Back | Next Question 2 Indicate the answer choice that best completes the statement or answers the question. Determine if the two figures are congruent by using transformations. Explain your reasonin a. congruent; a rotation followed by a reflection Ob. congruent; a reflection followed by another reflection Oc. congruent; a reflection followed by translation O d. not congruent
Answers
b. congruent; a reflection followed by another reflection
If grey shape is reflected across the x-axis and then the y-axis, or viceversa, white shape is obtained.
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In the expansion of (3a + 4b)^8, which of the following are possible variable terms?
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Remember the Binomial Theorem:
[tex](a+b)^n\text{ =}\sum_{i\mathop{=}0}^n\begin{bmatrix}{n} & \\ {i} & {}\end{bmatrix}a^{(n\text{ - i})}b^i[/tex]Now, consider the following polynomial:
[tex]\left(3a+4b\right)^8[/tex]Applying the Binomial Theorem, where:
a = 3a
b= 4b
we get:
[tex](3a+4b)^8\text{ =}\sum_{i\mathop{=}0}^8\begin{bmatrix}{8} & \\ {i} & {}\end{bmatrix}3a^{(8\text{ - i})}4b^i[/tex]thus, expanding the sum, we get:
[tex]\begin{gathered} \frac{8!}{0!(8\text{ -0})!}(3a)^8(4b)^0+\frac{8!}{1!(8\text{ -1})!}(3a)^7(4b)^1+\frac{8!}{2!(8\text{-2})!}(3a)^6(4b)^2 \\ +\frac{8!}{3!(8\text{ - 3})!}(3a)^5(4b)^3\text{ + ........+}\frac{8!}{8!(8\text{ -8})!}(3a)^0(4b)^8 \end{gathered}[/tex]Now, simplifying we get:
[tex]\begin{gathered} 6561a^8\text{ + 6998a}^7b\text{ + 326592a}^6b^2+870912a^5b^3+1451520a^4b^4 \\ +1548288a^3b^5+1032192a^2b^6+393216ab^7+65536b^8 \end{gathered}[/tex]then, we can conclude that the correct answer is:
Answer:The variable terms are:
[tex]\begin{gathered} a^8\text{ ,a}^7b\text{ , a}^6b^2,\text{ }a^5b^3,\text{ }a^4b^4 \\ ,\text{ }a^3b^5,\text{ }a^2b^6,\text{ }ab^7\text{ and }b^8 \end{gathered}[/tex]3. The results of the primary election are shown. Smith 15% Goron 35% Other 10% Fishman 40% (a) Order the popularity of the choices from greatest to least. (b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work. (c) 40 people voted for "Other." Was the estimate of total voters from Part (b) accurate? Explain. Answer: I C Focus 33
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a) The order is;
Fishman
Goron
Smith
Other
b) 98 people would have voted for Goron if the estimation was true
c) The estimate was not correct as the actual value obtained (40) is not same as what was estimated (28)
a) We want to order the popularity of choices from greatest to least
What we have to know and understand here is that the higher the percentage, the greater the popularity
Thus, we have it that;
Fishman
Goron
Smith
Other
b) As we can see from the data presented, Goron had 35% of the votes
So, the number of people that voted for Goron will be;
[tex]\begin{gathered} 35\text{ \% of 280} \\ =\text{ }\frac{35}{100}\times280\text{ = 98} \end{gathered}[/tex]98 people would have voted for Goron if the estimation was true
c) Here, we want to evaluate if the total we had from part B was correct
What we have to do here is get the number that would have been correct if at all 280 people voted
We have this as;
[tex]\begin{gathered} 10\text{ \% of 280} \\ =\text{ }\frac{10}{100}\times280\text{ = 28} \end{gathered}[/tex]The estimate was not correct as the actual value obtained (40) is not same as what was estimated (28)
What is the slope in c = 1.05p - 4?
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a linear equation is in the form
[tex]y=mx+b[/tex]in which the m is the slope that multiplies the independent variable and b will be the point for the y-intercept
The slope for the equation given is 1.05 since is the value multiplying the independet variable p
Find the solutions to the following quadric equation 2Xsquared -1x-2=0
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Given the quadratic equation:
[tex]2x{}^2-1x-2=0[/tex]We can use the general solution for the quadratic equation ax² + bx + c = 0:
[tex]x=\frac{-b\pm\sqrt{b{}^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-2 \end{gathered}[/tex]Finally, using the general solution:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-2)}}{2\cdot2}=\frac{1\pm\sqrt{1+16}}{4} \\ \\ \therefore x=\frac{1\pm\sqrt{17}}{4} \end{gathered}[/tex]Daria bought a bracelet at original cost $14 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet? Round to the nearest cent.
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Daria bought a bracelet at original cost $14 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet? Round to the nearest cent.
Remember that
100%+45%=145%=145/100=1.45
Multiply the original cost by the factor 1.45
so
$14*1.45=$20.30
the answer is $20.30A coin is tossed 10 times. It lands on heads 7 times and lands on tails 3 times. What is the experimental probability of the coin landing on tails?7/103/101/20
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The experimental probability is given by the following formula
[tex]\text{experimental probability=}\frac{successful\text{ tries}}{\text{total number of tries}}[/tex]In our case, the total number of tries is 10 and the successful number of tries is 3 (landing on tails); thus,
[tex]\Rightarrow\text{experimental probability}=\frac{3}{10}[/tex]The answer is 3/10
Which best represents the transformations for the coordinates of the verticals of the given pairs of triangles (1,6), (-1,3), (5,2), and (-1,6), (-3,3), (3,2) Is it a rotation (that my educated guess)Reflection or translation?
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No. It's not a rotation. It's translation.
for translation, there is a formula that is
[tex]x^{\prime}=x+a\text{ }[/tex]and
[tex]y^{\prime}=b+y[/tex][tex]y^{\prime}=b+y[/tex]where (x',y') is the new coordinate and (x,y) is the old one and (a,b) is the increasing value of (x,y)
so here we have the new coordinates are (-1,6), (-3,3), (3,2)
and the olds are (1,6), (-1,3), (5,2)
[tex]\begin{gathered} -1=a+1 \\ and\text{ }6=b+6 \\ this\text{ gives } \\ a=(-2)\text{ and b=0} \\ similarly\text{ you take each case you will get the value of a is \lparen-2\rparen and the value of b is 0.} \end{gathered}[/tex]Thus we can say that the triangle is translated by adding the horizontal value (a) =(-2) to the x-coordinate of each vertex and the vertical value (b)=0 to the y-coordinate.
now you can see
[tex]\begin{gathered} 1+(-2)=1\text{ \& 6+\lparen0\rparen=6 ie \lparen1,6\rparen+\lparen-2,0\rparen=\lparen-1,6\rparen} \\ similarly \\ (-1,3)+(-2,0)=(-3,3) \\ (5,2)+(-2,0)=(3,2) \end{gathered}[/tex]so the right answer is translation.
I would like to go step by step with this
Answers
The dice simulation method will be suitable according to the given sample space for Kwang to select which night of the week he will go to the shelter.
Step 1: What is the sample space of the outcome?
The sample space will be {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}.
Step 2: Choose a simulation method that matches the sample space.
The dice simulation method will be suitable. Because a dice has 6 faces and the given sample space has 6 elements.
Step 3: Assign each outcome to a random number.
Let's assign randomly:
1 = Monday,
3 = Tuesday,
5 = Wednesday,
2 = Thursday,
6 = Friday,
4 = Saturday.
Step 4: Run 4 simulations to select a night to volunteer for each of the next 4 weeks. List the result for each simulation is below:
1st Simulation: Let's say Kwang rolls the dice and got 4.
2nd Simulation: Let's say Kwang rolls the dice and got 6.
3rd Simulation: Let's say Kwang rolls the dice and got 3.
4th Simulation: Let's say Kwang rolls the dice and got 2.
Step 5: Based upon the simulations state the real-world outcomes for each event. Which day of the week will Tom volunteer for each of the next 4 weeks?
Week 1: Saturday
Week 2: Friday
Week 3: Tuesday
Week 4: Thursday
Thus, the dice simulation method will be suitable according to the given sample space for Kwang to select which night of the week he will go to the shelter.
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Paisley is going to invest in an account paying an interestrate of 34% compounded daily. How much would Paisleyneed to invest, to the nearest dollar, for the value of theaccount to reach $400 in 16 years?
Answers
Answer:
$2
Explanation:
To solve the given problem, we'll use the below compound interest formula;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A = future amount = $400
P = the initial amount( principal)
r = annual interest rate in decimal form = 34/100 = 0.34
n = number of compounding periods in a year = 365
t = time in years = 16
Let's go ahead and substitute the above values into our formula and solve for P;
[tex]\begin{gathered} 400=P(1+\frac{0.34}{365})^{365\times16} \\ 400=P(1.0009)^{5840} \\ 400=229.86P \\ P=\frac{400}{229.86} \\ \therefore P=2\text{ dollars} \end{gathered}[/tex]Chuck's age is five years less than twice Larry's age. If Chuck's age is 150% of Larry's age, then what is Larry's age, in years?A. 6B. 8C. 10D. 15
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Answer:
Larry's age is 10 years
Explanation:
Let Chuck's age be c
Let Larry's age be L
Chuck's age is five years less than twice Larry's age
Mathematically:
[tex]c\text{ = 2l-5}[/tex]Chuck's age is 150% of Larry's age
What this mean is that Chuck's age is 1.5 times multiplied by Larry's age
Mathematically, we have this as:
[tex]c\text{ = 1.5l}[/tex]Now, we can proceed to equate the two equations as follows:
[tex]\begin{gathered} 2l-5\text{ = 1.5l} \\ 2l-1.5l\text{ = 5} \\ 0.5l\text{ = 5} \\ l\text{ = }\frac{5}{0.5} \\ l\text{ = 10 } \end{gathered}[/tex]Find the sum of (3x2 + 18x – 7) and (-13x2 + 7x – 11)A –13x3 + 3x2 + 25x – 18B –13x3 + 10x2 + 7x – 7C-13x3 + 10x2 + 18x – 18D -10x2 + 25x – 18
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Answer:
The correct option is D, the sum of the given polynomials is
[tex]-10x^2+25x-18[/tex]Explanation:
To find the sum of:
[tex]3x^2+18x-7[/tex]and
[tex]-13x^2+7x-11[/tex]We write:
[tex]\begin{gathered} (3x^2+18x-7)+(-13x^2+7x-11) \\ =3x^2+18x-7-13x^2+7x-11 \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 3x^2-13x^2+18x+7x-7-11 \\ =-10x^2+25x-18 \end{gathered}[/tex]what would be a good upper bound for the number of jelly beans?
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From the picture:
• height of 1 bean: 1 unit
,• radius of 1 bean: 0.25 unit (assumed)
,• height of the jar: 11 units
,• radius of the jar 4 units
we assume that the jar and the bean are cylinders.
Volume of a cylinder = π*r²*h
where r is the radius and h is the height. Then:
Volume of 1 bean = π*0.25²*1 = 0.2 cubic units
Volume of the jar = = π*4²*11 = 553 cubic units
Therefore, an upper bound for the number of jelly beans is 553/0.2 = 2765
Round the number. Write the result as a product of a single digit and a power of 10 0.00063718
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EXPLANATION
Given the number 0.00063718, rounding and writting as a product of a single digit and a power of 10 give us:
6x10^-4
find the value of the investment at the end of 5 years
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Given: Following details for an amount compounded annually-
[tex]\begin{gathered} P=34900 \\ R=8\% \\ t=5\text{ years} \end{gathered}[/tex]Required: To determine the amount after 5 years.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{\frac{t}{n}}[/tex]Here, A is the amount accrued.
P is the principal amount.
r is the annual rate as a decimal.
t is the time.
n is the number of times interest is compounded in a year.
In this case, the value of n=1 as we are calculating for annual compounding if the interest is compounded semiannually, n=2. For monthly, n=12. Finally, for daily n=365.
Now substituting the values in the formula as-
[tex]\begin{gathered} A=34900(1+0.08)^5 \\ =34900(1.08)^5 \\ =\text{\$}51279.55 \end{gathered}[/tex]Final Answer: Investment after 5 years compounded annually is $51279.55
Bridget's father is building Champion a new stable,
and he needs to drive a nail through a 4 x 6 board
with an actual thickness of 31¹/2 inches. What length
of nail should he use? (Give your answer in inches and
write it as a mixed number.)
lesson 55)
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Answer:
Step-by-step explanation:
4x6 meaning the length is 4 and the width is 6 while as the thickness all around is 31 1/2 inches.
4x6=24
the area is 24 inches
He should use a 24 inch wide nail and the length should be 33/2 so it doesnt unloosen.
the linear function f(x)=mx+b is one to one for all slopes, expect when m=____ then find f exponent negative 1(x).
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how much money will be in Devon's retirement account if she continues to make the same monthly investment for 40 years
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Annuities
It refers to a special form to accumulate interest over a regular payment or cash flow (C) per period.
Devon decides to save money for her retirement by depositing C=$524 each month in an account that is expected to earn interest with an APR of r=5.25% compounded monthly.
We will calculate the future value (FV) of her investment over a period of n=40 years.
The future value can be calculated with the formula:
[tex]FV=C\cdot\frac{(1+i)^n-1}{i}[/tex]Where i is the interest rate adjusted for the compounding period. Since there are 12 months in one year:
[tex]i=\frac{r}{12}=\frac{0.0525}{12}=0.004375[/tex]The number of periods is also adjusted for monthly compounding:
n = 40*12 = 480
Now apply the formula:
[tex]FV=524\cdot\frac{(1+0.004375)^{480}-1}{0.004375}[/tex]Calculating:
[tex]\begin{gathered} FV=524\cdot1,629.45 \\ FV=853,832.69 \end{gathered}[/tex]There will be $853,832.69 in Devon's retirement account in 40 years
The distance from. Eight to point B is blank units. This is from. Eight to. C is blank units. The decision for point B de point C is blank units. The given points choose/does not form a right triangle?
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EXPLANATION
Since we have the given points:
A= (2,1)
B= (10,1)
C= (2,7)
We can represent this in a graphing calculator:
Now, in order to obtain the distance from A to B, we need to subtract both
x-coordinates points:
10-2 = 8 units
Therefore, the distance from A to B is 8 units.
Next, computing the distance from point A to the point C:
y_C - y_A = 7 - 1 = 6 units
Thus, the distance from point A to point C is 6 units.
In order to obtain the distance from the point B to C we need to apply the distance equation as shown as follows:
[tex]\text{distance}=\sqrt[]{(7-1)^2+(10-2)^2}[/tex]Subtracting numbers:
[tex]\text{distance}=\sqrt[]{6^2+8^2}[/tex]Computing the powers:
[tex]\text{distance}=10\text{ units}[/tex]The distance from point B to point C is 10 units.
Finally, we can conclude that the given points do form a right triangle.
[tex] 4\sqrt{109.6} [/tex]find the quotient
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The given division is
[tex]\frac{109.6}{4}[/tex]If we use the long division method, we get the following
As you can see in the image above, the quotient is 27.4.Quiz 1 Write an addition equation or a subtraction equation (your choice!) to describe the diagram. _15 10 -5 0 5 Report a prob
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Each arrow represents a subtraction. The beginning of the arrow is the number where the subtraction should start and the point of the arrow is the point where the subtraction should end. The first arrow begins in "0" and ends in "-4", while the second arrow begins on the point of the second one and ends in "-13".
We should first represent the arrow number 1, which is shown below:
[tex]0\text{ -4}[/tex]Because the arrow starts at 0 and go "4" units to the left, therefore we need to subtract 4.
The second arrow starts from the first and goes 9 units to the left, so we have:
[tex](0\text{ - 4) - 9}[/tex]Write a cosine function that Has a midline of 2 an amplitude of 3 and a period of 7pi/4
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Given:
Amplitude of cosine function, A=3.
Period, T=7π/4.
Midline, D=2.
The time period can be expressed as:
[tex]T=\frac{2\pi}{B}[/tex]Put T=7π/4 to find the value of B.
[tex]\begin{gathered} \frac{7\pi}{4}=\frac{2\pi}{B} \\ B=\frac{4\times2}{7} \\ =\frac{8}{7} \end{gathered}[/tex]The general cosine function can be expressed as,
[tex]f(x)=A\cos (Bx)+D[/tex]Substitute B=8/7, A=3 and D=2 in above equation.
[tex]f(x)=3\cos (\frac{8}{7}x)+2[/tex]Therefore, the cosine function is,
[tex]f(x)=3\cos (\frac{8}{7}x)+2[/tex]if the measure of the angles of a triangle are represented by 2x, 3x - 15 , and 7x + 15, the triangle is
Answers
Answer:
D An isosceles triangle
Explanation:
Given that the angles of a triangle are represented by;
[tex]\begin{gathered} 2x \\ 3x-15 \\ 7x+15 \end{gathered}[/tex]Recall that the sum of angles in a triangles is equal to 180 degrees.
Summing up the given angles we have;
[tex]\begin{gathered} (2x+3x-15+7x+15)^{\circ}=180^{\circ} \\ 2x+3x+7x-15+15=180 \\ 12x=180 \\ x=\frac{180}{12} \\ x=15 \end{gathered}[/tex]We have calculated the value of x.
We now need to calculate the value of each angle;
[tex]\begin{gathered} 2x=2(15)=30^{\circ} \\ 3x-15=3(15)-15=30^{\circ} \\ 7x+15=7(15)+15=120^{\circ} \end{gathered}[/tex]Therefore, the angles of the triangle are;
[tex]30^{\circ},30^{\circ},120^{\circ}[/tex]From the derived angles, we can notice that the triangle has two equal angles.
So it is an Isosceles triangle.
Flex Gym charges a membership fee of $150.00 plus $41.00 per month to join the gym. Able gym charges a membership fee of $120.00 plus $46.00 per month. Find the number of months for which you would pay the same total fee to both gyms.
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We have to write an equation for each gym of the cost as a function of the months, so:
[tex]\begin{gathered} We\text{ call c=the total cost and m=months.} \\ \text{For Flex Gym:} \\ c_F=41\cdot m+150 \\ \text{For Able Gym}\colon \\ c_A=46\cdot m+120 \end{gathered}[/tex]Now, we want to find the number of months at which the both gym have the same cost, so:
[tex]\begin{gathered} c_F=c_A \\ 41\cdot m+150=46\cdot m+120 \\ 150-120=46\cdot m-41\cdot m \\ 30=5\cdot m \\ m=\frac{30}{5}=6 \end{gathered}[/tex]At 6 months the cost of the both gyms is the same.
Yolanda bought 14 books. Yolanda bought 2 times as many books as Hans. Let n be the number of books that Hans bought.(a) Write an equation that relates the number of books that they bought.Use 2, 14, and n.
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number of books Yolanda bought = 14 books
Yoland bought 2 times as many books as Hans. Therefore, Yolanda number of books can be represented as 2n. Where n is the number of books Han bought.
n = number of books Hans bought
2n = 14
divide btoh
The equation V=31600(0.92)tV=31600(0.92)t represents the value (in dollars) of a car t years after its purchase. Use this equation to complete the statements below.
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Notice that:
[tex]0.92=1-0.08.[/tex]Therefore, we can rewrite the given equation as follows:
[tex]V=31600(1-0.08)^t.[/tex]From the above equation, we get that the price of the car is decreasing an 8% per year.
Evaluating the given equation at t=0, we get the purchase price:
[tex]V(0)=31600(0.92)^0=31600(1)=31600.[/tex]Answer:
The value of this car is decreasing at a rate of 8 percent per year.
The purchase price of the car was 31600 dollars.
Hi, can you help me answer this question please, thank you!
Answers
The t-statistic of the hypothesis is -2.1075 and the P value is 0.04 .
Given that
Sample Size п, = 80 proportion of mean P₁ = 45%
P₁ = 0·45
Sample size п₂ = 40
proportion of mean P₂ = 55%
P₂=0·55
q₁ = 1- P₁=1-0·45 = 0.55
q₂= 1 - P₂ =1-0.55 = 0.45
V₁ = 0.65
Mean= P₁- P₂ = 0.35 -0.55 =-0.20
standard deviation
SE (P₁ P₂) = 0.0949
Test statistic = 0.0949 = P₁- P₂ / SE( P₁- P₂) = -2.1075
t = -2-1075
DF = (N-1)+(N2-1)
Significance level=0.05
CS = 79+39
df = 118
This is a two tailed test for this hypothesis
P = 0.037236
P = 0.037
Hence the t-statistic of the hypothesis is -2.1075 and the P value is 0.037
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The floor of a square closet measures 7 feet on each side, as sho 7 feet What is the area of the floor of the closet?
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The formula to find the area of a square is:
[tex]\begin{gathered} A=s^2 \\ \text{ Where A is area and} \\ s\text{ is a side of the square} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} s=7ft \\ A=s^2 \\ A=(7ft)^2 \\ A=49ft^2 \end{gathered}[/tex]Therefore, the area of the floor of the closet is 49 square feet.
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than or equal to 2". Find P(not A). Outcome Probability 1 0.26 2 0.45 3 0.06 4 0.04 5 0.15 6 0.04
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A Probability
1 0.26
2 0.45
3 0.06
4 0.04
5 0.15
6 0.04
Probability to be less or equal than 2 = 0.45 + 0.26
= 0.71
write each in scientific notation with the answer simplified:(8•10^13) ÷ (2•10^8)(5•10^8) (6•10^9) ÷ (15•10^14)
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To write in scientific notation we must follow the formula below:
[tex]N=a\times10^b[/tex]where:
a is a number between 1 and 9;
b is a integer, i.e., can be a positive or negative number
We have also to do some power properties.
For the first question, we get:
[tex]\begin{gathered} \mleft(8•10^{13}\mright)\div2•10^8= \\ =\frac{8}{2}\times\frac{10^{13}}{10^8}= \\ =4\times10^{13-8}= \\ =4\times10^5 \end{gathered}[/tex]So the final answer is 4 x 10^5
For the second one:
[tex]\begin{gathered} \mleft(5•10^8\mright)6•10^9\div15•10^{14}= \\ =\frac{5\cdot6\cdot10^{8+9}}{15\cdot10^{14}}= \\ =\frac{30\cdot10^{17}}{15\cdot10^{}^{14}}= \\ =\frac{30}{15}\cdot10^{17-14}= \\ =2\cdot10^3 \end{gathered}[/tex]Our final answer here is 2 x 10^3.
We are stuck on this I will need some help trying to figure out which one is the right answer
Answers
The general form of represented of a number in scientific notation is,
[tex]a\times10^n[/tex]Here, the required conditions are,
[tex]\begin{gathered} 1\leq a<10 \\ n\in N \end{gathered}[/tex]Note that N represents the set of all possible natural numbers.
Consider the given numbers and match them with the above form.
Clearly, the rightmost number in the given image is in the proper form of the scientific notation,
[tex]8.98\times10^6[/tex]Here, 'a' is 8.98 and 'n' is 6.
Both the values satisfy the required conditions.
Therefore, it can be concluded that out of all the given numbers, the number represented in scientific notation is,
[tex]8.98\times10^6[/tex]