Answer:
73.24% probability that 6 or more people from this sample are unemployed
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.071[/tex]
So
[tex]\mu = E(X) = np = 10*0.071 = 7.1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.071*0.929} = 2.5682[/tex]
What is the probability that 6 or more people from this sample are unemployed
Using continuity correction, this is [tex]P(X \geq 6 - 0.5) = P(X \geq 5.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 5.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.5 - 7.1}{2.5682}[/tex]
[tex]Z = -0.62[/tex]
[tex]Z = -0.62[/tex] has a pvalue of 0.2676
1 - 0.2676 = 0.7324
73.24% probability that 6 or more people from this sample are unemployed
Given the following data, find the weight that represents the 53rd percentile.
Weights of Newborn Babies9.4 7.5 5.4 7.5 7.1
6.0 8.1 5.7 7.1 6.6
9.4 5.8 8.7 5.7 9.3
Answer:
Step-by-step explanation:
Rearranging the weights in ascending order, it becomes
5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4
The formula for determining the percentile is expressed as
n = (P/100)N
Where
n represents the value of the given percentile
P represents the given percentile
N represents the number of items(weights)
From the information given, the number of items, n is 15
P = 53
Therefore,
n = (53/100) × 15
n = 7.95
n = 8
Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1
53rd percentile is 7.1
A business office orders paper supplies from one of three vendors, V1, V2, or V3. Orders are to be placed on two successive days, one order per day. Thus, V2V3 might denote that vendor V2 gets the order on the first day and vendor V3 gets the order on the second day.
Required:
a List the sample points in this experiment of ordering paper on two successive days.
b Assume the vendors are selected at random each day and assign a probability to each sample point.
c Let A denote the event that the same vendor gets both orders and B the event that V2 gets at least one order. Find P( A), P( B), P( A U B), and P( A ∩ B) by summing the probabilities of the sample points in these events.
Find the given attachments
(please answer as soon as possible)If two lines intersect at a point, then vertically opposite angles are always: a)Complememtary b)Supplementary c)Unequal d)Equal
Answer:
D
Step-by-step explanation:
This is the veritcal angles theorem
Insurance Underwriters have established that the probability of city experiencing disasters in the next five years is 0.3 for a Tornado, 0.4 for Hurricane, and 0.1 for both Tornado and Hurricane. A) What is the probability of city experiencing only a Tornado in the next five years?B) What is the probability of city experiencing neither a Tornado nor Hurricane in the next five years?
Answer:
a. 20%
b. 40%
Step-by-step explanation:
We have the following from the statement:
P (T) = 0.3
P (H) = 0.4
P (T n H) = 0.1
Thus:
a. Tornado-only probability would be the probability of a tornado minus the probability of both tornado and hucaran
P (only T) = P (T) - P (T n H)
replacing:
P (only T) = 0.3 - 0.1
P (only T) = 0.2
In other words, the probability that only one tornado will occur is 20%
b. The probability that there is neither of the two would be the complement of the union between both events, that is:
P (T U H) '= 1 - P (T U H)
and the union is equal to:
P (T U H) = P (T) + P (H) - P (T n H)
replacing:
P (T U H) = 0.3 + 0.4 - 0.1
P (T U H) = 0.6
now if replacing in P (T U H) ':
P (T U H) '= 1 - 0.6
P (T U H) '= 0.4
That is to say that the probability that neither of the two happens is 40%
Please answer this correctly
Answer: 1/4
Step-by-step explanation:
The cheesiest recipe would be 1 cup and the least cheesy recipe would be 3/4 cups
1 - 3/4 = 1/4
Answer:
[tex]\frac{1}{4}[/tex] cup of cheese
Step-by-step explanation:
The least cheesiest recipe uses [tex]\frac{3}{4}[/tex] cup of cheese while the most cheesiest uses 1 cup of cheese.
[tex]1-\frac{3}{4} =\\\\\frac{1}{4}[/tex]
The most cheesiest uses [tex]\frac{1}{4}[/tex] cup more cheese than the least cheesiest.
Which of the following terminating decimals is equivalent to -1 3/4
Answer:
-1.75
Step-by-step explanation:
How can I make the red segment less steep than the blue segment , and more steep than the green segment ?
Please answer this correctly
Answer:
There are 5 number of temperature readings.
Step-by-step explanation:
9, 7, 9, 10, 9
5 readings recorded in the range of 6-10°C.
The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?
Answer:
4.6%.
Step-by-step explanation:
The probability that a can of paint contains contamination(C) is 3.23%
P(C)=3.23%
The probability of a mixing(M) error is 2.4%.
P(M)=2.4%
The probability of both is 1.03%.
[tex]P(C \cap M)=1.03\%[/tex]
We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]
In probability theory:
[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]
The probability that a randomly selected can has contamination or a mixing error is 4.6%.
PLEASE HELP ALGEBRA PROBLEM!!! 20 POINTS ANSWER A-D
Answer:
A. 1.5 seconds
B. 36 feet
C. 0 feet
D. After 3 seconds
Step-by-step explanation:
I graphed it on desmos.
Find the area and the circumference of a circle with radius 7 cm.
Use the value 3.14 for me, and do not round your answers. Be sure to include the correct units in your answers.
cm
7 cm
Area: 0
Circumference: 0
Х
[tex]answers \\ area = 153.86 \: {cm}^{2} \\ circumference = 43.96 \: cm \\ \\ solution \\ radius = 7cm \\ area \: of \: circle = \pi {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: 3.14 \times {7}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 49 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 153.86 \: {cm}^{2} \\ circumference \: of \: circle = 2\pi \: r \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 3.14 \times 7 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 43.96 \: cm \\ hope \: it \: helps \\ good \: luck \: on \: you r \: assignment[/tex]
Answer:
[tex] Area \: of \: circle = 153.86 \: {cm}^{2} \\ \\ Perimeter \: of \: circle = 43.96 \: cm [/tex]
Given:
Radius of circle (r) = 7 cm
Step-by-step explanation:
[tex]Area \: of \: circle = \pi {r}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times ({7}^{2} ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times 49 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3.14 \times 49 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 153.86 \: {cm}^{2} [/tex]
[tex]Circumference \: of \: circle = 2\pi r \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \pi \times 7\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \times \pi\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 14 \times 3.14\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 43.96 \: cm[/tex]
can someone help me please? its urgent
Answer:
Step-by-step explanation:
Answer:
972^1/4 = 4 ⁴√3
448^1/3 = 4 ³√7
3528^1/2 = 42√2
4050^1/4 = 3 ⁴√50
Hope this helps.
If f(x)=x³-2x², which expression equivalent to f(i)?
Answer:
f(x) = x³ - 2x²
=>
f(i) = i³- 2i²
Hope this helps!
:)
Christine has a motion detector light which gets activated an average of 16 times every 2 hours during the night. In order to find the probability that the motion detector light will be activated more than 4 times in a 25 minute period during the night using the Poisson distribution, what is the average number of activations per 25 minutes?
Answer:
The average number of activations per 25 minutes is 2.5.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In this question:
For 2 hours = 2*60 = 120 minutes, the mean is 16 times.
To find for 25 minutes, we use a rule of three.
120 minutes - 16 times
25 minutes - m times
[tex]120m = 12*25[/tex]
[tex]m = \frac{12*25}{120}[/tex]
[tex]m = 2.5[/tex]
The average number of activations per 25 minutes is 2.5.
In a particular region, for families with a combined income of $75,000 or more, 15% of these families have no children, 35% of the families have one child, 45% have two children, and 5% have three children. Use this information to construct the probability distribution for X, where x represents the number of children per family for this income group. Arrange x in increasing order and write the probabilities P(x) as decimals
Answer:
The probability distribution for x:"number of children per family for this income group" is:
[tex]\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\[/tex]
Step-by-step explanation:
With the information given we have the relative frequencies of each category.
We know:
[tex]\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\[/tex]
Which statements are true?
If all angles of a quadrilateral are right angles, then the quadrilateral must be a square.
Two shapes are similar if and only if their corresponding angles are equal.
All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º.
if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
There are three vertices in a triangle, or there are four sides in a pentagon.
Any two triangles are either similar or congruent.
Answer:
Step-by-step explanation:
1) If all angles of a quadrilateral are right angles, then the quadrilateral must be a square. This is not true because the quadrilateral can also be a rectangle.
2) Two shapes are similar if and only if their corresponding angles are equal. This is true.
3) All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º. This is false because the sum of the angles is 360°
4) if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus. This is true.
5) There are three vertices in a triangle, or there are four sides in a pentagon. This is false because a Pentagon has 5 sides.
6) Any two triangles are either similar or congruent. This is not true. Congruent triangles are always similar
Therefore, the true statements are 2 and 4
Answer:
its B and D
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Volume of cylinder = πr²h
= (3.14)(4)(0.75)
= 9.4
Since she'll fill it half so
Amount of water to be filled = 4.7
Find the inverse of f(x)=1/(x^3)
Answer:
Step-by-step explanation:
y[tex]f(x)^{-1} = inverse\\f(x)=y \\y = 1/(x^{3} \\Inverse: y=x ------------> x = 1/y^{3}\\y^{3} - \frac{1}{x} = 0\\y^{3} = \frac{1}{x}\\y = \sqrt[3]{\frac{1}{x}} \\y = \frac{\sqrt[3]{1} }{\sqrt[3]{x}} \\y = \frac{1}{\sqrt[3]{x}}[/tex]
rearrange the equation t = vf - vi /a
to make acceleration appear on the left hand side
Answer:
a= (vf - vi)/t
Step-by-step explanation:
t = vf - vi /a
a* t =(vf - vi /a)*a
at = vf - vi
at/t = (vf - vi)/t
a = (vf - vi)/t
Hope it works
The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.
Answer:
[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]
And we can find this probability with this difference:
[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200,50)[/tex]
Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]
We want to find the following probability:
[tex]P(170<X<220)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(170<X<220)=P(\frac{170-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{220-\mu}{\sigma})=P(\frac{170-200}{50}<Z<\frac{220-200}{50})=P(-0.6<z<0.4)[/tex]
And we can find this probability with this difference:
[tex]P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.655-0.274= 0.381 [/tex]
If a man takes 30 minutes to drive at work and it is 44 miles into work what is the average speed?
Answer:
1.46666 miles / minutes
88 miles per hour
Step-by-step explanation:
The speed is distance over time
44 miles / 30 minutes
1.46666 miles / minutes
or if we want in miles per hour
44 miles / .5 hours
88 miles per hour
Answer:
1.467 mile/minute
Step-by-step explanation:
you should divide the distance on the time i.e. 44/30
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
All of the following are examples of quantitative data EXCEPT ________.
a. the amount of sleep normally gotten by the students in a class
b. the number of siblings that students have
c. the cholesterol levels of the students in a class
d. the exam scores for the students in a class
d. the gender of the students in a class
Answer:
e. the gender of the students in a class
Step-by-step explanation:
Quantitative data is measured is numbers. For example 1, 2, 3.5,...
Qualitative data are labels, that is, tall, short, male, female, Brazilian, Colombian,...
In this question:
The only data that is not measured in numbers is the gender of the studens in class, which can be male or female, they do not assume any numeric value. So the answer is e.
The quantitive data example does not include option e. the gender of the students in a class.
Data:Quantitative data is measured in numbers. like 1, 2, 3.5,..While on the other hand, Qualitative data are labels i.e. tall, short, male, female, etc. Based on this, the last option is correct.learn more about the data here: https://brainly.com/question/20296761
What is 9/8 squaredto the power of 2 ?
Answer:
81/64
Step-by-step explanation:
(9/8)²=9²/8²=81/64
Solve x for the diagram below.
Answer:
20°
Step-by-step explanation:
These angles add up to 90° so we have:
x + 2x + x + 10 = 90
4x + 10 = 90
4x = 80
x = 20°
Solve for x and y
5x + 3y = 7
y=4
Answer:
-1
Step-by-step explanation:
plug in y, subtract 12 from seven, divide -5 by 5
The values of x and y are -1 and 4 respectively.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given are a system of linear equations.
5x + 3y = 7
y = 4
We already have the value of y as 4.
Substituting that value of y = 4 in the first equation 5x + 3y = 7, we get,
5x + (3 × 4) = 7
5x + 12 = 7
Subtracting both sides by 12, we get,
5x + 12 - 12 = 7 - 12
5x = -5
Dividing both sides by 5, we get,
5x / 5 = -5 / 5
x = -1
Hence the value of x is -1 and the value of y is 4.
To learn more about Linear Equations, click on the link :
https://brainly.com/question/29739212
#SPJ5
Which expression is equivalent to 36 a minus 27?
9 (4 a minus 3)
3 (18 a minus 9)
9 (4 a minus 27)
3 (12 a minus 6)
Answer:
[tex]9(4a)-9(3)[/tex]
Step-by-step explanation:
[tex]36a-27[/tex]
[tex]9(4a)-9(3)[/tex]
[tex]9(4a-3)[/tex]
Answer:
it is 9(4a-3)
Step-by-step explanation:
Which equation describes a relationship that is directly proportional?
(A) y = 9
(B) y = 1/5
(C) y = 3x
(D) y = x + 4
Answer:
(C) y = 3x
Step-by-step explanation:
Directly proportional relation is one in which the value of x and y gets increases or decreased in same proportion.
example of such relation can be y = kx
where k is the constant of proportionality which depicts by how much value of y will change in response to change of x.
_______________________________________________
now in the option
A and B
y= 9 , y =1/5
value of y is constant and does not depend on other variable. it value will remain same.
for y = x+4
value of y increases with x but it does not increase proportionally.
let see an example for x =1 , y = 1+4 = 5
x =2 , y = 2+4 = 6
(1,5) and (2,6) are not proportionally changing also this equation is not of form y = kx
thus, it is incorrect option.
_______________________________
(C) y = 3x
here equation is form y =kx . in place of k there is 3
let see an example for x =1 , y = 3*1 = 3
x =2 , y = 3*2 = 6
(1,3) and (2,6) are proportionally changing (1/3 = 2/6) also this equation is of form y = kx
thus, it is correct option.
Identify a reason why we should be skeptical of any claim or statistical evidence involving the following: A study shows that during the early 20th century, a strong correlation existed between the number of people who owned radios and the number of people put into insane asylums. Therefore, people who owned a radio were more likely to be declared insane and put into an insane asylum.a. correlation does not imply causality b. misleading graph c. self-interest survey d. voluntary response survey
Answer:
Option A
Step-by-step explanation:
Correlation does not imply causality. Correlation shows whether and how strongly pairs of variables are related.
Causality shows a situation between two events where one event is affected by the other
We would be skeptical of this survey because it is very difficult to assume that people who owned a radio were more likely to be declared insane and put into an insane asylum as listening to the radio cannot cause insanity unless proven.
An online furniture store sells chairs for $100 each and tables for $550 each. Every day, the store can ship at most 25 pieces of furniture and must sell no less than $7000 worth of chairs and tables. If 9 chairs were sold, determine all possible values for the number of tables that the store must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Answer:
(10, 11, 12, 13, 14, 15, 16)
Step-by-step explanation:
The minimum number of tables that the store has to sell in order to meet the requirements is given by:
[tex](25-t)*100+t*550=7,000\\(550-100)t=7,000-2,500\\t = 10\ tables[/tex]
The company must sell at least 10 tables.
Since the company already sold 9 chairs, and they can ship at most 25 items, they can sell at most 16 tables. Every integer number between the minimum and maximum is also possible:
(10, 11, 12, 13, 14, 15, 16).
Answer:
12,13,14,15,16
Step-by-step explanation:
\underline{\text{Define Variables:}}
Define Variables:
May choose any letters.
\text{Let }t=
Let t=
\,\,\text{the number of tables sold}
the number of tables sold
\text{Let }c=
Let c=
\,\,\text{the number of chairs sold}
the number of chairs sold
\text{\textquotedblleft at most 25 pieces"}\rightarrow \text{25 or fewer pieces}
“at most 25 pieces"→25 or fewer pieces
Use a \le≤ symbol
Therefore the total number of furniture pieces sold, t+ct+c, must be less than or equal to 25:25:
t+c\le 25
t+c≤25
\text{\textquotedblleft no less than \$7000"}\rightarrow \text{\$7000 or more}
“no less than $7000"→$7000 or more
Use a \ge≥ symbol
The store makes $550 for each table sold, so for tt tables, the store will make 550t550t dollars. The store makes $100 for each chair sold, so for cc chairs, the store will make 100c100c dollars. Therefore, the total revenue 550t+100c550t+100c must be greater than or equal to \$7000:$7000:
550t+100c\ge 7000
550t+100c≥7000
\text{Plug in }9\text{ for }c\text{ and solve each inequality:}
Plug in 9 for c and solve each inequality:
The store sold 9 chairs
\begin{aligned}t+c\le 25\hspace{10px}\text{and}\hspace{10px}&550t+100c\ge 7000 \\ t+\color{green}{9}\le 25\hspace{10px}\text{and}\hspace{10px}&550t+100\left(\color{green}{9}\right)\ge 7000 \\ t\le 16\hspace{10px}\text{and}\hspace{10px}&550t+900\ge 7000 \\ \hspace{10px}&550t\ge 6100 \\ \hspace{10px}&t\ge 11.09 \\ \end{aligned}
t+c≤25and
t+9≤25and
t≤16and
550t+100c≥7000
550t+100(9)≥7000
550t+900≥7000
550t≥6100
t≥11.09
\text{The values of }t\text{ that make BOTH inequalities true are:}
The values of t that make BOTH inequalities true are:
\{12,\ 13,\ 14,\ 15,\ 16\}
{12, 13, 14, 15, 16}
\text{(the final answer is this entire list)}
(the final answer is this entire list)
