and say that she will call her tomorrow with an update
Answer:
"ob" is the answer of this long question
Answer:
D
Step-by-step explanation:
reason:
not A cuz the customer has to wait for a long time, and she feel waste of time
not B cus it's the store's responsiblity, not customer. if she said that, the customer would feel be disrespected. and i swear she never comes back that store.
C if she said that, customer also feel waste of time when she has to talk with Aliana who cant solve her problem
and the boss will think Ali couldnt have no problem-solving skills
ZDAC = ZBAD.
What is the length of BD?
Round to one decimal place.
Answer:
BD = 4.1
Step-by-step explanation:
DA is an angle bisector which also divides the opposite side of the angle it bisects in a way that it is proportional to tye other two sides.
By implication, we would have the following:
AB/BD = AC/DC
AB = 5.3
AC = 5.5
DC = 4.3
BD = ?
Plug in the values
5.3/BD = 5.5/4.3
Cross multiply
BD*5.5 = 4.3*5.3
BD*5.5 = 22.79
Divide both sides by 5.5
BD = 22.79/5.5
BD = 4.1 (to 1 decimal place)
The measure of AD is v10. Find the AREA of the parallelogram below.
Leave answers in exact form (no decimals). Simplify all radicals and
rationalize the denominator. (You may write roots in the following ways:
2root5 or 2r5)
WILL GIVE BRAINLIEST
Math geometry worth 30 points
What is the value of x?
Answer:
x = 3
Step-by-step explanation:
First, use trigonometric function to find RT.
θ = 60°
Opposite = 2√3
Hypotenuse = RT
Apply SOH:
Sin θ = Opp/Hyp
Plug in the values
Sin 60° = 2√3/RT
RT*Sin 60° = 2√3
Divide both sides by Sin 60°
RT = 2√3/sin 60°
RT = 2√3 × √3/2 (sin 60° = √3/2)
RT = (2√3 × √3)/2
RT = (2 × 3)/2
RT = 3
✔️Find x
θ = 45°
Opposite = x
Adjacent = 3
Apply TOA:
Tan θ = Opp/Adj
Substitute
Tan 45° = x/3
3 × Tan 45° = x
3 × 1 = x (tan 45° = 1)
3 = x
x = 3
Place the labels in the chart
If you can draw this out for me or describe were they are that will be very helpful:)
Answer:
Check the image
Bạn được một cá nhân thuê làm tư vấn tài chính, anh ta nhận được 2 đề nghị hợp ký đồng làm
việc với thời hạn 5 năm theo 2 sự lựa chọn sau:
- Lựa chọn 1: Lương 3 triệu/năm
- Lựa chọn 2: Lương 1.5 triệu/năm và được thưởng 9 triệu khi kết thúc hợp đồng làm việc.
a. Nếu lãi suất 8% bạn sẽ khuyên anh ta nhận lựa chọn nào?
b. Nếu lãi suất tăng 10% theo bạn có cần phải đổi lựa chọn không?
For the function in the graph, find the values of f(-4), f(-1), and f(1).
Answer:
f(-4) = -1
f(-1) = -4
f(1) = 4
Step-by-step explanation:
We need to find the y value for the x values
f(-4) means find the y value for x= -4
f(-4) = -1
f(-1) = -4
f(1) = 4
The best basketball player
Answer:
c
Step-by-step explanation:
hope it helps!!!!!!!!!!!!!!
A restaurant interest survey of 230 citizens in a town showed that 80 want a new Chili's, 120 want a new Red Lobster, and 20 want both. Determine the probability that:
...
Answer:
2/23
6/23
5/23
Step-by-step explanation:
60 only want chilis
20 wants both
100 only want red lobster
50 want neither
The right solution to the given question is "[tex]\frac{2}{23}[/tex]", "[tex]\frac{6}{23}[/tex]" and "[tex]\frac{5}{23}[/tex]".
According to the question,
[tex]a+b+c+d = 230[/tex][tex]b = 20[/tex][tex]a+b = 80[/tex]By putting the value of "b", we get
[tex]a+20=80[/tex][tex]a = 80-20[/tex]
[tex]a = 60[/tex]
[tex]b + c=120[/tex]By putting the value of "b", we get
[tex]20+c=120[/tex]
[tex]c = 120-20[/tex]
[tex]c = 100[/tex]
[tex]d = 230-60-100-20[/tex]By putting the values of "a", "b", "c" and "d", we get
[tex]d = 50[/tex]
(a)
P(both Chili's and Red lobster),
= [tex]\frac{b}{a+b+c+d}[/tex]
= [tex]\frac{2}{23}[/tex]
(b)
P(only chili's),
= [tex]\frac{a}{a+b+c+d}[/tex]
= [tex]\frac{6}{23}[/tex]
(c)
P(neither),
= [tex]\frac{d}{a+b+c+d}[/tex]
= [tex]\frac{5}{23}[/tex]
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