Rewrite the product (3x2)(2x5) as a equivalent expression in simplest exponential form?
Answer:
[tex]3 {x}^{2} (2 {x}^{5} ) = 6 {x}^{7} [/tex]
A cylindrical tank is half-full of oil.
The cylinder has a base radius of 100cm. The height of the cylinder is 250cm.
1 litre= 1000cm^3
How many litres of oil are in a tank?
Round your answer to the nearest litre.
Answer:
3927 litres of oil to the nearest litre.
Step-by-step explanation:
The volume of the cylinder = π r^2 h
= π * 100^2 * 250.
When half full the volume is
1/2 * π * 100^2 * 250
= 3926991 cm^3 Dividing this by 1000:
= 3927 litres.
A cylindrical tank is half-full of oil.
There are 3928 liters of oil in the tank
Volume of CylinderVolume of cylinder is teh amount of material the cylinder holds. Volume is the density of the cylinder.
Volume Formula :
[tex]volume = \pi r^2h[/tex]
Given the radius of the cylinder is 100cm
Height of the cylinder is 250 cm
Substitute all the values inside the formula
[tex]V=\pi (100)^2(250)\\V=2500000\pi[/tex]
Cylinder tank is half full of oil . To find half of the volume , we divide the volume by 2
[tex]V=2500000\pi\\Half - full = \frac{2500000}{2}\pi \\Half-full =3926990.817 cm^3[/tex]
Given that 1 litre= 1000cm^3
convert cubic centimeter to litres
[tex]1000cm^3= 1litre \\3926990.817 cm^3=\frac{3926990.817 }{1000} \\1250000 cm^3=3927.99 liters[/tex]
There are 3928 liters of oil in the tank
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A bag contains 25 cents and 50 cent coins whose total value is $30 if the number of 25 cent coins is four times that of 50 cent coins, find the number of each type coins. please may I also have the equation.
Number of 25 cents coins is 80 and number of 50 cents coins is 20.
Step-by-step explanation:
Given,
A bag contains of total value $ 30.
Number of 25 cent coins is four times that of 50 cent coins.
To find number of 25 cents coin is x
Number of 50 cents coin is y
According to the problem,
[tex]\frac{x}{4} +\frac{y}{2} = 30[/tex] ----- eq 1
x = 4y------ eq 2
Now, we will solve these two equation.
Putting the values of x = 4y in eq 1 we get,
[tex]\frac{4y}{4} +\frac{y}{2} = 30[/tex]
or, [tex]y +\frac{y}{2} = 30[/tex]
or, [tex]\frac{3y}{2}[/tex] = 30
or, y = 20
So, x = 4×20 = 80
Hence,
Number of 25 cents coins = 80 and number of 50 cents coins = 20
Answer:
Step-by-step explanation:
Let 25 cent coin be A and 50 cent coin be B
Given
Total value of 25 cents coin and 50cents coin is $30
That’s
25A + 50B = 30
Also, 25 cents coin is equal to four times that of 50
So,
A = 4B
We now have
25A + 50B = 30
A = 4B
Substitute 4B for A into the first equation
25(4B) + 50B = 30
25 x 4B + 50B = 30
100B + 50B = 30
150B = 30
Divide both sides by 150 to isolate B
150B/150 = 30/150
B = 1/5
Recall
A = 4B
Therefore
A = 4 x 1/5
= 4/5
Number of 25 cents coin is 4/5 and that of 50 cents coin is 1/5
How do you subract integers?
Answer:
you could just add a negative if that makes since to you
Step-by-step explanation:
Adjust the sign on the integer to be subtracted to subtract integers. When all signs are positive, then the answer is positive. If both signs are negative, then the answer is negative. When the signs vary, deduct the lesser absolute value from the greater absolute value.
The function f is defined by f(x)=5x+k, where k is a constant. Find k, if the value of f at x=2 is equal to 14.
WILL MARK BRAINLIEST!
Answer:
k = 4
Step-by-step explanation:
f(x)=5x+k
Let x =2
f(2) = 5*2 +k
f(2) = 10+k
We know f(2) = 14
14 = 10+k
Subtract 10 from each side
14-10 = 10+k-10
4 =k
We are given the function f(x) = 5x + k when k is a constant, x equals 2, and f(x) equals 14
Steps to solve:
14 = 5x + k; x = 2
~Substitute
14 = 5(2) + k
~Simplify
14 = 10 + k
~Subtract 10 to both sides
14 - 10 = 10 - 10 + k
~Simplfy
4 = k
Best of Luck!
By visual inspection determine the best fitting repression model for the scatterplot
A. Quadratic
B. No pattern
C. Linear
D. Exponential
Answer:
exponential
Step-by-step explanation:
The y-value for the midline is equal to?
Answer:
answer is b (max y + min y)/2
Step-by-step explanation:
Answer:
(max y + min y)/2
Step-by-step explanation:
k=4
a 314
b 376.8
c 1256
d 942
Answer:
A. 314
Step-by-step explanation:
Volume of a cone= π*radius^2*height/3
Pi*radius^2=3.14*25=78.5
78.5 * height/3=78.5*12/3=78.5 x 4= 314
Which expressions are equivalent to 2 to the power of 5 / 6 to the power of 5
1. 1/3
2. 3 to the power of -5
3. (-4) to the power of -5
4. 2 to the 5th power times 6 to the -5 power
Answer:
2. 3 to the power of -5
4. 2 to the 5th power times 6 to the -5 power
Step-by-step explanation:
(2⁵)/(6⁵)
(2/6)⁵
(1/3)⁵
(3^-1)⁵
3^(-5)
(2/6)⁵
2⁵ × (6^-1)⁵
2⁵ × (6^-5)
Steps to solve:
2^5/6^5
~Apply exponent rules
(1/3)^5
1^5/3^5
~Simplify
1/243
Now, we can solve for each option.
Option 1:
1/3 ≠ 1/243
This is incorrect.
Option 2:
3^-5 = 1/243
This is correct.
Option 3:
-4^-5
-1/4^5
-1/1024 ≠ 1/243
This is incorrect.
Option 4:
2^5 * 6^-5
2^5 * 1/6^5
2^5/6^5
1^5/3^5
1/243 = 1/243
This is correct.
Therefore, the correct answers are options 2 and 4.
Best of Luck!
I need to find the the answer to this question thank you
Answer:
The answer is 116 degrees.
Step-by-step explanation:
The temperature at 4pm was 65 degrees Fahrenheit. The temperature dropped 5 degrees every hour from 4pm to 10pm. What is the temperature at 10pm? What are you doing dividing or multiplying? Can you write an equation to represent the problem and explain your process?
Answer: 35
Step-by-step explanation: It's an arith metic sequence that can be represented throigh the equation y= 65-5x where 5 is the amount of hous since 4pm and if you insert 6 for x you get 35
The mathematics problem involves subtraction, where the temperature drops 5 degrees per hour from 4pm to 10pm. The equation to represent this would be 65 - 5*6 = T. After performing the calculation, we find the temperature at 10pm is 35 degrees Fahrenheit.
Explanation:In this problem, you are dealing with a decline in temperature over time, which is considered as a subtraction problem. Since the temperature drops by 5 degrees every hour from 4pm to 10pm, that's a total of six hours (10pm - 4pm = 6 hours), so you'll subtract 5 degrees 6 times from the initial temperature of 65 degrees.
The equation to represent this problem is:
65 - 5*6 = T
This means you are subtracting 5 degrees six times from the initial temperature of 65 Fahrenheit to get the temperature (T) at 10pm. So, the calculation would be:
65 - (5*6) = 65 - 30 = 35
So, the temperature at 10pm is 35 degrees Fahrenheit.
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Alice will be serving punch at an event she is hosting next month. The graph below shows the number of servings based on the amount of punch available. What is the rate of change of the graph?
Answer:
There is no graph
Step-by-step explanation:
Answer: ben
Step-by-step explanation:b
e
n
ben
A rain barrel holds 47 gal. 1 qt of water. Mr. Jiko uses 12 gal. 2 qt to water his flower garden and 7 gal. 1 qt. to water his
trees. How much water is left in the rain barrel?
care sa nu mai
o proces po 2 e o water he tower an den ana 7 n. a over his
Answer:
27 gallons, 2 quarts
Step-by-step explanation:
The measurements are given in gallons and quarts. Lets convert everything to quarts.
We know:
4 quarts = 1 gallons
So,
Rain Barrel Capacity = 47*4 + 1 = 189 quarts
Jiko uses 12 gallon 2 quart to water flower garden = 12*4 + 2 = 50 quarts
Jiko uses 7 gallons 1 quarts to water trees = 7*4 + 1 = 29 quarts
He used up = 50 + 29 = 79 quarts
Remaining Water in Rain Barrel = 189 - 79 = 110 quarts
In gallons and quarts:
27 * 4 = 108 quarts
So, water left = 27 gallons, 2 quarts
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
28.46
Step-by-step explanation:
Use a^2+b^2=c^2 to find height
Then use the area formula bh/2 to find area :))
Answer: 44.1
Step-by-step explanation:
What’s is the index notation?
Given:
a) 3 × 3 × 3 × 3 × 3
b) 4 × 4 × 4 × 5 × 5
c) 9 × 7 × 9 × 9 × 7 × 9
To find:
The index notation.
Solution:
a) Using multiplication rule of indices:
[tex]a^{n} \times a^{m}=a^{n+m}[/tex]
[tex]3\times3\times3\times3\times3=3^{1+1+1+1+1}[/tex]
[tex]=3^5[/tex]
Therefore, [tex]3\times3\times3\times3\times3=3^{5}[/tex]
b) Using multiplication rule of indices:
[tex]4\times4\times4\times5\times5=4^{1+1+1}5^{1+1}[/tex]
[tex]=4^35^2[/tex]
Therefore, [tex]4\times4\times4\times5\times5=4^{3}5^{2}[/tex]
c) Using multiplication rule of indices:
[tex]9\times7\times9\times 9\times7\times9=9^{1+1+1+1}7^{1+1}[/tex]
[tex]=9^47^2[/tex]
Therefore, [tex]9\times7\times9\times 9\times7\times9=9^{4}7^{2}[/tex]
Volume and Surface Area! 30 POINTS
Answer:
Volume: 5200 cubic centimeters
Surface area: 1520 square centimeters
Step-by-step explanation:
Volume = [1/2 x 5 x side x apothem] x height
(The apothem is that little 8 cm mark, the height is 26, the side is 10.)
Plug those values in:
V = 1/2 * 5 * s * a * h
= 1/2 * 5 * 10 * 8 * 26 = 5200 cubic centimeters
Surface area = 2(base area) + 5(lateral area)
Perimeter of base = 10*5 = 50 cmBase area = pa/2 = 50*8 / 2 = 200 square centimetersLateral area = lw = 26*10 = 260 square centimetersSA = 2(200) + 5(260) = 1520 square centimeters
A baseball player got a hit of his last 40 at bats. What is the probability that he will get a hit in his next bat?
Answer: 41 out of 1
Step-by-step explanation:
Find the length of X.
Answer:
x=12
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
15/9=x/6
15/9 simplified by 3 equal 5/3
5/3=10/6 (multiplied by2 )
10/6=x/6
so x=10
A rectangle has a perimeter of 18cm. It’s length is 5cm greater than its width. Find the dimension
Answer:
The width is 2 cm and the length is 7 cm.
Step-by-step explanation:
Hope this helps!
Use 3.14 for pi.
Round to the nearest whole number.
The volume of this solid figure is
Answer:
[tex]v = 183 {cm}^{3} to \: the \: nearest \: whole \: number[/tex]
Step-by-step explanation:
Volume of a cone is given as:
[tex]v = \frac{1}{3} \times\pi \times \ {r}^{2} \times h[/tex]
where,
pi = 3.14
r = radius = half of diameter; 10cm/2 = 5cm
h = height = 3cm + 4cm = 7cm
Thus,
[tex]v = \frac{1}{3} \times 3.14cm \times {5}^{2} cm \times 7cm[/tex]
[tex]v = \frac{1}{3} \times 3.14cm \times 25cm \times 7cm[/tex]
[tex]v = \frac{1}{3} \times 549.50 {cm}^{3} [/tex]
[tex]v = \frac{549.50 {cm}^{3} }{3} [/tex]
[tex]v = 183.17 {cm}^{3} [/tex]
[tex]v = 183 {cm}^{3} to \: nearest \: whole \: number[/tex]
what's the least common denominator of 1/3 5/8 and 1/2?
The least common denominator of 1/3 5/8 and 1/2 will be 24.
What is Least common multiple?
The Least common multiple of two or more numbers are the smallest number that is multiple of two or more numbers.
Given that;
The numbers are,
⇒ 1/3, 5/8 and 1/2
Now,
To find the least common denominator of 1/3 5/8 and 1/2,
We need to find the least common multiple of 3, 8 and 2 as
The LCM of {3, 8, 2} = 24
Thus, The least common denominator of 1/3 5/8 and 1/2 will be 24.
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The least common denominator of 1/3, 5/8, and 1/2 is 24. It's the smallest number that all the denominators (3, 8, and 2) can divide into evenly, and it helps in adding or comparing fractions with different denominators.
Explanation:The least common denominator (LCD) of the fractions 1/3, 5/8, and 1/2 is the smallest number that all of the denominators can divide into evenly. When looking for the least common denominator, we can use the method of listing multiples or the method of prime factorization.
For the fractions given, we list the multiples of each denominator:
3's multiples: 3, 6, 9, 12, 15, 18, 21, 24, ...8's multiples: 8, 16, 24, 32, 40, ...2's multiples: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ...The smallest multiple that they all have in common is 24, which is the least common denominator. It's important to note that by finding the LCD, we can easily add or compare fractions with different denominators.
which angle pair relationships should be used to prove lines m and n are parallel?
What is 9 over 7 divided by 3?
The top of a pole is 15 feet high. The base is -3 feet underground. How tall is the pole?
Answer:
18
Step-by-step explanation:
tell if it helped
Answer:
18 feet
Step-by-step explanation:
We are 15 above ground and 3 feet below ground
Add the lengths together
15+3 = 18 feet for the pole length
J is the midpoint of CT CJ = 8x-5 and JT = 5x+4 find CT
The value of CT is 13x - 1.
What is a Line Segment?A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.
The figure given below shows a line segment CT, where the length of line segment CT refers to the distance between its endpoints, C and T.
Given that J is the midpoint of CT
CJ = 8x-5 and JT = 5x+4
C______________J______________T
⇒ CT = CJ + JT
Since J is the midpoint of CT, So CJ = JT
⇒ CT = CJ + JT
Substitute the values of CJ = 8x-5 and JT = 5x+4 in the above equation,
⇒ CT= (8x-5)+(5x+4)
⇒ CT= 8x-5+5x+4
Rearrange the likewise terms, and apply the arithmetics operation,
⇒ CT = 8x + 5x - 5 + 4
⇒ CT = 13x - 1
Hence, the value of CT is 13x - 1.
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Final answer:
To find the length of CT, solve the equation 8x-5 = 5x+4 to find x, then substitute the value of x into either CJ or JT to find the segment's length and double it.
Explanation:
The student is asking a geometry problem where they need to find the length of the segment CT given that J is the midpoint of CT with CJ being 8x-5 and JT being 5x+4. Since J is the midpoint, these two segments are equal in length, thus the equation to solve is 8x-5 = 5x+4.
To find the value of x, follow these steps:
Subtract 5x from both sides: 3x-5 = 4.Add 5 to both sides: 3x = 9.Divide both sides by 3: x = 3.Once x is found, substitute it back into either CJ or JT expression to find the length of one segment. Then, double that length to find CT, as CT is equal to 2 times CJ or 2 times JT.
A restaurant noted what type of food its customers ordered last week. Here are the results:
Burger
Fries
30%
40%
10%
20%
Find the probability that a randomly chosen customer ordered a burger given that they ordered fries.
P (burger fries) =
Answer:
0.80
Explanation:
Since the results are not shown properly, I attach the picture with full question inlcuding the diagram that shows the results correctly.
You need to determine P(burger|fries)
That is the ratio of people that ordered burgers from the set of people that ordered fries (the intersection of the two circles) to the total people who ordered fries (the blue circle, including the intersection of the two circles).
The venn diagram shows that the set of people who ordered fries was 10% + 40% = 50% (the percentage inside the blue circle, including the intersection with the purple circle)
And from that set, the subset of people who also ordered burgers is 40% (the intersection of the two circles).
Thus, the probability that a randomly chosen customer ordered a burger given that they ordered fries is:
[tex]P(burger\mid fries)=\dfrac{P(burger\cap fries)}{P(fries)}[/tex]
[tex]{P (burger\mid fries)=\dfrac{40\% }{50\% }=0.80=80\%[/tex]
The probability that a randomly chosen customer ordered a burger given that he ordered fries is 80%.
To determine the probability that a randomly chosen customer ordered a burger given that he ordered fries, the following calculation must be performed:
Fries = 10% Fries and burgers = 40% Burgers = 30% None = 20% Fries + Fries and burgers = 50% 50 = 100 40 = X 40 x 100/50 = X 80 = X
Therefore, the probability that a randomly chosen customer ordered a burger given that he ordered fries is 80%.
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Describe the type of correlation indicated by each correlation coefficient r=0.875
Answer:
A strong correlation
Step-by-step explanation:
The closer the correlation coefficient is to the number 1 the stronger the correlation is.
The correlation coefficient r = 0.875 indicates a strong correlation coefficient.
What is correlation?A statistical metric known as correlation shows how much two or more variables change in relation to one another.
The given correlation coefficient is r = 0.875.
Since the value of r is greater than 0.7, the correlation is strong.
Hence, the correlation coefficient r = 0.875 indicates a strong correlation coefficient.
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What is the mean of the data set shown below? 12 15 10 11
A 7.5 force is applied to a football, causing an acceleration of 15 m/s2. Calculate the mass
of the football.
Step-by-step explanation:
We know that we have the formula that F = ma
Given
Force (F) = 7.5 N
Acceleration (a) = 15 m/s²
Mass (m) = ?
Now
F = ma
7.5 = m * 15
m = 7.5/ 15
Mass = 0.5 kg
The mass of the football is 500 g.
Step-by-step explanation:
Given,
F = 7.5 N
Acceleration (f) = 15 m/s²
To find the mass (m) of the ball.
Formula
F = mf
According to the problem,
m×15 = 7.5
or, m = [tex]\frac{7.5}{15}[/tex] = 0.5 kg = 500 g
Hence,
The mass of the football is 500 g.
Explain the Pythagorean theorem to an alien. What is it? When do you use it? How does it work? What is the formula? Who discovered it? Etc.
Answer:
the pythagorean theorem is an equation to figure out the side of a triangle. theformula is a squared plus b squared equals c squared.
Step-by-step explanation:
Answer:
The pythagorean theorem is an equation to figure out the side of a triangle. And the formula is A squared plus B squared equal C squared and it better to always know the missing triangle
Step-by-step explanation: