Cube a and cube b are similar solids. the volume of cube a is 27 cubic inches, and the volume of cube b is 125 cubic inches. how many times larger is the base area of cube b than the base area of cube a?
The base area of cube B is 25/9 times larger than the base area of cube A.
What is area cubic?
Surface area of cube is the sum of areas of all the faces of cube, that covers it. The formula for surface area is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube. It is basically the total surface area.We know that volume of cube with each side of units is equal to .
First of all, we will find the each side of cube A and B as:
[tex]A^{3} = 27[/tex]
[tex]\sqrt[3]{A^{3} } = \sqrt[3]{27}[/tex]
A = 3
[tex]B^{3} = 125[/tex]
[tex]\sqrt[3]{B^{3} } = \sqrt[3]{125}[/tex]
B = 5
Now, we will find base area of both cubes as:
[tex]\frac{Base area of B}{Base area of A} = \frac{B^{2} }{A^{2} }[/tex]
[tex]\frac{Base area of B}{Base area of A} = \frac{5^{2} }{3^{2} }[/tex]
[tex]\frac{Base area of B}{Base area of A} = \frac{25}{9}[/tex]
Therefore, the base area of cube B is 25/9 times larger than the base area of cube A.
Learn more about cube
brainly.com/question/23728751
#SPJ4
An astronaut who weighed 150 pounds on earth found that his weight on jupiter was 400 pounds. he captured an alien that weighed 120 pounds on jupiter. what is the alien's weight on earth? a. 45 pounds c. 500 pounds b. 30 pounds d. 320 pounds
A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500?
The balance after 8 years is $22,942.67
What is the balance after 8 years?
We know that the savings account earns 15% annually, and the initial deposit is $7500, then the balance as a function of time in years is:
B = $7500*(1 + 15%/100%)^t
B = $7500*(1.15)^t
The balance after 8 years is what we get when we evaluate the above function in t = 8, so we get:
B = $7500*(1.15)^8 = $22,942.67
So the correct option is the last one.
If you want to learn more about exponentials:
https://brainly.com/question/2456547
#SPJ1
What must be added to: (a) x-y + 4z to get 5x - 4y + 8z?
Answer:
4x-3y+4z
Step-by-step explanation:
There are lot's of process to answer it but i will show one easy way to find the answer.
To find the required answer we need to subtract 5x - 4y + 8z by x-y + 4z, we get
5x - 4y + 8z
-x + y - 4z [Note: while subtracting we must change the sigh that one ___________who we are subtracting]
4x-3y+4z which is a required answer
Answer:
4x - 3y + 4z
Step-by-step explanation:
Let the unknown value that we have to add be 'a'.
Let us make an expression like this.
x -y + 4z + a = 5x - 4y + 8z
Now make 'a' the subject of the equation.
a = 5x - 4y + 8z - x + y - 4z
Now combine like terms.
a = 5x - x - 4y + y + 8z - 4z
a = 4x - 3y + 4z
Now let us check whether the answer is correct or wrong.
We can replace 'a' with ( 4x - 3y + 4z ).
Let us see.
x - y + 4z + 4x - 3y + 4z
Combine like terms.
5x - 4y + 8z
Yes, we are getting the same answer!
Therefore,
we need to add 4x - 3y + 4z to get 5x - 4y + 8z to x - y + 4z.
There are 25 prime numbers less than 100.
Some of these are two-digit prime numbers.
What fraction of two-digit prime numbers contain the digit 9?
Express this fraction in lowest terms.
Answer:
6/25.
Step-by-step explanation:
They are 19, 29, 59, 79, 89 and 97.
A total of 6.
So the required fraction is 6/25.
Hurrrry helpppp show your work
Answer: 17
Step-by-step explanation:
substitute -3 for a and -5 for b. the equation will be[tex]\frac{(-3)^{2}+(-5)^{2} }{-3-(-5)}[/tex]. then when you simplify, you will get [tex]\frac{9+25}{-3+5}[/tex]. finally, add and you will get [tex]\frac{34}{2}[/tex] which is 17.
Consider the sets below. u = {x | x is a real number} a = {x | x is an odd integer} r = {x | x = 3, 7, 11, 27} is r ⊂ a?
The correct option is (B) yes because all the elements of set R are in set A.
What is an element?In mathematics, an element (or member) of a set is any of the distinct things that belong to that set.Given sets:
U = {x | x is a real number}A = {x | x is an odd integer}R = {x | x = 3, 7, 11, 27}So,
A = 1, 3, 5, 7, 9, 11... are the elements of set A.R ⊂ A can be understood as R being a subset of A, i.e. all of R's elements can be found in A.Because all of the elements of R are odd integers and can be found in A, R ⊂ A is TRUE.Therefore, the correct option is (B) yes because all the elements of set R are in set A.
Know more about sets here:
https://brainly.com/question/2166579
#SPJ4
The complete question is given below:
Consider the sets below. U = {x | x is a real number} A = {x | x is an odd integer} R = {x | x = 3, 7, 11, 27} Is R ⊂ A?
(A) yes, because all the elements of set A are in set R
(B) yes, because all the elements of set R are in set A
(C) no because each element in set A is not represented in set R
(D) no, because each element in set R is not represented in set A
The mean of continuous data having term 100 is 20.find the sum of terms
Answer:
2000
Step-by-step explanation:
let the sum of the two terms be,x
Then,
x/100=20
where
100=no. of terms
20=mean
Then,
x/100=20
x=20×100
x=2000
So,
Sum of terms=2000
Factor the polynomial expression 3x² + 2.
A. (√3x + √2i)(√3x - √/2i)
B. (3x + √2i)(3x - √2i)
C. (√3x + √2)(√3x - √2)
D. (√3x + i)(√√3x - i)
Answer:
[tex]\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]
Step-by-step explanation:
Setting the expression equal to zero to find the roots,
[tex]3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}[/tex]
This means that
[tex]3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]
Geometry: complete these proofs, ASAP!!!
Answer:
1. Given.
2. <5 is supplementary to <4.
2. Angles 5 and 4 are consecutive angles, and by the consecutive angles theorem, the two are supplementary.
3. m<4 + m<5 = 180
3. By the definition of supplementary angles, m<4 + m<5 = 180.
4. m<2 = m<4
4. Angles 2 and 4 are corresponding angles, and by the corresponding angles postulate, the two are congruent. By the definition of congruent angles, m<2 = m<4.
5. m<5 + m<2 = 180
5. Substitution property of equality.
A blimp is 1600 meters high in the air and measures the angles of depression to two stadiums to the east of the blimp. if those measurements are 71.7° and 25.2°, how far apart are the two stadiums?
The two stadiums are 2,871 meters
A blimp = point A
stadium 1 = point B
stadium 2 = point C
height of the blimp , AD = 1600
depression angle of stadium 1 , ∠y = 71.7°
depression angle of stadium 2 , ∠x = 25.2°
distance between the two stadiums = d
So, it forms 2 triangles ABD and ACD,
Using the trigonometric ratios,
tan θ = Altitude / Base
DC = AD × tan (90° - x)
= 1600 × tan( 90° - 25.2° )
= 1600 × cot(25.2°)
= 1600 × 2.13
DB = AD × tan (90° - y)
= 1600 × tan( 90° - 71.7° )
= 1600 × cot(71.7°)
= 1600 × 0.33
∴ d = DC - DB
= 1600 * [ tan( 90° - 25.2° ) - tan( 90° - 71.7° ) ]
= 2,871 meters
To learn more about angle of depression from the given link
https://brainly.com/question/9723082
#SPJ4
3
OYes
O No
Is the following relation a function? (1 point)
x y
1 4
-1 -2
3 10
5 16
Answer: Yes
Step-by-step explanation:
Each value of y maps onto one value of x.
Step 3 of 6 : find the estimated value of y when x=30. round your answer to three decimal places
The estimated value of y when x=30. The answer rounded to three decimal places is 5.
Envisioned cost method, as of any date of willpower, with respect to any paintings of art, the most latest estimate of fee of such paintings of artwork, as determined every so often through the relevant Borrower in accordance with phase 5.12.
To discover the estimated value E(X), or imply μ of a discrete random variable X, in reality,y multiply every value of the random variable by way of its chance and upload the products. The method is given as E ( X ) = μ = ∑ x P ( x ) .
In opportunity theory, the estimated value is a generalization of the weighted common. Informally, the anticipated price is the mathematics suggestion of a big variety of independently decided effects of a random variable.
estimated Y when
b₁x + b
X = 30.
=( 0·302) (30) + (-3-772)
5.288
= 5
Learn more about the estimated value here https://brainly.com/question/24239771
#SPJ4
In two or more complete sentences, identify the parent function, and describe the transformations that were applied to
obtain the graph, f(x) = √2x+6 -1
Jaxon is training for a climbing competition.
He breaks his training up into strength and
endurance training in the ratio 5:3.
If he spends 4 hours on endurance training,
how long should he spend on strength training?
======================================================
Work Shown:
(x hours strength)/(4 hours endurance) = 5/3
x/4 = 5/3
3x = 4*5
3x = 20
x = 20/3
x = (18+2)/3
x = 18/3 + 2/3
x = 6 + 2/3
x = 6 & 2/3
He needs to spend 6 full hours, plus an additional 2/3 of an hour, on strength training.
1 hr = 60 min
2/3 hr = (2/3)*60 min
2/3 hr = 40 min
6 hr + 2/3 hr = 6 hr + 40 min
Therefore, he needs to spend 6 hours, 40 minutes on strength training.
This is equivalent to 6*60+40 = 360+40 = 400 minutes.
Ileana received a statement on her certificate of deposit showing that her investment had returned $5,084 over its life. if the certificate of deposit pays a simple interest rate of 4.1% and her initial investment was $15,500, how long had the money been invested? please help me! i'm dying!
Ileana have to invest for 8 years :
What is Simple interest?Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.
How do you calculate simple interest?The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.
Given Data:Principal amount = $15,500
interest = $5,084
Time = ?
Rate = 4.1% simple interest
Solution:to find the simple interest :
I = [tex]\frac{(p*t*r)}{100}[/tex]
Then:
Time = [tex]\frac{I*100}{P*R}[/tex]
= [tex]\frac{(5084*100)}{(15500*4.1)}[/tex]
= [tex]\frac{508400}{63,550}[/tex]
= 8 years
Ileana have to invest for 8 years
To know more about simple intertest visit:
https://brainly.com/question/24217271
#SPJ4
Heron's Formula:
The two bases of a trapezoid are 3 and 11 and the altitude is 8. What is the area of the trapezoid? Use Heron's formula.
Answer:
√s(s-a) (s-b) (s-c)
Step-by-step explanation:
123456
herons formula
Find the length of the function over the given interval. y = 3x from x = 0 to x = 2
The length of the function y = 3x over the given interval [0, 2] is 3.2 units
For given question,
We have been given a function y = 3x
We need to find the length of the function on the interval x = 0 to x = 2.
Let f(x) = 3x where f(x) = y
We have f'(x) = 3, so [f'(x)]² = 9.
Then the arc length is given by,
[tex]\int\limits^a_b {\sqrt{1+[f'(x)]^2} } \, dx\\\\= \int\limits^2_0 {\sqrt{1+9} }\, dx\\\\=\sqrt{10}\\\\ =3.2[/tex]
This means, the arc length is 3.2 units.
Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units
Learn more about the arc length here:
https://brainly.com/question/10729208
#SPJ4
UV has endpoint U(21.6, -8.2) and midpoint M(15.8, -17). What are the coordinates of the other endpoint, V?
(7, -22.8)
(10, -25.8)
(18.7, -12.6)
(27.4, 0.6)
Using the midpoint formula, the coordinates of the other endpoint, V is: B. (10, -25.8).
What is the Midpoint Formula?To find the coordinates of the midpoint of a segment, the midpoint formula is used, which is expressed as: M(x2 + x1/2, y2 + y1/2).
Given one endpoint of UV as, U(21.6, -8.2), and a midpoint of M(15.8, -17), let:
U(21.6, -8.2) = (x1, y1)
V(x, y) = (x2, y2)
Plug in the values into M(x2 + x1/2, y2 + y1/2):
M(15.8, -17) = (x2 + 21.6/2, y2 + (-8.2)/2)
Solve for x2
15.8 = (x2 + 21.6)/2
Multiply both sides by 2
2(15.8)= (x2 + 21.6)/2 × 2
31.6 = x2 + 21.6
Subtract both sides by 21.6
31.6 - 21.6 = x2 + 21.6 - 21.6
10 = x2
x2 = 10
Solve for y2:
-17 = (y2 + (-8.2))/2
Multiply both sides by 2
2(-17) = (y2 + (-8.2))/2 × 2
-34 = y2 + (-8.2)
-34 = y2 - 8.2
Add 8.2 to both sides
-34 + 8.2 = y2 - 8.2 + 8.2
-25.8 = y2
y2 = -25.8
The coordinates of the other endpoint, V is: B. (10, -25.8).
Learn more about the midpoint formula on:
https://brainly.com/question/13115533
#SPJ1
Answer: B
Step-by-step explanation: edge2023
Which point is the circumcenter of the triangle?
A) E
B) G
C) F
D) D
Answer: Point D
Reason:
The circumcenter is found by intersecting the perpendicular bisectors of each segment of the triangle.
As you can see, the circumcenter is the center of the circumcircle. This special circle is the smallest possible that wraps the triangle so to speak. The vertices of the triangle are on the circle. The distances AD, BD and CD are all the same.
A gardener wants to design a rectangular garden and has 100 feet of fencing available. A house is on one side of the garden, so no fencing will be needed there. What dimensions will give the maximum area?
Answer:
50 ft and 25 ft give the maximum area
Step-by-step explanation:
Let l and w be the dimensions of rectangle.
The length of fencing is 100 ft:
l + 2w = 100Then:
l = 100 - 2wThe area is:
A = lw = w(100 - 2w) = 100w - 2w²In order to have the maximum area we need to find the vertex of the quadratic function:
y = - 2w² + 100wThe vertex has x-coordinate:
w = - b/(2a) It comes from quadratic function y = ax² + bx + cor
w = - 100/(2*(-2)) = 25So the width is 25 ft.
Find the length:
l = 100 - 2*25 = 50 ftThe area is:
A = 50*25 = 1250 ft²See the attached graph.
Study island math pls helppp
I will love you if you answer
Answer:
Since <ABC ~= <DBE and <BAC ~= <BDE, the triangle s are similar by angle-angle.
A man has eight shirts, four pairs of pants, and five pairs of shoes. How many different outfits are possible
Answer:
160
Step-by-step explanation:
I multiplied the amount of each item to get to the answer:
- 8 shirts
- 4 pairs of pants
- 5 pairs of shoes
8 x 4 x 5 = 32 x 5
32 x 5 = 160
hope this helps!
Use 3.14 for pi. ROUND YOUR FINAL ANSWER TO THE NEAREST TENTHS PLACE!
Answer:
379.94
Step-by-step explanation:
3.14 x 11^2 = 379.94
The area of the given circle is 95 square ft.
Calculation for the Area of the Circle:
It is given in the diagram that,
The diameter of the circle, d = 11 ft.
Now, we know that the radius of a circle is equal to half of the diameter.
Therefore, radius of the given circle, r = 11/2 ft.
The formula for the area of the circle is given as follows,
A = π × r²
Substituting the values, π = 3.1, and r = 11/2, we get,
A = (3.14) × (11/2)²
A = (3.14) × 30.25
A = 94.985
A ≈ 95
Hence, the area of the given circle with diameter 11 ft. comes out to be 95 ft².
Learn more about a circle here:
https://brainly.com/question/11833983
#SPJ1
You buy four boxes of fish sticks on sale at $1.99 per
box. The fish sticks regularly sell for $2.49 per box. Lemons are also
on sale at two for $1.00. How much money did you save by buying
the fish sticks on sale
. Rashad is conducting an experiment at his high school to see how people feel about the school dress code. 1. Explain how Rashad could collect data to ensure that it is a random sample of the population. 2. Suppose Rashad has collected his data and has organized it in the table below. Create a visual plot of the data in the table by constructing a bar graph. 3. What is the average view of the dress code? How did you come to this conclusion? 4. The dress code will be changed if more than 60% of the school feels like a change is needed. If 40% of this majority agrees on the same change, that will be what is done with the dress code. Will the dress code change? Do we know which option will occur? Be sure to explain your reasoning.
Each sample has an equal chance of being picked as part of the sampling procedure known as random sampling. A randomly selected sample is intended to provide a fair reflection of the entire population.
How should Rashad proceed with the random sampling?Step 1: He should identify and decide which population he wants to study
Step 2: He should decide the size of the sample. He can do this using a sample size calculator.
Step 3: Select the Sample Randomly using:
Lottery technique; orRandom Number Technique.It is to be noted that the lottery and Random Techniques can be manual or computer simulated.
The sample bar graph for the above sample is attached.
What is the average view of the dress code?About 48 Students (boys and girls combined) indicated that the dress code is nice.13 said it wasn't nice6 on the average indicated that there were indifferent. If 40% of this majority agrees on the same change, that will be what is done with the dress code, will the dress code change?40% of 60% is not likely to catalyze a change in the needed change. A more proper percentage should be 90%.
Do we know which option will occur?Based on the figures given, 72% of the students agree that the dress code is nice (that is , it requires not change).
This means that it is highly unlikely that any changes will be made to the dress code soon.
Learn more about sampling:
https://brainly.com/question/24466382
#SPJ1
A number exceeds its four-sevenths by 18. Find the number.
Answer:
42
Step-by-step explanation:
let the number be x
4/7 of x
(4/7) × x
4x/7
As stated in the question:
x=4x/7+18
=x-4x/7=18
=(7x-4x)/7=18
=3x/7=18
3x= 18×17
3x= 126
x=126/3
x=42
An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?
The polygon is
Answer:
a polygon with an interior angle of 108 is a pentagon
Help!!! Brainliest to 1 or 2 answer!!
Answer:
35-17=3y
Step-by-step explanation:
3y+17=35
-17 -17
3y=35-17
The coordinates of the vertices of ΔDEF are D(2, 3), E(l, 1), and F(4, O).Find the coordinates for the image of ΔDEF after the translation (x, y) —i (x — 3, y — 2).Draw the preimage and image.
The translation 3 units to the right and 2 units down the plane will result in the coordinates D' (-1, 1),E'(-2, -1) and F' (1, -2)
Translation is a transformation technique used to change the position of an object on an y-plane.
For instance translating a coordinate (x, y) into (x-3,y -2) means a shift of the image 3 units to the right and 2 units down the plane. In order to get the corresponding coordinates, we will subtract 3 from the x-coordinates and 2 from the y-coordinates.
Given the coordinate of the triangle DEF as shown;
ΔDEF
D(2, 3),
E(l, 1), and;
F(4, O)
The translation 3 units to the right and 2 units down the plane will result in the coordinates D' (-1, 1),E'(-2, -1) and F' (1, -2)
Learn more on translation here: https://brainly.com/question/12861087
#SPJ1