Answer:
A
Step-by-step explanation:
Volume of a rectangular prism = l*b *h
Where base area = l*b
Volume = base area * h
Base area * height = Volume
15 * height = 180
height = 180/15
height = 12 inches
A right triangle has legs that are 10.1 inches and 12.2 inches long. what is the approximate length of the hypotenuse? 6.8 inches 15.8 inches 22.3 inches 125.5 inches
Answer:
about 15.8 inches
Step-by-step explanation:
Use the equation [tex]a^{2} + b^{2} = c^{2}[/tex]
Where "a" and "b" are the leg lengths and "c" is the hypotenuse.
The solution is, 15.8 inches is the approximate length of the hypotenuse.
here, we have,
given that,
A right triangle has legs that are 10.1 inches and 12.2 inches long.
We only need to apply Pythagoras theorem to solve this problem.
Pythagoras theorem state that in a right-angle triangle,
opposite² + adjacent² = hypotenuse²
From the question, the length of the leg = 10.1 inches
one of the leg, lets say adjacent = 12.2 inches
Let x be the hypotenuse of the other leg.
We can now proceed to insert our values into the formula;
opposite² + adjacent² = hypotenuse²
10.1² + 12.2² = x²
so, we get,
x² = 10.1² + 12.2²
x² = 102.01 + 148.84
x² = 250.85
Take the square root of both-side to get the value of x
√x² = √250.85
x = 15.83
x≈15.8
Therefore the approximate length of the other leg is 15.8 inches.
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Simplify the expression 8+(10+x).
Answer:
18+x
Step-by-step explanation:
since the plus is between the 8 and the perinthesis, you can basically just get rid of them and the expression is then
8+10+x
which is equal to 18+x
Answer:
18 + x
Step-by-step explanation:
combine 10 and 8 to make 18, then add x.
Which of the following is NOT a variation of a Pythagorean identity?
The expression that is not a variation of the Pythagorean identity is the third option.
What is the Pythagorean identity?The Pythagorean identity can be written as:
[tex]sin^2(x) + cos^2(x) = 1[/tex]
For example, if we subtract cos^2(x) on both sides we get the second option:
[tex]sin^2(x) = 1 - cos^2(x)[/tex]
Which is a variation.
Now, let's divide both sides by cos^2(x).
[tex]sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1[/tex]
Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.
Concluding, the correct option is the third one.
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Circle P has a radius of 3 centimeters. What is the length of Arc RS?
Round to the nearest tenth.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =143 \end{cases}\implies s=\cfrac{(143)\pi (3)}{180}\implies s=\cfrac{143\pi }{60}\implies s\approx 7.5[/tex]
In triangle ABC, angle bisectors line AD, line BE, and line CF meet at I. If DI = 3, BD = 4, and BI = 5, then compute the area of triangle ABC
The area of triangle ABC is the amount of space on the triangle
The area of the triangle is 54.84 square units
How to determine the area of triangle ABCStart by drawing the triangle (see attachment)
Next, calculate the measure of angle B using the following tangent ratio
[tex]\tan(B/2) = \frac 34[/tex]
This gives
[tex]\tan(B/2) = 0.75[/tex]
Take the arc tan of both sides
[tex]B/2 = 36.87[/tex]
Multiply by 2
[tex]B = 73.74[/tex]
Next, calculate the length of side AD using the following equation
[tex]AD = \tan(B) * BD[/tex]
This gives
[tex]AD = \tan(73.74) * 4[/tex]
[tex]AD =13.71[/tex]
The area of the triangle is then calculated as:
[tex]Area = AD * BD[/tex]
This gives
[tex]Area = 13.71 * 4[/tex]
[tex]Area = 54.84[/tex]
Hence, the area of the triangle is 54.84 square units
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Factor the polynomial: 3x^4+6^3+9^2
Answer:
3x^4+297
Step-by-step explanation:
First, simplify 6³ and 9².
6³ = 6•6•6 = 36•6 = 216
9² = 9•9 = 81
Add.
3x^4+216+81
3x^4+297
Note:
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How many grams of C4H10 are needed to make 27 grams of water?
(I missed the lesson for this and I’m totally lost)
Answer:
17.4 grams butane, C4H10
Step-by-step explanation:
I'll assume the water, H2O, is produced from the butane, C4H10, by a combustion process using oxygen, O2. We need a balanced equation to start the calculation.
The basic combustion reaction is:
C4H10 + O2 = CO2 + H2O
The basic equation needs to be balanced. The same numbers and types of atoms must be equal on both sides. We can see that one atom of C4H10 contains 4 carbons and 10 hydrogens.
Carbon: The carbons wind up in the CO2 molecule. But each CO2 only has 1 carbon, so we need at least 4 CO2 molecules:
C4H10 + O2 = 4CO2 + H2O
Hydrogen: Hydrogen atoms are used to form the water. 10 hydrogens from 1 C4H10 will be used to produce 5 H2O molecules, since each requires 2 hydrogens.
The leads to:
C4H10 + O2 = 4CO2 + 5H2O
Now all the carbons and hydrogens are accounted for. But the oxygens are still not balanced. As written, we have 1 molecule of O2, for 2 oxygen atoms. But from the last step in our balancing work, we need 8 from the 4CO2) and 5 for the H2O, for a total of 13 oxygen atoms. Normally, this would be easy to add more oxygen molecules, but since they comes in pairs (O2), we can only add two at a time, so there will never be an odd number of O atoms from the reactant side.
To solve this, try adding a coefficient of 2 to the C4H10 and rebalancing the H2O and CO2:
2C4H10 + O2 = 4CO2 + 5H2O
We need to adjust both the CO2 and H2O to accommodate the added C and H atoms (a total of 8C's and 20 H's):
2C4H10 + O2 = 8CO2 + 10H2O
Now we see we need more O2, since there is a total of 16 plus 10, or 26 O atoms in the 8CO2 and 10H2O molecules. To provide 26 O atoms, we need a coefficient of 13 in front of the O2 on the reactant side:
2C4H10 + 13O2 = 8CO2 + 10H2O
Now the equation is balanced. It tells us we'll need 2 moles of C4H10 to produce 10 moles of H2O. That's a molar ratio of 5 moles water/1 mole butane. Or, (0.2 moles butane)/(mole water).
Now convert 27 grams water into moles water:
The molar mass of water is 18 grams/mole. 27 grams of H2O is therefore:
(27 grams)(18 grams/mole) = 1.5 moles H2O
We discovered earlier that we need (1/5) that number of moles of butane. Therefore, we need:
(1.5 moles H2O)*((0.2 moles butane)/(mole water)) = 0.3 moles butane to produce 1.5 moles (or 27 grams) of water.
Now convert 0.3 moles butane into grams butane by multiplying by butane's molar mass of 58.0 g/mole:
(0.3 moles)(58.0 g/mole) = 17.4 grams butane to produce 27 grams of water.
=====
Wheh! That's a lot of work for 27 grams of water. But the heat released will be fun.
lighting if a 25-foot-tall house cast a 75-foot shadow at the same time that a streetlight casts a 60-foot shadow how tall is the streetlight
Answer:
The street light is 20 feet tall.
Step-by-step explanation:
This question depends on a proportion. Keep your height of the object in one ratio and the length of the shadow in the other.
25/x = 75/60 Notice the height of the structure is on the left. The length of the shadow is on the right. Cross multiply
75x = 60 * 25 Combine the right
75x = 1500 Divide by 75
x = 1500/75
x = 20
The street light is 20 feet tall.
answer quickly only if you know
Given f(x) = 3x-1 and g(x) = 2x-3, for which value of x does g(x)=f(2)?
Answer:
x = 4
Step-by-step explanation:
To see when g(x) = f(2)
First, find f(2)
f(2) = 3(2) - 1 = 5
Now g(x) = 2x-3 = f(2) = 5
2x - 3 = 5
Adding 3 to both sides
2x = 8
Dividing 2 on both sides
x = 4
Do you use the same set of parallel and perpendicular lines? Why?
PLEASE HELP! I WILL GIVE BRAINLIEST AND NO LINKS!
Answer:
8. 35
Step-by-step explanation:
An expression is evaluated for a particular value of a variable by replacing the variable in the expression with its value. Then the numerical expression is evaluated according to the Order of Operations. Here, that means the multiplication is carried out first, then the addition.
__
Put 5 where x is:
15 +4x
= 15 +4·5
Do the multiplication:
= 15 +20
Do the addition:
= 35
Derek Jeter challenges Albert Pujols to a batting battle. Each will earn 1 point for a hit other than a home run and 4 points for a home run in each round. Which player should you back given the statistics in the table below? Note that home runs are included as hits in the table. Data for Two Batters Batter At Bats Hits Home Runs Jeter 488 156 9 Pujols 448 125 26 E(Jeter) = 0. 38 and E(Pujols) = 0. 45, so back Pujols. E(Jeter) = 0. 39 and E(Pujols) = 0. 51, so back Pujols. E(Jeter) = 0. 34 and E(Pujols) = 0. 34, so it doesn’t matter who you back. E(Jeter) = 1. 22 and E(Pujols) = 0. 94, so back Jeter.
The player that should be backed is specified by: Option B: E(Jeter) = 0. 39 and E(Pujols) = 0. 51, so back Pujols.
How to find the mean (expectation) of a random variable?Supposing that the considered random variable is discrete, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i[/tex]
where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values
and [tex]f(x_i)[/tex] is the probability of [tex]X = x_i[/tex]
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For the considered case, the scores of Pujols and Jeter are specified as:
Bats Hits Home runs
Jetter 488 156 9
Pujols 448 125 26
The points that will be earned are:
On each hit : 1 point
On each home run: 4 points
From the statistics specified , the probability of Jetter scoring hits is estimated as:
[tex]P(\text{Jetter scoring hits})=\dfrac{\text{n(hits by Jetter)}}{\text{n(total bats for Jetter)}} = \dfrac{156}{488}\\\\[/tex]
The probability of Jetter scoring home run is estimated as:
[tex]P(\text{Jetter scoring home runs})=\dfrac{\text{n(home runs by Jetter)}}{\text{n(total bats for Jetter)}} = \dfrac{9}{488}\\\\[/tex]
Therefore, we get:
E(Jetter's score) = Score for hits × hits probability by Jetter + Score for home runs × home run's probability by Jetter
E(Jetter's score) = [tex]1 \times \dfrac{156}{488} + 4 \times\dfrac{9}{488} = \dfrac{192}{488} \approx 0.39[/tex]
Similarly, from the statistics specified , the probability of Pujol scoring hits is estimated as:
[tex]P(\text{Pujols scoring hits})=\dfrac{\text{n(hits by Pujols)}}{\text{n(total bats for Pujols)}} = \dfrac{125}{448}\\\\[/tex]
The probability of Pujol scoring home run is estimated as:
[tex]P(\text{Pujols scoring home runs})=\dfrac{\text{n(home runs by Pujols)}}{\text{n(total bats for Pujols)}} = \dfrac{26}{448}\\\\[/tex]
E(Pujol's score) = Score for hits × hit's probability by Pujol + Score for home runs × home run's probability by Pujol
E(Pujol's score) = [tex]1 \times \dfrac{125}{448} + 4 \times\dfrac{26}{448} = \dfrac{229}{448} \approx 0.51[/tex]
Thus, the player that should be backed is specified by: Option B: E(Jeter) = 0. 39 and E(Pujols) = 0. 51, so back Pujols.
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Answer:
a
Step-by-step explanation:
on edge 22
A realtor has been told that 43% of homeowners in a city prefer to have a finished basement. She surveys a group of 300 homeowners randomly chosen from her client list. Describe the sampling distribution model of the proportion of homeowners in this sample who prefer a finished basement. Round to the nearest tenth
The sample who prefer a finished basement is 126 homeowners
Percentages and ratiosGiven the following parameters
The total number of people surveyed = 300 homeowners
If a realtor has been told that 43% of homeowners in a city prefer to have a finished basement, the sample of owners that prefer a finished basement is expressed as:
Sample of owners = 43% of 300
Sample of owners = 0.43 * 300
Sample of owners = 126
Hence the sample who prefer a finished basement is 126 homeowners
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I think of a number.
If I subtract 10 from my number, then square the result,
I get the same answer as
if I square my number, then subtract 10 from the result.
What is my number?
You must show an algebraic method (use letter x in your working).
+
Answer:
Answer:
x =5.5
Step-by-step explanation:
The directions say to use x for the number.
"take 10 away from"
x - 10
"then square the result"
(x - 10)^2
"I get the same answer" means the two expressions will be equal to each other.
"if I square my number"
x^2
"then subtract 10 from the result"
x^2 - 10
SET EQUAL TO EACH OTHER.
(x - 10)^2 = x^2 -10
Multiply on the left side.
x^2-20x+100 =x^2-10
subtract x^2 from both sides.
-20x + 100 = -10
subtract 100.
-20x = -110
divide by -20
x = 11/2 or 5.5
CHECK:
(5.5-10)^2=20.25
5.5^2 - 10=20.25
The number would be equal to x =5.5
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The directions say to use x for the number means x - 10
"then square the result" means (x - 10)^2
"I get the same answer" means the two expressions will be equal to each other.
"if I square my number" means x^2
"then subtract 10 from the result" means x^2 - 10
therefore,
(x - 10)^2 = x^2 -10
Now Multiply on the left side.
x^2-20x+100 =x^2-10
Then subtract x^2 from both sides.
-20x + 100 = -10
-20x = -110
x = 11/2 or 5.5
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5. The Morrow family needed their bathroom
repaired. The service they used charged $65
an hour plus a $35 consultation fee. If their
repair bill was $262.50, how many hours did the
repairs take?
Answer:
3.5 hours
Step-by-step explanation:
First, subtract the consultation fee from $262.50 as it is a one off charge and is not applied hourly
$262.50 - 35 = $227.50
Then find how many times $65 fits into $227.50, in this case it is 3.5 times
To find this on a calculator:
$227.50 / $65 = 3.5
Hope this helps :)
Which of the following is equivalent to cos 32°?
a cos 58°
b cos 68°
c sin 32°
d sin 58°
Answer: Choice D
Step-by-step explanation:
cos(32) = 0.8480480962
cos(58) = 0.5299192642
cos(68) = 0.3746065934
sin(32) = 0.5299192642
sin(58) = 0.8480480962
Cos(58) = sin(32)
Cos(32) = sin(58)
The number of T-shirts a basketball team orders depends on the number of players on the team. **Remember: THE OUTPUT depends on THE INPUT
The total of T-shirts is proportional to the total of players, which means 15 players = 15 t-shirts.
What is a proportion?A proportion describes the number of elements from one category compared to the number of elements in another. For example, if there are 15 boys and 15 girls in a classroom the number of girls and boys is proportional.
How are the number of t-shirts and players related?These have a proportional relationship because for every player it is expected there is a determined t-shirts number and this number can only increase if the players increase.
1 t-shirt per player:
36 players = 36 t-shirts
2 t-shirts per player:
36 players = 72 t-shirts
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Please help with #14 , algebra
Answer:
x=26
Step-by-step explanation:
(0.5x-3)(x-14)=120
foil then solve for x
SM 7 – 8 On Monday, 329 students went on a trip to the zoo. All 8 buses were filled, and 9 students had to travel in cars. How many students were in each bus?
Answer:
40 students
Step-by-step explanation:
you have to minus 9 because of the cars then you have 320 divide 8 and you get 40.
Really need help on this graph
Answer:
The equation on the graph is: y = -(x+1)(x-6)
Question 5 of 5
A math textbook has a length of 21 cm, a width of 27 cm, and a height of 4
cm. A science textbook has a length of 22 cm, a width of 28 cm, and a height
of 3.5 cm
Which textbook has a greater volume?
A. The science textbook, with a volume of 2464 cm3
Ο Ο Ο
B. The math textbook, with a volume of 2268 cm3
O C. The math textbook, with a volume of 2376 cm3
OD. The science textbook, with a volume of 2156 cm3
SUBMIT
Answer:
I would say C not to sure tho
The pattern 0, 15, 30, 45, ________, follows the "add 15" rule. Use words to describe the rule and write the next term.
Answer:
The next term in the sequence can be found by adding 15 to the previous term in the sequence.
Therefore, the next term = 45 + 15 = 60
This is a arithmetic sequence having common difference d=15
If you want next term add 15to the previous one
Like
0+15=1515+15=30Next term is
45+15=60I need answer please
Answer:
4<sqrt24<5
Step-by-step explanation:
sqrt 16=4
sqrt 25= 5
16<24<25
sqrt 16< sqrt 24 < sqrt 25
Therefore 4< sqrt24 < 5
Heather is 1.6 m tall and casts a shadow of 3.5 m.
At the same time, a barn casts a shadow of
17.5 m. Find the height of the barn in meters.
Answer:
Heather is 1.6 m tall and casts a shadow of 3.5 m. At the same time, a barn casts a shadow of 17.5 m. Find the height of the barn in meters. (6y +11307 IH=71° 20.
Step-by-step explanation:
x-y=136
x+y=360
what do x and y equal?!
Answer:
x=13
y=234
Step-by-step explanation:
A transit train from Boston to New York and a passenger train from New York to Boston both departed at 3:00 pm. The distance between the New York station and the Boston station is 280 miles. The speed of the transit train was 80 mph. The speed of the passenger train was 60 miles per hour. Which train will arrive at their station first?
Answer:
The passenger train
Step-by-step explanation:
if its going 60 mph then it makes it way to a stop of 280 miles then the passenger train will just go 60 so thats 5 in a half hours
Answer:
5:00 pm
Step-by-step explanation:
The rate of closure is (80 mi/hr + 60 mi/hr) = 140 mi/hr
At 140 mi/hr, it will take 2 hours to travel 280 miles
The engines of the trains will meet in 2 hours past 3:00
use the graph to write a linear function that relates y to x when the slope is 4/3 and the yint is 2
Answer:
y = 4/3x +2
Step-by-step explanation:
The graph crosses the y-axis at y=2, so that is the y-intercept.
The points have a rise of 4 units for each horizontal run of 3 units, so the slope is ...
m = rise/run = 4/3
The slope-intercept equation for the line is ...
y = mx +b . . . . . . line with slope m and y-intercept b
y = 4/3x +2
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If f(x)=2x^2 + 5 sqrt(x-2), complete the following statement f(6)
Answer:
f(6) = 82
Step-by-step explanation:
substitute x = 6 into f(x) and evaluate
f(6) = 2(6)² + 5[tex]\sqrt{6-2}[/tex] = 2(36) + 5[tex]\sqrt{4}[/tex] = 72 + 5(2) = 72 + 10 = 82
Part a: Which relationship describes <1 and <2?
Part b: What is the value of x?
Part c: What is the m22?
Answer:
x = 8
Step-by-step explanation:
Part a: <1 and <2 are alternate exterior angles because line horizontal lines are parallel
Part b: the value of x can be calculated with the following equation
7x + 15 = 10x - 9 because alternate angles has same measure
15 + 9 = 10x - 7x
24 = 3x divide both sides by 3
8 = x