Answer:
The total possible outcomes that exist are:
2400
Step-by-step explanation:
We are given four dices:
first is a standard 6-faced die.
The second die has 4 faces.
Third dice has 10 faces.
Fourth dice has 10 faces.
Now when all the dice are thrown together then the total number of possible outcomes are:
( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)
The answer is:
2400
Find x round to the nearest whole number
Answer:
Below
Step-by-step explanation:
Instead of x , I assume you want the angle For RIGHT triangles, remember
cos (angle ) = adjacent leg / hypotenuse
cos ( angle ) = 5 /12
angle = arccos( 5/12) = 65 °
You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.
need help looking for the anwser
Answer:
need help looking for the anwser here it's the 2.5
Write a story that could represent this math problem. (2 points)
If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?
I believe that is what type of story you needed, if wrong let me know.
Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6
Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.
for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.
The answer after multiplying it is 6/24 or 1/4.
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Find the volume to each equation
(Directions listed above questions)
The volume of the cube is 444.19 in³
The volume of the rectangular prism is 661.2 ft³
The volume of the triangular prism is 30.04 yd³
The volume of the cylinder is 380.57 km³
How to find the volumeVolume of a cube is solved using the formula
= length³
= 7.63³
= 444.19 in³
Volume of a rectangular prism is solved using the formula
= Area of base * height
= 9.5 * 8.7 * 8
= 661.2 ft³
Volume of a triangular prism is solved using the formula
= 1/2 × base × height × length
= 1/2 * 5.84 * 3.08 * 3.34
= 30.04 yd³
Volume of a cylinder is solved using the formula
= π * radius² * height
= π * 3² * 13.46
= 380.57 km³
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ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
48ft²
Step-by-step explanation:
Visualize the trapezoid as consisting of a rectangle with two triangles on either side. To find its total area, find the area of each and add them up.
Note that the formula for the area of a square is (base*height) and the formula for the area of a triangle is (0.5*base*height). The bottom of the trapezoid is 15ft and the top is 9ft, which makes the combined bases of the two triangles 15-9=6ft, meaning each triangle's base is 3ft.
Area of left triangle = 0.5*3*4 = 6ft²
Area of square = 4*9 = 36ft²
Area of right triangle = 0.5*3*4 = 6ft²
Therefore the total area is: 6ft² + 36ft² + 6ft² = 48ft²
Answer:
48ft?
Visualize the trapezoid as consisting of
a rectangle with two triangles on either
side. To find its total area, find the area of
each and add them up.
Ramesh ran at a speed of 7 km/h for 3 h. He then 2 He took 6 h altogether to complete the whole journe (a) Find the total distance that Ramesh ran. (b) Find his average running speed for the whole j a mixed number in its simplest form.
Find the total distance that Ramesh ran is 23km. His average running speed for the whole journey is 3 5/6 km/h.
How to calculate Ramesh Total distance and average running speedTo find the average speed,
We find the total distance and divide it by the total time.
During the first part of the run, she ran 3 hours at a speed of 7 km/h.
To find the the distance she ran, multiply the speed times the time: 3 x 7 = 21 km.
From the second part of the run, she ran 2km.
So the total distance he ran is 21 + 2 = 23km.
The total time was 6 hours.
To find the the average speed;
Divide 23 by 6 to get the average speed, which comes to 3 5/6 km/h.
hence, the average speed is 3 5/6 km/h.
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13. Interpret the IQR and median in the context of the data set.
The interquartile range is 4 and the median is 27.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. On a box plot, the interquartile range is the difference between the first line and the third line on the box.
Interquartile range = 28 - 24 =4
Median is the central value of a data set. On a box plot, the median is the second line on the box.
The median is 27.
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An account that earned 23% annual interest compounded quarterly for 3 years and currently has a balance of $6258.
The initial balance of the account was approximately $3541.83.
What is interest is compounded?This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
We can utilise the compound interest formula to find a solution to this issue:
A = P(1 + r/n)ⁿⁿ
In this case, we have P = the initial balance of the account, r = 0.23 (23% expressed as a decimal), n = 4 (since interest is compounded quarterly), t = 3 years, and A = $6258. We can solve for P by rearranging the formula:
P = A / (1 + r/n)ⁿⁿ
Substituting the values we know, we get:
P = 6258 / (1 + 0.23/4)⁴ˣ³
Simplifying this expression gives:
P = 6258 / 1.76757
P ≈ $3541.83
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Convert 1,2kg to g to two decimal places where applicable
Answer: 1200g
Step-by-step explanation:
1 kilogram is equal to 1000 grams, so since you want 1.2, simply multiply by that quantity. So the answer is 1200 grams.
Points B and D are on the perpendicular bisector of ^ABC. The measure of
The measure of angle ABC in the figure of triangle attached is
< ABC = 46 degreesWhat are perpendicular bisectors?In geometry, a perpendicular bisector is a line or line segment that divides another line segment into two equal parts and is perpendicular to it.
From the definition of perpendicular bisector, we have that
< A = < C
and using triangle ABD
< A + < ABD = 90
< A + 28 = 90
< A = 90 - 28
< A = 62
Using triangle ABC
< A + < ABC + < C = 180
62 + < ABC + 62 = 180
< ABC = 180 - 62 - 62
< ABC = 56
OR
< ABD = < DBC = 28 degrees
and < ABC = < ABD + < DBC adjacent angles
< ABC = < ABD + < DBC
< ABC = 28 + 28
< ABC = 56 degrees
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complete question
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees
Yang Bai is investing $10,000 and wants a portfolio that is 80% stocks and 20% bonds. She has decided to accomplish this using just 2 exchange-traded funds (ETFs): a stock ETF trading for $50 per share and a bond ETF trading for $100 for share. What should she do to meet her asset allocation goal?
Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y2 = x, x = 3y; about the y-axis V=
The volume, V of the solid obtained by rotating the region bounded by the graphs of the expressions, y² = x, x = 3y; about the y-axis is equals to the 162π/5 cubic units.
We have a region bounded by the graphs of two expressions. These expressios are y² = x, x = 3y. We have to calculate the volume of solid obtained by rotating the bounded region about the y-axis. First determine the intersection points of
y² = x, x = 3y.
=> x = 3y --(1)
=> y² = 3y
=> y² - 3y = 0
=> y( y - 3 ) = 0
=> y = 0 or y - 3 = 0
=> y = 0 , y = 3
from (1), x = 3y => x = 0, x = 9
Let the intersection points be O(0,0) and P(3,9). Now, the volume of rotating region or due to shaded region is
[tex]V = π\int_{0}^{3} (R² - r²) dy [/tex]
where R = 3y , r = y²
[tex]V = π\int_{0}^{3} [(3y)² - (y²)²]dy [/tex]
[tex]V = π \int_{0}^{3} (9y² - y⁴)dy [/tex]
[tex]V = π[ \frac{9y³}{3}- \frac{y⁵}{5} ]_{0}^{3} [/tex]
[tex]V = π[ \frac{9(3)³}{3}- \frac{{3}^{5} }{5} - 0- 0 ][/tex]
[tex]V = π(81 - \frac{243}{5} ) = \frac{162π}{5} [/tex]
Hence, the required volume is 162π/5 cubic units.
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In the diagram, RSTU~ ABCD. Find the ratio of their perimeters.
U
R
18 S
36
T
D
A
24
The ratio of their perimeters is
B
C
Answer: Let's call the ratio of the perimeters of the two similar figures "k". That means that for every unit of length in RSTU, there are k units of length in ABCD.
Since UR = 18 and DA = 24, k = 24/18 = 4/3.
So for every length in RSTU, there are 4/3 times that length in ABCD. We can use this ratio to find the corresponding lengths in ABCD. For example, SR = 36, so BS = 36 * (4/3) = 48.
Now that we have the lengths of all sides of ABCD, we can find its perimeter:
Perimeter of ABCD = 24 + 48 + BC + 24 = 120 + BC
Perimeter of RSTU = 18 + 36 + 18 + 36 = 108
So the ratio of their perimeters is:
Perimeter of ABCD / Perimeter of RSTU = (120 + BC) / 108 = (120 / 108) + (BC / 108) = 20/18 + BC/108
Since the perimeters of the two figures are similar, the ratio of their perimeters is equal to the ratio of their corresponding side lengths:
20/18 + BC/108 = 4/3
Solving for BC:
BC = (4/3 - 20/18) * 108 = 36
Step-by-step explanation:
a toy manufacturer needs a piece of plastic in the shape of a right triangle with one leg 5 cm longer than the other and the hypotenuse 10 cm longer than the shorter leg. what is the perimeter of the triangle
The triangle's perimeter is roughly 25.29 cm.
In arithmetic, what is perimeter?The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.
Let's call the right triangle's shorter leg "x" for short.
The longer leg is then 5 cm longer than x, or x + 5, according to the situation.
The hypotenuse measures x + 10 cm longer than x.
By the Pythagorean theorem, we know that:
x² + (x+5)² = (x+10)²
Expanding and simplifying this equation gives:
2x² + 10x - 75 = 0
Dividing both sides by 2 gives:
x² + 5x - 37.5 = 0
We can find the value of x by using the quadratic formula:
x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2
x = (-5 ± sqrt(175)) / 2
x ≈ -8.68 or x ≈ 3.43
Since x represents a length, we must choose the positive solution x = 3.43 cm.
Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:
3.43 + 8.43 + 13.43 = 25.29 cm
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What is the location of point G, which partitions the directed line segment from F to D into an 8:5 ratio?
A number line goes from negative 5 to 10. Point D is at negative 4 and point F is at 9. A line is drawn from point D to point F.
The position of G in the given line segment is at point 1, which is between points F and D and the line segment between F and D in the ratio 8:5.
What is meant by line segment?
Two unique points on a line define the boundaries of a line segment. A line segment is a section of the path a line takes to join two locations. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given, the locations of D and F on the line segment.
D = -4
F = 9
Number of units between F and D = 9 - (-4) = 13
Point G partitions the line segment from F to D in the ratio 8:5.
So distance of G from F = [8/(8+5)] * 13 = 8
Distance of G from D = [5/(8+5)] * 13 = 5
So from F, it is 8 units behind F = 9 - 8 = 1
from D, it is 5 units in front of D = -4 + 5 = 1
Therefore the position of G in the given line segment is at point 1.
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Kara earns 9.75 per hour plus 15.50 in tips each night. If she works for 5 2/5 hours four nights this week how much money will she earn
Answer: $272.60
Step-by-step explanation:
9.75x5.4= 52.65
52.65+15.50=68.15
68.15x4=272.6
Find the number of ways to arrange the letters in HEDGEHOG.
There are blank ways to arrange the letters in HEDGEHOG.
Answer:
Step-by-step explanation:
The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.
The total number of arrangements of the eight letters is 8!:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
The number of arrangements of H's is 2!:
2! = 2 x 1 = 2
The number of arrangements of E's is 3!:
3! = 3 x 2 x 1 = 6
So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:
40320 / (2 x 6) = 40320 / 12 = 3360.
Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".
1. Items a company has purchased and paid for, but has not used are called
A. advanced
B.purchased
C.prepaid
D. long-term liability
items.
Answer:
the ans is advanced
I hope you get your ans
Which descriptions from the list below accurately describe the relationship
between AXYZ and AUVW? Check all that apply.
857-10
LSM
X62
16
37
← PREVIOUS
20
53M
12 W
A. Same size
B. Same shape
C. Similar
D. Congruent
SUBMIT
The same shape and similar are relationship between ΔXYZ and ΔUVW options (A) and (D) are correct.
What is the similarity law for triangles?
It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.
We have given two triangles with dimensions.
Take the ratio of the corresponding sides:
12/24 = 5/10 = 13/26 = 1/2
The ratios of the corresponding sides are same which means the triangle are similar and having same shape.
Hence, the same shape and similar are relationship between ΔXYZ and ΔUVW option (A) and (D) are correct.
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The complete question is in the attached image.
I need the first one
Answer:
∠1 = ∠2 = 135
Step-by-step explanation:
We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180° = 3 x 180°= 540°. Hence, the sum of interior angles of a pentagon is 540°.
so ∠1 + ∠2 + 3(90°) = 540°
since ∠1 = ∠2
∠1 + ∠1 + 3(90) = 540
2∠1 + 270 = 540
2∠1 = 540 - 270
2∠1 = 270
∠1 = 270/2 = 135
Find the total area of the shaded region. Ay 1.5- 14 x=5y3 (5,1) * = 5y? 0.5- х 07 0 2.5 5 7.5 Find the area of the region enclosed by the curves x= x = 7y?, x=0, and y=1. The area of the region enclosed by the curves is (Type a simplified fraction.)
The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).
From the attached graph :
The area of the shaded region :
x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :
= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]
= [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]
Substitute the lower limit and upper limit we get,
= (5 /3 )( 1 )³ - 0 - ( 5 / 4 )( 1⁴) + 0
= ( 5 / 3 ) - ( 5 / 4 )
= ( 20 - 15 ) / 12
= 5 / 12
Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .
The given question is incomplete, I answer the question in general according to my knowledge:
Find the total area of the shaded region x = 5y³ , x = 5y² for the interval
( 5, 1 ).
Graph is attached.
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As modeled, a movie is projected into a large outdoor screen. The bottom of the 60 foot-tall
Answer:
-
Step-by-step explanation:
the question isn't clear enough to answer it
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet of water weigh in pounds? In tons?
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
2. Sam spent $15 at an art store on paints, brushes, and paper. The paints cost $7.75 and the
brushes cost $3. Write and solve an equation you could use to find how much Sam spent on
paper.
PLSSS HELP ME DUE TODAY!!!
Meg is heading back to her car after a hike to Misty Falls. The waterfall is at an elevation of 4,000 feet, and the trail descends an average of 500 feet for every 1 mile she hikes. You can use a function to approximate Meg's elevation after she hikes x miles.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x.
Step-by-step explanation:
Since every single mile it descends the same amount (which is 500ft), that means it's linear, so we'll use that they gave us, the h(x) = mx+b
To find m, we use the following equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
to find b, we have to find out the starting point. luckily they gave it to us, which is 4,000ft. B = 4000
Now every 500 feet, we go down 1 mile
Which means at 1000 feet, we go down 2 miles
500 and 1000 can be our y1 and y2
1 and 2 can be our x1 and x2
[tex] \frac{1000 - 500}{2 - 1} = \frac{500}{1} = 500 = m[/tex]
Now that we have our m and b, we just put it together
[tex]h(x) = - 500x + 4000[/tex]
A negative was placed before the 500 because they are descending, not ascending.
Over the last 3 evenings, Laura received a total of 68 phone calls at the call center. The third evening, she received 2 times as many calls as the first evening. The first evening, she received 8 more calls than the second evening. How many phone calls did she receive each evening?
On first evening she receives 19 calls and on second evening she receives 11 calls while on 3rd evening she receives 38 calls.
What is equation?A mathematical equation is a fοrmula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences oοn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol, fοr instance, 2x – 4 = 2.
X, Y, and Z represents the 1st , 2nd, and 3rd evenings
X + Y + Z = 68
⇒ X = Y + 8
⇒ Z = 2(Y + 8)
⇒ Y + Y + 8 + 2(Y + 8) = 68
Y = 11 calls
And
X = (11)+ 8 = 19 calls
Z = 2((11) + 8) = 38 calls
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There are 15 students in an art class. Mr Popplewell has 300 colored pencils to distribute equally among the students. How many colored pencils will each student receive?
Answer:
Step-by-step explanation:
15 into 300 is 20
300÷ 15 = 20
Although 240° is a special angle on the unit circle, Aiden wanted to determine its coordinates using the sum and difference formulas.
Part A: Determine cos 240° using the cosine sum identity. Be sure to include all necessary work. (5 points)
Part B: Determine sin 240° using the sine difference identity. Be sure to include all necessary work. (5 points)
A. The value of cos 240° = [tex]\frac{-1}{2}[/tex]
B. The value of sin 240° = [tex]-\frac{\sqrt{3} }{2}[/tex]
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
Part A:
we know that, cos (a +b)=cos a cos b - sin a sin b
cos 240° = cos (60° +180°)
=cos 60° cos 180° - sin 60° sin 180°
=[tex]\frac{1}{2} *(-1)-\frac{\sqrt{3} }{2} *0[/tex]
=[tex]\frac{-1}{2}[/tex]
Part B:
we know that, sin(a- b)=sin a cos b - cos a sin b
sin 240° = sin(270° - 30°)
=sin 270° cos 30° - cos 270° sin 30°
=[tex]-1 *\frac{\sqrt{3} }{2}-0*\frac{1}{2}[/tex]
=[tex]-\frac{\sqrt{3} }{2}[/tex]
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Can someone help me with the step by step solutions to these? Thanks
Answer:
c. √2/30
f. 13√3/14
i. -11√10/24
Step-by-step explanation:
You want the sums of the fractions shown.
Sum of fractionsTwo fractions can be added like this:
[tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}[/tex]
If the denominators have a common factor (k), then this can be reduced to ...
[tex]\dfrac{a}{bk}+\dfrac{c}{dk}=\dfrac{ad+bc}{bdk}[/tex]
The product bdk is the least common denominator when k is the greatest common factor.
Here, the numerators have a common factor, so we can factor that out, perform the sum, then multiply the result by that numerator factor.
c[tex]\dfrac{\sqrt{2}}{5}-\dfrac{\sqrt{2}}{6}=\sqrt{2}\left(\dfrac{1}{5}-\dfrac{1}{6}\right)=\sqrt{2}\cdot\dfrac{6-5}{5\cdot6}=\boxed{\dfrac{\sqrt{2}}{30}}[/tex]
f[tex]\dfrac{3\sqrt{3}}{7}+\dfrac{\sqrt{3}}{2}=\sqrt{3}\left(\dfrac{3}{7}+\dfrac{1}{2}\right)=\sqrt{3}\cdot\dfrac{3\cdot2+7}{7\cdot2}=\boxed{\dfrac{13\sqrt{3}}{14}}[/tex]
iThe denominators have a common factor of 2: 6=3·2, 8=4·2.
[tex]\dfrac{-5\sqrt{10}}{6}+\dfrac{3\sqrt{10}}{8}=\sqrt{10}\left(\dfrac{-5}{6}+\dfrac{3}{8}\right)=\sqrt{10}\cdot\dfrac{-5\cdot4+3\cdot3}{3\cdot4\cdot2}=\boxed{-\dfrac{11\sqrt{10}}{24}}[/tex]
Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree to the nearest hundredth of a meter is 10.77m.
Detailed explanation:
An illustration of identical triangles is shown in the diagram. View the illustration I included with my response to see how triangles can be used to solve this issue.
Because they both share an internal angle, the triangles made by Alyssa and her shadow and the triangle created by the tree and its shadow are examples of comparable triangles.
The ratios of the comparable sides on both sides are proportionate according to the similar triangles theorem.
Therefore, in order to determine the height of the tree, we must make a percentage of the corresponding sides of both triangles. Let x equal the tree's height.
[tex]\frac{BE}{BC} =\frac{DE}{AC}[/tex]
BE = 4.25 meters
DE = 1.65 meters
BC = 27.75 meters
AC = x meters
[tex]\frac{4.25}{27.75} =\frac{1.65}{x}[/tex]
Cross multiply is now used to find x.
4.25x= 1.65(27.75)
x = 10.77
Therefore, the height of the tree is 10.77 meters.
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Complete question:
Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
