Answer:
[tex]V=\frac{1}{3}(2.5)(6)=5 \ in^{3}[/tex]
The volume of the pyramid is 5 cubic inches.
Step-by-step explanation:
Assuming that the triangle base dimensions are 1 inche and 5 inches, and the height of the pyramid is 6 inches, the volume would be
[tex]V=\frac{1}{3}Bh[/tex]
Where B is the area of the base (triangle) and h is the height.
[tex]B=\frac{1}{2}bh =\frac{1}{2}(1)(5)=2.5 \ in^{2}[/tex]
Then,
[tex]V=\frac{1}{3}(2.5)(6)=5 \ in^{3}[/tex]
Therefore, the volume of the pyramid is 5 cubic inches.
The sum of two numbers is 41. One number is 1 less than the other.
Answer:
s must be 21 and r is 20
Step-by-step explanation:
Represent the two numbers using variables r and s.
Then r + s = 41, and r = s - 1
Substituting the 2nd equation for r into the first equation, we get:
s - 1 + s = 41, or 2s = 42. Then s must be 21 and r is 20.
Suppose you have $200,000 in a bank term account. You earn 5% interest per annum from his account
Answer:
$190,000
Step-by-step explanation:
discount = x
original price = $200,000
discount% = 5%
x/200,000 = 5/100
x · 100 = 5 · 200,000
100x = 1,000,000
100x/100 = 1,000,000/100
x = 10,000
Sale price: $200,000 - $10,000 = $190,000
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
OP = OQ
Answer:
B
Step-by-step explanation:
Look at the shape closely observe the following the imaginary lines;
OC = OA , OB = OD {these is the raduis of the circle;
note also line CQ = CD { the perpendicular line bisects line CD in two equal halves;
Similarly ;
note also line AP= PB { the perpendicular line bisects line OP in two equal halves}
Hence;
OP is congruent to the OQ
In maths we say something is congruent when they are the same shape and have same angles but we are allowed to flip it's side.
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s circle t) (negative 7)?
Answer:
153
Step-by-step explanation:
Solve the inequality 6h−5(h−1)≤7h−11 and write the solution in interval notation. Use improper fractions if necessary.
Answer:
[tex]h \geq 2\frac{2}[3}[/tex]
Step-by-step explanation:
We solve the inequality similarly to how we would solve an equalitu.
[tex]6h - 5(h-1) \leq 7h - 11[/tex]
[tex]6h - 5h + 5 \leq 7h - 11[/tex]
[tex]h - 7h \leq -11 - 5/[/tex]
[tex]-6h \leq -16[/tex]
Multiplying everything by -1
[tex]6h \geq 16[/tex]
Simplifying by 2
[tex]3h \geq 8[/tex]
[tex]h \geq \frac{8}{3}[/tex]
8 divided by 3 is 2 with rest two. So as a improper fraction, the answer is:
[tex]h \geq 2\frac{2}[3}[/tex]
Answer:
[8,
3
Step-by-step explanation:
Diego's doctor has recommended that his daily diet should include 3 vegetables, 2 fruits, and 2 whole grains. At the grocery store, Diego has a choice of 9 vegetables, 9 fruits, and 11 whole grains. In how many ways can he get his daily requirements if he doesn't like to eat 2 servings of the same thing in 1 day
Answer:
166320 ways
Step-by-step explanation:
In this case we must calculate the number of combinations for each option, and then multiply the result of each one, like this:
Number of ways you can choose 3 vegetables out of 9 available:
nCr = n! / (r! * (n-r)!)
in this case n = 9, r = 3, replacing:
9C3 = 9! / (3! * (9-3)!) = 84
Number of ways you can choose 2 fruits out of 9 available:
9C2 = 9! / (2! * (9-2)!) = 36
Number of ways you can choose 2 whole grains out of 11 available:
11C2 = 11! / (2! * (11-2)!) = 55
So according to the rule of the products how many ways you can choose the daily diet
84*36*55 = 166320
Help ill give you brainliest and points !!!!!
Answer:
1.12
2.85
3.60
Step-by-step explanation:
1.
if m = 12 you solve by dividing 144/12
144/12 = 12
2.
when m = 11 you solve by computing 7(11) + 8
7(11) = 77 so you solve from there 77 + 8 which equals 85
3.
When g = 4 you solve my multiplying 15(4)
15(4) = 60
Answer:
first question: 12
second question: 85
third question: 60
Step-by-step explanation:
first question: plug in 12 for m and you would get 144/12 which equals 12.
Second question: plug in 11 for m and you have 7(11) + 8.
77+8 = 85
third question: plug in 4 for g and you have 15(4)
15 x 4 = 60.
*parentheses mean multiplication when next to a number
ex: 7(11)
not ex: 3 + (2/3) since it isn't directly next to the first number, instead its adding
What is the value of y?
Answer:
d. 54
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
y=(180º-72º)/2
y=108º/2
y=54º
D.
What is the range of the function?
all real numbers less than or equal to 4
all real numbers less than or equal to -3
all real numbers greater than or equal to 4
all real numbers greater than or equal to -3
10X
Answer:
1. all real numbers less than or equal to 4 = </= 4.
Answer = YES!
2. all real numbers less than or equal to -3 = </= -3.
Answer = YES!
3. all real numbers greater than or equal to 4 = >/= 4
Answer = YES!
4. all real numbers greater than or equal to -3 = >/= -3
Answer = NO!
Step-by-step explanation:
1. all real numbers less than or equal to 4 = </= 4.
1 + 1 = 2
1 + 2 = 3
2 + 2 = 4
2. all real numbers less than or equal to -3 = </= -3.
1 - 1 = 0
1 - 2 = -1
1 - 3 = -2
1 - 4 = -3
3. all real numbers greater than or equal to 4
1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
1 + 4 = 5
4. all real numbers greater than or equal to -3
1 - 1 = 0
1 - 2 = -1
1 - 3 = -2
1 - 4 = -3
Answer:
The range is all real numbers less than or equal to 4
Step-by-step explanation:
took the test on edge
2.1.40: The police records of a city contain the following statistics on offenses for the month of May: 430 assaults, 146 robberies, and 131 drug sales. The records also show that 26 people were involved in both assault and robbery and that 33 people were involved in both assault and drug sales. What is the greatest possible number of offenders for May who satisfy these statistics
Answer:
648
Step-by-step explanation:
Number of Assaults, n(A)=430
Number of Robberies, n(R)=146
Number of Drug Sales Offenses, n(D)=131
Number involved in both assault and robbery= [tex]n(A\cap R)=26[/tex]
Number involved in both assault and drug sales= [tex]n(A\cap D)=33[/tex]
Therefore, to find the greatest possible number of offenders for May who satisfy these statistics, we remove the number of those who were involved in more than one crime.
This gives us:
[tex]=n(A)+n(R)+n(D)-n(A\cap R)-n(A\cap D)\\=430+146+131-26-33\\=648[/tex]
The greatest possible numbers of offenders in May is 648.
What is the y value?
Answer:
y =34
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
63+ 2y+ y+15 = 180
Combine like terms
78+ 3y = 180
Subtract 78 from each side
78+3y-78 = 180-78
3y = 102
Divide each side by 3
3y/3 = 102/3
y =34
Answer:
[tex]y = 34[/tex]
Step-by-step explanation:
Sum of the angles in a triangle is 180 degrees
[tex]2y + 63 + y + 15 = 180 \\ 3y + 63 + 15= 180 \\ 3y +7 8 = 180 \\ 3y = 180 - 78 \\ 3y =10 2 \\ \frac{3y}{3} = \frac{102}{3} \\ y = 34 [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Dan got 45 out of 72 correct in his test.
What fraction of the marks did he get wrong?
Give your answer in its simplest form.
Answer:
3/8
Step-by-step explanation:
45/72=5/8
(5/8)+x=72/72
x=1-(5/8)
x=3/8
find the circumference
(3.14)(24)
Answer:
75.36unit^2
Step-by-step explanation:
Looking at the expression in the question, it is synonymous to the
equation for the circumference of a circle
π×d =3.14×24=75.36unit^2
If AB=x and x=4, then the transitive property states
1. AB+4=2x
2. X=4
3. AB+x=4
4. AB=4
Answer:
5
Step-by-step explanation:
i took the test
The transitive property states AB = 4.
What is transitive property?The transitive property of equality states that the first number is also equal to the third number if two numbers are equal and the second number is equal to the third number. In other words, if a is equal to b and b is equal to c, then a is equal to c. One of the many mathematical properties of equality is the transitive property.
Given AB = x and x = 4
Acc. to transitive property,
if a = b, b = c Then c = a.
so AB = 4
Hence option D is correct, AB = 4.
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You are shopping online for a new TV. The one you want costs $2,500. You live in New York where the state sales tax rate is 8.49%. Your sister lives a short distance over the border in CT where the state sales tax rate is 6.35%. If you have the TV shipped to her and you pick it up. How much will you save?
Answer:
$5350
Step-by-step explanation:
see attachment
Answer:
Its 53.50
Step-by-step explanation:
A phone company charges 12 cents per minute of call. If Gerardo made a call that took 75 minutes using this plan, how much did his call cost?
Answer:
900 cents, 9 dollars
Step-by-step explanation:
Twenty students from Sherman High School were accepted at Wallaby University. Of those students, eight were offered military scholarships and 12 were not. Mr. Dory believes Wallaby University may be accepting students with lower SAT scores if they have a military scholarship. The newly accepted student SAT scores are shown here.
Military scholarship: 850, 925, 980, 1080, 1200, 1220, 1240, 1300
No military scholarship: 820, 850, 980, 1010, 1020, 1080, 1100, 1120, 1120, 1200, 1220, 1330
Part A: Do these data provide convincing evidence of a difference in SAT scores between students with and without a military scholarship? Carry out an appropriate test at the α = 0.05 significance level.
Part B: Create and interpret a 95% confidence interval for the difference in SAT scores between students with and without a military scholarship.
Answer:
Step-by-step explanation:
For military scholarship,
Mean, x1 = (850 + 925 + 980 + 1080 + 1200 + 1220 + 1240 + 1300)/8
x1 = 1099.375
Standard deviation = √(summation(x - mean)²/n
n1 = 8
Summation(x - mean)² = (850 - 1099.375)^2 + (925 - 1099.375)^2 + (980 - 1099.375)^2 + (1080 - 1099.375)^2 + (1200 - 1099.375)^2 + (1220 - 1099.375)^2 + (1240 - 1099.375)^2 + (1300 - 1099.375)^2 = 191921.875
Standard deviation, s1 = √(191921.875/8
s1 = 154.89
For no military scholarship,
Mean, x2 = (820 + 850 + 980 + 1010 + 1020 + 1080 + 1100 + 1120 + 1120 + 1200 + 1220 + 1330)/12
x2 = 1070.83
Standard deviation = √(summation(x - mean)²/n
n2 = 12
Summation(x - mean)² = (820 - 1070.83)^2 + (850 - 1070.83)^2 + (980 - 1070.83)^2 + (1010 - 1070.83)^2 + (1020 - 1070.83)^2 + (1080 - 1070.83)^2 + (1100 - 1070.83)^2 + (1120 - 1070.83)^2 + (1120 - 1070.83)^2 + (1200 - 1070.83)^2 + (1220 - 1070.83)^2 + (1330 - 1070.83)^2 = 238091.6668
Standard deviation, s2 = =√(238091.6668/12
s2 = 140.86
Part A)
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean score of students with military scholarship and μ2 be the mean score of students without military scholarship.
The random variable is μ1 - μ2 = difference in the mean score between students with military scholarship and without military scholarship
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (1099.375 - 1070.83)/√(154.89²/8 + 140.86²/12)
t = 0.42
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [154.89²/8 + 140.86²/12]²/[(1/8 - 1)(154.89²/8)² + (1/12 - 1)(140.86²/12)²] = 21644133.914878543/1533280.3458504018
df = 14
We would determine the probability value from the t test calculator. It becomes
p value = 0.68
Since alpha, 0.05 < than the p value, 0.68, then we would fail to reject the null hypothesis. Therefore, at a significance level of 5%, these data do not provide convincing evidence of a difference in SAT scores between students with and without a military scholarship
Part B)
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (8 - 1) + (12 - 1) = 18
z = 2.101
x1 - x2 = 1099.375 - 1070.83 = 28.545
Margin of error = 2.101√(154.89²/8 + 140.86²/12) = 143.3
The 95% confidence interval is 28.545 ± 143.3
George is curious. He has been told that the average body temperature of humans is 98.6 degrees Fahrenheit. However, he believes it is much lower than that. He randomly selects 60 people from those passing by him on a street and takes their temperature. The average temperature of these 60 people is 98.2 degrees Fahrenheit. The standard deviation, sigma Subscript x,is known to be 0.62 degrees Fahrenheit. The p-value is less than 0.0001. What is the correct conclusion?
Answer:
[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.
Step-by-step explanation:
Information given
[tex]\bar X=98.2[/tex] represent the sample mean
[tex]\sigma=0.62[/tex] represent the population standard deviation
[tex]n=60[/tex] sample size
[tex]\mu_o =98.6[/tex] represent the value that we want to test
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean is equal to 98.6 F, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 98.6[/tex]
Alternative hypothesis:[tex]\mu \neq 98.6[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The degrees of freedom, on this case:
[tex]df=n-1=60-1=59[/tex]
The p value would be given by:
[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
domain: (-∞,∞)
range [-3,∞)
Step-by-step explanation:
The domain is the values that x can take
X can be any value so the domain is all real numbers
The range is the values that y can take
The minimum value is -3
The range is y ≥ -3
r(x−s)=sx+t what does x equal
Answer:
x = (rs + t)/(r-s)
Step-by-step explanation:
r(x - s) = sx + t
rx - rs = sx + t
rx - sx = rs + t
x(r - s) = rs + t
x = (rs + t)/(r-s)
The solution for x is x = (t + rs)/(r - s).
What is an equation?A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.
We can begin by simplifying the given equation:
First, solve the parenthesis,
r(x - s) = sx + t
Simplify, the equation, we get,
rx - rs = sx + t
rx - sx = t + rs
Take the like terms to one side, we get,
x(r - s) = t + rs
Now, solve for x, we get,
x = (t + rs)/(r - s)
Therefore, x is equal to (t + rs)/(r - s).
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Please answer this correctly
72+72+36= 144+36= 180
Answer:
Area of the figure = 176 m²
Step-by-step explanation:
Area of Rectangle = Length × Width
Dividing the whole figure
Rectangle 1:
6 × 18 = 108 m²
Rectangle 2 :
10 × 6 = 60 m²
Rectangle 3:
2 × 4 = 8 m²
Adding All
Area of the figure = 108 + 60 + 8
Area of the figure = 176 m²
Which expression is equivalent to StartRoot negative 80 EndRoot? Negative 4 StartRoot 5 EndRoot Negative 4 StartRoot 5 EndRoot i 4 StartRoot 5 EndRoot i 4 StartRoot 5 EndRoot
or
Which expression is equivalent to √-80
A. -4√5
B. -4√5i
C. 4√5i
D. 4√5
Answer:
C. 4√5i
Step-by-step explanation:
on edge
please vote brainliest i have never gotten it before
The tree diagram represents an
experiment consisting of two trials.
.4
.5
.6
D
.3
С
.5
.7
D
Þ(B and D) = [?]
ter
Answer:
0.35
Step-by-step explanation:
.5x.7
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
3
4
Ο Ο Ο Ο
5
9
Answer:
The answer is 4
Step-by-step explanation:
1.5(4+4)-3= 9
4.5(4-2)=9
9=9
Answer:
[tex]x=4[/tex]
Explanation:
[tex]1.5x+6+-3=4.5x+-9\\1.5x+3=4.5x-9\\-3x+3=-9\\-3x=-12\\x=4[/tex]
Tara has 1 3/5
yards of fabric. She needs
2 1/2
times this amount to make a shopping bag. How much fabric does Tara need to make the bag?
Answer:
amount of fabric to make the bag = 4 yards
Step-by-step explanation:
Tara has 1 3/5 yards of fabric . She needs extra 2 1/2 times the amount she have to make a shopping bag. The amount of fabric she needs to make the bag can be calculated as follows.
1 3/5 yards = 8/5 yards of fabrics
What she actually needs to make a shopping bag is two and half the amount she has . Mathematically, it can be express
2 1/2 × 8/5
Let us change 2 1/2 to improper fraction
amount of fabric to make the bag = 5/2 × 8/5
amount of fabric to make the bag = 40/10
amount of fabric to make the bag = 4 yards
Need help ASAP thank you!!!
Answer:
= 180 yd^3
Step-by-step explanation:
The volume of a triangle prism is
V= Bh where B is the area of the base
B = area of the triangle
= 1/2 *8* 5
= 20 yd^2
V = 20 yd^2 * 9 yd
= 180 yd^3
Brainliest to whoever gets this correct Which of the following is not a polynomial identity?
Answer:
Hi there!
The correct answer is C.
Step-by-step explanation:
A polynomial identity are equations that are true for all possible values of the variable. For example, x²+2x+1=(x+1)² is an identity.
You measure 50 textbooks' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 5.2 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places
Answer:
90% confidence interval for the true population mean textbook weight is [35.79 ounces , 38.21 ounces].
Step-by-step explanation:
We are given that you measure 50 textbooks' weights, and find they have a mean weight of 37 ounces.
Assume the population standard deviation is 5.2 ounces.
Firstly, the Pivotal quantity for 90% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean weight = 37 ounces
[tex]\sigma[/tex] = population standard deviation = 5.2 ounces
n = sample of textbooks = 50
[tex]\mu[/tex] = true population mean textbook weight
Here for constructing 90% confidence interval we have used One-sample z test statistics as we know about population standard deviation.
So, 90% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5%
level of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X -1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X +1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X -1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X +1.645 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]37-1.645 \times {\frac{5.2}{\sqrt{50} } }[/tex] , [tex]37+1.645 \times {\frac{5.2}{\sqrt{50} } }[/tex] ]
= [35.79 , 38.21]
Therefore, 90% confidence interval for the true population mean textbook weight is [35.79 ounces , 38.21 ounces].
Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between 0 million and 5.1 million?
Answer:
11.90% probability that the mean profit for the sample was between 0 million and 5.1 million
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 6.54, \sigma = 10.45, n = 73, s = \frac{10.45}{\sqrt{73}} = 1.2231[/tex]
In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between 0 million and 5.1 million?
This is the pvalue of Z when X = 5.1 subtracted by the pvalue of Z when X = 0. So
X = 5.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.1 - 6.54}{1.2231}[/tex]
[tex]Z = -1.18[/tex]
[tex]Z = -1.18[/tex] has a pvalue of 0.1190
X = 0
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0 - 6.54}{1.2231}[/tex]
[tex]Z = -5.35[/tex]
[tex]Z = -5.35[/tex] has a pvalue of 0
0.1190 - 0 = 0.1190
11.90% probability that the mean profit for the sample was between 0 million and 5.1 million
Rule multiply the last number by 3 then subtract 2
2 4 10 _ _
Answer:
[tex]28[/tex], [tex]82[/tex]
Step-by-step explanation:
[tex]10 \times 3 -2=28\\28 \times 3 - 2 = 82[/tex]
