Mr. Lin baked banana bread for a bake sale to raise money for the math team. He said that he added a spoonful of walnuts for each of the students in his three classes, and that he added more than 250 walnuts. He used the inequality
16w + 24w + 10w > 250 to represent this situation, where w represents the number of walnuts in each spoonful. How many walnuts can be in a spoonful?
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Related Questions
The Bureau of Justice Statistics reports that the number of Americans on probation increased 76% from 1980 to 1995 and that 3.09 million Americans were on probation in 1995. If the rate of increase continues in the same way for the next 15-year period, what might be the number of Americans on probation in 2010?
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x: current number of Americans.
y: number of Americans after the next 15 years.
We now write the expression to model the problem, assuming:
"the rate of increase continues in the same way for the next 15-year period".
We have then:
y = 1.76 * x
y = 1.76 * (3.09)
y = 5.44 million Americans
Answer:
the number of Americans on probation in 2010 might be:
y = 5.44 million Americans
A math test took 50 minutes to complete. The test ended at 3:55. What time did the test begin?
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A math test ended at 3:55 and it took 50 minutes to complete. What time did the math test start?
The math test started at 3:05.
If we know that the math test ended at 3:55 and lasted 50 minutes, we can subtract 50 minutes from 3:55 and we will get an answer of 3:05.
Therefore, the math test started at 3:05.
Lita,Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4:1. If Rose typed 48 words, how many words did Lita type?
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Then Lita types twice as fast so 192*2=384.
It should be 384 words.
A square playground has an area of 175 m2. What is the approximate length of each side of the playground? Round your answer to the nearest meter
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Therefore, for a known area A, the side length is
side = √ (area)
= √ (175)
= 13.2288 (to 4 places of decimals).
If the area of a square playground is 175 [tex]m^{2}[/tex] then the approximate length is 13 meters.
What is square?A square is a two dimensional figure having four vertices, four edges, four angles and all the sides are equal to each other. The perimeter is equal is equal to 4*side and the area is side*side.
How to find side of square?We have been given the area of the square playground equal to 175 meter square. We know that the area of a square is side*side means [tex]side^{2}[/tex].
Put the value of 175 equal to side square and we will get the value of slide.
Area =[tex]side^{2}[/tex]
175=[tex]side^{2}[/tex]
side=[tex]\sqrt{175}[/tex]
Side=13.22m
If we round to nearest meter then it will be equal to 13m.
Hence if the area of a square playground is 175 meter square then the side will be equal to 13m.
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how to do this 24:96 = 5:?
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In that case, x=20
Please help me with this question
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1. S=12²-10²=44 sq. ft.
2. S=10*12-6*8=120-48=72 sq. ft.
answers: 1-C; 2-C.
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
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It is best presented in the form of a table, where
x-component = Fcos(theta)
y-component = Fsin(theta)
For F=25 pounds, angle = 30
25cos(30)=21.65
Force angle x-component y-component
25 30 25cos(30)=21.65 25sin(30)=12.5
30 100 30cos(100)=-5.21 30sin(100)=29.54
Total Fx=16.44 Fy=42.04
Therefore angle = tan^(-1)(Fy/Fx)=tan^(-1)(42.04/16.44) = 68.64 °
magnitude = sqrt(Fx^2+Fy^2)=sqrt(16.44^2+42.04^2)=45.15 pounds
53b−7b−6b+1 if b=25
Please help me with this problem! And what is the simplified expression?
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Answer: 1001
B/c i said so
How many different possible outcomes are there when Jillana spins the spinner below and then flips the coin?
The spinner is from 1-6.
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Answer:
There are total 12 outcomes
Step-by-step explanation:
The number of outcomes in spinning a spinner is 6 (getting a number from 1 to 6)
The number of outcomes in flipping a coin=2 (head or tail)
Hence, total 12 outcomes are possible which are:
(1,H) (2,H) (3,H) (4,H) (5,H) (6,H)
(1,T) (2,T) (3,T) (4,T) (5,T) (6,T)
3^2•3^n simplifies to 3^20 what is the value of the exponent n?
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[tex]3^2 \times 3^n = 3^20 [/tex]
Solving for n.
Divide both sides by 3²
[tex] \frac{3^2 \times 3^n}{3^2} = \frac{3^{20}}{3^2} [/tex]
Simplify
[tex]3^n= 3^{20-2} \\ 3^n=3^{18} \\[/tex]
[tex]if \ a^{f(x)}=a^{g(x)} , \ then \ f(x)=g(x)[/tex]
So, n=18
Answer: n=18
6 Bands were going to play at a concert. How many ways can the concert manager send them on stage?
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there are two ways to resolve this task:
1. the 1st in this sequence is for 6 bands, the 2d in this sequence is for 5 rest bands, the 3d in this sequence is for 4 rest bands, the 4th in this sequence is for rest 3 bands, the 5th in this sequence is for rest 2 bands and the 6th in this sequence is for the last 1 band. Using the logical rule 'AND': A=6*5*4*3*2*1=720.
2. According to arrangement rules it is the formula: A=n!, where n - number of bands.
A=6!=720.
answer: 720.
Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation r(t) = <1+6t,−1+7t,7−6t> parametric equations (x(t), y(t), z(t)) =
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- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t
Explanation:
To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,
v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)
The vector equation of the line is given by
[tex]r(t) = v_0 + tv[/tex]
Where
[tex]v_0[/tex] = a point in the line (we choose point p(1,-1,7))
So, the equation of the line joining p and q is given by
[tex]r(t) = v_0 + tv \\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle \\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle \\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }[/tex]
In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.
Since the vector equation is given by
[tex]r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle[/tex]
The parametric equations of the line are given by:
[tex]x(t) = 1 + 6t \\y(t) = 1 + 7t \\z(t) = 7 - 6t[/tex]
The vector equation for the line segment joining the points p(1, -1, 7) and q(7, 6, 1) is r(t) = <1+6t, -1+7t, 7-6t> and the corresponding parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.
Explanation:To find the vector and parametric equations for the line segment joining two points p(1, -1, 7) and q(7, 6, 1), we first need to understand that the vector equation for a line segment in space is given by r(t) = p + t (q - p), where 0 ≤ t ≤ 1, and p and q are the coordinates of the points. The parametric equations are obtained by expressing the x, y, and z coordinates of r(t) as individual functions of t.
Substituting the given points into the vector equation we get: r(t) = <1+6t, -1+7t, 7-6t>. Then, the corresponding parametric equations will be x(t) = 1 + 6t, y(t) = -1 + 7t, and z(t) = 7 - 6t.
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can someone please help me with this equation? thank you.
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.. x +2y = 3 . . . . . . . . divide the given equation by 3
Now, the perpendicular line is easily written as
.. 2(x -(-4)) -(y -2) = 0 . . . . . swap x, y coefficients, negate one. Translate to the given point
Simplifying, we have
.. 2x -y +10 = 0
Solving for y gives
.. y = 2x +10 . . . . . . . . . . . . corresponds to selection B
Rob cuts a 15-foot wire into 8 equal pieces. about how long is each piece?
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15/8 = 1.875
Each piece is 1.875 foot long
hope this helps
I hope this helped! :-)
and are similar. Find the value of x. A. 5 B. 15 C. 60 D. 240
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Alicia buys a 5 pound bag of rocks for fish tank. She uses 1 1/8 pounds for a small fish bowl. How much is left
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Here is your answer:
The proper answer to this question is "4".
Here is how:
First convert the mix number into a fraction:
1 1/8=9/8
5*8=40
1*8=8
-
9*1=9
8*1=8
40-8=32
32/8=4
8/8=1
Which means your answer is 4/1 or 4!
If you need anymore help feel free to ask me!
Hope this helps!
Why do clouds tend to form around 3:00 pm and 6:00 am
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how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% compounded quarterly
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- Simple interest formula: [tex]A=P(1+rt)[/tex]
where
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex], so lets replace those values in our simple interest formula to find [tex]A[/tex]:
[tex]A=5000(1+(0.04)(5))[/tex]
[tex]A=5000(1.2)[/tex]
[tex]A=6000[/tex]
Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
where
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex]. Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded [tex] \frac{12months}{4months} =3[/tex] times per year, so [tex]n=3[/tex]. Now that we have all the vales, lets replace them in our formula:
[tex]A=5000(1+ \frac{0.04}{3} )^{(3)(5)} [/tex]
[tex]A=5000(1+ \frac{0.04}{3} )^{15} [/tex]
[tex]A=6098.95[/tex]
now that we know the final amounts of our investments, lets find how much difference is between them:
[tex]6098.95-6000=98.95[/tex]
We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.
find the product 3012 and 4
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The prism is completely filled with 1750 cubes that have edge length of 1/5 feet. What is the volume of the prism,
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the volume one cube=(1/5)*(1/5)*(1/5)=(1/125) ft³
the volume of prism=1750*(1/125)=14 ft³
the answer is 14 ft³
At noon, ship a is 60 km west of ship
b. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4:00 pm?
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base of our triangle if drawn is 60 km
to find dD/dt when t=4 hours we shall have:
(A+B)²+60²=D²
d/dt[(A+B)²+60²]=d/dt(D²)
[d(A+B)]/dt*2(A+B)(2)=dD/dt*2D
B=5km/h*4hr=20km
A=15km/hr*4=60km
20²+60²=D²
D=√4000
(15+5)*(2)*80*(2)=2*√4000*dD/dt
dD/dt=6400/√4000=101.192 km/hr
The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.
Therefore, from the below triangle, we have
[tex]\frac{dx}{dt} = 20 \text{ km/hr}[/tex]
Let the distance between the ships is y. On applying Pythagorous theorem, we have
[tex]y^2=x^2+60^2\\ \text{On differentiating, we get}\\ 2y\frac{dy}{dt} =2x\frac{dx}{dt}\\\frac{dy}{dt}= \frac{x}{y} \frac{dx}{dt}[/tex]
On substituting the value of y as [tex]y=\sqrt{60^2+x^2}[/tex]
[tex]\frac{dy}{dt} =\frac{x}{\sqrt{60^2+x^2}} \frac{dx}{dt}[/tex]
Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have
[tex]x=4 \times \frac{dx}{dt} \\ x= 4 \times 20 \\x=80[/tex]
On substituting the value in above, we get
[tex]\frac{dy}{dt} =\frac{80}{\sqrt{60^2+80^2}} (20[/tex]
[tex]\frac{dy}{dt} = 16.0 \text{ km/hr}[/tex]
Therefore, the distance between the ships changing at a rate of 16 km/hr at 4:00 pm
EXPERTS/ACE/GENIUSES
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A zoo has three panda bears and five giraffes. What is the ratio of panda bears to giraffes at that zoo?
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This is a ratio:
x:y
The ratio asks for panda bears to giraffes.
panda bears= 3
giraffes= 5
3:5 <== the ratio
I hope this helps!
~kaikers
The answer is 3:5
Hope this helps!
Always remember, you are a Work Of Art!
- Nicole <3 :)
A slice is made perpendicular to the base of a right rectangular prism as shown.
What is the area of the resulting two-dimensional cross section?
Drag and drop the answer into the box.
mm²
48
28
84
144
16
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Answer:
The correct option is 1. The area of cross section area is 48 mm².
Step-by-step explanation:
From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.
The area of a rectangle is the product of its dimensions.
[tex]A=l\times w[/tex]
Where, l is length of the rectangle and w is width of the rectangle.
The area of cross section is
[tex]A=4\times 12[/tex]
[tex]A=48[/tex]
Therefore the area of cross section area is 48 mm². Option 1 is correct.
What is 3^2/3 equal to? A.3√9 B.2√9 C.3√27 D.2√27
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[tex] 3^{\frac{2}{3}} = \sqrt[3] {3^2} = \sqrt[3] {9} [/tex]
The region r is bounded by the parabola y = x2 and the line y = 4. set up definite integrals to find the moment mx of r about the x-axis and the area a of the region r. then find (x, y )
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Volume is 256π/5, area is 32/3.
Details are in the attachment.
P.S. intersection points are (-2;4) and (2;4).
simplify the complex fraction
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the final answer is (y+z)/(y-z)
Shelly has a photo that is 7 1/3 inches tall. she wants to shrink it down to fit in a picture frame that is only 5 1/3 inches tall. the photo shop can only reduce photos by certin fractions. they can reduce it to 2/3 the original size, 3/4 the original size, or 5/9 the original size. which reduction should she use so the picture fills as much of the frame as possible, without being too large?
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the photo is 7 1/3 inches tall-----> 7 1/3=(7*3+1)/3=22/3 in ----- > (7.33 in)
the picture frame is 5 1/3 inches tall--> 5 1/3=(5*3+1)/3=16/3 in----> (5.33 in)
a) case A reduce 2/3 the original size------> (22/3)*(2/3)=44/9 in-----> (4.89 in)
b) case B reduce 3/4 the original size---> (22/3)*(3/4)=66/12 in-----> (5.5 in)
this is not solution because 66/12 (5.5 ) in >16/3 (5.33) in ( picture frame)
c) case C reduce 5/9 the original size---> (22/3)*(5/9)=110/27 in-----> (4.07 in)
the answer is the case A reduce 2/3 the original size----> 44/9 in (4.89 in)
Can somebody please help me out ?
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A = (1/2) * b * h
Where
b: base
h: height.
For the lower triangle we have:
A = (1/2) * (10) * (root ((8) ^ 2- (5) ^ 2))
A = 31 in ^ 2
We add this area with the area of the upper triangle:
31 in ^ 2 + 17 in ^ 2 = 48 in ^ 2
Answer:
The quadrilateral area will be:
48 in ^ 2 (option 3)
plz help ill give u branlist
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so...
48 + 7(x + 1) = 90
7(x + 1) = 42
x + 1 = 6
x = 5