Step-by-step explanation:
y=Kx
20=4k
k=5
when x=18
y=18 x 5
y=90
Use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in cost.
Function x-Value
C=0.025x^2 + 3x + 4 x=10
dC= ___________
ΔC= __________
Answer:
dC=3.5
DC is between 3.475 and 3.525
Step-by-step explanation:
So let dx=1 since the change there is a change in 1 unit.
Find dC/dx by differentiating the expression named C.
dC/dx=0.05x+3
So dC=(0.05x+3) dx
Plug in x=10 and dx=1:
dC=(0.05×10+3)(1)
dC=(0.5+3)
dC=3.5
Let D be the change in cost-the triangle thing.
Since dx=1 we only want the change in unit to be within 1 in difference.
So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.
Let's do from x=9 to x=10 first:
DC=C(10)-C(9)
DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]
DC=[2.5+30+4]-[0.025×81+27+4]
DC=[36.5]-[2.025+31]
DC=[36.5]-[33.025]
DC=3.475
Now let's do from x=10 to x=11
DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]
DC=[0.025×121+33+4]-[36.5]
DC=[3.025+37]-[36.5]
DC=[40.025]-[36.5]
DC=3.525
So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.
What is the area of a triangle with a base of 9 units and a height of 7 units? O A. 15.75 sq. units O B. 126 sq. units O c. 63 sq. units O D. 31.5 sq. units SUBMIT வன் PREVIOUS
Answer:
D. 31.5 sq. units
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
A = 1/2 ( 9)(7)
A = 63/2
A = 31.5 units^2
Step-by-step explanation:
For this, we'll use a formula for the area of a triangle.
Area (A) = ( Base (B) * Height (H) ) / 2
[tex]A = (B * H )/2[/tex]
Plug in given values.[tex]A = (9*7)/2[/tex]
Multiply within parentheses.[tex]A = (63)/2[/tex]
Divide by 2.[tex]A = 31.5[/tex]
Answer:
D. 31.5 sq. units
find the exact value of tan -75
Using the net below, find the surface area of the pyramid. (in the image) 2in 3in 3in
Answer:
Surface area = 21 in.²
Step-by-step explanation:
Surface area of the pyramid = sum of all areas of the faces or parts of the net = 4(area of triangle) + area of square base
✔️Area of the four triangles:
A = 4(½*b*h)
Where,
b = 3 in.
h = 2 in.
A = 4(½*3*2)
A = 2*3*2
A = 12 in.²
✔️Area of the square base = s²
s = 3 in.
Area = 3² = 9 in.²
✅Surface area of the pyramid = 12 + 9 = 21 in.²
Avi uses 11 toothpicks to form a row of 5 attached triangles, as shown. Suppose he continues this pattern, using 89 toothpicks in all. What is the total number of triangles formed? (sorry the picture wasn't uplodaing)
Answer:
44
Step-by-step explanation:
Given that Avi used 11 toothpicks to form a row of 5 attached triangles.
Total number of toothpicks used = 89
Let the total number of triangles formed be represented by x, so that:
11 toothpicks = 5 triangles
It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;
the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]
= 2.2
The number of toothpicks per triangle = 2.0
Thus,
x = [tex]\frac{89}{2.0}[/tex]
= 44.5
x = 44
The total number of triangles formed is 44.
Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92
people to interview.
Answer:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 41, standard deviation of 28:
This means that [tex]\mu = 41, \sigma = 28[/tex]
Sample of 92:
This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]
Distribution of the sample means:
By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=tcost, y=tsint, t=π
Step-by-step explanation:
the answer is in the image above
Find the perimeter of the quadrilateral in simplest form A quadrilateral has side lengths of 2 StartRoot 27 EndRoot inches, StartRoot 12 EndRoot inches, 3 StartRoot 3 EndRoot inches, 2 StartRoot 12 EndRoot inches.
Answer: c on edge
Step-by-step explanation:
just finished
Answer:
112.5 inches
Step-by-step explanation:
what is the average speed for the interval t=1 hour to t=3 hours
Answer:
7.5 miles per hour
Step-by-step explanation:
Average speed over the interval [1, 3] = (distance at 3 hrs -distance at 1 hr)/(3 hrs - 1 hr)
From the graph:
Distance at 3 hrs = 30 => (3, 30)
Distance at 1 hr = 15 => (1, 15)
Average speed = (30 - 15)/(3 - 1)
Average speed = 15/2
= 7.5
Therefore, average speed = 7.5 miles per hour
Which graph represents the function f (x) = StartFraction 5 minus 5 x squared Over x squared EndFraction? On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens up and to the left in quadrant 2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 2, and the other curve opens up and to the left in quadrant 3. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrants 3 and 4.
9514 1404 393
Answer:
2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3
Step-by-step explanation:
Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².
The function can be simplified to ...
f(x) = 5/x² -5
which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.
Researchers study the relationship between interpersonal violence and health in college age women. The researchers report an OR for somatic symptoms among abused versus non abused women (OR 1.03 95% CI 0.79-1.71). Based on this information, you know:_________-
a. Abused women are significantly more likely to have somatic symptoms.
b. There is no significant difference in somatic symptoms for abused and non-abused women.
c. This is a clinically significant result.
d. In this study women who were abused were less likely to report somatic symptoms.
Answer:
There is no significant difference in somatic symptoms for abused and non-abused women. ( B )
Step-by-step explanation:
Given that OR = 1 simply shows that there is no difference in data for both groups
and 95% of Cl for the variable OR = ( 0.79 - 1.71 )
given the relationship between Cl and OR we can conclude that Cl is inclusive in the value OR = 1
Finally : we can conclude that There is no significant difference in somatic symptoms for abused and non-abused women
Solve the following quadratic equation. Express your answers in exact form.
g(x) = -3x^2 + 4x + 2
Answer:
x = (2+√10)/ 3 and x= (2-√10/3)
Step-by-step explanation:
g(x) = -3x² +4x +2
use the quadratic formula x= (-b±√b²-4ac)/2a, when g(x) = ax² +bx +c
x= [-4 ±√4²-4*(-3)*2] / 2*(-3) , solve under the square root
x= (-4 ± √16 +24) / -6 , add under the radical
x= (-4 ±√40) / -6, simplify the square root
x= (-4 ±2√10) /-6, factor -2
x= -2 (2±√10)/-2 *3, simplify -2
x= (2±√10)/3
Therefore,
x = (2+√10)/ 3 and x= (2-√10/3)
A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence.
a. True
b. False
Answer:
a. True
Step-by-step explanation:
A series in the field of mathematics is defined as the operation of adding up or summation of infinitely many quantities of terms of a sequence. In other words, it is the sum of the terms of the sequence provided.
Another way of defining a 'series' is it is list of numbers with the "addition" operations between the numbers.
Thus the answer is (a). True
For this exercise assume that the matrices are all nn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer.
If there is an n x n matrix D such that Ax =0, then there is also an nxn matrix C such that CAI.
a. True
b. False
Answer:
A) True
Hope this helps!
The diameter of a circle is inches what is the area?
Answer:
Pie( r ^2)
Step-by-step explanation:
Here value of r is in inches
ms.+sanchez+bought+3+pounds+of+turkey+to+make+sandwiches+for+her+family+.+She+uses+.25+of+a+pound+for+each+sandwich+.+How+many+sandwiches+can+she+make+?
Answer:
she can make 12 sandwiches
Step-by-step explanation:
3/.25 is the solution
HELP!!!!!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not?
f(x) = ex
A) The base is x.
B) The base is e.
C) This is a polynomial.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
assuming that the equation was [tex]f(x) = e^{x}[/tex]
then the base is "e"
Step-by-step explanation:
first to answer gets brainiest
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
cm³
Answer:
V = 67 1/2 cm^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 4 1/2 * 6 * 2 1/2
Changing to improper fractions
V = 9/2 *6*5/2
V =270/4
V = 135/2
Changing to a mixed number
V = 67 1/2 cm^3
You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 2x - 3y = 12
-x + 2y = 13
O A. Multiply the left side of equation 2 by 2. Then subtract the result from equation 1.
O B. Multiply equation 1 by 2 and equation 2 by 3. Then add the new equations.
C. Multiply equation 2 by-2. Then add the result to equation 1.
Answer:
A.
Step-by-step explanation:
The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.
If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.
If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.
When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).
So, option B is not allowed (it is not allowed to multiply only one part of the equation)
The stopping distance on wet pavement at 20mph is about 60feet. The stopping distance at 30mph is 120feet. What would you estimate the stopping distance is at 40mph? Construct a formula
Answer:
[tex]y = 6x - 60[/tex] --- formula
The stopping distance at 40mph is 180ft
Step-by-step explanation:
Given
[tex](x,y) = (20,60)[/tex]
[tex](x,y) = (30,120)[/tex]
Solving (a): Construct a formula
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{120 - 60}{30-20}[/tex]
[tex]m = \frac{60}{10}[/tex]
[tex]m=6[/tex]
So, the equation is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 6(x - 20) + 60[/tex]
Open bracket
[tex]y = 6x - 120 + 60[/tex]
[tex]y = 6x - 60[/tex]
Hence, the formula to use is: [tex]y = 6x - 60[/tex]
Solving (b): y, when x = 40
[tex]y = 6x - 60[/tex]
[tex]y = 6 * 40 - 60[/tex]
[tex]y = 180[/tex]
Didi invested a total of $16125 in two accounts paying 8.5% and 4% simple interest. If her total return at the end of 2 years was 1740 , how much did she invest in each account?
Answer:
5000 ;
11125
Step-by-step explanation:
Given :
Total principal = 16125
Rates = 8.5% and 4%
Period, t = 2 years
Total interest = 1740
Let :
Principal amount invested at 8.5% = x
Principal amount invested at 4% = 16125 - x
Interest formula :
Interest = principal * rate * time
Hence, mathematically ;
(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740
(0.17x + 1290 - 0.08x ) = 1740
0.09x + 1290 = 1740
0.09x = 1740 - 1290
0.09x = 450
x = 450 / 0.09
x = 5000
Amount invested at 4% :
16125 - 5000 = 11125
Evaluate f (5)
f(5) =
Answer:
100
Step-by-step explanation:
f(5) means find the output value when x=5
When x =5 f(x) = 100
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
100Explanation:-
we have to find the value of f(5)
But in the questions attachment it tells that
f(5)=100
What is the slope formula?
Answer:
D is your answer
Step-by-step explanation:
Answer:
Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx
Step-by-step explanation:
The longest leg is Select one:
a. 5√3
b. 10√3
c. 5
d. 20
Answer:
D:20
sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20
Step-by-step explanation:
How do you know if a radical can be simplified? Explain.
Answer:
An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.
Which table repsents a linear function?
Answer:
Option 3
Step-by-step explanation:
Exclude option 1: a linear function will not have a repeated y coordinate
Exclude option 2: the y coordinate is - 3, - 4, - 5, gradually increasing. Thus the line is a curve, not linear function
Option 3: - 8 is the change in every y coordinate. The line is linear because the slope is constant
Exclude option 4: the difference of y coordinate is becoming greater and greater, thus the line is a curve. Not an linear function.
Brainliest please~
Someone help me?????
Step-by-step explanation:
4. b 612 (72/100) x 850)
5. c. 275 (33/100) x 835
6. b. 39% (3.24 - 2.85) x100%)
Help? Thanks!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
You can't really show work for this, but it's A because the angles are opposite each other.
Answer quick please.
Answer
The Answer is A C D
Step-by-step explanation:
What is the domain of the relation described by the set of ordered pairs (-2,8), (-1,1) (0,0) (3,5), (4,-2)?
Step-by-step explanation:
(-2,-1,0,3,4) are the domain
(x,y)=(domain,range)
simply x components are the domain whereas y components are the range
