Answers
5. Let the following inequality:
[tex]13-3m\text{ }<-2[/tex]this is equivalent to:
[tex]-13+3m\text{ }>2[/tex]this is equivalent to:
[tex]-13+13+3m\text{ }>2\text{ +13}[/tex]this is equivalent to:
[tex]3m\text{ }>15[/tex]solve for m:
[tex]m\text{ }>\frac{15}{3}=5[/tex]that is :
[tex]m\text{ }>5[/tex]6. Because of the graphic (real line), we can conclude that the correct interval would be:
[tex](-\infty,-3\rbrack\text{ = x}\leq-3[/tex]Then we have to find the inequalities that have this solution interval.
a) Let the inequality
[tex]\frac{x}{3}+2\leq1[/tex]this is equivalent to:
[tex]\frac{x}{3}+2-2\leq1-2[/tex]this is equivalent to:
[tex]\frac{x}{3}\leq-1[/tex]solve for x:
[tex]x\leq-3[/tex]then. A) represent the graph.
b)Let the inequality
[tex]8-5x\ge23[/tex]
this is equivalent to:
[tex]-8+5x\leq-23[/tex]this is equivalent to:
[tex]-8+8+5x\leq-23+8[/tex]this is equivalent to:
[tex]5x\leq-15[/tex]solve for x:
[tex]x\leq\frac{-15}{5}\text{ = -3}[/tex]then the solution interval would be:
[tex]x\leq\text{-3}[/tex]then. B) represent the graph.
c) Let the inequality:
[tex]-18\ge3+7x[/tex]this is equivalent to:
[tex]-18+18\ge3+18+7x[/tex]this is equivalent to:
[tex]0\ge21+7x[/tex]this is equivalent to:
[tex]-21\ge7x[/tex]solve for x:
[tex]x\text{ }\leq\frac{-21}{7}\text{ = -3}[/tex]that is:
[tex]x\text{ }\leq\text{-3}[/tex]then. C) represent the graph.
d) Let the inequality:
[tex]7x-3\leq18[/tex]this is equivalent to:
[tex]7x-3+3\leq18+3[/tex]this is equivalent to:
[tex]7x\leq21[/tex]solve for x:
[tex]x\leq3[/tex]We can conclude that this interval does not represent the graph because:
[tex]x\leq3\text{ }\ne\text{ }x\leq-3\text{ }[/tex]Finally:
e) Let the inequality:
[tex]1-\frac{x}{2}\text{ }\leq2\text{ +}\frac{1}{2}[/tex]this is equivalent to:
[tex]-1+\frac{x}{2}\text{ }\ge-2\text{ -}\frac{1}{2}[/tex]this is equivalent to
[tex]-2+x\text{ }\ge-4\text{ -}1[/tex]that is:
[tex]x\text{ }\ge-4\text{ -}1+2[/tex]that is:
[tex]x\text{ }\ge-3[/tex]THEN WE CAN CONCLUDE THAT THE CORRECT ANSWER ARE:
A), B), C) AND E)
Related Questions
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. Forexample b = 22 when a = -23. Which equation represents this
direct variation between a and b?
O b=-a
O-b=-a
Ob-a=0
Ob(-a)=0
Answers
The equation b=-a is the correct equation.
What is an equation?
An equation is a statement in maths that demonstrates the equivalence of two factors by linking them with the equivalent symbol =. Equations are used to define geometric patterns in Euclidean geometry. Because the equations beneath consideration, such as implicitly equations or descriptive equations, contain an unlimited variety of solutions, the goal has started to shift: instead of directly stating the alternatives or collecting them, which again is unattainable, one utilizes equations to analyze the features of figures. This is the fundamental concept of elementary algebra, a significant mathematics discipline. Differential equations is equations in which 1 or more polynomials and its implications are involved. They are addressed by locating a functional expression that doesn't employ derivatives. Differential equations are utilized to analyze rate-related phenomena.
The equation b=-a is the correct equation.
Hence, option (a) b=-a is correct.
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Complete both transformations below.
Then enter the final coordinates of the figure.
(1,-3)
A
C (2,-5)
B
(5,-1)
A" ([?], [])
B" ([ ], [])
C" ([],[])
1) Reflect across y - axis
2) <4.5>
Answers
Answer:
A''(3, 2), B''(-1, 4), C''(2, 0)
Explanation:
For the first step, negate the y coordinate.
For the second step, add 4 to the x coordinate and 5 to the y coordinate.
[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]
Mr. Jones and Mr. Evansbee both have gardens shaped as squares. The length of each side of Mr. Jones’ garden is 6 yd. The length of each side of Mr. Evansbee’s garden is 10 yd.
(a) Write an expression with exponents for the area of Mr. Jones’ garden. Then, find the area of the garden.
(b) Write an expression with exponents for the area of Mr. Evansbee’s garden. Then, find the area of the garden. Each plant takes up 2 yd(squared) of space in both gardens.
(c) How many plants can Mr. Jones place in his garden? How many plants can Mr. Evansbee place in his garden? Explain your reasoning.
(d) For each garden, the cost per plant is $4.99. Using your answers from part (c), how much will each gentleman spend on plants for his garden?
Answers need to be step-by-step please
Answers
Answer:
(a) expression: (6 yd)²; area: 36 yd²
(b) expression: (10 yd)²; area: 100 yd²
(c) Jones: 18; Evansbee: 50
(d) Jones: $89.82; Evansbee: $249.50
Step-by-step explanation:
You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.
Area of a squareThe formula for the area of a square of side length s is ...
A = s²
(a) Jones' gardenThe area of a square garden with a side length of 6 yards is ...
A = (6 yd)² . . . . . expression for the area
A = 36 yd² . . . . . the area of the garden
(b) Evansbee's gardenThe area of a square garden with a side length of 10 yards is ...
A = (10 yd)² . . . . . expression for the area
A = 100 yd² . . . . . the area of the garden
(c) Number of plants
The area used by the plants is the product of their number and the area taken by each.
For Jones' garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 36 yd²
n = (36 yd²)/(2 yd²/plant) = 18 plants
Mr. Jones can place 18 plants in his garden.
For Evansbee's garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 100 yd²
n = (100 yd²)/(2 yd²/plant) = 50 plants
Mr. Evansbee can place 50 plants in his garden.
(d) Cost of plantsAt $4.99 each, the cost of plantings will be $4.99 times the number of plants.
Plants for Jones' garden cost 18($4.99) = $89.82.
Pants for Evansbee's garden cost 50($4.99) = $249.50.
Select all equations that are equivalent to x² + 6x = 16
Answers
Answer
Options C and F are correct.
x² + 6x + 9 = 25
(x + 3)² = 25
are both equivalent to
x² + 6x = 16
Explanation
The equations that are equivalent to x² + 6x = 16 will all have to reduce to this exact equation on simplification.
x² + 6x + 9 = 0
Option A is not correct as this equation isn't equal to the equation given in the question.
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
Option B is not correct as this equation isn't equal to the equation given in the question.
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This option C is corect as it matches the equation given in the quesion.
(x + 3)² = 0
x² + 6x + 9 = 0
Option D is not correct as this equation isn't equal to the equation given in the question.
(x + 3)² = 16
x² + 6x + 9 = 16
x² + 6x = 16 - 9
x² + 6x = 7
Option E is not correct as this equation isn't equal to the equation given in the question.
(x + 3)² = 25
x² + 6x + 9 = 25
x² + 6x = 25 - 9
x² + 6x = 16
This option F is corect as it matches the equation given in the quesion.
Hope this Helps!!!
I need help with this question but no one is helping me! Can someone please help me
Answers
Answer:
13 + 13 = 26
13/26 * 12/25 = 6/25 = 0.24
Hey bb I know that it was ur b day and u said u were gonna come out to ur parents as bi. Did u do it and if u did how did it go. Just checking in, ofc u don’t know me so u don’t even have to tell me anything if you want.
Answers
An event can be said to be a set of possible outcomes which results from an experiment.
An individual can be said to create a theory after he observes events.
A theory is said to be a set of ideas that explains the results from an experiment.
Therefore, an individual creates a theory after he observes an event.
ANSWER:
Theory
You deposit $300 each month into an account earning 6% interest compounded monthly. a) How much will you have in the account in 30 years? $ b) How much total money will you put into the account? $ c) How much total interest will you earn?
Answers
Using the future value formula, it is found that:
a) You will have $301,355 in the account after 30 years.
b) You will have put $108,000 in the account.
c) You will have earned $193,355 in interest.
What is the future value formula?The future value formula is given by:
[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]
In which the parameters are described as follows:
P is the payment.n is the number of payments.r is the interest rate.Considering the $300 deposits, the interest rate of 6% and the monthly compoundings for 30 years, the values of the parameters are given as follows:
P = 300, r = 0.06/12 = 0.005, n = 12 x 30 = 360.
Hence the balance of the account after 30 years will be given by:
[tex]V(30) = 300\left[\frac{(1.005)^{360} - 1}{0.005}\right][/tex]
V(30) = $301,355.
The amount placed into the account is given by:
360 x 300 = $108,000.
The remaining amount is earned in interest, hence:
301355 - 108000 = $193,355.
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Trish's resting heart rate is 50 beats per minute. For every
minute she exercises, her heart rate increases 5 beats per
minute. How long will it take her to reach a heart rate of
120 beats per minute?
A 5 minutes
B 14 minutes
C 34 minutes
D 70 minutes
Answers
Answer:
B
Step-by-step explanation:
(120 - 50 b/m) / 5 b / m^2 = 14 minutes
5. If y = 1 and x = then in terms of x, y = (A)+1 (B) (C) (D)
Answers
The question states:
Notice that the angle for which its measure is arctan(a/b), is the angle that has "a" as the oposite side, and "b" as the adjacent side , so it is the angle on the bottom right of the triangle.
Then the cosine of that angle, is defined as:
cos(angle) = adjacent/hypotenuse = b / squareroot( a^2+b^2)
[tex]\cos (\theta)=\frac{b}{\sqrt[]{a^2+b^2}}[/tex]which agrees with answer D in the list of possible answers given.
A camera has a listed price of $788.99 before tax. If the sales tax rate is 7.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer:
$850.14
Step-by-step explanation:
7.75% as decimal: 0.0775
788.99 x 0.0775 = 61.146725
788.99 + 61.146725 = 850.136725
850.136725 rounded to nearest cent is 850.14
So the total price of the camera with sales tax included is $850.14
Question 12 of 47Solve kx - 2 = 7 for x.
Answers
ANSWER:
D. x = 9/k
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]kx-2=7[/tex]We solving for x:
[tex]\begin{gathered} kx=7+2 \\ \\ x=\frac{9}{k} \end{gathered}[/tex]The correct answer is D. x = 9/k
Plot (−1 3/4, 4 1/2) on the coordinate plane. Keyboard Instructions Initial graph state The horizontal axis goes from -5 to 5 with ticks spaced every 1 unit(s). The vertical axis goes from -5 to 5 with ticks spaced every 1 unit(s).
Answers
The point [tex](-1\frac{3}{4},4\frac{1}{2})[/tex] has been plotted on the coordinate plane.
Given the point [tex](-1\frac{3}{4},4\frac{1}{2})[/tex]
The coordinate plane is used to graph the points, lines and other objects.
First we have to convert the mixed fraction to the simple fraction
[tex]-1\frac{3}{4}[/tex] = -7/4
[tex]4\frac{1}{2}[/tex] = 9/2
Now we have to convert the simple fraction to decimal form
-7/4 = -1.75
9/2 = 4.5
The point is (-1.75,4.5)
Here the condition of axis is given, the horizontal axis is goes from -5 to 5, that is -5 < x < 5, and the vertical axis goes from -5 to 5 that is -5 < y < 8
Plot the points on the coordinate plane
Hence, the point [tex](-1\frac{3}{4},4\frac{1}{2})[/tex] has been plotted on the coordinate plane.
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Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height above ocean measured in feet as a function of time could be modeled by the function h(t) = -16t2 + 16t + 672, where t is the time in seconds and h is the height in feet. After how many seconds did Jason hit the water
Answers
You have the following function for the height respect to the water, Jason has after time t he jumped:
[tex]h(t)=-16t^2-16t+672[/tex]In order to determine the time Jason takes to hit the water, equal h = 0. Thus, you have a quadratic equation and it is necessary to find the zeros of the polynomial:
[tex]0=-16t^2-16t+672[/tex]use the following quadratic formula to find the zeros:
[tex]t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a,b and c are the coefficients of the polynomial:
a = -16
b = -16
c = 672
replace these values into the formula:
[tex]\begin{gathered} t=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(-16)(672)}}{2(-16)} \\ t=\frac{16\pm\sqrt[]{43264}}{-32} \\ t=\frac{16\pm208}{-32} \\ t=-0.5\pm(-6.5) \end{gathered}[/tex]Then, you obtain the following two values:
[tex]\begin{gathered} t=-7 \\ t=6 \end{gathered}[/tex]Select the positive values because negative time does not have physical meaning.
Hence, Jason takes 6 seconds to hit the water.
Please help with both ?s I’ll mark you brainly
Answers
Answer:
1) CW 270° or CCW 90°
Step-by-step explanation:
In each case, you want to identify two transformations that will map the preimage to the image.
1)We note the transformation maps ...
A(-7, 0) ⇒ A'(0, -7) . . . . . . CCW 90° or CW 270°
B(-4, -1) ⇒ B'(1, -4)
C(-7, 3) ⇒ C'(-3, -7)
These can be described by ...
(x, y) ⇒ (-y, x)
This transformation is equivalent to either of the two transformations ...
rotation CW 270° about the originrotation CCW 90° about the origin2)As above, rotation about the origin by 90° in one direction is the same as rotation 270° about the origin in the other direction. The attached graph shows the result either way. The two equivalent transformations are ...
rotation CW 90° about the originrotation CCW 270° about the originThe coordinate transformation is ...
(x, y) ⇒ (y, -x)
Sean is hiking the Appalachian Trail from Georgia to Maine. The distance of his hike is 2200 miles. It
took Sean 134 days to complete the hike. The data below represent the distance, D, he had hiked t
days after the start of his trip.
t
D(0)
0
0
19
308
In
34
578
67
1070
1. Determine the linear regression equation for this data.
Linear Regression Equation: D =
Round to the nearest tenth as needed.
2. Interpret the meaning of the slope of this regression model.
Sean hiked at a rate of approximately
91
1715
miles.
112
1902
Select an answer
3. Use your linear regression equation to estimate the total number of miles Sean had hiked in 52
days. Round your answer to the nearest mile.
In 52 days, Sean had hiked
4. Use your linear regression equation to estimate the total number of days it took for Sean to hike
377 miles. Round your answer to the nearest day.
days, Sean had hiked 377 miles.
134
2200
Answers
From the given table, it is found that:
1. The linear regression equation is: y = 16.96x + 3.
2. The meaning of the slope is that he hiked an average of 16.96 miles a day.
3. In 52 days, Sean had hiked 885 miles.
4. In 22 days, Sean had hiked 377 miles.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
In the context of this problem, the points are given as follows:
(0,0), (19,308), (34, 578), (67, 1070), (91, 1715), (112, 1902), (134, 2200).
Using a calculator, the equation is given as follows:
y = 16.96x + 3.
The input of the function and the output of the function are given as follows:
Input: number of days.Output: number of miles hiked.The slope is the rate of change, that is, change in the output divided by change in the input. Hence the slope of 16.96 means that he hiked an average of 16.96 miles a day.
In 52 days, the number of miles hiked is:
y = 16.96(52) + 3 = 885 miles.
The number of days is took to hike 377 miles is found as follows:
377 = 16.96x + 3
x = 374/16.96
x = 22 days.
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Which Similarity Theorem is described by the text below?If the lengths of three sides of one triangle are proportional to the lengths of three sides ofanother, then the triangles are similar.A. AAB. ASAC. SASD. SSS
Answers
Answer:
SSS.
Step-by-step explanation:
The text above described the Side-Side-Side Theorem, which states that two triangles are congruent if three sides of one are equal or proportional respectively to three sides of the other (SSS=SSS).
» Solve the equation 2y+6=y-7
Answers
Answer:
y = -13
Step-by-step explanation:
a) Subtract y from both sides.
2y + 6 − y = y − 7 − y
y + 6 = −7
b) Subtract 6 from both sides.
y + 6 − 6 = −7 − 6
y = -13
Describe how to determine the average rate of change between x=3 and x=5 for the function f(x)3x^3+2. Include the average rate of change in your answer.
Answers
Given the function:
[tex]f\mleft(x\mright)=3x^3+2[/tex]Select the correct answer.
What is the sum of this expression?
Answers
The mixed fraction 4 3/8 + 7 3/4 is equivalent to the fraction to 12 1/8
How to solve an equation?An equation shows the relationship between two or more numbers and variables.
The mixed fraction 4 3/8 is equivalent to the fraction (4 * 8 + 3)/8 = 35/8
The mixed fraction 7 3/4 is equivalent to the fraction (4 * 7 + 3)/4 = 31/4
Hence:
4 3/8 + 7 3/4
Substituting:
= 35/8 + 31/4
Simplifying:
= 97/8 = 12 1/8
4 3/8 + 7 3/4 is equal to 12 1/8
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Determine the area of the shaded triangle inside the square explain your strategy
Answers
To find the area of the shaded region, we have to find the area of the square first.
[tex]A_{\text{square}}=l^2=(10in)^2=100in^2[/tex]Then, we find the area of each yellow triangle inside (up and down). The base of each triangle is 10 inches, and the height of each of them is 7 inches.
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}bh=\frac{1}{2}\cdot10in\cdot7in=35in^2 \\ A_{\text{triangle}}=\frac{1}{2}\cdot10in\cdot7in=35in^2 \end{gathered}[/tex]Add the area of both triangles.
[tex]A_t=35in^2+35in^2=70in^2[/tex]At last, subtract the area of the triangles from the area of the square.
[tex]A_{\text{shaded}}=100in^2-70in^2=30in^2[/tex]Therefore, the area of the shaded region is 30 in^2.The strategy is to subtract the area of the yellow triangles (up and down) from the area of the square.
please help im stuck on this
Answers
04) The complementary angles are the angles whose sum is 90° thus { 26°,54°,48°,29°,22°} will be the corresponding angles.05)The supplementary angles are the angles whose sum is 180° thus {54°,48°,12°,135°,91°} will be the corresponding angles.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
If m∠A + m∠B = 90° then A and B will be the complimentary angle.
The complementary of 64° = 90° - 64° = 26°
The complementary angle of 36° = 90° - 36° = 54°
The complementary angle of 42°= 90° - 42° = 48°
The complementary angle of 51°= 90° - 51° = 29°
The complementary angle of 68°= 90° - 68° = 22°
If m∠A + m∠B = 180° then A and B will be the supplementary angle.
The supplementary of = 180° - 126° = 54°
The supplementary of = 180° - 132° = 48°
The supplementary of = 180° - 178° = 12°
The supplementary of = 180° - 45° = 135°
The supplementary of = 180° - 89° = 91°
Hence " { 26°,54°,48°,29°,22°} will be the corresponding complementary angle and {54°,48°,12°,135°,91°} will be the corresponding supplementary angles".
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Find missing side length
Answers
Answer:
7
Step-by-step explanation:
42 divided by 3 = 14 = total of triangle XYZ
14 divided by 2 = 7
line X/Y = 7
There are 15 members in a bicycle club this fall by next summer Bing home saying number of members will be 140% of this number what is the main goal for the number of members next summer 
Answers
The main goal is 140 percent i.e., 21 members.
What is meant by percentage?
In mathematics, a percentage (from Latin: percentage , "by a hundred") may be a number or ratio expressed as a fraction of 100. it's often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" also are used. A percentage may be a dimensionless number (pure number); it has no unit of measurement. The term "percent" springs from the Latin per centum, meaning "hundred" or "by the hundred". The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent." The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to 2 circles separated by a horizontal line, from which the fashionable "%" symbol is derived.
140 percent of 15 = 15x140/100 = 21 members
Hence, the main goal is 21 members.
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what percent of 29 is 13?
Answers
Answer:
45%
Step-by-step explanation:
x * 29 = 13
x = 13/29
x = 0.448
45%
Which set of ordered pairs represents y as a function of x? А A {(2,-1),(4,-2),(6,-3),(8,-4)} B {(0,0),(1,1),(1,0),(2, 1)} © {(3,3), (3,4),(4,3),(4,4)} {(1,-5),(1,5),(2,-10),(2, -15)}
Answers
Function:
A function is a relation in which every input x has a different output value y.
If there is more than 1 outputs for the same input then it doesn't represent a function.
Let us analyze each of the given options.
Option A:
{(2, -1), (4, -2), (6, -3), (8, -4)}
As you can see, each input x has a different output value y.
Therefore, it is a function
Option B:
{(0, 0), (1, 1), (1, 0), (2, 1)}
As you can see, the input (1) has two different outputs (1 and 0)
Therefore, it is not a function.
Option C:
{(3, 3), (3,4),(4,3),(4,4)}
g(x) = 4x + 4
f(x) = x3 − 1
Find (g ◦ f)(x)
Answers
Answer:
4x³
Step-by-step explanation:
substitute x = f(x) into g(x)
(g ￮ f)(x)
= g(f(x))
= g(x³ - 1)
= 4(x³ - 1) + 4
= 4x³ - 4 + 4
= 4x³
Solve the equations justify your response by showing mathematical steps
Answers
Given:-
[tex]undefined[/tex]5 In an experiment, the probability that event B occurs is -, and the probability that event A occurs given 8 5 that event B occurs is – 8 What is the probability that events A and B both occur? Simplify any fractions.
Answers
We have
probability of B occurs is 5/8
probability that event A occurs given B occurs is 5/8
We have the next formula, that is the conditional probability formula
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where
P(A|B)= probability of A given B
P(B)= probability of B
P(A∩B)=probability of A and B
so we need to isolate the P(A∩B) in order to obtain the probability that events A and B both occur
[tex]P\mleft(A\cap B\mright)=P(A|B)\cdot P(B)=\frac{5}{8}\cdot\frac{5}{8}=\frac{25}{64}[/tex]A pair of dice is rolled 3 times. What is the probability that a sum of 9 on the 2 dice will occur at least once?
Answers
The probability that a sum of 9 on the 2 die will occur at least once is 217/729.
Sum of 9 in a pair of dice can occur in the following 4 ways.
3 + 6
4 + 5
5 + 4
6 + 3
Also, total number of ways = 6*6 = 36
Hence, probability of getting a sum of 9 = 4/36 = 1/9.
We know that,
Probability of getting a sum of 9 + Probability of not getting a sum of 9 = 1
Hence, we can write,
1/9 + Probability of not getting a sum of 9 = 1
Probability of not getting a sum of 9 = 8/9
Also,
Probability of getting the sum of 9 atleast 1 + probability of getting the sum 9 none of the times = 1
Hence, we can write,
Probability of getting the sum of 9 atleast once = 1 - probability of getting the sum 9 none of the times/
Probability of getting the sum of 9 atleast 1 = 1 - (8/9)*(8/9)*(8/9) = 1 - 512/729 = 217/729.
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14. Use Structure Consider the rational
number.
a. What are the values of a and b in a)b wher
you use division to find the decimal form?
b. What is the decimal form for?3/11
Answers
The decimal form of this rational number is 0.27, where 27 in decimal is recurring.
What are the steps to solve a rational number?
The steps to solve a rational number problem are:
(a) Let 'a/b' be a rational number. From the sentence, we deduce that denotes the denominator of a rational integer, while represents the numerator. Consequently, is 3 and is 11.
(b) The decimal form is achieved by dividing by, and we described the procedure required to do so:
(i) Ten times the numerator:
Dividend is 30, and the result is known to be zero. Remainder: N/A
ii) Dividend less the dividend multiplied by the divisor by two:
Known outcome: 0.2; residuals: 8
iii) 10 times the residue:
Known outcome: 0.2; residuals: 80
iv) Divide the residue by the divisor and multiply it by 7:
0.27 as known result; 3 as residue
v) Ten times the residue:
0.27 as known result; 30 as residue
vi) Divide the divisor by two and deduct the result from the sum:
Results known: 0.272/Residue: 8
vii) 10 times the residue:
The known outcome is 0.272/Residue: 80.
viii) Divide the divisor by 7 and deduct the result from the sum:
A known outcome is 0.2727/Residue: 3.
Therefore, we can see that is a periodic decimal number in its decimal form.
As a result, we deduce that the decimal representation of this rational number is 0.27, where 27 is a regular integer.
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