The volume of square pyramid is 25 cubic inches. You want the height to be 2 inches less than the edge of the base. What are the dimensions?
Answers
Step-by-step explanation:
Related Questions
\(u'(s)=h^{-1} (u(s+h)-u(s-h))\)
Answers
The simplified form of the expression \(u'(s)=h^{-1} (u(s+h)-u(s-h))\) is \(u'(s) = \frac{du(s)}{ds}\)
Simplifying the expressionTo simplify the expression:
\(u'(s)=h^{-1} (u(s+h)-u(s-h))\)
We can first expand the terms inside the brackets:
\(u'(s) = h^{-1}u(s+h) - h^{-1}u(s-h)\)
Then, we can rewrite the expression with a common denominator:
\(u'(s) = \frac{u(s+h)}{h} - \frac{u(s-h)}{h}\)
Next, we can recognize that the expression inside the brackets is the definition of the forward difference quotient and the backward difference quotient, respectively.
Therefore, we can rewrite the expression as:
\(u'(s) = \lim_{h\to 0}\frac{u(s+h)-u(s)}{h} - \lim_{h\to 0}\frac{u(s)-u(s-h)}{h}\)
Finally, we can recognize that the first limit is the definition of the derivative of u at s, while the second limit is the negative of the derivative of u at s.
Therefore, we can simplify the expression as:
\(u'(s) = \frac{du(s)}{ds}\)
So the simplified form of the expression is \(u'(s) = \frac{du(s)}{ds}\)
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convert 5 2/5 into an improper fraction
Answers
Step-by-step explanation:
To write 5 as a fraction with a common denominator, multiply by 55 . Combine 5 and 55 . Combine the numerators over the common denominator. Simplify the numerator.
The convert of the mixed fraction into an improper fraction is \(\frac{27}{25}\)
Important information:The mixed fraction is \(5 \frac{2}{5}\)Calculation:\(= 5\frac{2}{5}\\\\ = \frac{27}{25}\)
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The circumference of a circle is 15pi centimeters what is the area of the circle in terms of pi?
Answers
\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)
e
value of x:
3/2 (x – 4) = 2(3x + 1)
Answers
3/2x-6x=6+2
-4.5x=8
X=-1.7
Answer:
Step-by-step explanation:
h, the points A(−5, 6), B(2, 6), C(2, -1) and D(-5, -1) are the vert of a square. what is the area of the square?
Answers
Answer:
so find dots, then count how many sections are beetween them, so you will find lenght of every side and use formula to find area(S=a²+b²).
An urn contains three red marbles, and six blue marbles. What is the probability of selecting at random, without replacement, two blue marbles?
A. 5/12
B. 4/9
C. 1/12
D. 1/9
show step bye step
Answers
The probability of selecting at random, without replacement, two blue marbles is 5/12 i.e. A.
What exactly is probability?
Probability is a measure of the possibility or chance of an event to be occurred. It is a mathematical concept that is used to describe the degree of uncertainty or randomness associated with an event.
The probability of an event is represented by a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. For example, the probability of rolling a 6 on a fair six-sided die is 1/6, because there is only one way to roll a 6 out of the six possible outcomes.
Now,
Using formula for probability:
P(A and B) = P(A) × P(B|A)
where P(A and B) is the probability of events A and B occurring together, P(A) is the probability of event A occurring, and P(B|A) is the probability of event B occurring given that event A has occurred.
In this case, we want to find the probability of selecting two blue marbles without replacement. Let's break this down into two events:
Event A: Selecting a blue marble on the first draw
Event B: Selecting a second blue marble on the second draw (without replacement)
For Event A, the probability of selecting a blue marble on the first draw is 6/9, since there are 6 blue marbles out of a total of 9 marbles.
For Event B, the probability of selecting a blue marble on the second draw given that a blue marble was selected on the first draw is 5/8, since there are 5 blue marbles remaining out of a total of 8 marbles.
So, using the formula for probability, we have:
P(Event A and Event B) = P(Event A) × P(Event B|Event A)
= (6/9) × (5/8)
= 30/72
= 5/12
Therefore, the probability of selecting at random, without replacement, two blue marbles is 5/12.
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Need help with factoring the trinomial and simplifying
Answers
Answer:
Hello
Step-by-step explanation:
From the answer to the second Question...
x²-6x+9 = -13 + 9
Factorize L.H.S
x² - 3x - 3x + 9 = -4
x(x - 3) - 3(x - 3) = -4
(x - 3)(x - 3) = -4
(x - 3)² = -4
Hence the answer is
\( \color{purple}{ \boxed{ {(x - 3)}^{2} = - 4}}\)
Answer:
-3 and -4 are the correct answers!!
Which expression is equivalent to pq
Answers
Answer:
D
Step-by-step explanation:
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According to a Human Resources report, a worker in the industrial countries spends on average 419 minutes a day on the job. Suppose the standard deviation of time spent on the job is 30 minutes.
a. If the distribution of time spent on the job is approximately bell shaped, between what two times would 68% of the figures be?
enter the lower limit for the interval where 68% of the values would fall
to enter the upper limit for the interval where 68% of the values would fall
b. If the distribution of time spent on the job is approximately bell shaped, between what two times would 95% of the figures be?
enter the lower limit for the interval where 95% of the values would fall
to enter the upper limit for the interval where 95% of the values would fall
c. If the distribution of time spent on the job is approximately bell shaped, between what two times would 99.7% of the figures be?
enter the lower limit for the interval where 99.7% of the values would fall
to enter the upper limit for the interval where 99.7% of the values would fall
d. If the shape of the distribution of times is unknown, approximately what percentage of the times would be between 360 and 478 minutes?
At least enter percentages rounded to 1 decimal place
% (Round the intermediate values to 3 decimal places. Round your answer to 1 decimal place.)
e. Suppose a worker spent 400 minutes on the job. What would that worker’s z score be, and what would it tell the researcher?
z score = enter the z score rounded to 3 decimal places
(Round your answer to 3 decimal places.)
This worker is in the lower half of workers but within select the distance from the mean
standard deviation of the mean.
Answers
Step-by-step explanation:
Ah statistics
68-95-99.7
a. 68% is between -1 and 1 standard deviation, which is between 389 and 449 minutes
b. 95% is between -2 and 2 standard deviations, which is between 359 and 479 minutes
c. 99.7% is between -3 and 3 standard deviations, which is between 329 and 509 minutes
d. Use table A with a z-score of (360-419)/30 = -1.96666667
and with a z-score of (478-419)/30 = 1.96666667
NOTE THESE ARE NOT THE ANSWERS, but use the z-scores to find the percentage on table A
e. (400-419)/30 = -0.633333333 as his z-score
now find that value on table A
We are given the mean and the standard deviation. If the distribution is normal(bell-shaped), the Empirical Rule is used, otherwise, if the distribution is unknown, Chebyshev's Theorem is used.
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by \(100(1 - \frac{1}{k^{2}})\).
In this question:
Mean of 419, standard deviation of 30.
Question a:
Within 1 standard deviation of the mean, so:
419 - 30 = 389.
419 + 30 = 449.
Between 389 and 449 minutes.
Question b:
Within 2 standard deviations of the mean, so:
419 - 60 = 359
419 + 60 = 479
Between 359 and 479 minutes.
Question c:
Within 3 standard deviations of the mean, so:
419 - 90 = 329
419 + 90 = 509
Between 329 and 509 minutes.
Question d:
Have to find how many standard deviations it is from the mean:
(478 - 419)/30 = 1.97
(360 - 419)/30 = -1.97
Considering \(k = 1.97\)
\(100(1 - \frac{1}{1.97^{2}}) = 74.2\)
At least 74.2% of the times would be between 360 and 478 minutes.
Question e:
The z-score is:
\(Z = \frac{X - \mu}{\sigma}\)
In which X is the measure, \(\mu\) is the mean and \(\sigma\) is the standard deviation.
For this question, X = 400, \(\mu = 419, \sigma = 30\)
So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{400 - 419}{30}\)
\(Z = -0.633\)
This worker is in the lower half of workers but within 0.633 standard deviations of the mean.
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A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+
ㅠ
2T
2πT
Answers
The graph that represents the function y= tanx is Option A.
What is the description of the above function?The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.
It oscillates between positive and negative infinity, creating a wave- like pattern.
It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.
Thus, option A is the correct answer.
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Translate the English phrase into an algebraic expression: the product of 9 and 7.
Answers
Answer: 9 × 7 = x
Step-by-step explanation:
Product means the solution to two numbers being multiplied, in this case it's 9×7. Answer to that equation is 63
What expression is equivalent to 1/3 divided by 1/6 plz help me
Answers
Answer:
The answer is B. 1/3 * 6/1
Step-by-step explanation:
When dividing fractions, you multiply the first term in the expression by the reciprocal of the 2nd term.
multiply the following decimals-0. 8 • (-0.3) • (-0.4) = -0. 096
Answers
Remember when we multiply negative numbers we need to be careful in the sign
\(-0.8\cdot-0.3\cdot-0.4=-0.096\)Remember when we multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
You are doing research on balance and fitness. To complete this research you will need a watch with a second hand. Identify a random sample of n = 12 men and n = 8 women. You must answer this question: How do you establish that this sample is truly random? STEP 2: Have each subject perform the following task: a) Have the subjects stand with their hands at their side, raise one knee, cross their ankle over the other knee, squat and bring their hands palms together in front of their chest. Time the subject until they put their foot back down on the floor. b) Ask the following questions: i) How many days per week do they exercise? ii) What is their favorite exercise? STEP 3: You will analyze your data and compute the following statistics for each group: 1) The Mean and standard deviation of the number of seconds the subject stayed balanced 2) The Median number of days per week exercised 3) The Mode of the favorite exercise 4) The 90% confidence interval of the mean STEP 4: Construct a complete hypothesis test and determine if the two groups have significantly different balance using α = 0.05. STEP 5: Write a one page introduction to your research, discuss how you selected your sample (is it a random sample?) and write a one page conclusion. Present your data in an organized manner.
Answers
Answer:
It should be a 2 sample t-test for the sample mean mu 1 - mu 2 at alpha = 0.05.
Step-by-step explanation:
To solve, you can just insert the data values into a graphing calculator and it should work. Remember to check the conditions and write out the null and alternate hypotheses.
Null: mu 1 - mu 2 = 0 There is no difference
Alternate: mu 1 - mu 2 =/= 0 There is a difference
Conditions:
-Random sample? Yes b/c assume that it is from a simple random sample.
-10%? Assume that there are more than 120 men and 80 women in the population"
-Normal Distribution? If the data for each respective sample is approx normal, assume they come from a normally distributed population. Large counts and the central limit theorem do not work here.
After this, insert ur data values into the graphing calculator n solve for p.
Once you get p, make a conclusion based on alpha = 0.05. If p is less than alpha, you can reject the null and conclude that you have significant evidence that the alternate is true. If p is greater than alpha, you cannot reject the null and conclude that you do not have significant evidence that the alternate is true.
When looking at a graph of a system of equations,
where can I find the solution(s) to the system?
Answers
Answer:
to solve a system of linear equations graphically we graph both equations in the same coordinate system, the solution to the system will be in the point where the 2 lines intersect.
An unopened bag of gummy bears weighs 2 1/3 ounces. Drayven has 3/4 of a bag of gummy bears and Akila has 2/3 of a bag. Who has more? If they put their bags together, would they have more than one bag? Explain your answer.
Answers
Answer:
Drayven has more
Step-by-step explanation:
If you look at the fractions through a drawing you would see that my claim is correct.
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
By what percent does the number of wolves change each year?
Answers
In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.
Percent calculation.
To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.
The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.
To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:
Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.
In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.
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The fair spinner shown in the diagram above is spun.
Work out the probability of getting a 5.
Give your answer as a fraction in its simplest form.
Answers
Answer:
1/5
Explanation:
There are five choices in the spinner. One of the choices is labeled '5'. That means you will have one out of the 5 choices to get the choice labeled '5'.
Good day :)
6x^2=-3x+1 to the nearest hundredth
Answers
The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
6x² = -3x + 1
To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:
6x² + 3x - 1 = 0
Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\)
Here; a = 6, b = 3, and c = -1.
Let's substitute these values into the quadratic formula:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23\)
Therefore, the values of x are -0.73 and 0.23.
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Write two ordered pairs for points that are on the graph of the line.
Answers
hope this helped! :)
Is 2/9 = 10/45 a true proportion?
Answers
Answer:
Yes
Step-by-step explanation:
To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other
\(45 \div 9 = 5\)
^ 45 and 9 were the denominators, we divide and get 5
Now for the numerators
\(10 \div 2 = 5\)
^ 10 and 2 we're the numerators, dividing also gave 5
Answer:
yes.
Step-by-step explanation:
let us check. to be a proportion they must be equivalent
however, what do we multiply to get there? let us check..
\(\frac{2x}{9x} =\frac{10}{45}\)
cross multiply...
2x * 45 = 9x * 10
90x = 90x
yes, they will be proportional!
you can even do it without the X, i just put x in to make it clearer.
At a peace summit, seven Hatfield and nine McCoy family
members sit down for a meeting. If the Sheriff orders two
randomly selected participants to shake hands at the end of
the meeting, what is the probability that the two are from
different families?
Answers
Answer:
0.525 = 52.5% probability that the two are from different families.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order in which the two participants are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Desired outcomes:
1 from the Harfield family(from a set of 7).
1 from the McCoy family(from a set of 9). So
\(D = C_{7,1}*C_{9,1} = \frac{7!}{1!6!}*\frac{9!}{1!8!} = 7*9 = 63\)
Total outcomes:
2 from a set of 16. So
\(T = C_{16,2} = \frac{16!}{2!14!} = 120\)
Probability:
\(p = \frac{D}{T} = \frac{63}{120} = 0.525\)
0.525 = 52.5% probability that the two are from different families.
i dont know if i am doing this wrong but i got non-fiction, fiction, children, school but it is not an option can someone double check
Answers
Answer:
non fic, fiction, children, school
Step-by-step explanation:
fiction: 1/4= 0.25
non fic: 1/2=0.50
school: 1/10= 0.10
children: 3/20= 0.15
What is the present value of R13 000 p.a. invested at the beginning of each year for 8years at 10%p.a. compound interest? (NB Use the compound interest tables provided or work to three decimal places only.)
Answers
Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:
PV = A *\((1 - (1 + r)^(-n)) / r\)
Where:
PV = Present value
A = Annual payment or cash flow
r = Interest rate per period
n = Number of periods
In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).
Using the formula and substituting the given values, we can calculate the present value:
PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)
Calculating this expression:
PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)
= 13000 * (1 - 0.46318) / 0.10
= 13000 * 0.53682 / 0.10
= 6977.66 / 0.10
= 69776.6
Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
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Jose is building a rectangular shaped garden and needs to know how many square feet it will cover. The dimensions of the garden will be 8 feet in length and (3n+2) in width. What is the area of the garden space?
A) 24n+16
B) 11n+10
C) 40n
Thank you!!!
Answers
Answer:
The equation for the area of a rectangle is length*width. For this problem, it says the length is 8 and the width is (3n+2). All you have to do is multiply 8 by (3n+2).
8(3n+2)=A
24n+16=A
Option A is correct
To find the end behavior
Answers
Answer:
hope this helps
Step-by-step explanation:
To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph
HELP ME. I HATE MATH DUDE.
Answers
Find the square root of the following numbers by division method.
Answers
Answer:
Answer is in picture
Step-by-step explanation:
Hope it is helpful.....
Quick please, If f(x) = 2x + 3 and g(x) = 5 - f(x), what is g(3)?
Answers
if f(x) = 2x + 3 and g(x) = 5 - f(x) then g(3) value is 2.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that function f(x) = 2x + 3 and
g(x) = 5 - f(x),
We need to find the g(3).
g(x)=5-2x+3
g(x)=8-2x
Now to find g(3) we have to replace x by 3
g(3)=8-2(3)
=8-6
=2
Hence, if f(x) = 2x + 3 and g(x) = 5 - f(x) then g(3) value is 2.
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What is the correct proportion to find 22% of 86?
Answers
Answer:
its either 18.92
or 25.58%
but I believe it is 18.92 I may be wrong though