Answer:
total cost = 8x^2 +17280/x
Step-by-step explanation:
Let x represent the base length. Then the area of the base is x^2, and the height is h = 720/x^2.
The area of the four sides is ...
(4x)(h) = (4x)(720/x^2) = 2880/x
The cost of the base is ...
base cost = 8x^2
And the cost of the sides is ...
side cost = 6(2880)/x = 17280/x
The total cost of the box is ...
total cost = base cost + side cost
total cost = 8x^2 +17280/x
_____
Comment on the cost function
You will find this function has a minimum at x=∛1080 ≈ 10.260 in. The total cost is about $2526.35, and the box is 2/3 times as tall as wide. That aspect ratio makes any pair of opposite sides cost the same as the base, the generic solution to a cost optimization problem of this sort.
I need help
On these two
Answer:
10.
A. 10240
6.
B. 2^18 = 262144
Step-by-step explanation:
Give your answers in pi
Answer:
36π
Step-by-step explanation:
area=πr²
=πx6x6
6x6=36
area = 36π
what is the solution set for the equation (x+3)(x-8)=0
Answer:
x= -3 x=8
Step-by-step explanation:
(x+3)(x-8)=0
We can use the zero product property to solve
x+3 =0 x-8 =0
x= -3 x=8
Answer:
x=8
Step-by-step explanation:
(02.04 MC) Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3. y = −3x − 13 y = −3x + 11 y = −3x + 13 y = −3x + 1
Answer:
it is b
Step-by-step explanation:
the answer is b because
Describe the rate of change of f(x)=lnx. Your answer should explain how the slope changes when x is small and when x is large.
Answer:
By plotting the graph of f(x)=lnx, you can conclude that when x is small, dy/dx has a larger value. For instance, the gradient of the curve when x=0.5 is 2. However, as you move along the x axis, you will see that the graph levels off, indicating a decrease in the slope, or dy/dx. For example, if x=10, dy/dx = 0.1 and when x=20, dy/dx= 0.05 and so on. Eventually, when x is large enough the value of dy/dx will be negligible.
Thus, as x increases, the slope decreases.
Answer:
Explanation shown below
Step-by-step explanation:
f(x)=lnx;
The rate of change is defined as dy/dx;
dy/dx[Inx] = 1/x
and dy/dx is defined as the slope
The nature of the slope is as x increases ; the slope decreases and conversely meaning as x decreases, the slope increases.
On a coordinate plane, triangle A B C has points (negative 9, 3), (negative 9, 6), (0, 3) and triangle A double-prime B double-prime C double-prime has points (3, negative 1), (3, negative 2), and (0, negative 1).
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
a reflection over the x-axis, then a dilation by a scale factor of 3
a reflection over the x-axis, then a dilation by a scale factor of One-third
a 180° rotation about the origin, then a dilation by a scale factor of 3
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Answer: D 180 degrees rotation about the origin.then a dilation by a scale factor of one-third.
Step-by-step explanation:
A( -9,3) B(-9,6) C (0,3)
After a rotation of 180 degrees you will have the new points as
A (9,-3) B( 9,-6) C (0, -3)
The you after dilating it by a scale factor of 1/3
you will get the coordinates
A ( 3,-1) B( 3,-2) C(0,-1)
which match is what was given in the question.
Answer:
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Step-by-step explanation:
took the test
52 is what percent of 93?
Answer:
55.9139785%
Step-by-step explanation:
Is means equals and of means multiply
52 = P * 93
Divide each side by 93
52/ 93 = P
.559139785
Change to percent form
55.9139785%
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
Answer:
Step-by-step explanation:
The formula is y = mx + b
m being the slope, rise over run. And b being the y-intercept. Right off the bat we can visually see the y-intercept is -4.
To find slope, we need to take two sets of coords and apply the slope fomula. The slope fomula is change in y divided by the change in x. The function itself is straight, so that means the slope will be the exact same no matter which points you choose.
(4, -1) and (8, 2) are coords on the line. Do 2 - (-1) to get 3. then do 8 - 4 to get 4. Finally, we just gotta do 3/4 which is simply [tex]\frac{3}{4}[/tex].
We have the slope of 3/4 and we have the y-intercept of -4. Just plug it in the standard formula of y = mx + b to get:
[tex]y=\frac{3}{4} x-4[/tex]
algebra parabola question see picture above
Answer:
see below
Step-by-step explanation:
(-1, -9) is a vertex or minimum.
(-4, 0) is an x-intercept / zero of the function / solution
(2, 0) is also an x-intercept / zero of the function / solution
The parabola has a minimum.
How many degrees was ABCD rotated?
the answer is 180°
Step-by-step explanation:
because it rotated 2x and 90+90 is 180
Round 90.2844097979 to 3 decimals
Answer:
only allow 3 decimals
90.284 is the answer we removed all others except for 3
The number of seconds, t it takes for an object to fall a distance of d meters can be found using the formula t=2dg−−√, where g is the constant acceleration due to gravity, 9.8msec2. How many meters does an object fall in 5 seconds? Round your answer to the nearest whole number.
Answer:
d = 61.25 m
Step-by-step explanation:
The number of seconds, t it takes for an object to fall a distance of d meters can be found using the formula :
[tex]t=2\sqrt{\dfrac{d}{g}}[/tex] .....(1)
It is required to find the distance covered by ab object in 5 seconds
Solving equation (1) for d. So,
[tex]d=\dfrac{t^2g}{4}[/tex]
Putting all the values we get :
[tex]d=\dfrac{(5)^2\times 9.8}{4}\\\\d=61.25\ m[/tex]
So, the distance covered by the object is 61.25 m.
The object will fall at a distance of 122.5 meters.
What is acceleration?Acceleration is the rate of change of velocity with time, both in terms of speed and direction.
Given that, t = √(2d/g).
t = √(2d/g
t√(g/2) = √d
t²(g/2) = d
Or, d = t²(g/2)
Substitute g = 9.8 and t = 5:
d = 5²(9.8/2)
d = 122.5 meters
Hence, the object will fall at a distance of 122.5 meters.
Learn more on acceleration here:
https://brainly.com/question/12550364
#SPJ2
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =
Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
If x = 45, then is between _____. 6 and 7 22 and 23 44 and 46 4 and 5
Step-by-step explanation:
The last option 45 and 46
Answer:
its 4-5 not 45-46 \
Step-by-step explanation:
Age (years) Population Under 15 2600 15 - 64 16000 Over 64 4000 Calculate the child dependency ratio from the chart above. Round to 3 decimals places.
Answer:
16.25%
=0.163 (correct to 3 decimal places)
Step-by-step explanation:
The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]
From the given table:
Population Under 15 years = 2600
Population of the working class (between 15-64) = 16000
Therefore:
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]
=0.163 (correct to 3 decimal places)
Alex is paid $30/hr at full rate, and $20/hr at a reduced rate. The hours of work are paid at a ratio of 2:1, full rate : reduced rate. For example, if he worked 3 hours, he would be paid 2 hours at full rate and 1 hour at reduced rate. Calculate his pay for 4 hours of work
Answer:
His pay for 4 hours of work is $106.67.
Step-by-step explanation:
2:1, full rate : reduced rate.
This means that for each 2+1 = 3 hours that he works, 2 he has full pay and 1 he has reduced pay.
4 hours
How much are full pay?
For each 3, 2 are full pay. For four?
3 hours - 2 full pay
4 hours - x full pay
[tex]3x = 8[/tex]
[tex]x = \frac{8}{3}[/tex]
So for [tex]\frac{8}{3}[/tex] hours he makes the full pay($30) and for [tex]4 - \frac{8}{3} = \frac{12}{3} - \frac{8}{3} = \frac{4}{3}[/tex] he makes reduced pay($20).
Calculate his pay for 4 hours of work
[tex]30*\frac{8}{3} + 20*\frac{4}{3} = 106.67[/tex]
His pay for 4 hours of work is $106.67.
What is a word problem for 15-28?
Answer:
valarie had 28 pencils , she gave 15 pencils away to people. How many pencils will she have left?
Step-by-step explanation:
hope this helps:)
Examine the details of the chi‑square test and conclude in context. There is good evidence (cite P-value) of an association between treatment and outcome in the population of women just treated for a UTI. There were substantially fewer than expected women getting a UTI recurrence in the study among those drinking cranberry juice daily. The conditions for inference are not met. There is good evidence (cite P-value) of an association between treatment and outcome in the population of women just treated for a UTI. There were substantially fewer than expected women getting a UTI recurrence among those abstaining from both drinks. There is good evidence (cite P-value) of an association between treatment and outcome in the population of women just treated for a UTI. There were substantially fewer than expected women getting a UTI recurrence among those drinking Lactobacillus drink. There is good evidence (cite P-value) that, in the population of women just treated for a UTI, women drinking cranberry juice daily have fewer UTI recurrences, on average. Question Source: Baldi 4e - The Practice Of Statistics
Answer:
Step-by-step explanation:
We will examine and outline the details of this chi-square test and then conclude in context.
(A) A population of women have just been treated for a urinary tract infection.
(B) Since the chi-square test is done for categorical variables, we will pick out the variable involved here.
That variable is: "UTI Recurrence"
Hence, we are looking at the recurrence of a urinary tract infection, among samples of the population of women who have recently been treated of it.
(C) There are three samples from this population and they are distinguished thus:
SAMPLE 1: Those drinking cranberry juice daily
SAMPLE 2: Those taking lactobacillus drink
SAMPLE 3: Those abstaining from both drinks (the placebo sample)
(D) The result of the test gave good evidence that SAMPLE 1 has the lowest value of the categorical variable involved; as compared to the values from SAMPLE 2 and SAMPLE 3.
In other words, on the average (average here is equal to mode or frequency of occurrence of the variable), the lowest number of UTI recurrences stems from Sample 1, as compared to the numbers of UTI recurrences in the other two samples
Dan earns £8.10 per hour how much will he earn for 7 hours work
A hose fills a hot tub at a rate of 3.84 gallons per minute. How many hours will it take to fill a 305-gallon hot tub?
Answer:
1.56 hours
Step-by-step explanation:
300 gal × 1 min 3.2 gal × 1 hr 60 min = 1.56 hr.
Answer:
i thought the question said a 'HORSE' fills a hot tub...
Step-by-step explanation:
lol dont mind me i just want points :D
Please answer this correctly
Answer:
The answer is 2.5ft².
Step-by-step explanation:
Given that the area of trapezoid formula is A = 1/2×(a+b)×h where a and b is the length and h is the height. Then substitute the following values into the formula :
[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]
Let a = 1.2,
Let b = 0.8,
Let c = 2.5,
[tex]area = \frac{1}{2} \times (1.2 + 0.8) \times 2.5[/tex]
[tex]area = \frac{1}{2} \times 2 \times 2.5[/tex]
[tex]area = 2.5 {feet}^{2} [/tex]
What is the surface area of a hemisphere with a radius 10
Answer:
Maths keeps one mentally active. The total surface of a hemisphere = 3(pi)r^2. So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
Step-by-step explanation:
hope this helps you :)
Answer:
The total surface of a hemisphere = 3(pi)r^2.
So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
Solve using
elimination 5y+3x=9 and 4y-3x=32
Answer:
(x,y)= (-124/27, 41/9)
Step-by-step explanation:
1) Add the equation to eliminate x.
5y+3x=9
4y-3x=32
2) Add 5y and 4y.
5y=9
4y=32 --> 9y=41
3) Get y by itself by dividing 9 on both sides:
y=41/9
4) Substitute Value in the equation 5y+3x=9
5(41/9)+3x=9
5) solve for x
x=-124/27
Step-by-step explanation:
5y + 3x = 9
4y - 3x = 32
using elimination method
subtracting equation 1 from 2 gives
y = -23
substitute to get value of X
5(-23) + 3X = 9
-115 +3x = 9
3x= 124
x = 41.33
Convert decimal +61 and +27 to binary using the signed 2’s complement representation and enough digits to accommodate the numbers. Then perform the binary equivalent of (27) + (-61), (-27) + (+61), and (-27) + (-61). Convert then answers back to decimal and verify that they are correct.
Answer:
the sum is 01011000₂ = 88
Step-by-step explanation:
For numbers of magnitude less than 128, it is convenient to use an 8-bit representation. I find it works will to convert back and forth through the octal (base-8) representation, as each base-8 digit converts nicely to three (3) base-2 bits.
61 = 8·7 +5 = 075₈ = 00 111 101₂
27 = 8·3 +3 = 033₈ = 00 011 011₂
Then ...
[tex]\begin{array}{cc|ccc}&61&&00111101\\+&27&+&00011011\\ &\overline{88}&&\overline{01011000}\end{array}[/tex]
__
Starting from the right, we can convert the binary back to octal, then to decimal by considering 3 bits at a time:
01 011 000₂ = 130₈ = 1·8² +3·8 +0 = 64 +24 = 88
The binary sum is the same as the decimal sum.
Suppose that a population of people has an average weight of 160 lbs, and standard deviation of 50 lbs, and that weight is normally distributed. A researcher samples 100 people, and measures their weight. Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170. [Round your answer to four decimal places]
Answer:
0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 160, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]
Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
This is the pvalue of Z when X = 170 subtracted by the pvalue of Z when X = 150. So
X = 170
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{170 - 160}{5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 150
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 160}{5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
Mai deposited $4000 into an account with 4.8% interest, compounded quarterly. Assuming that no withdrawals are made, how much will she have in the
account after 7 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
5,586.17
Step-by-step explanation:
A = $ 5,586.17
A = P + I where
P (principal) = $ 4,000.00
I (interest) = $ 1,586.17
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
What's 2|–9| – |–2|?
Answer:
Step-by-step explanation: AS YOU KHOW THW ABSOLUTE VALUE OF A QUESTION IS NUMBER ITSELF IF THERE IS MINUS SIGH THEN THE SIGH OF A NUMBER WILL BECOME PLUS OR IF THERE IS A PLUS SIGH THEN THERE IT WILL REMAIN AS IT IS. IF THERE IS NO NUMBER WITH THE MINUS SIGH THEN THE MINUS SIGH WILL REAMIN AS IT IS.
+2 +9 - +2
The answer has same sigh, then Plus answer will you get is
+11 - 2 then you will minus the answer will be
+9
HOPE IT HELP YOU
Please answer this correctly
Answer:
10-19 ⇒ 3
50-59 ⇒ 4
Answer:
# of ties # of racks
10-19 3
50-59 4
Step-by-step explanation:
Using the Stem and Leaf plot, our data is:
11, 12, 16
21
32, 34, 36, 37, 39
41, 45
51, 52, 53, 56
# of ties # of racks
10-19 3 (11, 12, 16)
50-59 4 (51, 52, 53, 56)
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. F(x) = 3(x - 2)² - 2
Step-by-step explanation:
→The function F(x) narrowed, meaning the absolute value being multiplied to the function is greater than 1.
→The function F(x) flipped over the x-axis, this means that the number being multiplied has to be a negative.
→The function F(x) shifted to the left 2 units, this means there needs to be a 2 being added.
→The function F(x) shifted downwards 2 units, meaning there needs to be a 2 being subtracted from the whole function.
This gives us the correct answer of "B. F(x) = 3(x - 2)² - 2."
Amar wants to make lemonade for a birthday party. He wants to mix 12 tablespoons of sugar in water. He only has a teaspoon which needs to be used 4 times to be equivalent to one tablespoon. At this rate, how many teaspoons of sugar will Amar need to make the lemonade?
Answer:48
Step-by-step explanation:
Given
Amar wants 12 tablespoons of sugar in water.
Amar has teaspoon whose four times is equivalent to 1 tablespoon
i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]
therefore
[tex]12 tablespoon is 4\times 12[/tex]
[tex]\Rightarrow 4\times 12[/tex]
[tex]\Rightarrow 48\ \text{teaspoons}[/tex]
So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade
Answer:6328565394729
Step-by-step explanation:213
sorry