PLEASE HELP
7.06
1. Find the first six terms of the sequence.
a1 = -7, an = 4 • an-1
A) -7, -28, -112, -448, -1792, -7168
B) -28, -112, -448, -1792, -7168, -28,672
C) -7, -28, -24, -20, -16, -12
D) 0, 4, -28, -24, -20, -16
2. Find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2, ...
an = -13 x 5(n - 1)
an = -13 + 5(n - 1)
an = -13 + 5(n + 2)
an = -13 + 5(n + 1)
3. Find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5
A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)
4. Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...
A) Diverges
B) Converges; 231
C) Converges; 3751
D) Converges; 935
5. Find an equation for the nth term of the sequence.
-4, -16, -64, -256, ...
A) an = 4 • -4n
B) an = 4 • -4n + 1
C) an = -4 • 4n
D) an = -4 • 4n - 1
6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.
A) an = 1 • (-2)n - 1
B) an = 1 • 2n
C) an = 1 • (-2)n + 1
D) an = 1 • 2n - 1
7. Write the sum using summation notation, assuming the suggested pattern continues.
4 - 24 + 144 - 864 + ...
A) summation of four times six to the power of n from n equals zero to infinity
B) summation of four times negative six to the power of n from n equals zero to infinity
C) summation of four times negative six to the power of the quantity n minus one from n equals zero to infinity
D) summation of four times six to the power of the quantity n plus one from n equals zero to infinity
8. Write the sum using summation notation, assuming the suggested pattern continues.
-3 + 6 + 15 + 24 + ... + 132
A) summation of negative 27 times n from n equals 0 to infinity
B) summation of negative 27 times n from n equals 0 to 15
C) summation of the quantity negative 3 plus 9 n from n equals 0 to infinity
D) summation of the quantity negative 3 plus 9 n from n equals 0 to 15
9. Write the sum using summation notation, assuming the suggested pattern continues.
343 + 512 + 729 + 1000 + ... + n3
A) summation of the quantity n minus 1 cubed from n equals 7 to infinity
B) summation of n cubed from n equals 7 to infinity
C) summation of n cubed from n equals 8 to infinity
D) summation of the quantity n plus 1 cubed from n equals 7 to infinity
10. Find the sum of the arithmetic sequence.
3, 5, 7, 9, ..., 21
A) 39
B) 120
C) 20
D) 23
11. Find the sum of the geometric sequence.
4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3
A) 1363 divided by 3
B) 1364 divided by 15
C) 1364 divided by 3
D) 1363 divided by 15
12. An auditorium has 20 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 390
B) 580
C) 620
D) 400
13. Use mathematical induction to prove the statement is true for all positive integers n.
10 + 20 + 30 + ... + 10n = 5n(n + 1)
14. A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.
Answers
2. B. The sequence is -13, -8, -3, 2... It's obvious that each term is equal to the previous term plus 5. This is an arithmetic sequence with initial term -13 and common difference 5. We know a1=-13, so a_n=-13+5*(n-1). The answer is B.
3. A. We are given a15=-53, a16=-5. The common difference of the arithmetic sequence is -5-(-53)=48. The formula for a_n term is a1+48*(n-1). We know that a15=-13; plug in n=15, a15=-53=a1+48*(15-1), a1=-725. So a_n=-725+48*(n-1).
4. Diverge. We are given a few terms, 11, 44, 176, 704... Observe that each term is four times the previous one. 11*4=44, 44*4=176, 176*4=704... This is a geometric series with common ratio>1. You can keep multiplying by 4 and the series goes to infinity, so it diverges.
5. D. We have -4, -16, -64, -256... Same as above, each term is four times the previous one. The initial term is a1=-4. The common ratio d=4. So a_n=a1*d^(n-1)=-4*4^(n-1)=-4^n. (D).
6. The answer is A. a2=-2, a5=16. Suppose the common ratio is D. a_n=a1*d^(n-1). a2=a1*d; a5=a1*d^4. Plug in a2 and a5: -2=a1*d, 16=a1*d^4. 16/-2=d^3=-8, d=-2, a1=1. So a_n=1*(-2)^(n-1).
7. B. We are given the sequence 4, -24, 144,... Each term is -6 times the previous one. The first term a0=4, the n^th term a_(n-1) is a1*d^n=4*(-6)^n. To express the sum, we simply have to use the sigma notation and sum 4*(-6)^n from n=0 to infinity. The answer is B.
8. D. We are given -3 + 6 + 15 + 24... 132. Each term is equal to the previous one plus 9. First term a0=-3, n^th term a_n-1 is -3+9*n. The last term is 132. 132 =-3+9n, n=15. So we have to sum -3+9n from n=0 to n=15.
9. B. 343 + 512 + 729 + 1000+... 343=7^3, 512=8^3, 729=9^3, 1000=10^3. This is a sequence of perfect cubes. Therefore, the sum is n^3 from n=7 to infinity. (The initial term is 343=7^3).
10. B. We are given 3, 5, 7, 9, ... 21. The common difference is 2. There are (21-3)/2+1=10 terms. The initial term a1=3, and last term is a10=21. The sum is (a1+a10)*10/2=(3+21)*10/2=120.
11. C. 4/3, 16/3, 64/3, 256/3, 1024/3. Each term is four times the previous one. This is a geometric series with initial term a1=4/3 and common ratio r=4. 1024/3 is the 5th term of the sequence. So sum=a1*(1-r^n)/(1-r)=4/3*(1-4^5)/(1-4)=-4/9*-1023=1364/3.
12. B. 10,12,14,... This is an arithmetic sequence. a1=10, and common difference d=2. There are 20 terms (20 rows). a20=a1+d*(n-1)=10+2*(20-1)=48. So the sum S=(a1+an)*n/2=(10+48)*20/2=580.
13. 10 + 20 + 30 + ... + 10n = 5n(n + 1). When n=1, this expression is true, since 10=5*1*(1+1). Suppose when n=k, this statement is true, then when n=k+1, the left side is 10+...+10n+10(n+1), the right side is 5(n+1)(n+2). The left side adds 10(n+1) compared to the previous one. The right side adds 5(n+1)(n+2)-5n(n+1)=5(n+1)(n+2-n)=10(n+1). So the statement holds true.
14. The height at week 0 is a0=300 (initial height). Common difference is 4.2 (weekly increment). a_n=300+4.2n. At week n, the height of the tree is 300+4.2*n centimeters.
Please, see the detailed solution in the attached files.
Thanks
Related Questions
Joseph squares a number and subtracts 8 from the answer. He then divides this result by 7. Finally he adds 12 and the result is now 20. What was Joseph's original number?
Answers
[tex]( {x}^{2} - 8) \div 7 + 12 = 20[/tex]
[tex]( {x}^{2} - 8) \div 7 = 8[/tex]
[tex]( {x}^{2} - 8) = 56[/tex]
[tex] {x}^{2} = 64[/tex]
[tex]x = \sqrt{64} \: \: \: \: \: x = - \sqrt{64} [/tex]
[tex]x = 8 \: \: \: \: \: x = - 8[/tex]
Final answer:
We use reverse operations to solve Joseph's equation and find that the original number could have been either 8 or -8.
Explanation:
The question asks us to determine Joseph's original number based on a series of mathematical operations. We can set up an equation to represent the problem statement: let x be the original number. The sequence of operations given is:
Square x and subtract 8.
Divide this result by 7.
Add 12 to the result from step 2.
The final result is 20.
Representing this mathematically: ((x2 - 8) / 7) + 12 = 20. To find x, we need to work backward through these operations:
Subtract 12 from both sides: ((x2 - 8) / 7) = 8.
Multiply both sides by 7: x2 - 8 = 56.
Add 8 to both sides: x2 = 64.
Take the square root of both sides: x = 8 or x = -8 (considering both positive and negative square roots).
Therefore, Joseph's original number could have been either 8 or -8.
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Answers
The third choice is the correct one
Explanation:
Square root means that what is under the root has power of 1/2
8 = 4 * 2
Therefore:
√8 = √4 * √2 = 2√2
The given expression:
(8 * x^7 * y*8)^1/2 = (8)^1/2 * (x^7)^1/2 * (y^8)^1/2
= 2√2 * x^7/2 * y^4
= 2√2 * x^3 * y^4 * √x
= 2* x^3 * y^4 √2x
Hope this helps :)
How can you find the number of inches in 1 mile, show your work.
Answers
1 foot=12 inches
63360 is the correct answer
The value of number of inches in 1 mile is,
⇒ 15,096 inches
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
To find the number of inches in 1 mile.
Since, We know that;
1 mile = 1258 foot
And, 1 foot = 12 inches
Thus, The value of number of inches in 1 mile is,
⇒ 1258 x 12
⇒ 15,096 inches
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WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!! PLEASE HELP ME!!!!!!
A specialty ice cream manufacturer collected data for the number of ice creams sold each day and the temperature on that day. The data was displayed in the following table.
Ice Creams Sold - 34, 39, 40, 36, 46, 47, 54, 27, 31, 56
Temperature (in °F) - 71.0, 73.8, 74.9, 71.4, 75.0, 76.9, 79.4, 68.6, 70.0, 81.4
What is the best interpretation of the correlation coefficient between the temperature and the number of ice creams sold?
* Because the correlation coefficient is close to -1, the ice cream sales decrease markedly with a rise in temperature.
* Because the correlation coefficient is close to 1, the ice cream sales increase markedly with a rise in temperature.
* Because the correlation coefficient is close to 1, the ice cream sales increase vaguely with a rise in temperature.
* Because the correlation coefficient is close to 0, the ice cream sales decrease vaguely with a rise in temperature.
Answers
S:[34, 39, 40, 36, 46, 47, 54, 27, 31, 56]
T:[71.0, 73.8, 74.9, 71.4, 75.0, 76.9, 79.4, 68.6, 70.0, 81.4]
n=10 = number of observations in each list.
We need the correlation coefficient ρ to select the right choice of answers.
We first calculate the mean μ and standard deviation σ of each list
[tex]\mu_s=\sum_{i=1}^{10}S_i=41.0[/tex]
[tex]\sigma^2_s=\sum_{i=1}^{10}(S_i-\mu_s)^2/n=83[/tex]
[tex]\sigma_s=\sqrt{\sigma^2_s}=\sqrt{83}=9.1104[/tex]
[tex]\mu_t=\sum_{i=1}^{10}T_i=74.24[/tex]
[tex]\sigma^2_t=\sum_{i=1}^{10}(T_i-\mu_t)^2/n=15.4524[/tex]
[tex]\sigma_t=\sqrt{\sigma^2_t}=\sqrt{15.4524}=3.9310[/tex]
We are now ready to calculate the correlation coefficient ρ :
[tex]\rho=\frac{E[(S-\mu_s)(T-\mu_t)]}{\sigma_s*\sigma_t}[/tex]
[tex]=\frac{\sum_{i=1}^{n}[(S_i-\mu_s)(T_i-\mu_t)]/n}{\sigma_s*\sigma_t}[/tex]
[tex]=\frac{\sum_{i=1}^{n}[(S_i-\mu_s)(T_i-\mu_t)]/n}{9.1104*3.9310}[/tex]
[tex]=\frac{35.27}{35.8127}[/tex]=0.9848
Because the correlation coefficient, ρ , is close to one, the ice cream sales increase markedly with a rise in temperature.
Note:
a correlation close to 1 means both increase (or decrease)
a correlation close to -1 means one increases while the other decreases
correlation close to 0 means one does not quite affect the other.
A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer as a simplified mixed number or a decimal
Answers
The volume of a rectangular prism is:
[tex]V=l*w*h[/tex]
Where
l=lenght,
w=width
h=height
So, as this prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches, the volume is calculated as follows:
[tex]V=l*w*h=312 in*5 in*112 in=174 720 inches^3[/tex]
Select the correct product. ( a + 8)( b + 3)
ab + 8 a + 3 b + 24
ab + 3 a + 8 b + 24
11 ab
24 ab
Answers
ab + 3a + 8b + 24
i hope this helps :)
Answer:
ab + 3 a + 8 b + 24
Step-by-step explanation:
just did this question
which expression represents the volume of the box?
use the formula v=lwh.
please help....
Answers
V=lwh
V is the volumen of the box.
l is the length of the box.
w is the widht of the box.
2. When you substitute the values shown in the figure attached, into the formula V=lwh, you obtain:
V=(2x-1)(x+2)(3x+1)
3. You must apply the "Distributive property". Then, you have:
V=6x³+11x²-3x-2
Which expression represents the volume of the box?
The second expression, which is: 6x³+11x²-3x-2
What are the slope and the y-intercept of the linear function that is represented by the graph?
Answers
The y-intercept is the point where the line cuts the y-axis, hence the y-intercept is (0,3)
Slope and intercept of a lineThe formula for calculating slope of a line is expressed as:
Slope = y2-y1/x2-x1
Using the coordinate points (0, 3) and (4, 0)
Slope = 0-3/4-0
Slope = -3/4
Since the y-intercept is the point where the line cuts the y-axis, hence the y-intercept is (0,3)
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what is the lateral area of the cone? base 10 yd height 12.1 yd
a. 242.6 yd2
b. 190.07 yd2
c. 603.19 yd2
d. 96.4 yd2
Please help me get this answer correct ! asap
Answers
L= r x [tex] \pi [/tex] x l
where: L = Lateral area
l = length or height
r = radius
[tex] \pi [/tex] = 3.1416
Now sorting out your given:
base = 10 yd
Height = 12.1 yd
To work out the lateral area, you will need the radius. Your base 10 yd, is the measure from one side to the other of the circle base, this is what you call diameter. What you need is radius, which is the measure of a circle from the middle of the circle to the outside, so it is half of a diameter.
So to get radius (r), divide the base by 2.
r = 10yd/2 = 5yd
Now that you have all that you need just input it into your formula:
L = r x [tex] \pi [/tex] x l
= 5 yd x [tex] \pi [/tex] x 12.1 yd
= 190.07 yd[tex] ^{2} [/tex]
So your answer is B.
base=10 yd-----------------> r=5 yd
lateral area=pi*r*h--> pi*5*12.1= 190.07 yd²
the answer is option b. 190.07 yd2
Select the correct answer. What is the LCM of the numbers 3, 6, and 9? 9 18 36 54
Answers
Answer:
18
Step-by-step explanation:
3 times 5
6 times 2
9 times 2
all 18
Jake carries a green and yellow and a black guitar pick in his pocket he randomly chooses a guitar pick from his pocket before every concert what is the probability will he select the same color pic for two concert in a row?
Answers
Answer:
[tex]\bf\textbf{The required probability = }\frac{4}{9}[/tex]
Step-by-step explanation:
The total number of ways that he can pick a pic are 3 × 3 × 3 = 27 ways
If Jake selects the black pic in the first concert, then number of ways of success are :
B B G
B B Y
B G G
B Y Y
Total number of success = 4
If Jake selects the green pic in the first concert, then number of ways of success are :
G G B
G G Y
G B B
G Y Y
Total number of success = 4
If Jake selects the yellow pic in the first concert, then number of ways of success are :
Y Y B
Y Y G
Y B B
Y G G
Total number of success = 4
Therefore, in all the three cases total number of successes are :
4 + 4 + 4 = 12
[tex]Probability = \frac{\text{Number of successful ways}}{\text{Total number of ways}}\\\\\implies Probability = \frac{12}{27}=\frac{4}{9}[/tex]
[tex]\bf\textbf{Hence, The required probability = }\frac{4}{9}[/tex]
Answer:
For the people coming for the iready question answer, the answer is 1/3 lol
Step-by-step explanation:
If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to
decrease
stay the same
increase
Answers
If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to decrease.
What is the correlation of the sets?For a message to be processed by a certain orchestration, a correlation set specifies a collection of qualities and values for these properties. A maximum of three parameters are supported by each correlation set.
If two sets are negatively correlated, as the values in one of the sets increase, the values in the other set tend to decrease.
This means that there is an inverse relationship between the two sets, such that when one variable increases, the other variable tends to decrease.
This type of correlation is often expressed by a negative correlation coefficient,
which ranges from -1 to 0, with -1 indicating a perfect negative correlation.
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What pair of numbers has the geometric mean of 44
Answers
so 16×121 = 1936
so the pair is 16 and 121
The possible pair of numbers that has the geometric mean of 44 is 16 and 121 and this can be determined by using the concept of geometric progression.
Given :
The geometric mean of 44.
The following steps can be used in order to determine the pair of numbers that has the geometric mean of 44:
Step 1 - The concept of geometric progression can be used in order to determine the pair of numbers that has the geometric mean of 44.
Step 2 - Let the two numbers be 'a' and 'b'.
Step 3 - According to the given data, the geometric mean of 44, that is:
[tex]\rm \sqrt{ab} = 44[/tex]
Step 4 - Simplify the above expression.
ab = 1936
Step 5 - So, the possible pair of numbers that has the geometric mean of 44 is 16 and 121.
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Jessica has $4 left in her pocket. She spent $7 on a ticket to a baseball game, $2 on a hot dog, and $11 on a hat. How much money did she have at the beginning of the day?
Answers
4 + 7 + 2 + 11 = 24
Jessica had $24 at the beginning of the day.
Answer:
Money Jessica had at the beginning of the day was:
$24
Step-by-step explanation:
Let Jessica had $x in the beginning of the day.
She spent $7 on a ticket to a baseball game, $2 on a hot dog, and $11 on a hat and left with $4
⇒ x=7+2+11+4
⇒ x=24
Hence, money Jessica had at the beginning of the day was:
$24
helppppppppppppppppppppppppppppppppppp
Answers
-16 + 37i
Explanation:
Note that i^2 = -1
(4+7i)(3+4i) = 4*3 + 4*4i + 7i*3 + 7i*4i
= 12 + 16i + 21i + 28i^2
= 12 + 37i + 28(-1)
= 12 + 37i - 28
= -16 + 37i
Hope this helps :)
Choose the correct simplification of the expression a to the 7th power times b to the 8th power all over a to the 4th power times b to the 4th power
Answers
(a^7b^8)/(a^4b^4)
According to the rules of indices, when you divide numbers with the same base, it's the same as subtracting their powers. Hence we shall have:
(a^7b^8)/(a^4b^4)
=(a^(7-4))(b^(8-4))
=a^3b^4
the answer is a^3b^4
Letter grades earned by a particular student in history class.
a. qualitative/nominal
b. qualitative/ordinal
c.quantitative/continuous
d.quantitative/ discrete
i think the answer is d
Answers
How much will it cost to mail a first-class letter that weighs 3.7 oz? The rate is $.22 for the first ounce and $.17 for each additional ounce or fraction of an ounce. a. $.81 b. $.73 c. $.63 d. $.07
Answers
3.7 ounces minus the first ounce = 2.7 ounces
2.7 ounces x $.17/ounce = $0.459 = $0.46
$0.46 (the rate for 2.7 ounces + $0.22 (the rate for the first ounce) = $0.68
Ellen is drawing two polygons. One of tue polygons has 3 more angles than the other. What shapes could she be drawing?
Answers
Polygon- A shape with at least three straight sides.
Triangle and a Hexagon is what I recommend
Hope this helps:D
Have a great rest of a brainly day!
"AB84"
Answer:
Pentagon and an OCTAGON
Step-by-step explanation:
Polygons are are plane figures with three or more sides. Since plane figures with 3sides are triangles and those with 4sides are quadrilaterals, I will take a plane figure of 5sides as one of the two polygons Ellen is drawing
A plane figure with 5sides and 5angles is a PENTAGON
If one of the polygons has 3 more angles than the other, then the other polygon she is drawing was a polygon with (5+3) i.e 8sides and 8angles. This polygon is known as an OCTAGON
Based on the conclusion, the shape Ellen could be drawing is a PENTAGON and an OCTAGON
Judi is 9 years older than Baz.Baz is twice as old as Caleb.All their ages add up to 64.What are their ages?
Answers
Baz is 22
Caleb is 11
Caleb is 11 years old, Baz is 22 years old, and Judi is 31 years old, which adds up to 64 years in total.
If Caleb's age is C, then Baz, being twice as old, is 2C. Judi is 9 years older than Baz, so her age is 2C + 9.
C + 2C + 2C + 9 = 64
5C + 9 = 64
Subtracting 9 from both sides gives:
5C = 55
C= 11
Special-effects artists often use scale models.the actual height of a velociraptor is estimated to have been approximately 2 ft.an artist draws the dinosaur with a height of 4 in. on paper.
a. what would be an appropriate scale for a model of the velociraptor?
b. the same scale is used for a model of a tyrannosaurus, whose actual height was 16 ft.what is the height of the model?
Answers
part A)
[scale]=[model height]/[actual height]
[scale]=[4 in]/[2 ft]=2 in/ft
that means
(2 in) in the model is -------------> (1 ft) in the actual
part B)
[actual height]=16 ft [model height]=? [scale]=2 in/ft
[scale]=[model]/[actual height]
[model height]=[scale]*[actual height]
[model height]=[2]*[16]=32 in
the answer part B) is 32 in
factor the trinomial x^2+6x-16
Answers
-16 = -1(16) or 16(-1)
-16 = -2(8) or 8(-2)
-16 = -4(4) or 4(-4)
Out of these 6 possibilities, the only one that sums to 6 is 8(-2), because 8+(-2)=6.
This gives us the factors (x+8)(x-2).
There are 8 runners in a race.
The 4 fastest runners will win trophies.
Halfway through the race, 2 of the
runners drop out of the race. What
fraction of the remaining runners will win
a trophy?
Answers
Halfway, 2 dropped out, remaining 8 - 2 = 6 runners
4 fastest runners win
Fraction = 4/6 = 2/3
There are 6 runners left, and 4 will win a trophy. 4/6 simplifies to 2/3
What is the definition of a circle?
A circle is a set of all points that are the same distance form a fixed point called the center.
A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
A circle is the distance from a set of points to a fixed point called the center.
A circle is the set of all points in a plane that are a given distance from a given line.
Answers
Answer:
A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
Step-by-step explanation:
see picture
Circle can be defined as a set of all points in a plane that are the same distance from a fixed point called the center.
What is a circle?A circle has defined the set of all points in a plane that are the same distance from a fixed point called the center. The circle is a 2D shape.
In geometry, the circle is defined as the closed 2-dimensional curved shape. The distance from between the center of the circle to any point on the circle is known as the radius of the circle.
As we have discussed the definition of a circle, therefore, the correct option is 'A circle is the set of all points in a plane that are the same distance from a fixed point called the center.'
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WILL GIVE BRAINLIEST!!! PLEASE HELP!!! 11 POINTS!!!
Given that a function, f(x), has a domain of -70 ≤ x ≤ -15 and a range of 30 ≤ f(x) ≤ 110 and that f(-60) = 80 and f(-17) = 40, select the statement that could be true for f(x).
* f(-10) = 25
* f(-60) = 95
* f(40) = -55
* f(-65) = 90
Answers
Answer:
Step-by-step explanation:
[tex]slope=\frac{40-80}{-17+60} =-\frac{40}{43}\\f(x)-80=-\frac{40}{43}(x+60)\\\\x=40\\f(x)=-\frac{40}{43}*100+80 \approx -93+80=-13\\x=-65\\f(-65)=-\frac{40}{43}*(-15)+80 \approx 14+80=94[/tex]
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. the store manager assures you that 13 of the 47 boxes on the shelf have the secret decoder ring. the other 34 boxes on the shelf have a different gift inside. if you randomly select two boxes of cereal from the shelf to purchase, what is the probability that both of them have the secret decoder ring?
Answers
The probability that both selected boxes have the secret decoder ring is approximately 7.20%
Explanation:To find the probability that both selected boxes have the secret decoder ring, we can use the concept of independent events. Since the boxes are randomly selected, the probability of selecting a box with the secret decoder ring is 13/47 for the first box. After selecting the first box, there will be 12 boxes with the secret decoder ring left out of 46 total boxes. So, the probability of selecting a second box with the secret decoder ring is 12/46. To find the probability of both events occurring, we multiply the probabilities: (13/47) * (12/46) = 156/2162 ≈ 0.07197 or about 7.20%
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A rectangle is 25 inches long and 13 inches wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form
Answers
25*13=325
The area of the rectangle is 325 sqr inches.
Match term with the definition
__A) shape created when a right triangle is rotated about the y-axis
__B) shape created when a rectangle is rotated about the y-axis
__C) perpendicular cross section of a cylinder
__D) parallel cross section of a sphere
__E) perpendicular cross section of a pyramid
Triangle
Rectangle
Circle
Cylinder
Cone
Answers
I got A,B,E,D,C
Correct me if im wrong
It may be wrong.
Janet has a square-shaped sheet of wrapping paper. To cover the top of a box, she cuts off 11 centimeters of the sheet along the width. The new area of the sheet is given by the expression below, where x represents the length, in centimeters, of the sheet of wrapping paper before being cut.
x^2-11x
Which statement best describes the term 11x?
the area cut from the sheet of wrapping paper
the area of the sheet of wrapping paper after being cut
the area of the sheet of wrapping paper before being cut
the width of the sheet of wrapping paper after being cut
Answers
The expression she has, x² - 11x, represents the area of the sheet of wrapping paper after she's cut it.
Answer:
The correct option is 1. It means 11x is the area cut from the sheet of wrapping paper.
Step-by-step explanation:
The shape of sheet is square.
Let x represents the length, in centimeters, of the sheet of wrapping paper before being cut.
The area of a square is
[tex]A=a\times a[/tex]
Where, a is side length.
The area of sheet before being cut is
[tex]A=x\times x=x^2[/tex]
The width of the piece cut from the sheet is 11 and length is x. So, the area of piece is
[tex]A=x\times 11=11x[/tex]
The remaining area of sheet is
[tex]A=\text{Area of sheet}-\text{Area of piece cut from the sheet}[/tex]
[tex]A=x^2-11x[/tex]
Therefore correct option is 1. It means 11x is the area cut from the sheet of wrapping paper.
If the endpoints of AB have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?
A. 5,3
B. 4,5
C. 5,5
D. 4,3
Answers
D. (4,3)
Explanation:
The endpoints of the line are given as (9,8) and (-1,-2)
1- Computing the x-coordinate of the midpoint:
Xmidpoint = (x1+x2) / 2 = (9+-1)/2 = 8/2 = 4
2- Computing the y-coordinate of the midpoint:
Ymidpoint = (y1+y2) / 2 = (8+-2) / 2 = 6/2 = 3
Based on the above, the midpoint is (4,3)
Hope this helps :)