The rectangular box shown in the figure has dimensions 8" × 7" × 4" (a = 8, b = 7, c = 4). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 7" × 4" side. (Round your answer to two decimal places.)
Answers
Answer:
Rectangle
four
Length and width
Step-by-step explanation:
Related Questions
Find the area of the surface. the part of the cylinder y^2+z^2=9 that lies above the rectangle with vertices (0,0),(4,0),(0,2), and (4,2)
Answers
To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.
Explanation:To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.
The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.
John has painted 4/5 of his house the next day he painted 2/3 of what he had left what fraction of the house is left to paint
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so... he painted 4/5 of the house first..... now the whole house is 5/5, from 4/5 to 5/5 is just 1/5, so 1/5 was left for the next day.
the next day, he painted only 2/3 of what was left, what is 2/3 of 1/5? well is just their product.
[tex]\bf \cfrac{2}{3}\cdot \cfrac{1}{5}\implies \cfrac{2}{15}\impliedby \textit{only painted the next day the slacker} \\\\\\ \textit{so he has painted in total }\cfrac{4}{5}+\cfrac{2}{15}\impliedby \textit{LCD of 15}\implies \cfrac{12+2}{15} \\\\\\ \stackrel{painted}{\cfrac{14}{15}}\qquad \qquad \stackrel{whole}{\cfrac{15}{15}}-\stackrel{painted}{\cfrac{14}{15}}\implies \stackrel{unpainted}{\cfrac{1}{15}}[/tex]
THe cost of a hamburger is $2.50. Each additional hamburger cost $2.00. Sully wrote this explicit rule to explain the sequence of costs: f(n) = 2 + 2.5(n-1). Using the rule, he found the cost of 12 hamburgers to be 29.50. Is this number correct?
Answers
Answer:
Yes, the number is correct.
Step-by-step explanation:
The cost of a hamburger is $2.50.
Each additional hamburger cost $2.00.
Sully wrote this explicit rule to explain the sequence of costs:
[tex]f(n) = 2+2.5(n-1)[/tex]
Using the rule, he found the cost of 12 hamburgers to be 29.50.
Lets check by putting n = 12.
[tex]f(12) = 2+2.5(12-1)[/tex]
= [tex]2+2.5(11)[/tex]
= [tex]2+27.5 [/tex]
= $29.50
So, yes Sully is correct.
s=n(a1+an)/2 gives the partial sum of an arithmetic sequence. What is the formula solved for an?
Answers
[tex]S= \frac{n}{2} (a_{1}+a_{n})[/tex]
Multiply each side by 2.
[tex]2S=n(a_{1}+a_{n}) [/tex]
Divide each side by n.
[tex] \frac{2S}{n} =a_{1} + a_{n}[/tex]
Subtract a₁ from each side.
[tex] \frac{2S}{n} - a_{1} = a_{n}[/tex]
Answer: [tex]a_{n} = \frac{2S}{n} - a_{1} [/tex]
"THIS IS A 90 POINT QUESTION"
A) F IS A INCREASING ON THE INTERVAL X < 0
B) F IS A DECREASING ON THE INTERVAL X < 0
C) F IS A INCREASING ON THE INTERVAL 0 < X < 1
D) F IS A DECREASING ON THE INTERVAL 0 < X < 1
E) F IS A INCREASING ON THE INTERVAL 1 < X < 3
F) F IS A DECREASING ON THE INTERVAL 1 < X < 3
G) F IS A INCREASING ON THE INTERVAL X > 3
H) F IS A DECREASING ON THE INTERVAL X > 3
"SELECT ALL THAT APPLY"
Answers
A) F IS A INCREASING ON THE INTERVAL X < 0
hope this helps
Use the distributive property in two different ways to find the product of 127 and 32.
Answers
2.) 32(100+20+7)= 3200+640+224=4064
Answer and explanation:
Use the distributive property in two different ways to find the product of 127 and 32.
Distributive property says that,
[tex]a(b+c)=ab+ac[/tex]
We have to find product of 127 and 32,
1) Split 127 as 100+27
[tex]127\times32=(100+27)\times 32[/tex]
Apply distributive property,
[tex]127\times32=100\times 32+27\times 32[/tex]
[tex]127\times32=3200+864[/tex]
[tex]127\times32=4064[/tex]
2) Split 32 as 30+2
[tex]127\times32=127\times (30+2)[/tex]
Apply distributive property,
[tex]127\times32=127\times 30+127\times 2[/tex]
[tex]127\times32=3810+254[/tex]
[tex]127\times32=4064[/tex]
Solve the simultaneous equations
5x-4y=19
x+2y=8
Answers
For this equation we’re going to multiply the bottom equation by 2 so that the y’s will cancel out when we ad the equations together so that we can solve for x
5x-4y=19
2(x+2y=8)
Distribute the 2
5x-4y=19
2x+4y=16
Next add the two equations together
7x=35
As you can see the y was cancelled out. Now divide each side by 7 to solve for x
x=5
Now take this answer and plug it back into either equation to solve for y. I am going to plug it into the second equation, but you can choose either
x+2y=8
Replace x with its value, 5
5+2y=8
Subtract 5 from each side
2y=3
Divide each side by 2
y=3/2 (or 1.5)
ANSWER:
x = 5
y = 3/2 (or 1.5)
Robert can swim the first 50 meters of a race in 1 minute. Then he slows down by 12 seconds for each of the next 50 meters of a race. How long will it take Robert to swim a 400 meter race?
Answers
It takes Robert 13 minutes and 36 seconds to complete a 400 meter swimming race when he swims the first 50 meters in 1 minute and slows down by 12 seconds for each subsequent 50 meters.
Explanation:In this mathematical problem, Robert swims the first 50 meters in 1 minute. He slows down by 12 seconds for each subsequent 50 meters of the race. The total distance Robert needs to swim is 400 meters. The 400 meters is split into eight 50 meter increments.
For the first increment, it takes Robert 1 minute (or 60 seconds). For the next seven increments, Robert swims each in 12 seconds slower than the previous increment.
Therefore, the total time in seconds for Robert to complete the 400 meters swimming race is:
60 + 72 + 84 + 96 + 108 + 120 + 132 + 144 = 816 seconds
This is equivalent to 13 minutes and 36 seconds.
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A certain airplane has two independent alternators to provide electrical power. the probability that a given alternator will fail on a one-hour flight is 0.019. (a) what is the probability that both will fail? (round your answer to 4 decimal places.) probability (b) what is the probability that neither will fail? (round your answer to 4 decimal places.) probability (c) what is the probability that at least one fails? (round your answer to 4 decimal places.) probability referencesebook & resources
Answers
The probability that both alternators fail is approximately 0.0004, the probability that neither fails is approximately 0.9612, and the probability that at least one fails is approximately 0.0388, all rounded to four decimal places.
(a) The probability that both Alternator will fail is calculated by multiplying the probabilities of each failing:
P(Both Fail) = P(Alternator 1 Fails) x P(Alternator 2 Fails) = 0.019 x 0.019 ≈ 0.000361 = 0.0004 (rounded to four decimal places).
(b) The probability that an alternator does not fail is 1 minus the probability that it fails.
P(Neither Fail) = (1 - P(Alternator Fails))^2 = (1 - 0.019)^2 ≈ 0.9612 (rounded to four decimal places).
(c) To find the probability of at least one alternator failing, we subtract the probability of neither failing from 1:
P(At Least One Fails) = 1 - P(Neither Fail) = 1 - 0.9612 ≈ 0.0388 (rounded to four decimal places)
A rocket is launched with an initial velocity of 360 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds. h(t)=‒10t2 + 360t Which statement is true?
A. The rockets maximum height is 324 feet.
B. The rockets maximum height is 3240 feet.
C. In the interval from 9 seconds to 18 seconds, the rocket is descending.
D. The rocket hits the ground in 18 seconds.
Answers
hope it helps
Find the distance between the points given. (2, 5) and (6, 8) √(37) 5 √(22)
Answers
Answer: The correct option is (B) 5.
Step-by-step explanation: We are given to find the distance between the points (2, 5) and (6, 8).
We will be using the following formula :
DISTANCE FORMULA : The distance between the points (a, b) and (c, d) is given by
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points (2, 5) and (6, 8) is given by
[tex]D\\\\=\sqrt{(6-2)^2+(8-5)^2}\\\\=\sqrt{4^2+3^2}\\\\=\sqrt{16+9}\\\\=\sqrt{25}\\\\=5.[/tex]
Thus, the required distance between the given points is 5 units.
Option (B) is CORRECT.
David is playing a trivia game where he gains points for correct answers and loses points for incorrect answers. At the start of round 3 his score is −1500 points. During round 3 he answered five 1000 point questions correctly and three 500 points questions incorrectly. What is his score at the end of round 3?
A) −2000
B) −500
C) 2000
D) 3500
Answers
he answered 5 one thousand point questions....5 * 1000 = 5000
so he now has -1500 + 5000 = 3500
he answered 3 five hundred point question incorrectly...3 * -500 = -1500
3500 + (-1500) = 3500 - 1500 = 2000
so he ended up with 2000
Answer:
2000 points
Step-by-step explanation:
Topic: Substraction, Addition and Products
You have to organize the problem, as you can see
at Start of Round 3 David Has: - 1500
During Round 3:
5 Questions: 1000 each correctly
so 5 x 1000 = 5000
3 Questions: - 500 each incorrectly
so 3 x -500 = -1500
at the End of Round 3:
Starting: -1500
During Round 3: 5000 - 1500 = 3500
the end of round 3: -1500 + 3500 = 2000
Trina's employer purchased a health insurance plan that cost $550 per month Trina pays $85 toward the plan each month what is the annual value of the employer's contribution
Answers
The annual value of the employer's contribution towards Trina's health insurance plan is $5,580.
Here, we have to find the annual value of the employer's contribution, we need to determine how much the employer pays towards the health insurance plan in one month.
Trina's employer purchased a health insurance plan that costs $550 per month, and Trina pays $85 toward the plan each month.
Therefore, the employer's contribution is the difference between the total cost of the plan and what Trina pays:
Employer's contribution = Total cost of the plan - Trina's contribution
Employer's contribution = $550 - $85
Employer's contribution = $465 per month
Now, to find the annual value of the employer's contribution, we multiply the monthly contribution by 12 (since there are 12 months in a year):
Annual employer's contribution = $465 * 12
Annual employer's contribution = $5,580
So, the annual value of the employer's contribution towards Trina's health insurance plan is $5,580.
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Right triangle ABC is shown below.
Answers
Thanks
Jessica wants to serve 3/4 of a pint of orange juice to each of her guests. Her juice jar can hold 12 full pints of juice. Jessica can serve the juice to guest
Answers
Answer:16
Step-by-step explanation:
What is 2x-4y=20 for y
Answers
2x - 4y = 20
subtract the 2x over
-4y = -2x + 20
divide everything by -4
y = 1/2x - 5 <------- this is your answer
The savings account offering which of these APRs and compounding periods offers the best APY?
4.0784% compounded monthly
4.0798% compounded semiannually
4.0730% compounded daily
Answers
[tex]\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2 \end{cases} \\\\\\ \left(1+\frac{0.040798}{2}\right)^{2}-1\\\\ -------------------------------\\\\ [/tex]
[tex]\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 4.0730\%\to \frac{4.0730}{100}\to &0.040730\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\to &365 \end{cases} \\\\\\ \left(1+\frac{0.040730}{365}\right)^{365}-1[/tex]
Answer:
Option C is correct.
Step-by-step explanation:
The formula is = [tex](1+\frac{r}{n})^{n}-1[/tex]
r = rate of interest
n = number of times its compounded
1. 4.0784% compounded monthly
here n = 12
[tex](1+\frac{0.040784}{12})^{12} -1[/tex] = 1.0403-1 = 0.0403
2. 4.0798% compounded semiannually
here n = 2
[tex](1+\frac{0.040798}{12})^{2} -1[/tex] = 1.0066-1 = 0.0066
3. 4.0730% compounded daily
here n = 365
[tex](1+\frac{0.040730}{12})^{365}[/tex] = 3.328-1 = 2.328
Select "Rational" or "Irrational" to classify each number. Rational Irrational 0.25 √ 0.25 √0.33
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√0.25: Rational (=0.5)
√0.33: Irrational
whats the slope of (0,1) and (2,7)
Answers
7-1/2-0 or 1-7/0-2, the answer will equal 3 in either form as long as the y-coordinates are on the top and the x-coordinates are on the bottom.
The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.
Answers
is zero where h(t) is maximum.
The derivative is h'(t) = -32 t + 96 .
At the maximum ... h'(t) = 0
32 t = 96 sec
t = 3 sec .
___________________________________________
If you haven't had any calculus yet, then you don't know how to
take a derivative, and you don't know what it's good for anyway.
In that case, the question GIVES you the maximum height.
Just write it in place of h(t), then solve the quadratic equation
and find out what 't' must be at that height.
150 ft = -16 t² + 96 t + 6
Subtract 150ft from each side: -16t² + 96t - 144 = 0 .
Before you attack that, you can divide each side by -16,
making it a lot easier to handle:
t² - 6t + 9 = 0
I'm sure you can run with that equation now and solve it.
The solution is the time after launch when the object reaches 150 ft.
It's 3 seconds.
(Funny how the two widely different methods lead to the same answer.)
The answer is from AL2006
Cours hero a simple random sample of 64 8th graders at a large suburban middle school indicated that 89% of them are involved with some type of after school activity. find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.
a.[0.799, 0.981]
b.[0.699, 0.931]
c.[0.849, 0.854]
d.[0.799, 0.781]
e.[0.719, 0.981] f) none of the above
Answers
Final answer:
Using the formula for the confidence interval of a proportion, and after calculating standard error and margin of error, the 98% confidence interval for the proportion of 8th graders involved in after school activities is [0.799, 0.981]. Therefore, option a is correct.
Explanation:
To find the 98% confidence interval for the proportion of 8th graders involved in some type of after school activity, we can use the formula for the confidence interval of a proportion:
CI = ± z * √((p*(1-p))/n), where p is the sample proportion, n is the sample size, and z is the z-score corresponding to the confidence level.
In this case, we have p = 0.89 (since 89% of the sample is involved in after school activities), n = 64, and for a 98% confidence interval, the z-score (from z-tables or statistical software) is approximately 2.33.
First, let's calculate the standard error (SE): SE = √((0.89*(1-0.89))/64) = √((0.89*0.11)/64) = √(0.0989/64) = 0.0392.
Next, calculate the margin of error (ME): ME = z * SE = 2.33 * 0.0392 = 0.09136.
Now we can calculate the confidence interval: the lower limit is p - ME = 0.89 - 0.09136 = 0.79864 and the upper limit is p + ME = 0.89 + 0.09136 = 0.98136.
After rounding to three decimal places, the 98% confidence interval for the proportion is [0.799, 0.981]. Hence, option a is correct.
A rainstorm in Portland Oregon wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 60 Portland households is taken after the rainstorm. a. Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is the expectation of the relevant random variable do not round your response.) b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution run your response to at least three decimal places.
Answers
ps Portland is the most fun city in Oregon.
What is 1.5 x 10^-1 in standard form?
Answers
Its scientific notation:
Its negative so your going to the left:
1.5×10^-1
=0.015
Answer:
the answer is .15
Step-by-step explanation:
What is the area of a parallelogram whose vertices are A(−4, 9) , B(11, 9) , C(5, −1) , and D(−10, −1) ?
Answers
Let
[tex]A(-4,9)\\B(11,9)\\C(5,-1) \\D(-10,-1)\\E(-4.-1)[/tex]
using a graphing tool
see the attached figure to better understand the problem
we know that
Parallelogram is a quadrilateral with opposite sides parallel and equal in length
so
[tex]AB=CD \\AD=BC[/tex]
The area of a parallelogram is equal to
[tex]A=B*h[/tex]
where
B is the base
h is the height
the base B is equal to the distance AB
the height h is equal to the distance AE
Step 1
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-4,9)\\B(11,9)[/tex]
substitute the values
[tex]d=\sqrt{(9-9)^{2}+(11+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(15)^{2}}[/tex]
[tex]dAB=15\ units[/tex]
Step 2
Find the distance AE
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-4,9)\\E(-4.-1)[/tex]
substitute the values
[tex]d=\sqrt{(-1-9)^{2}+(-4+4)^{2}}[/tex]
[tex]d=\sqrt{(-10)^{2}+(0)^{2}}[/tex]
[tex]dAE=10\ units[/tex]
Step 3
Find the area of the parallelogram
The area of a parallelogram is equal to
[tex]A=B*h[/tex]
[tex]A=AB*AE[/tex]
substitute the values
[tex]A=15*10=150\ units^{2}[/tex]
therefore
the answer is
the area of the parallelogram is [tex]150\ units^{2}[/tex]
The area of the parallelogram is 0 units.
Explanation:To find the area of a parallelogram, we can use the formula A = base * height. We can find the length of the base by finding the distance between points A and D, which is 11 units. To find the height, we can find the distance between points A and B, which is 0 units. Therefore, the area of the parallelogram is 0 units.
Solve the problem as directed. The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of travel. An automobile averages 80 miles per hour. Using the inverse variation relationship, show what the time would be for the automobile to complete the trip. a0 hours
Answers
65*8 = 520 miles traveled
520/80 = 6.5 hours for the car
Answer:
The automobile would take 6.5 hours to complete the trip.
Step-by-step explanation:
This is a case of a inverse variation relationship because when you increase the speed of traveling the time of arriving will reduce, now we have to define the equation and the variables:
Inverse variation equation: [tex]x1y1=x2y2[/tex]
[tex]x1[/tex]: speed of the bus, 65 miles per hour
[tex]y1[/tex]: time to Austin by bus, 8 hours
[tex]x2[/tex]: speed of the automobile, 80 miles per hour
[tex]y2[/tex]: time to Austin by automobile, unknown
Now we can replace the values in the equation and clear [tex]y2[/tex], this is:
[tex]65*8=80*y2\\y2=\frac{65*8}{80} =\frac{520}{80} =6.5\\[/tex]
The automobile would take 6.5 hours to complete the trip.
Two worded maths questions. Even if you know one answer it would help! Please also give working out if possible.
Answers
Answer:
675 litres 80 mLStep-by-step explanation:
1. The total amount of oil in the two tanks at the start is ...
total oil = n + (n +150) + 0 = 2n+150 . . . . litres
The amount of oil in tank C at the end is 1/3 this amount, or
oil in tank C = (total oil)/3 = (2n+150)/3 . . . . litres
The amount pumped into tank C was 500 litres, so we have ...
(2n +150)/3 = 500
2n +150 = 1500 . . . . . . multiply by 3
2n = 1350 . . . . . . . . . . . subtract 150
1350/2 = n = 675 . . . . . divide by the coefficient of n
___
2. Let x represent the amount remaining in container A. Then 4x is the amount in tank B. Before the transfer, the amount in each container was the same, so ...
x +120 = 4x -120 . . . . . A had 120 more than remains; B had 120 less
240 = 3x . . . . . . . . add 120-x
240/3 = x = 80 . . . divide by the coefficient of x
The amount of liquid left in container A is 80 mL.
Tony and some friends went to the movies. They bought 4 drinks and 2 tubs of popcorn and spent a total of $32.50 on the food. Each drink cost $3.50 less than a tub of popcorn. Define a variable. Write and equation that can be used to find the cost of one tub of popcorn.
Answers
1 drink = t - 3.5
4(t - 3.5) + 2t = $32.50
4t - 14 + 2t = 32.5
6t = 32.5 + 14
6t = 46.5
t = 46.5 / 6
t = $7.75
Which expression shows how to multiply 5 times 381 by using place value and expanded form
Answers
The shadow of a vertical tower is 50 m long when the angle of elevation of the sun is 35°. find the height of the tower. © k12 inc. 2. an airplane is flying 12,330 feet above level ground. the angle of depression from the plane to the base of a building is 11°. how far must the plane fly horizontally before it is directly over the building?
Answers
2. To find how far the plane must fly, you must calculate the tangent of 11. Tan. (11) = 12,330 / x. X = 12,330/ tan (11). X = 63,432. The plane must fly 63,432 feet before it is directly over the building.
Hope this helps.
A major league baseball pitcher throws a pitch that follows these parametric equations:
x(t) = 143t
y(t) = –16t2 + 5t + 5.
Recall that the speed of the baseball at time t is
s(t)=√ [x '(t)]2 + [y ' (t)]2 ft/sec.
What is the speed of the baseball (in mph) when it passes over homeplate?
Answers
The speed of the baseball when it passes over the home plate is 97.67 mph.
Given :
[tex]x(t) = 143t[/tex] ---- (1)[tex]y(t) = -16t^2+5t+5[/tex] ---- (2)The distance between the pitcher's plate and the home plate is 60.5 ft.Differentiate the function x(t) and y(t) with respect to t.
[tex]x'(t)=143[/tex]
[tex]y'(t)= -32t+5[/tex] ---- (3)
Now, put the value of x(t) in equation (1).
60.5 = 143t
t = 0.423 sec
Now, put the value of t in equation (3).
[tex]y'(t) = -32(0.423)+5=-8.536[/tex]
Now, [tex]s(t) = \sqrt{(x'(t))^2+(y'(t))^2}[/tex]
[tex]s(t)=\sqrt{143^2+(-8.536)^2}[/tex]
[tex]\rm s(t)=\sqrt{20521.8633} = 143.2545\;ft/sec[/tex]
[tex]\rm s(t) = 97.67 mph[/tex]
Therefore, the speed of the baseball when it passes over the home plate is 97.67 mph.
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