The formula to find the nth term of the AP is 8 + 3(n - 1).
How to calculate the values?a = first term = 8
d = common difference = 3
The nth term will be:
= a + (n - 1)d
= 8 + (n - 1)3
= 8 + 3(n - 1)
The age of the 4th student will be:
= a + (n - 1)d
= 8 + (4 - 1)3
= 8 + 9
= 17 years
The sum of total ages if there are 20 students in a row will be:
= n/2[2a + (n - 1)d]
= 20/2 [2×8 + (20 - 1)3]
= 10 [16 + (19 × 3)]
= 10(16 + 57)
= 10(73)
= 730
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You and two friends plan to walk your dogs together. You want the meeting place to be the same distance from each person’s residence. Explain how you can use the diagram to locate the meeting place.
The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets. Regular price 138 124 89 112 116 123 98 Reduced price 124 134 154 135 118 126 133 132 i. Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)
ii. Compute the test statistic. (Round your answer to 2 decimal places.)
iii. State your decision about the null hypothesis.
The pooled estimate of the variance is 187.650 and the test statistic is -2.32
Pooled estimate of the varianceThe dataset is given as:
Regular price 138 124 89 112 116 123 98
Reduced price 124 134 154 135 118 126 133 132
Let the regular price be dataset 1 and the reduced price be dataset 2.
So, we have:
#1: 138 124 89 112 116 123 98
#2: 124 134 154 135 118 126 133 132
Calculate the sample means and the sample standard deviations using a graphing calculator.
#1
[tex]\sigma_1 = 16.56[/tex]
[tex]\bar x_1 = 114.29[/tex]
[tex]\sigma_1^2 = 274.24[/tex]
#2
[tex]\sigma_2 = 10.65[/tex]
[tex]\bar x_2 = 132[/tex]
[tex]\sigma_2^2 = 113.43[/tex]
The pooled estimate of the variance is:
[tex]\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}[/tex]
This gives
[tex]\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}[/tex]
Evaluate the factors
[tex]\sigma_p^2 = \frac{2439.45}{13}[/tex]
Divide
[tex]\sigma_p^2 = 187.65[/tex]
Hence, the pooled estimate of the variance is 187.650
The test statisticThis is calculated using:
[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]
This gives
[tex]t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}[/tex]
This gives
[tex]t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}[/tex]
Evaluate the product
[tex]t = \frac{-17.71}{\sqrt{58.08214}}[/tex]
Evaluate the exponent
[tex]t = \frac{-17.71}{7.62}[/tex]
Divide
t = -2.32
Hence, the test statistic is -2.32
The decision about the null hypothesisThe critical value at 0.025 significance level is -1.96
-2.32 is less than -1.96
This means that we accept the null hypothesis
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Do exponent laws apply all the time when simplifying variables?
It is true that exponent laws apply all the time when simplifying variables
How to determine the true statement?The laws of exponent state that:
[tex](ab)^m = a^m * b^m[/tex]
[tex](a+ b)^m \ne a^m + b^m[/tex]
[tex](a- b)^m \ne a^m - b^m[/tex]
[tex](a/b)^m \ne a^m / b^m[/tex]
The above laws must be followed in all variables.
When any of the law is misinterpreted, misrepresented or misused in simplifying variables, the result would be incorrect
Hence, it is true that exponent laws apply all the time when simplifying variables
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Angela is starting a new business, selling shirts and dresses that she sews herself, The materials for the skirts cost 13.56 and the materials for the dresses cost 18.79. She only has $80 to spend. She still has a regular job, so she is limited on the time she has to sew her products. She only wants to spend 15 hours sewing; it takes 2 hours to sew a skirt, and 4 hours to sew a dress
Select all ratios that are in their simplest form. a29:26 b4:28 c25:10 d28:5 e12:19
The correct answer is Option A , D , E.
What is meant by ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.
What is meant by ratio in simplest form?Ratio in it's simplest form means when the ratio can't be simplified anymore by cancelling out the common factors.
The ratio in Option(A) can't be simplified anymore because 29 is a prime number.
The ratio in Option(B) can be simplified to 1 / 7.
The ratio in Option(C) can be simplified to 5 / 2.
The ratio in Option(D) can't be simplified.
The ratio in Option(E) can't be simplified because 19 is prime number.
Hence, the correct answer is Option A , D , E.
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c=pd for d pls help with steps
The given equation, when solved for d gives d = c/p
Subject of formulaeFrom the question, we are to solve for d in the given equation
The given equation is
c = pd
To solve for d, we will divide both sides by p
c/p = (pd)/p
c/p = d
∴ d = c/p
Hence, the given equation, when solved for d gives d = c/p
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Five regular six-sided dice are rolled. How many ways are there to roll the dice so that the total of the numbers on the five dice is 14
If five regular six sided dice are rolled then there are 540 ways through which sum of numbers coming after rolling will be 14.
Given Five regular six sided dices are rolled.
From stars and bars the number of n tuples of natural numbers summing up to k is given by
[tex](k-1\\n-1)[/tex]
For k=14 and n=5
[tex](14-1 \\5-1)[/tex]
=[tex](13\\4)[/tex]
=715
Some of these will contains a number greater than 6.To get the number of 5 tuples that correspond to 5 rolls of a six sided dice we need to subtract from 715.
Total 5 tuples summing up to 14 for which no element is greater the 6 is given as under:
N=[tex](13/4)-5(6/3)-5(5/3)-5(4/3)-5(3/3)[/tex]
where last term comes from the 5 tuples containing one 10 and fours'
=715-100-50-20-5
=540
Hence there are 540 such ways which sum to 14 when five six sided dices are rolled.
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If a/(b+c+d)=4/3 and a/(b+c)=3/5, find the value of d/a
Answer:
I did this quickly, so please check carefully.
d/a = -(11/12)
Step-by-step explanation:
a/(b+c+d)=4/3
3a = 4(b+c+d) [Cross multiply]
3a = 4((b+c)+d) [Note that b and c can be grouped as (b+c)]
---------------------
We can see the second equation also has a (b+c) group. Isolate it to one side:
a/(b+c)=3/5
5a = 3(b+c)
(b+c) = (5a/3)
------------------
Now use this definition of (b+c) in the first equation:
3a = 4((b+c)+d)
3a = 4((5a/3)+d) [Use the new value of (b+c), which is (5a/3)]
3a = 4(5a/3+3d/3)
3a = 4((5a + 3d)/3)
3a = (4/3)(5a + 3d)
3a = (20/3)a + 4d
9/3a = (20/3)a + 4d
-(11/3)a = 4d
4d = -(11/3)a
d = -(11/12)a
d/a = -(11/12)
-5 5/6-(-2 1/3)+5 1/6
Answer: 1.66666666667
If -8. min 19 are in an AP, find the values of m and n
Answer:
m = 1 and n = 10.
Step-by-step explanation:
I am assuming you mean -8, m , n, 19.
If they are in AP the 4 terms will have a common difference.
19 - (-8) = 19 + 8 = 27.
So the increase over 3 terms (from -8 to 19) is 27 so we have:
27 / 3 = 9
Therefore the common difference is 9 and the A P is
-8, 1, 10, 19.
Grogg has two bags of marbles, each of which contains some red marbles and some blue marbles (and no marbles of any other color). The ratio of red marbles to blue marbles in the first bag is 3:5. The ratio of red marbles to blue marbles in the second bag is 3:2. When the two bags of marbles are mixed together, the ratio of red marbles to blue marbles is 11:9. What is the ratio of the number of marbles in the first bag to the number of marbles in the second bag?
The ratio of the number of marbles in the first bag to the number of marbles in the second bag is 2:7.
How to determine the required ratio?First of all, we would assign the variables x and y to the marbles in the first and second bag respectively. Also, let F and S represents the first and second bag respectively.
For the first bag, we have:
Ratio = 3:5 = 3x:5x = 3x + 5x = 8x
For the first bag, we have:
Ratio = 3:2 = 3y:2y = 3y + 2y = 5y
Tabulating these values, we have:
Red Blue
First bag 3x 5x
Second bag 3y 2y
The two red marbles = 3x + 3y.
The two blue marbles = 5x + 2y.
Next, we would write the ratio of the total red marbles to the total blue marbles:
Total red/Total blue = 11/9
(3x + 3y)/(5x + 2y) = 11/9
Cross-multiplying, we have:
27x + 27y = 55x + 22y
27y - 22y = 55x - 27x
5y = 28x
y = 28x/5
y = (28/5)x
y = 5.6x
Remember from the second bag, S = 5y:
S = 5(5.6x)
S = 28x.
Thus, the ratio of the number of marbles in the first bag to the number of marbles in the second bag is given by:
F/S = 8x/28x
F/S = 8/28
F/S = 2/7
F:S = 2:7.
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Compare using <,=,or >.
-5/12 and -3/4
Answer:
-9/12 < -5/12
Step-by-step explanation:
-5/12 = -5/12
-3/4 = -9/12
-9/12 < -5/12
The magnitude of the electrical force acting between a 2.4 × 10–8 c charge and a 1.8 × 10–6 c charge that are separated by 0.008 m is n, rounded to the tenths place.
The magnitude of the electrical force acting between both the given charges which are separated by 0.008 m is 6.07 N.
Given Charges 2.4*[tex]10^{-8} C[/tex] and 1.8 *[tex]10^{-6} C[/tex] that are separated by 0.008 m.
We have to find the magnitude of the electrical force acting between the charges. Magnitude is the property which determines the size of an object or process. Force is an influence that can change the direction of an object.
To find the magnitude we have to use Coulomb's law which says that
[tex]F_{E}=K*(q_{1}*q_{2}/d^{2}[/tex]
where K is Coulomb's constant whose value is [tex]8.9910^{9}Nm^{2} C^{2}[/tex].
[tex]q_{1}[/tex]=[tex]2.6*10^{-8} C[/tex] and
[tex]q_{2}=1.8*10^{-6} C[/tex] are the electric charges.
d=0.008m is the separation distance between the charges.
Putting the values in the given formula we get:
[tex]F_{E} =8.99(10)^{9}Nm^{2}/C^{2} *(2.4(10)^{-8}C(1.8(10)^{-6}C)/(0.008m)^{2}[/tex]
=6.07 N
Hence the magnitude of force acting between [tex]2.4*10^{-8} C[/tex] and [tex]1.8*10^{-6}C[/tex] is 6.07 N.
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Answer:
6.1Step-by-step explanation:
** Which of the following is parallel to the line 2x + 4y = 16 (A) y = 2x + 5 (B) y = -x + 4 (C) y = -x + 8 (D) y = 2x + 5 =-
Answer:
None of them.
Step-by-step explanation:
Each and every straight line is of one kind in terms of its pattern: it can be presented in the view of [tex]y = kx + b[/tex]: [tex]k[/tex] is the slope or gradient of the line, [tex]b[/tex] is the y-intercept of the line. I will not let the cat out of the bag if I say that any parallel lines do not intersect one another, hence they should have the same value of coefficient [tex]k[/tex].
[tex]2x + 4y = 16 \Leftrightarrow x + 2y = 8 \Leftrightarrow 2y = -x + 8 \Leftrightarrow y = - \frac{1}{2}x + 4[/tex]
Therefore, our line has [tex]k = - \frac{1}{2}[/tex] and [tex]b = 4[/tex] coefficients.
(A) [tex]k = 2, b = 5;[/tex]
(B) [tex]k = -1, b = 4;[/tex]
(С) [tex]k = -1, b = 8;[/tex]
(D) [tex]k = 2, b = 5;[/tex]
Recapitulating this: none of them have the same coefficient [tex]k[/tex], thus none of them suit us.
Suppose that a classroom has 4 light bulbs. The probability that each individual light bulbs work is 0. 6. Suppose that each light bulb works independently of the other light bulbs. What is the probability that none of the 4 light bulbs work?.
Answer:
(0.4)⁴
Step-by-step explanation:
• The probability that each individual light bulbs work is :
1 - 0. 6 = 0.4
Then
•• the probability that none of the 4 light bulbs work is :
(0.4)×(0.4)×(0.4)×(0.4)
= (0.4)⁴
= 0.0256
2 six-sided dice, one colored green and one red, are released. Find the probability that : either the score on the green die is 1, or the score on the red die is 6, but not both.
The probability that either the score on the green die is 1 or the score on the red die is 6, but not both, is 11/36.
To find the probability that either the score on the green die is 1 or the score on the red die is 6 (but not both), we can break it down into two mutually exclusive events and then calculate their probabilities separately.
Event A: The score on the green die is 1.
Event B: The score on the red die is 6.
We need to find the probability of either event A or event B occurring but not both.
The probability of event A occurring is the probability of rolling a 1 on the green die.
Since each die is six-sided, the probability of rolling a 1 on the green die is 1/6.
The probability of event B occurring is the probability of rolling a 6 on the red die. Similarly, the probability of rolling a 6 on the red die is 1/6.
To calculate the probability of either event A or event B occurring but not both, we need to subtract the probability of both events occurring simultaneously from the sum of their individual probabilities.
The probability of both event A and event B occurring simultaneously is the product of their individual probabilities, which is (1/6) x (1/6) = 1/36.
So, the probability of either event A or event B occurring but not both is:
Probability = (Probability of event A) + (Probability of event B) - (Probability of both events occurring)
= (1/6) + (1/6) - (1/36)
= 6/36 + 6/36 - 1/36
= 11/36
Therefore, the probability is 11/36.
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Glenn the owner of a hardware store originally paid $54.60 for 15 tool sets. at his year-end clearance sale he sold the last tool set for$24.00 how much money did he lose on the last tool set
The amount of money that Glenn lost on last tool set is $30.60.
Given sale value of 15 tool set 1 year before is $54.60 and the sale value of last tool at year end is $24.00 by Glenn.
Sale value is the price which we get by selling the good including the profit and cost of the product.
In this question it is given that 15 tools sets, it does not mean that 15 sets are sold.
Using the formula
Amount lose=Original amount paid- selling price.
Now put the values in the formula:
Amount lose=$54.60-$24.00
Amount lose=$30.60.
Hence the amount of money he lost on the last tool set is $30.60.
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I’m confused, can someone explain?
Answer:
-3 < x < 7
Step-by-step explanation:
The domain of a graph is all of the x-values that are included in the function. Since the graph is continuous (one connected line), you can determine the domain by identifying the x-values associated with the line's endpoints. These values are x = -3 and x = 7. Remember, the x-value located on a closed dot is not included in the domain. Therefore, the domain of the graph is -3 < x < 7.
Please assist me with this problem
Answer:
x = 192
Step-by-step explanation:
The three right triangles in the figure are all similar, so their sides are proportional.
ProportionThe length marked x is the long side of the smallest triangle, and the short side of the middle-size triangle. The long side of the middle-size triangle is ...
400 -144 = 256
We now have enough information to write the proportion ...
long side/short side = x/144 = 256/x
Multiplying by 144x gives ...
x² = (144)(256)
x = √(144×256) = 12×16 = 192
The length x is 192 units.
simplify (x^-1y^2)(-3x^2y^0)
Please help and explain
We have [tex]x^{-n} = \frac1{x^n}[/tex] if [tex]n[/tex] is a positive integer and [tex]x\neq0[/tex], as well as [tex]x^0 = 1[/tex] if [tex]x\neq0[/tex]. So right away we can simplify to
[tex]\left(x^{-1} y^2\right) \left(-3 x^2 y^0\right) = \left(\dfrac{y^2}x\right) \left(-3x^2\right) = -\dfrac{3x^2y^2}x[/tex]
If [tex]x=0[/tex], then the starting expression is undefined. So we accept that [tex]x=0[/tex], in which case [tex]\frac xx = 1[/tex], and the overall expression simplifies to
[tex]\left(x^{-1} y^2\right) \left(-3 x^2 y^0\right) = \boxed{-3xy^2}[/tex]
What’s the property of equality of r-20=30
The addition property of equality is applied to find the value of r which equals 50.
What is the Addition Property of Equality?The addition property of equality states that, if a - b = c, then a = c + b.
Given the expression, r - 20 = 30, to find the value of r, apply the addition property of equality as shown below:
Add 20 to both sides
r - 20 + 20 = 30 + 20
r = 50
The value of r using the addition property of equality is: 50.
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Baby rabbits were sorted into three groups, based upon which food they preferred when given a choice: Brand A rabbit food, Brand B rabbit food, or a diet of raw vegetables. For two months each group was restricted to their preferred diet (they were no longer given a choice in diet). Measurements for the height, weight, and length of the rabbits was taken each week for two months. The rabbits in the group with the diet of raw vegetables had significantly more growth that the other two groups. What conclusion can be drawn from this study?
Answer: That raw vegetables are better for the rabbit's growth than rabbit food.
Answer:
The rabbit food that was strictly a diet of raw vegetables is healthier for the rabbits.
Step-by-step explanation:
You have a bag of marbles that has 12 red, 5 green, 6 yellow, and 4 blue. If you draw one at random. what is P(red)? (What would the percent of choosing red be)
[tex]|\Omega|=12+5+6+4=27\\|A|=12\\\\P(A)=\dfrac{12}{27}=\dfrac{4}{9}=44.4\%[/tex]
Answer: 44.44% approximately
Work Shown:
P(red) = (number of red)/(number total)
P(red) = (12 red)/(12 red + 5 green + 6 yellow + 4 blue)
P(red) = (12 red)/(27 total)
P(red) = 12/27
P(red) = 4/9
P(red) = 0.4444 approximately
P(red) = 44.44% approximately
6x+7=-5 i got it wrong
Answer:
x = -2
Step-by-step explanation:
Subtract 7 from both sides :
6x = -12
Divide both sides by 6 :
x = -2
Hope this helped and have a good day
help me please ASAP
Answer:
on the percentage of the buses on time ,30 is not included
Answer:
the numbering on the y axis
Im so confused please help me :((
Answer:
[tex]A) \sf \ \sf \dfrac{x^8}{16y^4}[/tex]
Explanation:
[tex]\sf \left(\dfrac{2y}{x^2}\right)^{-4}[/tex]
inverse of the expression
[tex]\sf \left(\dfrac{x^2}{2y}\right)^{4}[/tex]
distribute power inside parenthesis
[tex]\sf \left(\dfrac{(x^2)^4}{(2y)^4}\right)[/tex]
apply exponent rules: [tex]\s(a^b )^c = a^{bc}[/tex]
[tex]\sf \dfrac{x^8}{16y^4}[/tex]
It was a 5ft. by 5ft. sandbox. how many square feet would mr. potato head be able to walk inside the box?
25 square feet would mr. potato head be able to walk inside the box.
What is square ?A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is side square.Each side of square is 90° .Given,
length and breadth of sandbox is 5 ft.
Now, We apply formula of area of square.
5 × 5 = 25 ft²
Therefore, 25 ft² would mr. potato head be able to walk inside the box.
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Which statement about this figure is true?
It has reflectional symmetry with one line of symmetry
It has rotational symmetry with an angle of rotation of 90%
It has no reflectional symmetry
It has no rotational symmetry
Option C. The truth statement about the figure is that it has no reflectional symmetry.
What is reflectional symmetry?
This is the term that is also used to refer to mirror symmetry. It is known to be used in respect to reflections.
The shape that we have here can be seen that it does not have this type of symmetry.
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If we changed the 2 to a 5 in the domain restriction x < 2 what would happen to the graph?
Answer:
what would happen is that the dotted line that is at 2 and down right now would go up to 5
Hope This Helps!!!
coach tim needs to fill five
volleyballs with air. if each
volleyball has a diameter of 8
inches, what is the total volume
of air that coach tim will
need? round to the nearest
whole number
The total volume of air that coach Tim will need to fill is [tex]1,340^{3} inches[/tex].
To find the total volume of air that coach Tim will need:
The formula of volume = [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × [tex]r^{3}[/tex]
Given - Diameter of volleyball = 8 inches
So, the radius of volleyball = [tex]\frac{8}{2}[/tex] = 4 inches
Now, put the values in the formula of volume as follows:
[tex]\frac{4}{3} * \pi * 4^{3}[/tex]
[tex]\frac{4}{3} * \pi * 64[/tex]
[tex]\frac{4}{3} * 3.14 * 64\\\frac{4}{3} * 201.06\\4 * 67.02\\268.08[/tex]
To find total volume = [tex]268.08 * 5[/tex]
[tex]= 1340.4[/tex]
Rounding off to the nearest whole number = [tex]1,340^{3} inches[/tex]
Therefore, the total volume of air that coach Tim will need to fill is [tex]1,340^{3} inches[/tex].
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