Yes it can be, it will be a fraction
Answer:
[image]
Step-by-step explanation:
follow the steps provided in the picture
A deck of 52 cards has only one queen of diamonds. The deck is well-shuffled and you draw the first and last card (without replacement). What is the chance that the first card is a queen of diamonds or the last card is a queen of diamonds
Answer:
3.8% chance
Step-by-step explanation:
A prism with a base area of 8 cm² and a height of 6 cm is dilated by a factor of 54 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
cm³
Answer:
New base area = 8 x 25/16 = 25/2 = 12•5 cm²
New height = 7•5 cm²
V = 7•5 x 12•5 cm³
V = 93•75 cm³
Step-by-step explanation:
HELP PLEASEEEEEEE
can you help me find the period of the function from this table?
Answer: It’s either 6, or 2, though the answer is most likely 6, because of the way the table is created.
Step-by-step explanation:
Period is 12.
We can see the pattern 50, 33, 50, 67 that keeps repeating every m=12 points.
Chloé had 100 math problems to complete over the 3-day weekend. She recorded the number of problems in her math journal. She completed 39/100 of the problems on Friday,5/10 of the problems on Saturday,and another 15 problems on Sunday. Did chloe fill out her math journal correctly ?
The answer is no, Chloe did not fill out her math journal correctly.
To determine if Chloe completed all 100 math problems correctly, we need to calculate the total number of problems she completed over the weekend.
On Friday, Chloe completed [tex]\( \frac{39}{100} \)[/tex] of the problems. This fraction represents the portion of the total problems she completed on Friday. To find out how many problems this corresponds to, we multiply the total number of problems by this fraction:
[tex]\[ \text{Problems on Friday} = \frac{39}{100} \times 100 = 39 \text{ problems} \][/tex]
On Saturday, Chloe completed [tex]\( \frac{5}{10} \)[/tex] of the problems. Again, we multiply the total number of problems by this fraction to find out the number of problems completed on Saturday:
[tex]\[ \text{Problems on Saturday} = \frac{5}{10} \times 100 = 50 \text{ problems} \][/tex]
On Sunday, Chloe completed another 15 problems.
Now, we add up the problems completed each day to find the total number of problems completed over the weekend:
[tex]\[ \text{Total problems completed} = \text{Problems on Friday} + \text{Problems on Saturday} + \text{Problems on Sunday} \][/tex]
[tex]\[ \text{Total problems completed} = 39 + 50 + 15 \][/tex]
[tex]\[ \text{Total problems completed} = 104 \][/tex]
Chloe completed a total of 104 problems, which is more than the 100 problems she was supposed to complete. Therefore, she did not fill out her math journal correctly, as she recorded more problems than were assigned.
Chloé's math journal is not filled out correctly.
Let's calculate how many problems Chloé completed each day:
Friday: She completed [tex]\frac{39}{100}[/tex] of 100 problems, which equals 39 problems.Saturday: She completed [tex]\frac{5}{10}[/tex] (or 50%) of 100 problems, which equals 50 problems.Sunday: She completed 15 problems.Adding these up: 39 (Friday) + 50 (Saturday) + 15 (Sunday) = 104 problems.
This must be incorrect since she only had 100 problems to start with. Therefore, Chloé's math journal is not filled out correctly.
8. Mr. Mercado bought a bond with a face value of $5000 and a coupon rate of 7.5%. The bond will mature in 15 years. How much interest will he receive semiannually?
Answer: $187.5
Step-by-step explanation:
The interest = 5000× ( 7.5/100 )÷2
=5000 × 0.075 ÷2
= 5000 ×0.0375
= 187.5 has interest semiannually
Hence, he gets 187.5
Brynn ate 4/10 funnel cakes and 37/100 of the food was cotton candy. The rest of the food was popcorn. What fraction of the food brynn are was funnel cakes or cotton candy?
Answer:
?
Step-by-step explanation:
Convert 4/10 into 40/100(so you can have same denominator as other fraction) and then add 40/100 and 37/100 and you will get the answer!
On a river you must release any fish that you catch ifvit measures less than 12 inches. Define a variable and then write an algebraic inequality for each senario. can you keep a fish that is 11.99 inches?
Let f = fish
If f < 12, let the fish go.
We cannot catch a fish measuring 11.99 inches.
If f = fish, then f < 11.99. It must be released.
Find the volume of a right circular cone that has a height of 8.8 cm and a base with a diameter of 18.6 cm. Round your answer to the nearest tenth of a cubic centimeter.
Final answer:
The volume of the cone is approximately 860.6 cm³.
Explanation:
To find the volume of a right circular cone, we can use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. In this case, the diameter of the base is 18.6 cm, so the radius is half of that, which is 9.3 cm. The height of the cone is 8.8 cm. Plugging these values into the formula, we get V = (1/3)π(9.3 cm)²(8.8 cm). Calculating this, we find that the volume of the cone is approximately 860.6 cm³.
In the following set, the mode is the most effective measure of central tendency if you want to emphasize how small the values are. 32, 21, 68, 21 True False
Answer:
FALSE
Step-by-step explanation:
The mode is a measure of the number with the highest frequency in a group of data. In the set of values (32, 21, 68, 21), the number that appears most is 21 and this is the mode.
If a set of data has two modes, it is bi-modal. If it has several modes, it is multi-modal
Consider the set of data below
2,2,3,3,5,7,8
The numbers 2 and 3 appears with the same frequency, therefore this set of data is bi-modal.
HELP ASAP!! Write the inverse variation function given that y varies inversely with x, and y = 2 when x = 8.
Answer: y= 16/x
Step-by-step explanation:
Triangle ABC is reflected across the line y = x. What are the coordinates of the vertex B' of the resulting triangle A'B'C'?
A. (2, -5)
B. (-2, 5)
C. (5, -2)
D. (-5, -2)
a + b = 10
a - b = 2
Solve the system of equations.
Answer:
a=6 b=4
Step-by-step explanation:
they can't both equal 5 so you need to find 2 numbers that add up to equal 10 but when you subtract one from the other it equals 2
A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of 79, 95, 89, and 81. Alan received an 81 on his term paper. His final examination score was 85. Use the weighted mean formula to find Alan's average for the course.
Answer:
The Alan's average for course is 72.65.
Step-by-step explanation:
Given that,
Each test counts as 15% of the course grade. 20% of course grade is counted term test paper. Alan has test scores of 79, 95, 89, and 81. Alan got 81 score on his term paper . Alan's final examination score = 85.
[tex]\sum w=1[/tex]
Let n number x₁,x₂,.......,[tex]x_n[/tex] with respect to assigned weight[tex]w_1[/tex],[tex]w_2[/tex],.......,[tex]w_n[/tex] is
[tex]{\textrm{weighted mean}}= \frac{\sum w.x}{\sum w}[/tex]
Where [tex]\sum w.x[/tex] is the sum of the products the number with the relevant weight.
weighted mean [tex]=\frac{79\times 15\%+95 \times 15\%+89\times 15\%+81\times 20\%+85\times20\%}{1}[/tex]
=72.65
The Alan's average for course is 72.65.
Look at the system of equations below.
{y = − 2 x + 3
4 x − 3y = 11
What is the solution to the system? Show your work.
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=-1[/tex]
Step-by-step explanation:
Considering the system of the equation
[tex]\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=-2x+3[/tex]
[tex]\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}[/tex]
[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11[/tex]
[tex]4x-3\left(-2x+3\right)=11[/tex]
[tex]4x+6x-9=11[/tex]
[tex]10x-9=11[/tex]
[tex]10x-9+9=11+9[/tex]
[tex]10x=20[/tex]
[tex]x=2[/tex]
[tex]\mathrm{For\:}y=-2x+3[/tex]
[tex]\mathrm{Subsititute\:}x=2[/tex]
[tex]y=-2\cdot \:2+3[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=-1[/tex]
Dustin bought 9 pencils. Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, how many green pencils did he buy?
Answer: he bought 5 green pencils
Step-by-step explanation:
Let x represent the number of green pencils that Dustin bought.
Dustin bought 9 pencils. The remainder of the pencils were purple. This means that the number of purple pencils that he bought is 9 - x
Some of the pencils were green and cost $0.90 each. The remainder of the pencils were purple and cost $0.65 each. If Dustin paid $7.10 for all of the pencils, it means that
0.9x + 0.65(9 - x) = 7.1
0.9x + 5.85 - 0.65x = 7.1
0.9x - 0.65x = 7.1 - 5.85
0.25x = 1.25
x = 1.25/0.25
x = 5
Someone has 240$ for a road trip this is 2/5of the coast of the trip how much dose the trip coat
Answer:
$600
Step-by-step explanation:
Divide 240 by 2/5
Sociologists want to test whether the number of homeless people in a particular urban area is increasing. In 2010, the average number of homeless people per day who sought shelter was 42.3 (σ = 6.2). Data from the current year reveal that the mean number of people seeking shelter per day is 45.3. Compute the test statistic using an alpha = .01 and n = 1000.
Answer:
The test statistic value is 15.3.
Step-by-step explanation:
The hypothesis for this test is:
H₀: The average number of homeless people is not increasing, i.e. μ = 42.3.
Hₐ: The average number of homeless people is increasing, i.e. μ > 42.3.
Given:
[tex]\bar x=45.3\\\sigma=6.2\\n=1000[/tex]
As the population standard deviation is provided use a single mean z-test for the hypothesis testing.
The test statistic is:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}=\frac{45.3-42.3}{6.2/\sqrt{1000}}=15.3[/tex]
Thus, the test statistic value is 15.3.
Using the z-distribution, it is found that the test statistic is of z = 15.3.
At the null hypothesis, it is tested if the mean number has not increased, that is, it still is of 42.3, hence:
[tex]H_0: \mu = 42.3[/tex]
At the alternative hypothesis, it is tested if it has increased, that is, the mean is greater than 42.3, hence:
[tex]H_1: \mu > 42.3[/tex]
We have the standard deviation for the population, hence, the z-distribution is used.
The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are:
[tex]\overline{x} = 45.3, \mu = 42.3, \sigma = 6.2, n = 1000[/tex]
Hence:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{45.3 - 42.3}{\frac{6.2}{\sqrt{1000}}}[/tex]
[tex]z = 15.3[/tex]
The test statistic is of z = 15.3.
To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918
Factor completely. If the polynomial is not factorable, write prime.
5.) 3x^3y+x^2y^2+x^2y
6.) 8r^3-64s^6
Step-by-step explanation:
5)
3x³y + x²y² + x²y
x²y (3x + y + 1)
6)
8r³ − 64s⁶
8 (r³ − 8s⁶)
8 (r − 2s²) (r² + 2rs² + 4s⁴)
The cost, in dollars, of producing x belts is given by Upper C (x )equals 751 plus 12 x minus 0.067 x squared. Find the rate at which average cost is changing when 256 belts have been produced.
Answer:
-$0.07846 per belt
Step-by-step explanation:
The average cost per belt is ...
[tex]c(x)=\dfrac{C(x)}{x}=\dfrac{751+12x-0.067x^2}{x}=751x^{-1}+12-0.067x[/tex]
Then the rate of change of average cost is ...
[tex]c'(x)=-751x^{-2}-0.134\\\\c'(256)=\dfrac{-751}{256^2}-0.067\approx -0.07846[/tex]
The rate at which average cost is changing is about -0.078 dollars per belt.
_____
Note that the cost of producing 256 belts is -$567.91, so their average cost is about -$2.22 per belt.
The student is asked to calculate the rate of change of average cost for producing belts when 256 belts are produced, by finding and evaluating the derivative of the average cost function.
Explanation:The question asks about the rate at which the average cost is changing for the production of belts given a certain cost function C(x) = 751 + 12x - 0.067x2. To find this rate when 256 belts are produced, we need to first calculate the average cost, which is C(x) divided by x, and then take the derivative of the average cost to find its rate of change. The derivative of the average cost function gives us the rate at which the average cost is changing with respect to the number of belts produced. We evaluate this derivative at x = 256 to find the specific rate of change at the production of 256 belts.
please help
As x increases by 1 unit, what is the exponential growth factor?
Answer: The answer is 3, I just finished doing the assignment.
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
We would like to construct a 66% confidence interval for the proportion of voters that support building a new prison. What is the appropriate multiplier (z) that would be used in this situation?
Answer:
The appropriate z multiplier for 66% confidence interval is 0.95
Step-by-step explanation:
We are given the following in the question:
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
We have to make a 66% confidence interval for the proportion of voters.
Confidence level = 66%
Significance level =
[tex]\alpha = 1 - 0.66 = 0.34[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.34} = \pm 0.95[/tex]
Thus, the appropriate z multiplier for 66% confidence interval is 0.95
Please help!!! ASAP someone please
Answer:
0.31 yr
Step-by-step explanation:
The formula for interest compounded continuously is
[tex]FV = PVe^{rt}[/tex]
FV = future value, and
PV = present value
If FV is twice the PV, we can calculate the doubling time, t
[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]
1. Brianna's doubling time
[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}[/tex]
2. Adam's doubling time
The formula for interest compounded periodically is
[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]
where
n = the number of payments per year
If FV is twice the PV, we can calculate the doubling time.
[tex]\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}[/tex]
3. Brianna's doubling time vs Adam's
10.663 - 10.355 = 0.31 yr
It would take 0.31 yr longer for Brianna's money to double than Adam's.
Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide. How far is the bottom of the ladder from the bottom of the slide
Answer:
the bottom of the ladder from the bottom of the slide is 15 feet far from
the bottom of the slide
Step-by-step explanation:
Given that Mitchel climbs 8 feet up the vertical ladder of a slide and zips down the 17-foot slide.
The slide the vertical ladder and the floor together form a right triangle if we can vizualise.
The hypotenuse would be the slide , and one leg is ladder and other the bottom of the ladder from the bottom of the slide
We have hypotenuse = 17 feet and one leg = 8 feet
So use Pythagorean theorem to find other leg
Other leg = [tex]\sqrt{17^2-8^2} \\=\sqrt{(17+8)(17-8)} \\= 15[/tex]
the bottom of the ladder from the bottom of the slide is 15 feet far from
the bottom of the slide
A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 5 ft, the length is 15 ft, and the top of the tank is 10 feet under the ground. Assume the tank is full and all of the gasoline will be pumped to the surface of the ground. The density of gasoline is 42 lb/ ft3. Consider a slice of gasoline that is delta y ft thick and located y ft above the center of the cylinder. Use delta or the CalcPad for delta . Leave pi in your answer. Volume of slice : ft3 Displacement of slice : ft Find the endpoints of the integral needed to find the exact work required to pump all the gasoline to the surface of the ground. Lower endpoint = Upper endpoint =
Answer:
The exact work required to pump all the gasoline to the surface of the ground is π × 5.094 × 10⁶ j
Step-by-step explanation:
Here, we note that volume of a slice is given by
Length × Width × Height
Length of slice = Length of cylinder = 15 ft
Since the slice height is Δy ft thick and located y ft above the center of the cylinder, then
Width of slice = 2 × √(r² - y²)
Where:
r = Radius of the cylinder =5 ft
∴ Width of slice = 2 × √(25 - y²)
∴Volume of slice = 15 ×2 × √(25 - y²)×Δy
Mass of slice then = 42 × 15 ×2 × √(25 - y²)×Δy = 1260 × √(25 - y²)×Δy
The force required to lift the slice is the weight of the slice, which is given by
32.2 × 1260 × √(25 - y²)×Δy = 40572 × √(25 - y²)×Δy N (Newtons)
The work done by the force is the product of the force and the distsnce through which the force acts.
Work done = 40752×(10-y) × √(25 - y²)×Δy
Therefore total work done is given by
[tex]W = \int\limits^5_{-5} {40752\times (10-y) \times \sqrt{ (25 - y^{2} )} } \, dy[/tex]
= 5094000·π J = π × 5.094 × 10⁶ j
The exact work required to pump all the gasoline to the surface of the ground = π × 5.094 × 10⁶ j
The calculation requires determining the volume and displacement of each slice of gasoline in the tank and then integrating over these from the bottom to the top of the tank (from -5 to 5 feet).
Explanation:
To calculate the exact work required to pump all the gasoline to the surface, we need to first determine the displacement of each slice of gasoline and then integrate over the total volume. The displacement of a slice at height y is the distance it needs to be moved to the surface, which is (10 - y) feet. The volume of a cylindrical slice of thickness delta y is given by the area of the cylinder's cross section times the slice's thickness, i.e., volume = pi * r^2 * delta y. Here, r = 5ft and delta y is the thickness of the slice. Therefore, the volume of the slice is 25*pi*delta y ft3. The endpoints of the integral are defined by the top and bottom of the tank relative to the center, which in this case are -5 and 5 feet. Therefore, the lower endpoint is -5 and the upper endpoint is 5.
Learn more about Work required to pump gasoline here:
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Two companies charge differently for canoe rentals, as shown below. What is the rate of change for each function? What is the cost to rent a canoe for 4 hours for each company? Company A: c = 8h + 10, where c = totals cost (in dollars) and h = number of hours Company B: $15 per hour
The rate of change for company A is $8 an hour and it would cost $42 to rent a canoe for four hours from company A.
The rate of change for company B is $15 an hour and it would cost $60 to rent a canoe for four hours from company B.
Step-by-step explanation:
Step 1:
For company A, [tex]c = 8h + 10,[/tex] where c is the cost after h hours.
When [tex]h=1,[/tex] [tex]c = 8(1) + 10 = 18.[/tex]
When [tex]h=2,[/tex] [tex]c = 8(2) + 10 = 26.[/tex]
The rate of change for company A [tex]= 26 - 18 = 8.[/tex]
The rate of change for company A is $8 an hour.
When [tex]h=4,[/tex] [tex]c = 8(4) + 10 = 42.[/tex]
So it would cost $42 to rent a canoe for four hours from company A.
Step 2:
For company A, the cost is $15 per hour so [tex]c = 15h,[/tex] where c is the cost after h hours.
When [tex]h=1,[/tex] [tex]c =1(15) =15.[/tex]
When [tex]h=2,[/tex] [tex]c = 2(15)= 30.[/tex]
The rate of change for company B [tex]= 30 - 15 = 15.[/tex]
The rate of change for company B is $15 an hour.
When [tex]h=4,[/tex] [tex]c = 4(15) = 60.[/tex]
So it would cost $60 to rent a canoe for four hours from company B.
walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. For a fundraiser, the softball team will be selling bags of mixed nuts. How many punds of walnuts and how many pounds of peanuts should the team buy in order to make a 60 pound . ixture that will sell for $3.00 per pound?
Answer: 20 pounds of walnuts should be mixed with 40 pounds of peanuts.
Step-by-step explanation:
Let x represent the number of pounds of walnuts that should be in the mixture.
Let y represent the number of pounds of peanuts that should be in the mixture.
The number of pounds of the mixture to be made is 60. This means that
x + y = 60
Walnuts cost $3.60 per pound and peanuts cost $2.70 per pound. The mixture will sell for $3.00 per pound. It means that the total cost of the mixture is 3 × 60 = $180. The expression would be
3.6x + 2.7y = 180- - - - - - - - - - - - -1
Substituting x = 60 - y into equation 1, it becomes
3.6(60 - y) + 2.7y = 180
216 - 3.6y + 2.7y = 180
- 3.6y + 2.7y = 180 - 216
- 0.9y = - 36
y = - 36/ - 0.9
y = 40
x = 60 - y = 60 - 40
x = 20
If a member variable is declared , all objects of that class share that variable. A(n) function is not a member of a class, but has access to the private members of the class. A(n) tells the compiler that a specific class will be declared later in the program. When the operator is overloaded, its function must have a dummy parameter. The class Stuff has both a copy constructor and an overloaded = operator. Assume that blob and clump are both instances of the Stuff class. For each of the statements, indicate whether the copy constructor or the overloaded = operator will be called: Staff blob = clump ; clump = blob ; blob.operator =(clump) ; showValues(blob) ; // blob is passed by value Consider the following class declaration: class Thing { private: int x ; int y ; static int z ; public: Thing() { x = y = z ; } static void putThing(int a) { z = a ; } } ; int Thing:: z = 0 ; Assume a program containing the class declaration defines three Thing objects with the following statement: Thing one, two, three ; How many separate instances of the x member exist? How many separate instances of the y member exist ? How many separate instances of the z member exist? What value will be stored in the x and y members of each object? Write a statement that will call the putThing member function before the Thing objects are defined. Explain why the parameter of a copy constructor must be a reference.
Answer:
a shs s s s ss bsbsbsbs s s s s s s s s s s s s s
1) Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep
up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his
vlog and he has watched 1250 movies. He has watched twice as many horror movies as action
movies. Write two equations that can model this situation.
two equations which can model this situation is : [tex]y=2x[/tex] and [tex]x+y=1250[/tex]
Step-by-step explanation:
Here we have , Bronson is an action and horror movie junkie. He started a movie review vlog and needs to keep up with his movie viewing at a high pace. It has been a total of 50 weeks since he has stated his vlog and he has watched 1250 movies. He has watched twice as many horror movies a action movies. We need to Write two equations that can model this situation. Let's find out:
Let Bronson watched x action movies and y horror movies , than according to question horror movies he watched is twice that of action movies i.e.
⇒ [tex]y=2x[/tex] ........(1)
Now , he has watched 1250 movies i.e.
⇒ [tex]x+y=1250[/tex] .......(2)
⇒ [tex]x+2x=1250[/tex]
⇒ [tex]3x=1250[/tex]
Therefore , two equations which can model this situation is : [tex]y=2x[/tex] and [tex]x+y=1250[/tex] .
Math-The park department wants to have new tree planted. They agreed that 1/10 of the tree will be oak,3/10 will be pine, and 2/10 will be willow. They are undecided about the rest. What fraction of trees will be oak, or pine?
Factor the expression. 16j2 + 24j + 9
(4j – 3)Factor the expression. 16j2 + 24j + 9
(4j – 3)2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)^2
(4j + 3)(4j – 3)
(4j + 3)^2
(4j – 9)(4j + 1)
Option C: [tex](4 j+3)^{2}[/tex] is the correct answer.
Explanation:
The given expression is [tex]16 j^{2}+24 j+9[/tex]
We need to factor the expression.
Let us rewrite the expression as
[tex](4j)^{2}+24 j+(3)^2[/tex]
Also, we can rewrite the term [tex]24j[/tex] as [tex]2(4)(3)j[/tex]
Thus, we have,
[tex](4j)^{2}+2(4j)(3)+(3)^2[/tex]
Hence, the equation is of the form,
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
where [tex]a=4 j[/tex] and [tex]b=3[/tex]
Hence, the factor of the expression can be written as [tex](4 j+3)^{2}[/tex]
Thus, the factored expression is [tex](4 j+3)^{2}[/tex]
Therefore, Option C is the correct answer.
Final answer:
The factored form of the expression 16j^2 + 24j + 9 is (4j + 3)².
Explanation:
To factor the expression 16j2 + 24j + 9, we look for two binomials ((aj + b)(cj + d)) that when multiplied together, give us the original quadratic expression. The factors of 16j2 are 4j imes 4j, and the factors of 9 are 3 imes 3. Our binomial factors will have the format (4j + 3).
Expanding the binomial (4j + 3)², we have:
(4j + 3) imes (4j + 3)
= 16j2 + 12j + 12j + 9
= 16j2 + 24j + 9
This matches the original expression exactly, so the factored form of the expression is (4j + 3)².