The volume of the rectangular prism can be calculated by multiplying the base area (20cm2) with the height (9.2cm), giving a volume of 184cm3.
Explanation:The volume of a rectangular prism can be calculated as the product of its base area and its height. This is a formula that mathematically represents the process of 'filling' the three-dimensional shape with tiny cubes, each having a side length of 1 cm. In this case, the given base area of the rectangular prism is 20cm2, and the height is 9.2cm.
To find the volume, you multiply these two measurements together. So, 20cm2 * 9.2cm = 184cm3. Hence, the volume of the rectangular prism is 184cm3.
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One day, River writes down the numbers $1,$ $2,$ $\dots,$ $999.$ River chooses one of the digits written down at random. What is the probability that River chooses a $7$?
Answer:
100/963
Step-by-step explanation:
The number 1,2,3,...,999 is written down.
First, we determine the total number of digits written down
1-9 =9 digits 10-99= 2(99 - 10 + 1) =2(90) digits100-999=3(999 - 100 + 1) =3(900) digitsTotal Number of digits=9+2(90)+3(900) =2889
Number of Digit 7 between 1 and 999
In the Units’ place, 7 occurs once every decade (7, 017… 997)=10 X 10= 100 times In the Tens place, 7 occurs in the ten times every century (70–79, 170–179, …, 970–979) =10 X 10= 100 times In the hundreds’ place, 7 occurs once in the hundreds’ place (700, 701, …, 799) = 100 timesTherefore, the number 7 will be found a total of 300 times between 1 and 999.
Therefore, the probability of selecting a "7" = 300/2889
= 100/963
Final answer:
The probability that River chooses a 7 from the numbers 1 to 999 when randomly selecting a digit is approximately 0.111 or 11.1%. This is calculated by dividing the total occurrences of the digit 7 (321 times) by the total number of digits written (2889 digits).
Explanation:
To calculate the probability that River chooses a 7 from the numbers 1 to 999 when randomly selecting a digit, we must first determine the total number of times the digit 7 appears in this range. In numbers 1-9, 7 appears once; in numbers 10-99, it appears 10 times in the units place plus 10 times in the tens place; and in numbers 100-999, it appears 100 times in the units place, 100 times in the tens place, and 100 times in the hundreds place. Therefore, there are a total of 1 + 10 + 10 + 100 + 100 + 100 = 321 occurrences of the digit 7.
Next, we calculate the total number of digits written down from 1 to 999. For numbers 1-9, there are 9 digits. For 10-99, there are 90 numbers times 2 digits each, totaling 180 digits. For 100-999, there are 900 numbers times 3 digits each, totaling 2700 digits. The sum of all digits is 9 + 180 + 2700 = 2889 digits.
The probability that River chooses a 7 is the number of 7s divided by the total number of digits, which is 321/2889. Simplifying this fraction, we get a probability of approximately 0.111 or 11.1%.
What expression is equivalent to 5/2
Answer:
2 1/2
You didnt give us any option or choices
Step-by-step explanation:
I would like to help but there is no choices
Rockin' Reggie's Music Shop sells about 200 guitar picks each week. Reggie orders picks by the gross (144) from a distributor. About how many gross should Reggie order for a three month supply.
Answer:
1872 gross should Reggie order for a three month supply.
Step-by-step explanation:
Given:
200 guitar picks each week.
To Find:
How many gross should be ordered for three months period
Solution:
Now the guitar picks corresponds to the order picks by gross as follows;
given that 200 guitar picks corresponds to 144 gross orders
Now 200 are sold for each weeks i.e 7 days
Now for 3 months there are approximately 13 weeks
so Total sell for 3 months=13*200=2600 guitars
Now The ratio of guitar picks to gross orders is ,
144/200
=1/1.39=0.72
So 2600 guitars corresponds to 2600*(1/1.39)
i.e. 2600/1.39
=1872 Gross orders are required to get three month of supply
True or False: If your expression contains more than one set of parentheses, you should evaluate all of them
before doing anything else.
B
False
Answer:
You should evaluate whatever is in the parenthesis first.
By standardization of algebra, we can say that the statement is true, you should evaluate the parentheses at the beginning.
In general problems, we usually use parentheses to separate larger problems in smaller ones. The benefit of doing this is that we can tackle these smaller problems one by one instead of a larger problem all at once.
Whit this in mind, when an expression has several sets of parentheses, the first thing that you need to do is simplify them by evaluating them, so yes, the statement is correct.
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Mali performed an experiment with a standard deck of 52 cards. She wanted to see if the face cards (Ace, King, Queen, and Jack) came up the expected number of times when she randomly selected 13 cards from the deck. A 3-column table with 4 rows. Column 1 is labeled Card with entries ace, king, queen, jack. Column 2 is labeled Theoretical (predicted frequency) with entries 1, 1, 1, 1. Column 3 is labeled Experimental (Observed frequency) with entries 0, 1, 1, 0. Mali noticed that the observed frequencies did not match the predicted frequencies. What does she need to change in her experiment to get closer to the predicted values based on the theoretical probability for all the face cards?
Answer:
Increase the number of trials...
Step-by-step explanation:
The number of experiment trials should be increased as to match the predicted frequencies.
What is Probability?Probability is the likeliness of an event to happen.
In probability experiments are performed to determine the probability of a required event.
Mali performed the experiments and found that the observed frequencies did not match the predicted frequencies.
To make the data closer to the predicted values, more number of trials to determine the frequencies should be done.
Your question seems incomplete, the complete question is attached as an image with the answer.
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Christina bought a purse for $29.95 and x belts for $3.99 each. Which of the following expressions shows the total amount of money she spent?
29.95x + 3.99 29.95x + 3.99x 29.95 + 3.99 + x 29.95 + 3.99x
Answer:
29.95 + 3.99x
Step-by-step explanation:
she bought one purse and x number of belts for 3.99
Answer:
29.95+3.99x
Step-by-step explanation:
Part of the population of 5,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50
elk shows that 6 of them are infected. How many elk are likely to be infected?
Based on the sample, there will likely be
————- infected
in the wildlife preserve.
Answer:
720 elk I think (sorry if wrong)
what is the circumference of a circle when the radius is 7
Answer:
43.98
Step-by-step explanation:
pier2
Please Help ASAP!!!
Question in image below.
Y=-3x+3
Y=5x+19
Solve this system by substitution
Answer:
x=-2
Step-by-step explanation:
You can substitute the first equation into the second:
-3x+3=5x+19
Add 3x on both sides:
3=8x+19
Subtract 19 on both sides:
-16=8x
Divide 8 on both sides:
x=-2
Answer:
x = -2
y = 9
Step-by-step explanation:
to evaluate this system of equation we would say that
let
Y=-3x+3................................................. equation 1
Y=5x+19................................................... equation2
substitute equation 2 into equation 1
5x + 19 = -3x + 3
collect the like terms together
5x + 3x = 3 -19
8x = -16
divide both sides by the coefficient of x which is 8
8x/8 = -16/8
x = -2
put x = -8 into equation 1
Y=-3x+3................................................. equation 1
y = -3(-2) + 3
y = 6 + 3
y = 9
therefore the value of x and y is -2 and 9 respectively.
Rewrite the function by completing the square h(x) =4x^2+4x+1
Answer:
4(x + [tex]\frac{1}{2}[/tex] )²
Step-by-step explanation:
Given
h(x) = 4x² + 4x + 1
To complete the square the coefficient of the x² term must be 1
Factor out 4 from 4x² + 4x
h(x) = 4(x² + x) + 1
add/subtract ( half the coefficient of the x- term )² to x² + x
h(x) = 4(x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) + 1
= 4(x + [tex]\frac{1}{2}[/tex] )² - 1 + 1
= 4(x + [tex]\frac{1}{2}[/tex] )²
Answer:
Step-by-step explanation:
4(x+1/2)^2+0
The first box is 4
The second box is 1/2
the third box is 0
The tree diagram shows Pam's choices for her appetizer and meal at a restaurant How many choices include chicken?
A) 1
B) 2
C) 3
D) 4
Can somebody help me with the next question
Yep, sure. Which question?
help me with the question below
Answer:
122
Step-by-step explanation:
a^2 + b^2 = c^2
(only in right angled triangles)
Answer:
122
Step-by-step explanation:
Use the graph to identify the amplitude for each
function shown.
The amplitude of the function shown in orange is
The amplitude of the function shown in blue is
The amplitude of the function shown in green is
Answer:
6
4
3
Step-by-step explanation:
Answer:
Use the graph to identify the amplitude for each function shown.
The amplitude of the function shown in orange is
✔ 6
.
The amplitude of the function shown in blue is
✔ 4
.
The amplitude of the function shown in green is
✔ 3
.
Step-by-step explanation:
This from my answers.
EASY POINTS!!!!! FIRST CORRECT ANSWER GETS 5 STARS PLUS A THANK YOU, AND MORE THAN 20 POINTS!!!
Answer:
D
Step-by-step explanation:
D, because it has infinite solutions, or both sides simplify down to 0.
Hope this helps!
Simplify the expression:
P +7p + 5p
Oh
Answer:
Option A, 13p
Step-by-step explanation:
Step 1: Simplify
[tex]p + 7p + 5p[/tex]
[tex](p + 7p) + 5p[/tex]
[tex]8p + 5p[/tex]
[tex]13p[/tex]
Answer: Option A, 13p
What number between 18 and 22 is a prime number?
Answer:
I think
19 has no factors other than 1 and itself
please help me I need hlp
x^2<64 find solution
Answer:
(-8,8)
Step-by-step explanation:
19.64851 2 s .f help please
Answer: 20
Step-by-step explanation:
19.64851 to 2s.f
To 2 significant figures
Looking at the digit behind the decimal
It is 6,meaning it is more than 5
So you round up to 1 and add to the digit in front
=20
Greatest common factor of x4 and x3
Answer:
x^3 is the greatest common factor of x4 and x3
Step-by-step explanation:
The greatest number that is a factor of two (or more) other numbers. When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor. Abbreviated "GCF". Also called "Highest Common Factor"
2(x − 6) − 24 = 13 − 5x
x =
Answer:
X=5
Step-by-step explanation:
Given a+b=7 and a–b=3, find:
2^a*2^b
Answer:
128
Step-by-step explanation:
5+2=7
5-2=3
2^5=32
2^2=4
32*4=128
Hope this helps:)
The quantity R, in grams, of a certain radioactive substance decreases according to the exponential decay model dRdt=−0.05R, where t is measured in seconds. During an experiment, a scientist determines that the rate of decay of a second substance with the quantity S, in grams, can be represented by a linear model dSdt=−4, where t is measured in seconds. If at time t=0, R(0)=100 and S(0)=125, at what time t, in seconds, will there be equal quantities of both substances?
Answer:
24 secondsExplanation:
1. Quantiy R
Decay model:
[tex]\dfrac{dR}{dt}=-0.05R[/tex]
That is a first order reaction, whose solution is:
[tex]R=R_0e^{-0.05t}[/tex]
The value at t = 0, R(0) = 100 is R₀.
Thus, the law is:
[tex]R(t)=100e^{-0.05t}[/tex]
2. Quantity S
Decay model:
[tex]\dfrac{dS}{dt}=-4[/tex]
That is a zero order kinetic, whose solution is:
[tex]S=S_0-4t[/tex]
The value at t = 0, S(0) = 125 is S₀
Thus, the law is:
[tex]S(t)=125-4t[/tex]
3. At what time will there ve equal quantities of both substances?
You must solve the system doing R(t) = S(t)
[tex]100e^{-0.05t}=125-4t[/tex]
That equation must be solved by graphing or by consecutive iterations
Note that when t = 0 R(t) = 100 and S(t) = 125. From, that the quantities decreases.
Subsitute with t = 10.
The left-hand side yields: 61 and the right-hand side yields 85.Then, the time is greater than 10.
Substitute with t = 15
Left-hand side = 47Right-hand side = 65t = 20
Left-hand side = 3745t = 25
Left-hand side = 29Right-hand side =25t = 24
Left-hand side =3 0Right hand side = 29Hence, 24 seconds is a satisfactory solution.
The graph attached shows that the intersection point is at t ≈ 23.548 seconds, confirming that 24 seconds is the best solution rounded to an integer number.
At t= 24 , in seconds, will there be equal quantities of both substances.
Given that,
The quantity R, in grams, of a certain radioactive substance decreases, according to the exponential decay model dR\dt=−0.05R, Where t is measured in seconds
The rate of decay of a second substance with the quantity S, in grams, can be represented by a linear model dS\dt=−4,
Where t is measured in seconds. If at time t=0, R(0)=100 and S(0)=125.
We have to determine,
At what time t, in seconds, will there be equal quantities of both substances.
According to the question,
Exponential decay model,
[tex]\dfrac{dR}{dt} = 0.05R[/tex]
The solution of first order reaction,
[tex]R = R_o.e^{0.05t}[/tex]
Substitute the value t = 0 ,R(0)= 100,
Then,
[tex]R(t) = 100.e^{0.05t}[/tex]
The decay model,
[tex]\frac{dS}{dt} = -4[/tex]
That is a zero order kinetic, whose solution is:
[tex]S= S_0-4t[/tex]
The value at t = 0, S(0) = 125 is S₀,
Therefore,
[tex]S(t) = 125-4t[/tex]
At what time will there +ve equal quantities of both substances,
Solve the system doing R(t) = S(t),
[tex]100.e^{-0.05t} = 125-4t[/tex]
The equation must be solved by graphing or by consecutive iterations
When t = 0 R(t) = 100 and S(t) = 125. From, that the quantities decreases.
Substitute with t = 10.
The left-hand side yields: 61 and the right-hand side yields 85.
Then, the time is greater than 10.
Substitute with t = 15
Left hand side = 47
Right-hand side = 65
t = 20
Left-hand side = 37
45
t = 25
Left-hand side = 29
Right-hand side =25
t = 24
Left-hand side =3 0
Right hand side = 29
Hence, 24 seconds is a satisfactory solution.
The graph attached shows that the intersection point is at t ≈ 23.548 seconds, confirming that 24 seconds is the best solution rounded to an integer number.
Hence, At t= 24 , in seconds, will there be equal quantities of both substances.
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Select the correct answer.
What is a demand schedule?
A.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C. a chart that shows the demand for a product at various prices
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WILL GIVE BRAINLIEST!!Which graph shows the following system of equations and its solution?
-4x-3y=4
4x-y=-4
Answer:
C, I believe?
Step-by-step explanation:
2=1/4 4+ b how do I find the y intercept?
Answer:
you intercept 2 with the 46721
Step-by-step explanation:
2=64=1/4/5_=24
please help
pleaze plz
Given:
Deposit (P) = £2000
Rate of interest (r) = 3%
Time (t)= 2 years
Number of time interest calculated per year (n) = 1
To find:
Amount in the account after 2 years
Solution:
Compound interest formula:
[tex]$A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
Substitute the given values.
[tex]$A=2000\left(1+\frac{3\%}{1}\right)^{1\times 2}[/tex]
To convert percentage into fraction divide by 100.
[tex]$A=2000\left(1+\frac{\frac{3}{100} }{1}\right)^{1\times 2}[/tex]
[tex]$A=2000\left(1+\frac{0.03 }{1}\right)^{ 2}[/tex]
[tex]$A=2000\left(1+0.03\right)^{ 2}[/tex]
[tex]$A=2000\left(1.03 }\right)^{ 2}[/tex]
[tex]$A=2121.8[/tex]
Therefore, £2121.8 will be in the account after 2 years.
Simplify [tex]\sqrt{4}[/tex]
_____________
[tex]\sqrt[3]{4}[/tex]
Taking the square root of a number means finding a number that when you square it, it equals the number in the square root.
√4 = 2 because 2² = 4
³√4 is already simplified.
Best of Luck!