Identify an equation in point-slope form for the line perpendicular to
y= - 1/3x - 6 that passes through (-1,5).
O A. y + 1 = 3(x - 5)
O B. y + 5 = 1/3(x - 1)
O C. y - 5 = 3(x + 1)
O D. y - 5 = - 1/3(x + 1)
Answer:
hope you get it....sorry for any mistake calculations
I need answers for 1 , 2, 4
Answer:
(3) x ≥ -3
(4) 2.5 gallons
(4) -12x + 36
Step-by-step explanation:
Hey there!
1)
Well its a solid dot meaning it will be equal to.
So we can cross out 1 and 2.
And it's going to the right meaning x is greater than or equal to -3.
(3) x ≥ -3
2)
Well if each milk container has 1 quart then there is 10 quarts.
And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.
(4) 2.5 gallons
4)
16 - 4(3x - 5)
16 - 12x + 20
-12x + 36
(4) -12x + 36
Hope this helps :)
Help!! It’s much appreciated in this time
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
Help ASAP it’s Math I need this rightnow 31 points
Answer:
AC (b)
Step-by-step explanation:
Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)
Answer:
[tex]\boxed{\sf C}[/tex]
Step-by-step explanation:
The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.
[tex]75\%*\sqrt{20} = 3.354102[/tex]
[tex]\sqrt{10}= 3.162278[/tex]
AC is almost half of AE.
[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]
[tex]\sqrt{10} = 3.16227766017[/tex]
It isn’t close to the option C.
please answer asap. there are two pics :)
Answer:
[tex]\boxed{\sf A. \ 0.34}[/tex]
Step-by-step explanation:
The first triangle is a right triangle and it has one acute angle of 70 degrees.
We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.
The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.
The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.
[tex]\sf \frac{3.4}{10} =0.34[/tex]
A crew clears brush at a rate 2/3 acre in 2 days. How long will it take the same crew to clear the entire plot of 4 acres?
Answer:
It takes the crew 12 days to clear the bush.
Step-by-step explanation:
Given clears 2/3 acres / 2 days, or 1/3 acre per day
Time to clear 4 acres
= 4 / (1/3)
= 4 * (3/1)
= 12 days
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence interval for mu is:______.
Answer:
The 90% confidence interval for population mean is [tex]14.7 < \mu < 19.1[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 16.9[/tex]
The confidence level is [tex]C = 0.90[/tex]
The sample size is [tex]n = 45[/tex]
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as
[tex]\alpha = 1-0.90[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table. The values is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of that of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]
[tex]MOE = 2.207[/tex]
The 90% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
substituting values
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]14.7 < \mu < 19.1[/tex]
Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 54,000 + 130x + 4x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ per unit
Answer:
Step-by-step explanation:
Given that:
If C(x) = the cost of producing x units of a commodity
Then;
then the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
We are to consider a given function:
[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]
And the objectives are to determine the following:
a) the total cost at a production level of 1000 units.
So;
If C(1000) = the cost of producing 1000 units of a commodity
[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]
[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]
[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]
[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]
[tex]C(1000) = $310491.1064[/tex]
[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]
(b) Find the average cost at a production level of 1000 units.
Recall that :
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
SO;
[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]
Using the law of indices
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]
c(1000) =$ 310.49 per unit
(c) Find the marginal cost at a production level of 1000 units.
The marginal cost is C'(x)
Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:
[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]
[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]
[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 319.7366596[/tex]
[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]
(d) Find the production level that will minimize the average cost.
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
the production level that will minimize the average cost is c'(x)
differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]
Also
[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]
[tex]x^2 = 27000\sqrt{x}[/tex]
[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]
x= 0; or [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900
Since production cost can never be zero; then the production cost = 900 units
(e) What is the minimum average cost?
the minimum average cost of c(900) is
[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]
c(900) = 60 + 130 + 4(30)
c(900) = 60 +130 + 120
c(900) = $310 per unit
Click on the solution set below until the correct one is displayed.
Answer:
{ } or empty set.
Step-by-step explanation:
The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.
Hope this helps!
Answer:
{ } or empty set
Step-by-step explanation:
It's because these lines are parallel so they don't intersect to give you a coordinate.
A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400
Find the value of a A.130 B.86 C.58 D.65
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5\text{ m}^213.5 m 2 13, point, 5, start text, space, m, end text, squared of material to build the cube. What is the volume inside the giant sugar cube?
Answer:
3.375
Step-by-step explanation:
Answer:
3.375
Step-by-step explanation:
Had it on Khan
PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.
6(x+8) ≥ ‒43+4x
Answer:
[tex]x \geq -91/2[/tex]
Step-by-step explanation:
[tex]6(x+8) \geq -43 + 4x[/tex]
Resolving Parenthesis
[tex]6x+48 \geq -43 + 4x[/tex]
Collecting like terms
[tex]6x - 4 x \geq -43-48[/tex]
[tex]2x \geq -91[/tex]
Dividing both sides by 2
[tex]x \geq -91/2[/tex]
Answer:
x ≥ - 91 / 2
Step-by-step explanation:
In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.
Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]
[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,
[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,
[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,
[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.
A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?
Answer:-95 1/7 feet
Step-by-step explanation:
-120 4/7+25 3/7=-95 1/7 feet
Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
When the input is 4, the output of f(x) = x + 21 is
Answer:
25Step-by-step explanation:
When the input is 4, the output of f(x) = x + 21 is f(4).
Substitute x = 4 to f(x):
f(4) = 4 + 21 = 25
Answer:
25
Step-by-step explanation:
We can find the output by plugging in 4 as x into the function:
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high
Answer:
0.0526ft/minStep-by-step explanation:
Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.
Volume of a cone V = πr²h/3
If the diameter and the height are equal, then r = h
V = πh²h/3
V = πh³/3
If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min
Using chain rule to get the expression for dV/dt;
dV/dt = dV/dh * dh/dt
From the formula above, dV/dh = 3πh²/3
dV/dh = πh²
dV/dt = πh²dh/dt
20 = πh²dh/dt
To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.
20 = π(11)²dh/dt
20 = 121πdh/dt
dh/dt = 20/121π
dh/dt = 20/380.133
dh/dt = 0.0526ft/min
This means that the height of the pile is increasing at 0.0526ft/min
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answer:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Step-by-step explanation:
For this case we have the following probability density function
[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]
And for this case we can find the expected value with this formula:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 amount of sugar (mg) 180 182 184 186 188 190 192 194 Frequency What is the sample size for this data set?
Answer:
The sample size is 30.
Step-by-step explanation:
The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set
From the question the frequency is given as
Frequency = 2 4 6 8 10
The sample size n =
2 + 4 + 6 + 8 + 10
= 30
Therefore the sample size n of the data set = 30
W varies inversely as the square root of x when x=4 w=4 find when x=25
Answer:
8/5
Step-by-step explanation:
w = k / √x
4 = k / √4
k = 8
w = 8 / √x
w = 8 / √25
w = 8/5
50 points + brainliest!
Answer:
( x+2) ^2 = 11
x =1.32,-5.32
Step-by-step explanation:
x^2 + 4x -7 = 0
Add the constant to each side
x^2 + 4x -7+7 = 0+7
x^2 + 4x = 7
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 = 4
Add this to each side
x^2 + 4x +4 = 7+4
Take the 4/2 as the term inside the parentheses
( x+2) ^2 = 11
Take the square root of each side
sqrt( ( x+2) ^2) =±sqrt( 11)
x+2 = ±sqrt( 11)
Subtract 2 from each side
x = -2 ±sqrt( 11)
To the nearest hundredth
x =1.32
x=-5.32
Answer:
[tex](x+2)^2=11[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2+4x-7=0[/tex]
[tex]x^2+4x=7[/tex]
[tex]x^2+4x+4=7+4[/tex]
[tex](x+2)^2=11[/tex]
[tex]x+2=\pm\sqrt{11}[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
A rectangle has a width of 3/4 inches and a length of 9/10 inches. Another rectangle
is larger but still proportional to the first rectangle. It has a width of 30 inches and a length of 36 what proportion could model this situation
Answer:
Bigger size / smaller size = 40
Step-by-step explanation:
Notice that we
36 / (9/10) = 30 / (3/4) = 40
Therefore the proportion model would be
Bigger size / smaller size = 40
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
About 9% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
Answer:
The mean for all such groups randomly selected is 0.09*800=72.
Step-by-step explanation:
The value of the standard deviation is 7.
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The standard deviation is calculated by using the formula,
[tex]\sigma = \sqrt{Npq}[/tex]
N = 600
p = 9%= 0.09
q = 1 - p= 1 - 0.09= 0.91
Put the values in the formulas.
[tex]\sigma = \sqrt{Npq}[/tex]
[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]
[tex]\sigma[/tex] = 7
Therefore, the value of the standard deviation is 7.
To know more about standard deviation follow
https://brainly.com/question/475676
#SPJ2
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
Enter your answer in the box
____
Answer:
[tex]\boxed{2144}[/tex]
Step-by-step explanation:
The sum can be found by adding the parts:
[tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]
__
The sum of numbers 1 to n is n(n+1)/2.