Answer:
D. Cluster sampling
Step-by-step explanation:
Dealing with the whole population can be cumbersome, time-consuming and very expensive. In order to make it more feasible for researchers they can employ cluster sampling. In cluster sampling, the population are divided into precincts, or gropus. The researcher then selects the groups that will be included in the study through simple random samping or systematic sampling. The researcher can opt to choose let the whole cluster or group to participate in the study or they can randomly select the individuals within the groups.
Answer:
d
Step-by-step explanation:
Emma and Kyle combine their eamings to pay their
bills. Emma's eamings can be modeled by the
equation E(x) = 22.75x + 74, where x is the number
of hours worked in a week. Kyle's eamings are
modeled by the equation K(x) = 17 85x + 127, where
x is the number of hours if they each work the same
number of hours in a week?
a. C(x) = 241.60x
b. Cix) = 40,60x + 201
c.Cix) = 40.60x + 53
d. Cix)= 4.90x - 53
The answer is:
The second option,
b.) [tex]C(x)=40.60x+201[/tex]
Why?We are given the functions E(x) and K(x), since they both are function of the same variable, we need to add them in order to find the correct option.
From the statement we know the functions:
[tex]E(x)=22.75x+74[/tex]
and
[tex]K(x)=17.85x+127[/tex]
So, adding the functions we have:
[tex]C(x)=E(x)+F(x)[/tex]
[tex]C(x)=(22.75x+74)+(17.85x+127)[/tex]
[tex]C(x)=22.75x+17.85x+74+127[/tex]
[tex]C(x)=40.60x+201[/tex]
Hence, the answer is the second option,
b.) [tex]C(x)=40.60x+201[/tex]
Have a nice day!
Answer:
The answer is b
Step-by-step explanation:
C(x)=40.60x + 201
The population of a town is decreasing at a rate of 1% per year in 2000 there were 1300 people write an exponential decay function to model this situation then find the population in 2008.
A.) 1200 people
B.) 1300 people
C.) 1500 people
D.) 1100 people
Answer:
b
Step-by-step explanation:
Based on the rate at which the population is decreasing, we can calculate that population in 2008 is A. 1,200 people
The population after a certain number of years is:
= Population now x (1 - rate) ^ number of years
The number of years is:
= 2008 - 2000
= 8 years
The population in 2008 is therefore:
= 1,300 x ( 1 - 1%)⁸
= 1,199.57
= 1,200 people
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Find the reference angle of 10pi/13
Answer:
3π/13
Step-by-step explanation:
In order to find the reference angle of a given angle, first of all, its quadrant is determined
In order to determine the quadrant,
10π/13=10(180)/13
=138.46
As the given angle belongs to 2nd quadrant, it will be subtracted from 180 degrees also denoted by pi.
So,
Reference angle for 10π/13= π-10π/13
=(13π-10π)/13
=3π/13
So the reference angle for 10π/13 is 3π/13 ..
Which of the sets of ordered pairs represents a function?
A = {(3, −5), (4, 6), (−3, 9), (2, 7)}
B = {(2, 4), (−1, −7), (5, 6), (4, 3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
Both A and B
Step-by-step explanation:
A = {(3, −5), (4, 6), (−3, 9), (2, 7)}
-Each x goes to a different y so this is a function
B = {(2, 4), (−1, −7), (5, 6), (4, 3)}
-Each x goes to a different y so this is a function
which answers are equivalent to Q + p + Q + p + Q
Answer:
3Q + 2pStep-by-step explanation:
[tex]Q+p+Q+p+Q\\\\\text{combine like terms}\\\\=(Q+Q+Q)+(p+p)=3Q+2p[/tex]
Can someone help me this is due tonight
Answer:
Step-by-step explanation:
x% of y equals to 0.01*x*y
Just put the numbers in the formula
33% of 507 = 167.31
48% of 375 = 180
76% of 285 = 216.6
60% of 398 = 238.8
89% of 150 = 133.5
26% of 430 = 111.8
81% of 216 = 174.96
5% of 584 = 29.2
18% of 725 = 130.5
2% of 115 = 2.3
90% of 152 = 136.8
12% of 649 = 77.88
55% of 216 = 118.8
43% of 108 = 46.44
97% of 235 = 227.95
twenty-five members of the eighth grade class at Park Center Middle School are going to a museum and then to lunch each student must pay an entrance fee to the museum and 7.25 for lunch the cost for the trip is for for 443.75 what is the entry fee for one student
Answer:
$10.50
Step-by-step explanation:
The first step is to determine the cost per student for the trip.
It cost $443.75 for 25 students, so
TS = 443.75 / 25 = $17.75 per student.
From that $17.75, we know we should remove $7.25 for the lunch in order to get the entrance fee:
EF = 17.75 - 7.25 = 10.50
The entrance fee for one student was $10.50
Which graph shows the solution set of
Answer:
Hence final answer is [tex](1,3)[/tex].
correct choice is D because both ends are open circles.
Step-by-step explanation:
Given inequality is [tex]\frac{x-1}{x-3}<0[/tex]
Setting both numerator and denominator =0 gives:
x-1=0, x-3=0
or x=1, x=3
Using these critical points, we can divide number line into three sets:
[tex](-\infty,1)[/tex], [tex](1,3)[/tex] and [tex](3,\infty)[/tex]
We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.
Test for [tex](-\infty,1)[/tex].
Clearly x=0 belongs to [tex](-\infty,1)[/tex] interval then plug x=1 into [tex]\frac{x-1}{x-3}<0[/tex]
[tex]\frac{0-1}{0-3}<0[/tex]
[tex]\frac{-1}{-3}<0[/tex]
[tex]\frac{1}{3}<0[/tex]
Which is False.
Hence [tex](-\infty,1)[/tex] desn't belongs to the answer.
Similarly testing other intervals, we get that only [tex](1,3)[/tex] satisfies the original inequality.
Hence final answer is [tex](1,3)[/tex].
correct choice is D because both ends are open circles.
The Math Club raised money for its spring banquet by washing vehicles. The club charged $3 per car and $5 per truck. The club earned a total of $510 for washing 122 cars and trucks combined. How many cars did the club wash?
Answer:
3C + 5 T = 550
C+T= 122
PUT IN 1 T= 122-C
3C + 5 (122-C)=550
3C -5C + 610=550
-2C= 550 - 610= -30
C= 15
T= 122-15 = 107
Step-by-step explanation:
Answer: 50
Step-by-step explanation:
Let x be the number of cars and y be the number of trucks .
By considering the given information, we get
[tex]x+y=122-----------------(1)\\\\3x+5y=510-------------------(2)[/tex]
Multiply (1) by 3 , we get
[tex]3x+3y=366--------------(3)[/tex]
Eliminate equation (3) from (2), we get
[tex]2y=144\\\\\Rightarrow\ y=72[/tex]
Put y= 72 in equation (1), we get
[tex]x+72=122\\\\\Rightarrow\ x=122-72=50[/tex]
Hence, the number of cars did the club = 50
Solve the simultaneous equation 2x+5y=29, 3x+5y=-19
Answer:
x = -48, y = 25
Step-by-step explanation:
Both equations have a 5y term, we can work with that.
Let's first convert them into 5y = ... form:
2x + 5y = 29 => 5y = 29 - 2x
3x + 5y = -19 => 5y = -3x - 19
Now we can equate the right-hand sides:
29 - 2x = -3x - 19
And simplify:
29 + 19 = -3x + 2x => x = -48
Let's put this x value in the first:
2*(-48) + 5y = 29 =>
-96 - 29 = -5y =>
-5y = -125 =>
y = 25
Please help me thank you
solution for #18 is C and for #19 is D
QUESTION 18
Use the Pythagorean Identity.
[tex] \cos^{2}( \theta) +\sin^{2}( \theta) = 1[/tex]
We substitute the given value into the formula,
[tex] \cos^{2}( \theta) +( { \frac{4}{7} })^{2} = 1[/tex]
[tex] \cos^{2}( \theta) + \frac{16}{49} = 1[/tex]
[tex] \cos^{2}( \theta) = 1 - \frac{16}{49} [/tex]
[tex]\cos^{2}( \theta) = \frac{33}{49} [/tex]
Since we are in the first quadrant, we take positive square root,
[tex]\cos( \theta) = \sqrt{\frac{33}{49} } [/tex]
[tex]\cos( \theta) = \frac{ \sqrt{33}}{7} [/tex]
The 3rd choice is correct.
QUESTION 19.
We want to simplify;
[tex]18 \sin( \theta) \sec( \theta) [/tex]
Recall the reciprocal identity
[tex] \sec( \theta) = \frac{1}{ \cos( \theta) } [/tex]
This implies that,
[tex]18 \sin( \theta) \sec( \theta) =18 \sin( \theta) \times \frac{1}{ \cos( \theta) } [/tex]
[tex]18 \sin( \theta) \sec( \theta) =18 \times \frac{\sin( \theta) }{ \cos( \theta) } [/tex]
This will give us:
[tex]18 \sin( \theta) \sec( \theta) =18 \tan( \theta) [/tex]
The correct choice is D.
Which ratio represents sin A?
A)817B)1517C)1715D)178
Answer:b
Step-by-step explanation:
Find the value of x in this figure.
ANSWER
The value of x is 47°
EXPLANATION
PQ is a tangent to the circle at Q.
This tangent meets the diameter at 90°.
The sum of interior angles of a triangle is 180°
This implies that:
[tex]90 \degree + x + 43 \degree = 180 \degree[/tex]
[tex]133 \degree + x = 180 \degree[/tex]
Group similar terms to obtain;
[tex] x = 180 \degree - 133 \degree[/tex]
Simplify similar terms to get;
[tex]x = 47\degree[/tex]
Answer:
The value of x = 47°
Step-by-step explanation:
From the figure we can see that a circle with center O.
PQ is a tangent to the circle fro point P.
m<P = 43°
Therefore <Q = 90°
To find the value of x
From the given triangle we can write,
x + m<Q + m<P = 180
x = 180 - (m<Q + m<P)
= 180 - (90 + 43)
= 180 - 133 = 47°
Therefore the value of x = 47°
Find the distance between the points (3, -5) and (-6, -5).
ANSWER
9
EXPLANATION
We want to find the distance between the points (3, -5) and (-6, -5).
The given points have the same y-coordinates .
This means it is a horizontal line.
We use the absolute value method to find the distance between the two points.
We find the absolute value of the distance between the x-values.
The distance between the two points is
|3--6|=|3+6|=|9|=9
1. Which statement is true about the solutions to
x^2 - 1 = 24
Hint:
Isolate the squared term.
Take the square root of both sides.
Is this number rational? (Can you simplify?) Or is it irrational? (Does a square root remain?)
A
There is only one irrational solution.
B
There are two distinct rational solutions.
C
There are two distinct irrational solutions.
2. Marcus wants to solve the quadratic equation 2x^2 - 7x+3=0 Which expression could be one of the factors that he writes in order to solve the equation?
a. 2x-1
b. x-6
c. 2x+1
3. True or False
The solutions to 5x^2 = -2x are x = - 2/5 and x = 0
Hint:
Get all the terms to one side so the equation equals zero.
Factor out the GCF.
Set each term equal to zero.
Solve.
Compare solutions to those given in the problem.
a. true
b. false
4. True or False
The solutions to ( x + 3 )^2 - 4 = 0 are x = - 1 and x = - 5
Hint:
Isolate the squared quantity.
Take the square root of both sides.
Don't forget the plus or minus.
Solve for x.
Determine the two solutions. Compare with those given in the question.
a. true
b. false
Step-by-step explanation:
(B).(x=5 or -5) is the homogeneous mixture
The first equation has two distinct rational solutions, the expression 2x - 1 can be one of the factors to solve the second equation, the solutions to the third equation are x = -2/5 and x = 0, and the solutions to the fourth equation are x = -1 and x = -5.
Explanation:1. To find the solutions to the equation x^2 - 1 = 24, we can start by isolating the squared term:
x^2 = 24 + 1
x^2 = 25
Next, we take the square root of both sides to find the values of x:
x = ±√25
Therefore, there are two distinct rational solutions to the equation.
2. In order to solve the quadratic equation 2x^2 - 7x + 3 = 0, Marcus can use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). One of the factors he can write is 2x - 1.
3. The solutions to the equation 5x^2 = -2x are found by getting all the terms to one side and setting the equation equal to zero:
5x^2 + 2x = 0
Next, we factor out the greatest common factor:
x(5x + 2) = 0
Setting each term equal to zero, we get two values for x:
x = 0 or x = -2/5
Therefore, the statement that the solutions are x = -2/5 and x = 0 is true.
4. To find the solutions to the equation (x + 3)^2 - 4 = 0, we isolate the squared quantity:
(x + 3)^2 = 4
Next, we take the square root of both sides, considering both the positive and negative square roots:
x + 3 = ±√4
x + 3 = ±2
Solving for x, we get two solutions:
x = -3 - 2 = -5
x = -3 + 2 = -1
Therefore, the statement that the solutions are x = -1 and x = -5 is true.
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*** PLEASE HELP ASAP
two cylinders have the same size base, but one is twice as tall. explain why the taller cylinder does not have double the surface area.
Answer:
The top isn't closed.
Step-by-step explanation:
The bottom is enclosed, creating more surface area, but the top is opened.
Answer:
The surface area of a cylinder is given by :
SA=[tex]2 \pi rh+2\pi r^{2}[/tex]
When the base is same but the height is doubled. Doubling the height replaces h with 2h:
New formula becomes:
SA=[tex]2 \pi r(2h)+2\pi r^{2}[/tex]
SA = [tex]4\pi rh+2\pi r^{2}[/tex]
We can see that only the height is doubled not the radius. The formula changes a little bit.
We can take an example-
Lets say the height of cylinder is 10 cm and radius is 4 cm
So, SA in 1st case :
SA=[tex]2\times3.14\times4\times10+ 2\times3.14\times (4)^{2}[/tex]
=[tex]251.2+100.48=351.68[/tex] cm square
SA in 2nd case:
[tex]4\times3.14\times4\times10+ 2\times3.14\times(4)^{2}[/tex]
= [tex]502.4+100.48=602.88[/tex] cm square
We can see that area of lateral surface doubles up in case 2 but the base area remains the same.
Which statement describes the graph of function g?
Answer:
The graph of G is 3 units to the left of graph F
Step-by-step explanation:
I used Desmos graphing calculator to check my answer, but generally you can use this formula.
a(x + or - h) + or - k = y
h is vertical movement and k is horizontal movement.
Answer: Never mind that answer was incorrect it is not B!!
Step-by-step explanation:
Bentley went into a bakery and bought 4 donuts and 10 cookies, costing a total of $23. Skylar went into the same bakery and bought 8 donuts and 6 cookies, costing a total of $25. Determine the price of each donut and the price of each cookie.
Answer:
Donuts cost $2.00 and Cookies cost $1.50
Step-by-step explanation:
D = cost of a donut
C = cost of a cookie
4D + 10C = $23.00
8D + 6C = $25.00
Eliminate a variable when subtracting the two equations. Change both values with C to 60 in order to eliminate the C variable and solve for D.
80D + 60C = $250.00 subtracted from 24D + 60C = $138
56D = $112.00 (Divide by 56 to single out the variable)
56D/56 = $112.00/56
D = $2.00
Use the D value to solve for C.
4(2) + 10C = $23.00
8 + 10C = $23.00
8 - 8 + 10C = $23.00 - 8
10C = $15.00
10C/10 = $15/10
C = $1.50
Check:
Bentley:
4D + 10C = $23
4(2) + 10(1.50) = $23
8 + 15 = $23
23 = 23
Skylar:
8D + 6C = $25
8(2) + 6(1.50) = $25
16 + 9 = $25
25 = 25
Answer:
Each donut costs $2 and each cookie costs $1.5
Step-by-step explanation:
1. Let´s name the variables as the following:
x = price of one donut
y = price of one cookie
2. Write in an equation form which Bentley bought:
[tex]4x+10y=23[/tex] (Eq.1)
3. Write in an equation form which Skylar bought:
[tex]8x+6y=25[/tex] (Eq.2)
4. Solve for x in Eq.1:
[tex]4x+10y=23[/tex]
[tex]4x=23-10y[/tex]
[tex]x=\frac{23-10y}{4}[/tex] (Eq.3)
5. Replace Eq.3 in Eq.2 and solve for y:
[tex]8*(\frac{23-10y}{4})+6y=25[/tex]
[tex]\frac{184-80y}{4}+6y=25[/tex]
[tex]\frac{184-80y+24y}{4}=25[/tex]
[tex]184-80y+24y=100[/tex]
[tex]-80y+24y=100-184[/tex]
[tex]-56y=-84[/tex]
[tex]y=\frac{84}{56}[/tex]
[tex]y=1.5[/tex]
6. Replacing the value of y in Eq.3:
[tex]x=\frac{23-10*(1.5)}{4}[/tex]
[tex]x=\frac{23-10*(1.5)}{4}[/tex]
[tex]x=\frac{23-15}{4}[/tex]
[tex]x=\frac{8}{4}[/tex]
[tex]x=2[/tex]
Therefore each donut costs $2 and each cookie costs $1.5
What are the coordinates of p?
A.(0,5)
B.0,7
C.7,0
D.5,0
Answer:
(5,0)
Step-by-step explanation:
Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)
Answer:
(5,0)
Step-by-step explanation:
Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)
Find the midpoint between A and C.
(1, 1)
(5, -7)
(-5, 7)
(0.5, 0.5)
Answer:
(0.5, 0.5)Step-by-step explanation:
The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):
[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
From the graph we have the points A(-2, 4) and C(3, -3).
Substitute:
[tex]M_{AC}(x,\ y)\\\\x=\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\y=\dfrac{4+(-3)}{2}=\dfrac{1}{2}=0.5[/tex]
Answer:
0.5 0.5
Step-by-step explanation:
because it is logically correct now deal with it! hehehe have a grate day un like me!;)
Choose the correct answer. The collection of investments in a mutual fund is called a .
The collection of investments in a mutual fund is referred to as a portfolio, which can include a variety of stocks and bonds. Index funds are examples of mutual funds that track the performance of market indexes. Mutual funds are significant in the financial landscape, with many U.S. households investing in them.
Explanation:The collection of investments in a mutual fund is called a portfolio.
Mutual funds gather stocks or bonds from various companies into one investment vehicle, making it simpler for investors to own a diversified collection without purchasing each security individually.
Investors purchase shares of the mutual fund and receive returns based on the collective performance of the fund's portfolio.
For instance, index funds are types of mutual funds that aim to mimic the performance of a specific market index.
This strategy offers broad market exposure and low operating expenses.
There are also specialized mutual funds that focus on particular sectors or regions, offering different levels of risk and potential return.
In the modern financial landscape, mutual funds play a significant role, with a substantial percentage of U.S. households holding investments in these funds.
The radius of a right circular cylinder is increasing at the rate of 6 in./s, while the height is decreasing at the rateof 3 in./s. At what rate is the volume of the cylinder changing when the radius is 5 in. and the height is 11 in.?
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is
[tex]V=\pi r^2h[/tex]
Differentiate both sides with respect to time:
[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dr}{\mathrm dt}+\pi r^2\dfrac{\mathrm dh}{\mathrm dt}[/tex]
We're given that
[tex]\dfrac{\mathrm dr}{\mathrm dt}=6\dfrac{\rm in}{\rm s}[/tex]
[tex]\dfrac{\mathrm dh}{\mathrm dt}=-3\dfrac{\rm in}{\rm s}[/tex]
so that at the point when [tex]r=5\,\rm in[/tex] and [tex]h=11\,\rm in[/tex], the volume is undergoing a total change of
[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi(5\,\mathrm{in})(11\,\mathrm{in})\left(6\dfrac{\rm in}{\rm s}\right)+\pi(5\,\mathrm{in})^2\left(-3\dfrac{\rm in}{\rm s}\right)[/tex]
[tex]\boxed{\dfrac{\mathrm dV}{\mathrm dt}=585\pi\dfrac{\mathrm{in}^3}{\rm s}}[/tex]
The volume of the right circular cylinder is changing at a rate of 255π cubic inches/sec with the radius increasing at 6 in./s and height decreasing at 3 in./s.
Explanation:The question involves the application of calculus concepts particularly related to volume flow rate. The volume (V) of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. We can take the derivative in respect to time (t) of both sides, which will result in dV/dt = πrh(dr/dt) + πr²(dh/dt).
According to the problem, dr/dt = 6 in./s and dh/dt = -3 in./s. The volume is changing when the radius (r) is 5 in. and the height (h) is 11 in. Substituting all these values into the formula, we get: dV/dt = π(5)(11)(6) + π(5)²(-3). This equals 330π - 75π = 255π cubic inches/sec.
Thus, the volume of the cylinder is changing at a rate of 255π cubic inches/sec.
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A contractor is building a set of stairs out of concrete. Each step is exactly the same length and width is the same and height from the last step.
A) Which solid figures can the staircase be broken into?
B) What are the dimensions of each solid figure?
C) How much concrete will be needed to form the staircase?
QA) Which solid figures can the staircase be broken into?
A) The staircase can be broken into 3 rectangular prisms.
QB) What are the dimensions of each solid figure?
A) We are given the height (2.5 ft) and the length (3 ft) of the entire staircase. To find the height and length of each step, just divide by 3:
2.5 / 3 = 5/6 ft high
3 / 3 = 1 ft long
Looking at the image given, we can see that the staircase is 6 ft wide.
Bottom prism: 3 ft long, 6 ft wide, and 5/6 ft high.
Middle prism: 2 ft long, 6 ft wide, and 5/6 ft high.
Top prism: 1 ft long, 6 ft wide, and 5/6 ft high.
QC) How much concrete will be needed to form the staircase?
A) To answer this question, we have to find the volume of each rectangular prism. The formula for the volume of a rectangular prism is
V = lwh; where l = length, w = width, and h = height.
We need to apply this formula to each prism. I'll go from the bottom up.
(1.) V = lwh; l = 3, w = 6, h = 5/6
V = (3)(6)(5/6)
V = 15 ft²
(2.) V = lwh; l = 2, w = 6, h = 5/6
V = (2)(6)(5/6)
V = 10 ft²
(3.) V = lwh; l = 1, w = 6, h = 5/6
V = (1)(6)(5/6)
V = 5 ft²
To find the amount of concrete needed to form the staircase, just add the volumes of the three rectangular prisms:
15 + 10 + 5 = 30 ft²
The contractor will need enough concrete to cover 30 ft² to form the staircase.
Hope this helps!
Final answer:
The staircase can be broken into rectangular prisms, each representing a step. The volume of each step is calculated using the given dimensions, which are then summed to find the total concrete needed.
Explanation:
To determine the amount of concrete needed to form a staircase, we need to calculate the volume of concrete required for each step and then sum them up. Since each step is of the same size, we can break down the staircase into a set of rectangular prisms, where each prism represents a step.
Dimensions of each solid figure (step): Given a stage height of 400 mm and 3 steps, the height of each step would be 400 mm / 3, which is around 133.33 mm or 13.33 cm. The length of the horizontal part of each step is 800 mm or 80 cm. Assuming a step width of 1,200 mm or 120 cm (since the steps must be wide enough for two people), we obtain the dimensions for each step.
To calculate the volume of each step, we use the formula for the volume of a rectangular prism: Volume = Length × Width × Height. Therefore, we have Volume = 80 cm × 120 cm × 13.33 cm for each step. To find the total volume for the staircase, we multiply the volume of one step by the number of steps (3 in this case).
Calculating the total concrete required: After finding the volume of one step, we multiply it by 3 (since there are 3 steps) to find the total concrete needed.
The zeroes of f(x)=x^3+3x^2+2x are
x = 0, -1, -2
When the function is set equal to zero and solved for, you end up with these three numbers.
show the first step when factoring 5a^2b- 5a^2c -5db +5dc by grouping?
Answer:
[tex]5(a^2b-a^2c-db+dc)[/tex]
Step-by-step explanation:
Given expression is [tex]5a^2b- 5a^2c -5db +5dc[/tex].
Now we need to show the first step of factoring.
We know that first step of factoring in any problem is to find the GCF that is find the greatest common factor. We see that 5 is the only largest number that can divide each term so 5 is the GCF.
Now we write 5 outside parenthesis and divide given terms by 5 to find the terms that goes inside parenthesis.
Hence first step of factoring is given by :
[tex]5a^2b- 5a^2c -5db +5dc[/tex]
[tex]=5(a^2b-a^2c-db+dc)[/tex]
The first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group
Let's factor the expression [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping.
First, let's group the terms:
[tex]\( (5a^2b - 5a^2c) + (-5db + 5dc) \)[/tex]
Now, let's factor out the common terms from each group:
[tex]\( 5a^2(b - c) + 5d(-b + c) \)[/tex]
Now, we can factor out the common factor of 5 from both terms:
[tex]\( 5(a^2(b - c) + d(-b + c)) \)[/tex]
So, the factored expression is [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]
In the given expression, we have four terms[tex]: \(5a^2b\), \(-5a^2c\), \(-5db\), and \(5dc\).[/tex]
The first step in factoring by grouping is to group the terms in pairs. Here, we pair [tex]\(5a^2b\)[/tex] with [tex]\(-5a^2c\)[/tex] and [tex]\(-5db\)[/tex] with [tex]\(5dc\).[/tex]
Next, we factor out the common terms from each group. From the first group, we factor out [tex]\(5a^2\)[/tex], and from the second group, we factor out [tex]\(5d\).[/tex] This leaves us with [tex]\(b - c\)[/tex] in the first group and [tex]\(-b + c\)[/tex] in the second group.
Finally, we factor out the common factor of 5 from both terms to get the final factored expression [tex]\(5(a^2(b - c) + d(-b + c))\).[/tex]
So, the first step when factoring [tex]\(5a^2b - 5a^2c - 5db + 5dc\)[/tex] by grouping is to group the terms and then factor out the common terms from each group.
Complete question:
show the first step when factoring [tex]5a^2b- 5a^2c -5db +5dc[/tex] by grouping?
Pleaseeee help me! 8 points! What is x-value?
Answer:
[tex]\frac{7\pi }{2}[/tex]
Step-by-step explanation:
Given
sin x = - 1
x = [tex]sin^{-1}[/tex] ( - 1 )
= [tex]\frac{3\pi }{2}[/tex] + 2kπ k ∈ Z
For 2π < x < 4π, then
x = [tex]\frac{7\pi }{2}[/tex]
Due to ever-changing technology, a new XYZ Smartphone decreases in value 20% each year.
1. How much will this $1000 phone be worth in 2 years?
2. How long until it is worth less than 10% of it's original price?
Answer:
1. $640
2. About 10.3 years later
Step-by-step explanation:
This is a compound decay problem. The formula is
[tex]F=P(1-r)^t[/tex]
Where
F is the future amount
P is the initial amount
r is the rate of decrease (in decimal), and
t is the time in years
Question 1:
We want to find F after 2 years of a phone initially costing 1000. So,
P = 1000
r = 20% or 0.2
t = 2
plugging into the formula, we solve for F:
[tex]F=P(1-r)^t\\F=1000(1-0.2)^2\\F=1000(0.8)^2\\F=640[/tex]
The phone is worth $640 after 2 years
Question 2:
We want to find when will the phone be worth 10% of original.
10% of 1000 is 0.1 * 1000 = 100
So, we want to figure this out for future value of 100, so F = 100
We know, P = 1000 r = 0.2 and t is unknown.
Let's plug in and solve for t (we need to use logarithms):
[tex]F=P(1-r)^t\\100=1000(1-0.2)^t\\100=1000(0.8)^t\\\frac{100}{1000}=0.8^t\\0.1=0.8^t\\ln(0.1)=ln(0.8^t)\\ln(0.1)=t*ln(0.8)\\t=\frac{ln(0.1)}{ln(0.8)}\\t=10.32[/tex]
So, after 10.32 years, the phone would be worth less than 10% of original value.
Umm can anyone answer this I need the area please
Answer:
21503 feet²
Step-by-step explanation:
Area of Square 1 = 69 x 69 = 4761
Area of Triangle = 69 x 92 ÷ 2 = 3174
Area of Square 2 = 92 x 92 = 8464
Area of Circle = 57.5² x π ÷ 2 ≈ 5104
Total Area = 21503
What is five ninths of 540? PLEASE HELP! lol
Answer:
three hundred
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
5,9 times 540
Your child weighs 16 kg. Your research indicates that 40 mg/kg/day is the recommended dosage. What would the safe dosage be for your child in milligrams per day?
Answer:
The safe dose for the child is: [tex]640\ \frac{mg}{day}[/tex]
Step-by-step explanation:
We know that the conversion factor is 40 mg/kg/day
The child weighs 16 kg. This means that 40 mg per day corresponds to each kilogram of the child.
So to know how many milligrams per day correspond per day we must multiply 16 kg by the conversion factor
[tex]16\ kg * 40\ \frac{\frac{mg}{kg}}{day} = 640\ \frac{mg}{day}[/tex]
Answer:
The safest dose would be 640 mg per day.
Hope this helps!