Answer:
She can fit 9 cubic feet of clothing in the two boxes.
Step-by-step explanation:
She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.
3 + 6 = 9
Answer:
9 cu ft.
Step-by-step explanation:
That is the sum of the capacities of the 2 boxes
= 3 + 6
= 9 cu ft.
Find the area of the triangle
Answer:
54
Step-by-step explanation:
A = (9*12)/2
A = 9*6
A = 54
Answer:54
Step-by-step explanation:
multiply 9 and 12 then divide by 2 because a triangle is half of a square
List the steps taken and find the area of the figure below
6cm
6 CM
6 cm
6 cm
Answer:
36 cm
Step-by-step explanation:
Since all measurements of the figure are the same, that means that this figure is a square. To find the area of a figure multiply length by width. Since this figure is a square and all sides are equal, we multiply 6 by 6 for an area of 36 cm.
sider F and C below. F(x, y, z) = yz i + xz j + (xy + 4z) k C is the line segment from (1, 0, −2) to (6, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = xyz+2z2+c (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
Answer:
a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]
b) The value of the integral is 18
Step-by-step explanation:
a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that
[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]
From here, we have that
[tex] yz = \frac{\partial f}{\partial x}[/tex]
if we integrate both sides with respect to x, we get that
[tex] f(x,y,z) = xyz+ g(y,z)[/tex]
where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is
[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]
This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form
[tex] f(x,y,z) = xyz+g(z)[/tex]
If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get
[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]
This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]
So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]
b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is
[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]
2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
Let uequalsleft angle 4 comma negative 3 right angle, vequalsleft angle negative 2 comma 5 right angle, and wequalsleft angle 0 comma negative 6 right angle. Express 7 Bold u minus 5 Bold v plus Bold w in the form left angle a comma b right angle.
Answer:
[tex]<38,52>[/tex]
Step-by-step explanation:
[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]
We are required to express 7u-5v+w in the form <a,b>.
[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]
Please answer this correctly
Answer:
pic wont load
Step-by-step explanation:
Answer:
The quarter circle's area is 38.47 yard²
Step-by-step explanation:
The area of a full circle is pi * r ²
The area of a quarter circle is 1/4 * pi * r ²
Given:
Use 3.14 for pi
Round to the nearest hundredths.
Perimeter of quarter circle is 24.99 yards
For r you must leave it as 'r' because we do not know it for now...
1. Circumference of a full circle = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * r )
1/2 * 3.14 * r
1.57 * r
3 Since r = 'r'
We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.
4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch
1.57 * r + 2 * r = 24.99
( 1.57 + 2 ) * r = 24.99
3.57 * r = 24.99
Divide left and right of the = sign by 3.57
3.57 / 3.57 * r = 24.99 / 3.57
1 * r = 24.99 / 3.57
r = 7
The area of a quarter circle is 1/4 * pi * r ²
1/4 * pi * 7²
1/4 * 49 * pi
49/4 * pi
49/4 * 3.14
38.465
Round to the nearest hundredths gives 38.47 yard²
The quarter circle's area is 38.47 yard²
sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project
Answer:
It will take them approximately 51.43 minutes to complete the project together
Step-by-step explanation:
This is what is called a "shared job" problem.
The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.
So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project
Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.
We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).
Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.
In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:
[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]
So it will take them approximately 51.43 minutes to complete the project together.
Find the equations for a conical helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane). Include a plot of your conical helix.
Answer:
The equation are
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
z = z
Step-by-step explanation:
From the question we are told that
The radius of the conical helix is [tex]r= 8[/tex]
The height of the conical helix is [tex]h = 12[/tex]
The angular frequency is [tex]w = 2[/tex]
The plot of the conical helix is shown on the first uploaded image
Generally the parametric equation of a conical helix is mathematically represented as
for x -axis
[tex]x =\frac{ h-z }{h} r cos (wz)[/tex]
substituting values
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
for y-axis
[tex]y = \frac{h-z }{h} rsin (wz)[/tex]
substituting values
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
for z-axis
z = z
A commuter train travels 65 kilometers in 27 minutes. What is it’s speed in kilometers per hour?
Answer:
Per hour: 2.40740740741
Step-by-step explanation:
you have to divided 65 and 27 so
65/27
which is 2.40740740741
Please answer this correctly
Answer:
0-4: Make it 1 unit tall
5-9: Make it 5 units tall
10-14: Make it 4 units tall
15-19: Make it 1 unit tall
20-24: Make it 2 units tall
Step-by-step explanation:
0-4: 3 (1 number)
5-9: 5, 5, 7, 8, 8 (5 numbers)
10-14: 10, 11, 12, 13 (4 numbers)
15-19: 17 (1 number)
20-24: 22, 23 (2 numbers)
What’s the correct explanation for this question?
Step-by-step explanation:
=> The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid
=> The volume of a cone can be found by V = 1/3(Ab)(H) where Ab is base area and H is the height of the cone
The difference between both is that is it's base. A cone has a polygonal base while a pyramid has a tetragonal base
Write down the 1st term in the sequence given by: T(n) = n² + 3
Answer:
4
Step-by-step explanation:
T(n) = n² + 3
T(1) = 1² + 3 = 1 + 3 = 4
The average math SAT score is 511 with a standard deviation of 119. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was selected, and the mean math SAT score was 528. Is the high school justified in its claim? Explain. ▼ No Yes , because the z-score ( nothing) is ▼ unusual not unusual since it ▼ does not lie lies within the range of a usual event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means. (Round to two decimal places as needed.)
Answer:
No, because the z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Unusual
If X is more than two standard deviations from the mean, x is considered unusual.
In this question:
[tex]\mu = 511, \sigma = 119, n = 55, s = \frac{119}{\sqrt{55}} = 16.046[/tex]
A random sample of 55 students from this school was selected, and the mean math SAT score was 528. Is the high school justified in its claim?
If Z is equal or greater than 2, the claim is justified.
Lets find Z.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{528 - 511}{16.046}[/tex]
[tex]Z = 1.06[/tex]
1.06 < 2, so 528 is not unusually high.
The answer is:
No, because the z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
The statement that could be made regarding the high school about the justification of its claim would be:
- No, because the z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
Given that,
μ = 511
σ = 119
Sample(n) = 55
and
s = [tex]119/\sqrt{55}[/tex]
[tex]= 16.046[/tex]
As we know,
The claim of the high school could be valid and justified only when
[tex]Z > 2[/tex]
To find,
The value of Z
So,
[tex]Z = (X -[/tex] μ )/σ
by putting the values using Central Limit Theorem,
[tex]Z = (528 - 511)/16.046[/tex]
∵ [tex]Z = 1.06[/tex]
Since [tex]Z < 2[/tex], the claim is not justified.
Learn more about "Standard Deviation" here:
brainly.com/question/12402189
Need help finding the answer
Answer:
D
Step-by-step explanation:
When there is an negative sign inside in a radical, then we remove that and put out of the radical classifying as "i". Then, reduce 63 into smallest form and we can write it as 9 and 7. 9 is a perfect square of 3 so we put it outside and the answer is D.
Colgate claims that 90% of dentists recommend Colgate toothpaste. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answer:
the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;
P(X) = 0.0043
P(X) = 0.43%
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 90% = 0.9
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.9 = 0.1
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.9)^8 × (0.1)^2
P(X) = 0.0043
P(X) = 0.43%
The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.
Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.
Probability of dentist, who recommend Colgate toothpaste = 0.9
Probability of dentist, who does not recommend Colgate toothpaste,
= 1 - 0.9 = 0.1
When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend Colgate toothpaste and 2 recommend other tooth paste.
Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,
[tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]
Learn more:
https://brainly.com/question/20046335
g Suppose the company operates mine #1 for x1 days and mine #2 for x2 days. Write a vector equation in terms of v1 and v2 whose solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver. Do not solve the equation.
Answer:
The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]
Step-by-step explanation:
Solution
The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.
Thus,
Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.
Now,
If the company operates mine 1 for x1 days and mine #2 for x2 days
Then,
The total output becomes x₁v₁ +x₂v₂ which is the same output to b = [296 2454]
Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]
So, the vector equation becomes x₁v₁ +x₂v₂ = [296 2454]
Any help would be great
Answer:
[tex]\frac{56}{96}[/tex] is your answer
Step-by-step explanation:
[tex]\frac{7}{12}[/tex]=[tex]\frac{x}{96}[/tex]
to get to 96 you must multiply by 8
and since you did that for the bottom then you need to do the same for the top,
[tex]\frac{56}{96}[/tex] is your answer
what is the slope from 1 to 5.3 seconds?
Answer:
3/2
Step-by-step explanation:
The graph rises 3 feet for each 2 seconds to the right. The slope is ...
rise/run = (3 ft)/(2 s) = (3/2) ft/s
The numerical value of the slope is 3/2 or 1.5. The associated units are feet per second.
A triangular plate with base 3 m and height 5 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
The hydro-static force [tex]F=245000N[/tex]
Step-by-step explanation:
given data
base = 3 m
height = 5 m
density of water = 1000 kg/m3
Acceleration due to gravity = 9.8
The area if the strip needs to be calculated using similar triangular formula as well as the hydrostatic force
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
The volume of the box shown in the diagram is 40π3 cubic units. Find the length of ‘x’.
Answer:
4: 4[tex]\pi^2[/tex]
Step-by-step explanation:
2[tex]\pi[/tex] x 5 x [tex]x[/tex] = 10[tex]\pi x[/tex]
10[tex]\pi x[/tex] = 40[tex]\pi ^3}[/tex]
x = 4[tex]\pi^2[/tex]
Answer:
4π units
Step-by-step explanation:
v=lwh
40π^3=2π×5×h
40π^3=10π^2×h
h=40π^3/10π^2
h=4π units
mark brianliest if my answer suit your question please.
A swimming pool is to be drained. The pool is shaped like a Rectangular prism with length 12m , with 10 m, and depth 3m. Suppose water is pumped out of the pool at a rate of 18 m3 per hour.if the pool starts completely full , how many hours does it take to empty the pool ?
Answer:
20 hours
Step-by-step explanation:
first calculate volume:
12x10x3=360
then divide by 18
360/18=20
So 20 hours in total
Find all zeros of f(x)=x^3−17x^2+49x−833
Answer:
x = 17 or x = ±7i
Step-by-step explanation:
x³ − 17x² + 49x − 833 = 0
x² (x − 17) + 49 (x − 17) = 0
(x² + 49) (x − 17) = 0
x = 17 or ±7i
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. what is the height of the bridge
Answer:
100
Step-by-step explanation:
When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.
Answer:
100
Step-by-step explanation:
:3
which is the equation of a circle with center (-3, -5) and radius of 4
Answer: -8
Step-by-step explanation:
find the area of the triangle. ? square units
Answer:
54 square units
Step-by-step explanation:
The formula for the area of a triangle is:
[tex]\frac{1}{2}[/tex] x base x height
The base is 12
The height is 9
So 1/2 x 12 x 9 = 54 square units
NEED ASAP!!!!
Which equation represents the grafted function
Answer:
sorry i meant c
Step-by-step explanation:
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
P(greater than 1.25 minutes) = 0.8611 (Approx)
Step-by-step explanation:
Given:
Waiting time = 0 - 9 minutes
Find:
Probability that selected passenger has a waiting time greater than 1.25 minutes.
Computation:
⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =
⇒ P(greater than 1.25 minutes) = [9-1.25] / 9
⇒ P(greater than 1.25 minutes) = [7.75] / 9
⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)
find the square root of 12 to the nearest hundredth
Answer:
\sqrt(12) hope this helped.
Identify the word form of this number: 139,204,539,912
One hundred thirty-nine billion, two hundred four million, five hundred thirty-nine thousand, nine hundred twelve.
Hope this helped!
A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
