Answers
Given:
Given that the triangular prism with height 10 inches.
The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.
We need to determine the surface area of the prism.
Surface area of the prism:
The surface area of the prism can be determined using the formula,
[tex]SA=bh+(s_1+s_2+s_3)H[/tex]
where b is the base and h is the height of the triangle.
s₁, s₂, s₃ are the side lengths of the triangle and
H is the height of the prism.
Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;
[tex]SA=(12)(5)+(12+5+13)(10)[/tex]
[tex]SA=60+(30)(10)[/tex]
[tex]SA=60+300[/tex]
[tex]SA=360 \ in^2[/tex]
Thus, the surface area of the triangular prism is 360 square inches.
Hence, Option b is the correct answer.
Answer:
360 sq in
Step-by-step explanation:
i did it trust me
Related Questions
which cannot be a cross section of the figure? A cross section of the figure cannot be a ____
Answers
Answer:
it is circle
Step-by-step explanation:
just got it correct
A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the desert for vacation. How many individuals were surveyed in total? How many people are planning on going to the mountains for their vacation?
Answers
Answer:
140 individuals were surveyed
42 people are planning on going to the mountains
Step-by-step explanation:
The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.
If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:
[tex]21=n*0.15\\n=140\ individuals[/tex]
140 individuals were surveyed
Since 30% responded "the mountains", the number of people planning on going to the mountains is:
[tex]m = 140*0.30\\m=42\ people[/tex]
42 people are planning on going to the mountains
Takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. Her data are shown in the plots below. A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Shaded plants (inches). There are 0 dots above 1.5, 4 above 2, 3 above 2.5, 2 above 3, 0 above 3.5 and 4, and 1 above 4.5. A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Full Sun plants (inches). There are 0 dots above 1.5, 1 above 2, 0 above 2.5, 2 above 3, 0 above 3.5, 4 above 4, and 3 above 4.5. Which best explains the variability of the sets? The shaded plants set has greater variability because more data is clustered around the median. The sets are equally variable because the ranges of the data sets are equal. The full sun plants set has greater variability because the IQR for full sun plants is greater. The full sun plants set has greater variability because the median for full sun plants is greater.
Answers
Answer:
c
Step-by-step explanation:
its not a b or d so its c
Answer: C
Step-by-step explanation: on edge
volume of a sphere with a radius of 10
Answers
Answer:
4189 cubic units
Step-by-step explanation:
Put the value in the volume formula and do the arithmetic. The formula for the volume of a sphere is ...
V = (4/3)πr³
Filling in 10 for r, we have ...
V = (4/3)π(10³) = 4000π/3 ≈ 4189 . . . cubic units
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the margin of error at 90% confidence?
A. 0.3 grams
B. 0.5133 grams
C. 0.8391 grams
D. 1.5 grams
E. 0.06 grams
Answers
Answer:
A.0.39 grams
margin of error at 90% confidence intervals is
M.E = 0.39 grams
Step-by-step explanation:
Explanation:-
Given a sample of size n = 25
mean of the sample x⁻ = 15 grams
Standard deviation of the sample 'S' = 1.5 grams
margin of error at 90% confidence intervals is determined by
[tex]Margin error = \frac{t_{0.90} S.D}{\sqrt{n} }[/tex]
The degrees of freedom ν = n-1 = 25-1 =24
The tabulated value t₀.₉₀ = 1.318
[tex]Margin error = \frac{1.318X 1.5}{\sqrt{25} }[/tex]
Margin of error = 0.3954
Conclusion:-
Margin of error at 90% confidence intervals = 0.3954
The chart describes how four of Susan’s friends handle their money. Handling Money Person Description of Spending Sylvia She uses her whole paycheck to buy food and necessities and pay the minimum amount on her bills each month. Then, she buys new clothes and pays for them with a credit card. Nancy She uses her whole paycheck to buy food and necessities and then takes a trip each month, which she pays for by adding to a personal loan with her credit union. Fiona She buys food and necessities and pays more than the minimum due on her bills each month. She goes out with her friends using some of the money that is left over in her checking account. Uli She buys food and necessities and pays the minimum amount on her bills each month. She goes out with her friends using the money that is left over in her savings. Which person is most creditworthy? Nancy Sylvia Fiona Uli
Answers
Answer: C. Fiona
Step-by-step explanation:
what is the area of a circle if the diameter is 16 millimetres
Answers
Answer:
201.1 mm²
Step-by-step explanation:
given that the diameter is 16mm,
radius = diameter ÷ 2 = 16÷2 = 8 mm
area of a circle is given by
A = πr², where
π=3.142
r = radius = 8 mm
Substituting these into the equation,
A = πr²
= 3.142 (8)²
= 201.088 mm²
= 201.1 mm² (rounded to nearest tenth)
NEED ANSWER ASAP WILL GIVE BRAINLIEST!!!!!!!
A teacher had 1 apple, he gave 1 to his student. How many apples does the teacher have and how much apples does his student have?
Answers
Answer:
Teacher has 0 . Student has 1 apple
Step-by-step explanation:
Any jogs 1/3 of a mile in 1/5 of an hour while john takes 1/30 of an hour to jog 1/5 of an mile if they continued at this rate who would jog farther in one hour and by how much?
Answers
Answer:
At the end of one hour, John would be ahead of Anny by 4.33 miles
Step-by-step explanation:
In this question, we are to state who jogs Farther between these. 2 persons per hour.
Any jogs 1/3 of a mile in 1/5 of an hour, what this means that he jogs one-third of a mile in 1/5 * 60 in 12 minutes
John however jogs 1/5 miles in 1/30 of hour. This means he jugs one-fifth of a mile in 1/30 * 60 in 2 minutes
Let’s go back to Any
if Any jogs 1/3 in 12 minutes, then the whole lap will be completed in 36 minutes
Thus if he can jog 1 mile in 36 minutes, then in 60 minutes he would have jogged 1.67 miles
If he Jogs 1/5 in 2 minutes, this mean that the whole lap of 1 mile would be completed in 10 minutes
Thus if he can jug 1 mile in 10 minutes, then in 60 minutes, he will be able to jug a whopping 6 miles
This shows that John is actually faster than Any.
By how much distance? that would be 6 - 1.67 = 4.33 miles
What is the inner quartile range for 72,80,81,84,92,92,94,95?
Answers
Answer:
the inter quartile range is 12.5
Step-by-step explanation:
Ten people at two local restaurants were randomly surveyed and asked to rate their experience, with “1” representing very poor and “10” representing very good. The data is shown in the dot plots. Find the mean for each set of data. Blue Terrace: Paradiso Grill:
Answers
Answer:
Blue Terrace: 6.1
Paradiso Grill: 6.3
Step-by-step explanation This is the right answer
Answer:
6.1 and 6.3
Step-by-step explanation:
1.
Solve the following inequalities:
- 4x >72
Answers
Answer:
x<18
Step-by-step explanation:
-4x>72 / divide both side ÷-4
x<-18
xe(-œ,-18)
Paddling with the current in a river, jake traveled 16 miles. Even though he paddled upstream for an hour longer than the amount of the time he paddled downstream jake could only travel 6 miles against the current. I'm still waterJake paddles at a rate of 5 mph. What is the speed of the current I the river
Answers
Answer: the rate of the current is 3 mph.
Step-by-step explanation:
Let x represent the rate of the current.
In still water, Jake paddles at a rate of 5 mph. Paddling with the current in a river, Jake traveled 16 miles. It means that the speed with which she travelled downstream (with the current) is (5 + x) mph
Time = distance/speed
Time spent in paddling downstream is
16/(5 + x)
While paddling upstream, it took an hour longer. The speed with which he paddled upstream is (5 - x) mph.
Jake could only travel 6 miles against the current. It means that the time spent in travelling upstream us
6/(5 - x)
Since it took 1 hour longer, then
6/(5 - x) = 16/(5 + x) + 1
Cross multiplying by (5 - x)(5 + x), it becomes
6(5 + x) = 16(5 - x) + 1(5 + x)(5 - x)
30 + 6x = 80 - 16x + 25 - 5x + 5x - x²
30 + 6x = - x² - 16x + 5x - 5x + 25 + 80
30 + 6x = - x² - 16x + 105
x² + 16x + 6x + 30 - 105 = 0
x² + 22x - 75 = 0
x² + 25x - 3x - 75 = 0
x(x + 25) - 3(x + 25) = 0
x - 3 = 0 or x + 25 = 0
x = 3 or x = - 25
Since x cannot be negative, then x = 3 mph
Answer: x=3
Step-by-step explanation:
Took test
A ball is thrown vertically upward. After seconds, its height (in feet) is given by the function 56t - 16t^2 . What is the maximum height that the ball will reach?
Answers
Answer:
Therefore the maximum height that the reach is 49 feet after 1.75 seconds.
Step-by-step explanation:
Given that,
A ball is thrown vertically upward. After t seconds its height is given by the function
[tex]h=56t-16 t^2[/tex]
where h is height in feet.
Maximum value:
Given function f(x)= at²+bt+c.
Find the value [tex]-\frac{b}{2a}[/tex] Putting [tex]x= -\frac{b}{2a}[/tex] in the given function. The maximum value of the given function is [tex]f(-\frac{b}{2a})[/tex].Here a= -16 , b=56 and c=0
The ball attains its maximum height when [tex]t=-\frac{56}{2.(-16)}=1.75[/tex] s.
Putting the value of t in the given function
[tex]h=(56\times 1.75)-16(1.75)^2[/tex]
=49 feet
Therefore the maximum height that the reach is 49 feet after 1.75 seconds.
The maximum height the ball will reach is given by the vertex of the parabola represented by the equation 56t - 16t^2. This is reached at t = 1.75 seconds, giving a maximum height of 49 feet.
Explanation:The equation 56t - 16t^2 represents the trajectory of the ball thrown upwards over time. To identify the maximum height reached by the ball, we should look for the vertex of the parabola this equation graphically represents. This equation is a quadratic function given in the standard form at^2 + bt + c, where a = -16, b = 56, and c = 0. The time at which the maximum height is reached is found by the formula -b / (2.a). This yields t = -56 / (2 * -16) = 1.75 seconds. When substituted back into the equation, the maximum height (h) would be h = 56 * 1.75 - 16 * (1.75)^2 = 49 feet.
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Determine the value of the expression given below. 121 / 2÷(−1 3/8)
Answers
Answer:
-44
Step-by-step explanation:
A bank offer 3% interest each yr you invest 1500. Write a equation to model this situation for x years. How much will be in the account after 10 years?
Answers
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1500
r = 3% = /100 = 0.0
n = 1 because it was compounded once in a year.
t = x years
Therefore, the equation to model this situation is
A = 1500(1 + 0.03/1)^1 × x
A = 1500(1.03)^x
When x = 10 years, then
A = 1500(1.03)^10
A = $2016
The original price of a shirt was $20. It was decreased to $15. What is the percent decrease of the price of this shirt?
Answers
Answer:
25%
Step-by-step explanation:
Price reduction = 20 - 15 = $ 5
Percent decrease of price = (5/20)*100 = 5*5 = 25%
two-fifth of the students in a mixed school are boys. if there are 30 girl in the school how many are boys
Answers
Answer:
12
Step-by-step explanation:
One fifth of 30 would mean u divide 30 by 5 which equals 6. Since it's two fifths you would have 12.
Jim had $2,052.24 in his checking account. He wrote a check to pay for
two airplane tickets. His account now has $1,084.12. How much did each
ticket cost? *
Answers
Answer:
$485.06
Step-by-step explanation:
Answer:
$484.06
Step-by-step explanation:
$2,052.24 - 1,084.12 = 916.12
916.12 divided by 2 = 484.06
The combination of Wendell and Maggie’s ages is 33. Wendell’s age is 3 less than 3 times the age of Maggie. How old is Wendell?
Answers
Answer:
Wendell is 24 years old.
Step-by-step explanation:
First write an equation to represent the situation.
x=Maggie's age
x+(3x-3)=33
Then solve for x
x+3x-3=33
4x-3=33
4x-3+3=33+3
4x=36
4x/4=36/4
x=9
Then solve for Wendell's age
y=Wendell's age
y=3x-3
y=3(9)-3
y=27-3
y=24
Wendell is 24 years old.
By setting up and solving a system of equations based on the information given, we find that Wendell is 24 years old.
Explanation:In this question, we are asked to find out Wendell's age. First, we assume that Maggie's age is x. According to the problem, the sum of Wendell and Maggie's ages is 33, so we can write the first equation as Wendell's age + Maggie's age = 33. Next, we know that Wendell's age is three less than three times Maggie's age, so Wendell's age = 3*x - 3. Now, if we insert Wendell's age expression from the second equation into the first equation, we get 3*x - 3 + x = 33. When we solve this equation, we found that x equals to 9, hence, Maggie is 9 years old. That means, Wendell is 33 - 9 = 24 years old.
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The first 4 terms of a geometric sequence are 108, 36, 12, 4, ... What is the eighth term of the sequence?
Answers
Answer:
4/81
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
hope it helps
Find the profit function for the given marginal profit and initial condition. Marginal Profit Initial Condition dP dx = −20x + 290 P(5) = $670 P(x) =
Answers
Answer:
[tex]P(x) = -10x^2+290x-530[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dP}{dx} = -20x + 290[/tex]
Initial condition:
[tex]P(5) = $670[/tex]
Solving the given differential equation, we get,
[tex]\dfrac{dP}{dx} = -20x + 290\\\\dP=(-20x + 290)dx\\\text{Integrating both sides}\\\\\displaystyle\int dP = \int (-20x + 290)dx\\\\P(x) = -20\dfrac{x^2}{2} + 290x + C\\\\\text{where C is constant of integration}\\P(x) = -10x^2+290x + C\\P(5) = 670\\670 = -10(5)^2+290(5) + C\\670 = 1200 + C\\\Rightarrow C = -530\\P(x) = -10x^2+290x-530[/tex]
is the required profit function.
To determine the profit function, integrate the given marginal profit function. After integration, apply the initial condition to find the integration constant. The final profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]
Explanation:The subject matter of this question is calculus, specifically how to determine the profit function based from the given marginal profit and initial condition. To determine the profit function, you need to integrate the marginal profit function. The marginal profit is given as dP/dx = -20x + 290. When you integrate this, you will get [tex]P(x) = -10x^2 + 290x + C[/tex], where C is an integration constant that we determine using the initial condition P(5) = 670.
To do this, substitute 5 into x in the equation and set P(x) equal to[tex]670: 670 = -10*5^2 + 290*5 + C.[/tex] Solving for C, you will find that C equals -60. So the profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]
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what is the range for this set of data 38,17,55,40
a)2
B)38
C)39
D)72
Answers
Answer:
b.38
Step-by-step explanation:
suppose the diameter is a circle 8 units what is the circumference in units
Answers
Answer:
C = 8π
Step-by-step explanation:
C = 2πr
C = 2π(8/2)
C = 2π × 4
C = 8π
Answer:
18.84 units
Step-by-step explanation:
diameter is 6 units so radius will be 3 units.
circumference = 2πr = 2×22/7×3
= 18.84 units
Twenty college students experience the effects of alcohol on reaction time. They perform very basic timed responses in a driving simulator both before and after consuming several alcoholic beverages. The researcher collects a reaction-time result for each of the 20 students before and after intoxication, for a total of 40 measures. What is the null hypothesis for this paired-samples study?
Answers
Answer:
For this case the hypothesis would be that after consuming alcoholic beverages the reaction time increases, so then the system of hypothesis for this case are:
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
We can define the difference as: [tex]d_i=y_i-x_i[/tex]
And the system of hypothesis are:
Null hypothesis:[tex] \mu_d \leq 0[/tex]
Alternative hypothesis: [tex] \mu_d >0[/tex]
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
Solution to the problem
For this case the hypothesis would be that after consuming alcoholic beverages the reaction time increases, so then the system of hypothesis for this case are:
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
We can define the difference as: [tex]d_i=y_i-x_i[/tex]
And the system of hypothesis are:
Null hypothesis:[tex] \mu_d \leq 0[/tex]
Alternative hypothesis: [tex] \mu_d >0[/tex]
A cylindrical waste can has a volume of 5,667.7 cubic inches and its base has a radius of 9.5 inches. Find the height of the waste can. Round to the nearest tenth.
Answers
Answer:
20.0 inches
Step-by-step explanation:
The formula for the volume of a cylinder is useful here.
V = πr²h
Filling in the given numbers, we see ...
5667.7 = (3.14)(9.5²)h
Dividing by the coefficient of h, we get ...
h = 5667.7/283.385 = 20 . . . . inches
The height of the waste can is 20.0 inches.
_____
Comment on the solution
If you use a more exact value of pi, the height is closer to 19.9899 inches. It still rounds to 20.0.
What is the domain of the function y = StartRoot x EndRoot?
Answers
Answer:
C
Step-by-step explanation:
0 is less than or equal to x is less than infinity. PERIODT.
The domain of the function y = √x will be [0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = √x
The graph of the function is similar to the rightward parabola, the function is not defined for the negative value of x, because the function becomes imaginary.
For the domain of the function, the value of x should be greater than equal to zero.
Because the value under the square root should be greater than or equal to zero.
Then the domain of the function y = √x will be
x ≥ 0
Thus, the domain of the function y = √x will be [0, ∞).
The graph of the function is given below.
More about the domain and range link is given below.
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Victor has already taken 4 pages of notes on his own, and he will take 2 pages during each hour of class. Write an equation that shows the relationship between the time in class h and the number of pages p.
Write your answer as an equation with p first, followed by an equals sign
Answers
Answer:
The answer is p = 4 + 2h .
Step-by-step explanation:
It is given that Victor has already taken 4 pages and he will take 2 pages per hour of class. So you have to make an equation of p in terms of h :
Let p be pages,
Let h be hours,
p = 4 + (2×h)
p = 4 + 2h
A check is written pay to the order of Matthew Carter. Examine the check. For Mathew Carter, the check would be a . The amount would be the balance in his checking account.
Answers
Answer:The first one is deposit and the second one is added to.
Answer:
Deposit and Added To
Step-by-step explanation:
which cannot be a cross section of the figure? A cross section of the figure cannot be a ____
Answers
Answer: The answer is circle
Step-by-step explanation: The explanation is that you can see by looking at the shape you can easily make a rectangle, etc but you can not make a circle :).
Answer:
circle
Step-by-step explanation: