Final answer:
The volume of a cube with each edge measuring 7 cm is calculated using the formula V = s^3, which results in a volume of 343 cubic centimeters (cm3).
Explanation:
To find the volume of a cube that is 7 cm on each edge, we use the formula for the volume of a cube, which is V = s3, where s is the length of one side of the cube. In this case, s is 7 cm. Therefore, the volume can be calculated as follows:
V = 7 cm imes 7 cm imes 7 cm = 343 cm3
So the volume of the cube is 343 cubic centimeters (cm3).
Which of the following shows the true solution to the logarithmic equation 3log2(2x)=3
A.x=-1
B.x=1
C. x=-1 and x=1
D. x0 x=-1 and x=1
Answer:
Option B is correct.
Step-by-step explanation:
Given logarithmic equation,
[tex]3log_2(2x)=3[/tex]
[tex]log_2(2x)=\frac{3}{3}[/tex]
[tex]log_2(2x)=1[/tex]
since base of the log function is 2.
we take power of 2 on both sides.
[tex]2^{log_2(2x)}=2^1[/tex]
2x = 2
x = 1
Therefore, Option B is correct.
The area of a sector of a circle is given by the formula below. What is the solution for S?
The density of water is 1000 kilograms per cubic meter and the density of ice is about 916 kilograms per cubic meter of 700 kilograms of water and 450 kilograms of ice is combined in a container what is the volume of the water
The volume of water can be calculated by dividing the mass of water by the density of water.
Explanation:The question asks for the volume of water when 700 kilograms of water and 450 kilograms of ice are combined in a container. To find the volume of water, we need to subtract the volume of ice from the total volume. The density of water is 1000 kg/m³, so the volume of water can be calculated by dividing the mass of water (700 kg) by the density of water (1000 kg/m³).
Volume of water = Mass of water / Density of water
Volume of water = 700 kg / 1000 kg/m³
Volume of water = 0.7 m³
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The perimeter of a rectangle is 32 cm. The difference between the length and the width is 4cm. find the width
A circle has a circumference of 10. It has an arc of length 9/2
Describe the locus that the figure represents.
Question 13 options:
all points equidistant from line l
all points equidistant from point A and point B
none of these
all points 1 cm from line l
Determine if the following data set follows a linear, quadratic, or exponential model. (0, 1), (1,3), (2, 9), (3, 19), (4, 33)
show your work
PLEASE SOMEONE HELP!
I think that it would be a linear model.
Answer:
Step-by-step explanation:
quadratic C
Simplify i^41. (2 points) i −1 −i 1
Answer:
[tex]\large\boxed{i^{41}=i}[/tex]
Step-by-step explanation:
[tex]i=\sqrt{-1}\\\\i^2=-1\\\\(-1)^2=1\\\\\text{Use}\ a^n\cdot a^m=a^{n+m}\ \text{and}\ (a^n)^m=a^{nm}:\\\\i^{41}=i^{40+1}=i^{40}\cdot i=i^{2\cdot20}\cdot i=(i^2)^{20}\cdot i=(-1)^{20}\cdot i=1\cdot i=i[/tex]
Answer:
i
I got this right on the test!!
The volume of a solid gold statue can be approximated as 1000 cm3. If the density of gold is about 20/cm3, what is the mass of the statue?
PLEASE HELP will give brainiest if correct
99 POINTS
suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2176 pounds. when carrying 46 gallons of fuel, it weighs 2399 pounds. how much does the airplane weigh if it is carrying 54 gallons of fuel?
At the start of the year northern lights had $8000 worth of merchandise. What do we know about northern lights?
A. The company ended with a net income last year
B. It’s a retail business
C. The company ended with a net loss last year
D. It’s a service business
Answer:
B. It's a retail Business
Step-by-step explanation:
Just by knowing that they have money worth in merchandise, you can say that they sell as a retail business, the first option A. is not posible because they dont have an income they just have inventory worth money. the C. is not possible because having $ 8000 positive value does not constitute loss and D. it's a service business, could be but the merchandise does not suffice all information.
the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of the line after dilation
The equation that represent that image of the line after dilation is
[tex]y = 2x-6[/tex]
Given :
The line [tex]y=2x-4[/tex] is dilated by a scale factor of [tex]3\div2[/tex] and centered at the origin.
Solution :
The given line has slope 2 and y intercept -4.
As dilation conserves the parallelism, the dilated line will have the same slope = 2 and the y intercept of the dilated line is
[tex]= -4\times \dfrac{3}{2}=-6[/tex]
Therefore the equation that represent that image of the line after dilation is
[tex]y = 2x-6[/tex]
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There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 3?
Answer:
1/15
Step-by-step explanation:
The probability of spinning a number on a spinner with 15 equal areas that is a multiple of 5 or a multiple of 3 is 7/15, as there are 7 favorable outcomes (3, 5, 6, 9, 10, 12, 15) out of 15 possible results.
Explanation:The question asks for the probability of spinning a number that is either a multiple of 5 or a multiple of 3 on a spinner with 15 equal areas numbered 1 through 15. To solve this, we need to identify the multiples of each within the range of numbers on the spinner and then use the principles of probability to find the chances of landing on one of those multiples when the spinner is spun once.
The multiples of 5 between 1 and 15 are 5, 10, and 15. The multiples of 3 are 3, 6, 9, 12, and 15. Note that 15 is a multiple of both 5 and 3, so it should only be counted once. To avoid overcounting, we will list each multiple only once, which gives us the numbers 3, 5, 6, 9, 10, 12, and 15. The probability of landing on any specific number on the spinner is 1 out of 15 because there are 15 equally likely outcomes.
Since we have 7 such favorable outcomes, the probability is calculated as the number of favorable outcomes over the total number of possible outcomes, which is 7/15. So, the probability of spinning a number that is a multiple of 5 or a multiple of 3 on one spin is 7/15.
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Zack borrowed $1,087 for 12 months at 11 percent interest. If he must pay 11.00 per $100, what is zacks monthly payment
please help compare these integers by typing the symbol that would make the statement true
12 ________ - 18
An ice chest contains 88 cans of apple juice, 44 cans of grape juice, 55 cans of orange juice, and 66 cans of mango juice. suppose that you reach into the container and randomly select three cans in succession. find the probability of selecting three cans of appleapple juice.
The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?
can someone please explain how to do this.
Jane is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
A town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number?
The population of a town with an intial population of 5000, that grows at 2% every year would be 5520 after 5 years
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the population of the town after x years.
The population of 5000 grows at 2% every year. Hence:
100%+2% = 1.02, this gives:
y = 5000(1.02)ˣ
After 5 years:
y = 5000(1.02)⁵ = 5520
The population of a town with an intial population of 5000, that grows at 2% every year would be 5520 after 5 years
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The length of a rectangle is 10 feet longer than it is wide. if each side is increased 10 feet, then the area is multiplied by 4. what was the size of the original rectangle?
Final answer:
The original rectangle had a width of 20 feet and a length of 30 feet (20 feet + 10 feet). After solving a quadratic equation, we determined the original dimensions by setting up an equation that represented the area before and after the increase.
Explanation:
The original rectangle has a length that is 10 feet longer than its width. Let the width be represented by w feet. Therefore, the length would be w + 10 feet. After increasing each side by 10 feet, the new width is w + 10 and the new length is w + 20. The area of the new rectangle is 4 times larger than the original rectangle's area.
The area of the original rectangle is given by w(w + 10). The area of the larger rectangle is given by (w + 10)(w + 20). By multiplying the larger area, we get 4 times the original area, so (w + 10)(w + 20) = 4w(w + 10). We can simplify this equation to solve for w.
Step-by-step solution:
Set up the equation: (w + 10)(w + 20) = 4w(w + 10).Expand and simplify to: w² + 30w + 200 = 4w² + 40w.Rearrange to: 3w² + 10w - 200 = 0.Factor the quadratic equation: (3w - 20)(w + 10) = 0.Solve for w: w = 20 or w = -10 (we discard the negative solution).Thus, the original width is 20 feet and the original length is 30 feet (20 + 10).
one serving of crackers is 3/10 of the whole box of crackers. bella ate 3 servings last week. what fractonof the box did she eat?
PLEASE HELP!!!Which pair of angles are corresponding? Two horizontal lines cut by a diagonal transversal. Angles 1, 3, 5, and 7 are located on the left-hand side of the transversal starting from the top. Angles 2, 4, 6 and 8 are located on the right-hand side of the transversal starting at the top. Question 2 options: 1 and 3 1 and 4 4 and 8 1 and 8
Answer:
According to the description of the case, the angles should be named after this picture.
The congruents angles among each other are:
Blue: 1,4,5,8
Purple: 2,3,6,7
Therefore the three possibilities are:
a. 1 and 4
b. 4 and 8
c. 1 and 8
Step-by-step explanation:
A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability of a lock without all even digits? There to get a lock code with all even digits. There are 3,024 different 4-digit lock codes. There are to get a lock code without all even digits. The probability of a 4-digit lock code without all even digits is
Answer:
it's 24, 3000, and 3000/3024
Step-by-step explanation:
The probability for a 4-digit lock code using numbers 1-9 with no repeats and not all even is 2,904/3,024.
Explanation:To solve this, we need to find the total number of possible 4-digit lock codes using digits 1-9 with no repeats and not all even, then divide it by the total number of 4-digit lock codes using digits 1-9 with no repeats. Specifically, the lock code includes 5 different even numbers (2,4,6,8), and 4 different odd numbers (1,3,5,7,9). If the lock code is all even, we will have 5*4*3*2 = 120 possibilities. However, the total possibilities for 4-digit lock codes are 9*8*7*6 = 3,024. Thus the number of codes that are not all even digits is 3,024 - 120 = 2,904. Therefore, the probability for a 4-digit lock code not having all even digits is 2,904/3,024.
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Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)
A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?
Answer:
4.6
Step-by-step explanation:
Which quadratic equation is equivalent to (x+2)2+5(x+2)-6=0
A woman can bicycle 27 miles in the same time it takes her to walk 9 miles. she can ride 10 mph faster than she can walk. how fast can she walk
What is the surface area of a square pyramid with a height of 12 mm and a base that measures 10 mm on each side? Round to the nearest tenth if necessary.
The surface area of the square pyramid is [tex]\(360 \, \text{mm}^2\)[/tex]
To calculate the surface area of a square pyramid, we need to find the area of its base and the area of its four triangular faces. Given the following:
The base side length [tex](\(s\))[/tex] is [tex]10\ mm[/tex].
The height of the pyramid [tex](\(h\))[/tex] is [tex]12 \ mm[/tex]
Step-by-Step Calculation:
1. Area of the base:
The base is a square with side length [tex]\(s = 10\) mm.[/tex]
[tex]\[\text{Area of the base} = s^2 = 10^2 = 100 \, \text{mm}^2\][/tex]
2. Slant height of the pyramid:
To find the slant height [tex](\(l\))[/tex], we need to use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle where one leg is half the side length of the base [tex](\(\frac{s}{2} = \frac{10}{2} = 5\) mm)[/tex] and the other leg is the height of the pyramid [tex](\(h = 12\) mm)[/tex].
[tex]\[l = \sqrt{\left(\frac{s}{2}\right)^2 + h^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, \text{mm}\][/tex]
3 Area of the four triangular faces:
Each triangular face has a base of [tex]10\ mm[/tex] and a slant height of [tex]13 \ mm[/tex].
[tex]\[\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 10 \times 13 = 65 \, \text{mm}^2\][/tex]
Since there are four triangular faces:
[tex]\[\text{Total area of the four triangular faces} = 4 \times 65 = 260 \, \text{mm}^2\][/tex]
4. Total surface area:
The total surface area of the square pyramid is the sum of the area of the base and the area of the four triangular faces:
[tex]\[\text{Total surface area} = \text{Area of the base} + \text{Total area of the four triangular faces} = 100 + 260 = 360 \, \text{mm}^2\][/tex]