Step-by-step explanation:
the ratio of boys and girls is equal to 4:5
let the number of boys be x
and the number of girls be y
so form 1st statement
x:y=4:5
now 2nd statements
x:y-100=6:7
Therefore solving equations 1 and 2
x=1200
y=1500
Show that 4^(x+2)+4^(x+1)+4^x is divisible by 7 for all positive integers of x.
Answer:
Below.
Step-by-step explanation:
4^(x+2)+4^(x+1)+4^x
= 4^x*4^2 + 4^x*4 + 4^4
= 4^x(16 + 4 + 1)
= 21*4^x.
As 21 is divisible by 7, 21*4^x is also divisible by 7 for all positive integers of x.
Thus the original expression must be also divisible by 7 for all positive integers of x.
I need help with this I don't understand
Answer:
Sin ? = 4/7
? = arcSin (4/7)
? = 35° (rounded to the nearest degree)
So the answer is 35°
Answered by GAUTHMATH
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Total amount she wants to raise = $3200
Amount she'll get for each kilometer = $35
So, number of kilometers she need to run
= Total amount she wants to raise/Amount she'll get for each kilometer
= $3200/$35
= 91.42....
Since her sponser is will donate only for whole kilometers she'll have to run 92 km.
what is the square root of 25
the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!
Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
the second option : w should be 25 units
Step-by-step explanation:
the area of the rectangle is length×width = L×W
the perimeter of a rectangle = 2L + 2W
now, we know that the perimeter is 100 units.
and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.
in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?
now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.
W = 0 would render the whole rectangle to a flat line with L = 50 because of
100 = 2L + 2W = 2L + 0 = 2L
L = 50
and A = L×W = 50×0 = 0
an area of 0 is for sure not the largest possible area.
w = 50 would cause L = 0
100 = 2L + 2W = 2L + 2×50 = 2L + 100
0 = 2L
L = 0
and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.
so, the only remaining useful answer is W = 25
100 = 2L + 2W = 2L + 2×25 = 2L + 50
50 = 2L
L = 25
A = L×W = 25×25 = 625 units²
and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.
Can someone help me with this math homework please!
Answer:
The answers are options A and C.
They are (-2,0) and (0,0).
Step-by-step explanation:
x-intercept
(-2,0) and (0,0)
In a recent storm, an 18-foot utility pole broke and fell leaving a 5-foot tall portion upright. How far is the top of the pole from the base of the pole?
Answer: [tex]12\ ft[/tex]
Step-by-step explanation:
Given
Total height of utility pole is 18 ft
After breakage, only 5 foot tall portion is standing
The fallen part is [tex]18-5=13\ ft[/tex] in length
From the figure, apply the Pythagoras theorem
[tex]\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft[/tex]
Thus, the fallen part is [tex]12\ ft[/tex] away from the base of the pole.
American airlines requires that total outside dimensions (length+width+height) of a checked bag not exceed 62 inches.Suppose you want to check a bag whose height is same as its width.What is the biggest volumn bag of this shape that you can check on an american flight
Answer:
The maximum volume is 35316.4 in^3.
Step-by-step explanation:
Length + width + height is less than equal to 62 inches
Height = width = W
Let the length is L .
[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]
So, the maximum volume is
[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]
Dilate the figure by the scale factor. Then enter
the new coordinates.
A(1,3)
B(4,2)
K=3
A'([?],[ ]
B'([ ],[])
c'[[)
C(1,-3)
Answer:
i think (4,2)
Step-by-step explanation:
differentiate with product rule
Answer:
[tex]{ \boxed{ \bf{ \frac{dy}{dx} = v \frac{du}{dx} + u \frac{dv}{dx} }}}[/tex]
u = ( x + 1 )
v = ( 2x + 5 )²
[tex]{ \tt{ \frac{dy}{dx} = {(2x + 5) {}^{4} .(1) + (x + 1).(2)(2x + 5) {}^{3} } }} \\ = { \tt{ {(2x + 5)}^{3} ((2x + 5) +(2x + 2) }} \\ = { \tt{ \frac{dy}{dx} = {(2x + 5)}^{3}(4x + 7) }}[/tex]
Two factory plants are making TV panels. Yesterday, Plant A produced 8000 panels. Four percent of the panels from Plant A and 1% of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 2%?
Answer:
The answer is "16,000"
Step-by-step explanation:
In this question the amounts of panels created by B the x.
[tex]\therefore[/tex]
Calculating the amounts of defective panels from B:
[tex]\to \frac{1}{100} \times x = 0.01x[/tex]
Calculating the amounts of defective panels from A:
[tex]\to \frac{4}{100} \times 8000 = 320[/tex]
Calculating the total defective panels are :
[tex]\to 320+ 0.01x[/tex]
Calculating the total panels manufactured:
[tex]\to 8000 + x[/tex]
when the overall percentage of the defective panels is [tex]2\%[/tex]
[tex]\to \frac{(320 + 0.01x)}{(8000 + x)} = 0.02\\\\\to (320 + 0.01x) = 0.02 (8000 + x)\\\\\to 320 + 0.01x = 160 + 0.02x\\\\\to 320 -160 = -0.01x + 0.02x\\\to 160 = 0.01x\\\\\to x=\frac{160}{0.01}\\\\\to x=16,000\\\\[/tex]
A boy on top of a building observe that the angle of depression of a goat in horizontal ground is 47.if the goat is 23m away from the foot of the building,how high is the building,correct to the nearest meter? (ignore the height of the boy)
Answer:
Step-by-step explanation:
tan 47° = opposite side /adjacent side
=>1.072 = AB/BC
=>1.072 × BC = AB(height of the building)
=>1.072 × 23 = h ( As assumed height of building is h )
h = 24.656
= 25 metres ( nearest metre )
Find the surface area of the solid given the net
WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!!
Answer:
For 25) it's option C. -1/2
For 26) it's option D. 7π/6, 11π/6
Step-by-step explanation:
If you are finding sin−1 of a positive value, the answer will be between 0 and π/2. Using the unit circle, the angle with a sine of 1/2 in the first quadrant is π/6.
Answer:
-1/2
7π/6, 11π/6
Step-by-step explanation:
First problem:
31π/6 = 31/6 π = 5 1/6 π
A full circle is 2π radians. π radians = 180°
Start at 0 radians (positive x axis), and go 5 half circles counterclockwise.
You end up at π radians, or 180°, or the negative x axis.
Now go π/6 radians more counterclockwise.
You end up at 7π/6 or 210°.
Read the y-coordinate of the point on the unit circle.
Answer: -1/2
Second problem:
Look in the figure of the first problem.
The sine corresponds to the y-coordinate.
Look at the points on the circle, below the x-axis, that have a y-coordinate of -1/2.
They correspond to 7π/6 and 11π/6
Identify the transformations of the graph of f(x) = x3 that produce the graph of the given function
g(x). Then graph g(x) on the same coordinate plane as the graph of f(x) by applying the
transformations to the reference points (-1,-1),(0,0), and (1,1).
Answer:
Step-by-step explanation:
Find questions attached.
Show workings.
Answer:
Solution given:
7.<OYM=15°base angle of isosceles triangle
<OYL=50°base angle of isosceles triangle.
<OYL=<OYM+<MYL
50°=15°+<MYL
<MYL=50°-15°
<MYL=35°
again;
<MOL=35*2=70°central angle is double of a inscribed angle.
18.
Solution given:
<PQR+<PSR=180°sum of opposite angle of a cyclic quadrilateral is supplementary
<PQS+42°+78°=180°
<PQS=180°-120°=60°
<PQS=60°
<SPR=42°inscribed angle on a same arc is equal
:.<QPS=18°+42°=60°
<QSR=18°inscribed angle on a same arc is equal
again.
<PSR=78°
<QSR+<PSQ=78°
18°+<PSQ=78°
<PSQ=78°-18°
<PSQ=60°
In ∆ PQS
<PSQ=60°
<QPS=60°
<PQS=60°
In triangle ∆PQS all the angles are equal.
so it is a equilateral triangle.Which of the following is the equation of a line that passes through the point
(1.4) and is parallel to the x-axis?
A.x=1 B.y=4 C.x=4 D.y=1
Given:
A line passes through the point (1,4) and is parallel to the x-axis.
To find:
The equation of the line.
Solution:
If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.
The point-slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.
The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:
[tex]y-4=0(x-1)[/tex]
[tex]y-4=0[/tex]
[tex]y-4+4=0+4[/tex]
[tex]y=4[/tex]
The required equation is [tex]y=4[/tex].
Therefore, the correct option is B.
can someone answer this
Answer:sadwer
Step-by-step explanation:
please help with math properties I need 5 and 8 :)
Answer:
Step-by-step explanation:
Statements Reasons
1. m∠A = 6x - 10 1. Given
2. m∠B = 2x 2. Given
3. m∠C = 8x - 2 3. Given
4. m∠A + m∠B + m∠C = 180° 4. Triangle sum theorem
5. (6x - 10) + (2x) + (8x - 2) = 180° 5. Substitution
6. 16x - 12 = 180 6. Algebra
7. 6x = 192 7. Addition property of equality
8. x = 12 8. Division property of equality
if we put a marble in 10 ml of water how can we find its volume
please answer
i will mark brainliest
Answer: See below
Step-by-step explanation:
This relates to the usage of water displacement.
Have the 10 ml of water ready in a measuring flask (or any container that has a scale)Put the marble into the waterObserve how much did the water riseSubtract the current water level by the original 10 mlThe final answer would be the volume.------------------------------------------------------------------------
EXTRA (Only for advanced purposes, if you do not understand, it is totally fine)
Refer to the attachment below to finish the question.
Assuming the water levels are integer,
The original water level is 13.33 mlAfter the rock is put in, the water level is raised to 30 mlThen, we do the fourth step which is subtraction
30 - 13.33 = 16.66 mlHope this helps!! :)
Please let me know if you have any quesitons
Simplify this expression.
Can anyone help pls
Answer:
Step-by-step explanation:
First one gram equals 1000 grams, so a 39 kilogram equals 39000 grams. Then, 1000 pillows times 300 equals a 39 kilogram sofa. Is my answer correct?
Answer:
No
Step-by-step explanation:
Kilogram is the unit of weight. Kilogram is the measure of how much matter or the mass an object has in it. Kilogram is the bigger unit of measurement while gram and milligram are the smaller units to measure the weight of any object.
We know,
1 kilogram = 1000 gram x 1
So, 1000 gram is equal to 1 kilogram
That means, 39,000 gram is equal to 39 kilogram.
In the question it is asked whether 1000 pillows times 300 is equal to 39 kilogram sofa or not.
The answer is not correct, because we do not know the weight of the 1000 pillows.
And also, 1000 x 300 will give you 300,000 and not 39 kilogram or 39,000 grams.
There is a bag with 50 popsicles inside. 5 are red, 15 are orange, 12 are blue, 8 are
yellow and 10 are purple. If you were to
grab one popsicle from the bag, what is
the probability that it is red or not orange?
P(red or not orange)
Find the missing segment in the image below
Answer:
If there are two line which is parallel in a triangle the triangle has a ratio
Step-by-step explanation:
So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8
Answer:
Step-by-step explanation:
what is the solution to this equation?
3x+x-13+4-6x=12
A. x= -21/2
B. x= 21/2
C. x= 3/2
D. x= -3/2
Answer:
A.
Step-by-step explanation:
3x + x - 13 + 4 - 6x = 12
we try to combine the elements with the same power of x (including the ones without any x) :
3x + x - 6x
-13 + 4
so, we get
-2x - 9 = 12
-2x = 21
x = -21/2
Answer:
A
Step-by-step explanation:
group the like terms
3x+x-6x-13+4=12
-2x=12+9
divide both sides by -2
-2x/-2=21/-2
x= -21/2
hope it helps
Help Now!!!!
The Base Of A triangle prism
Answer:
Volume=Area × height
=35×7
volume = {245} m³
OAmalOHopeO
Answer:
Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.
7 x 35 = 245 m3 is your answer
You can picture it too:
(sorry my drawing is bad with the marker)
A 90 ° angle is divided into 2 angles. Find the size of the angles. 5x+10 and 6x-41 Not drawn to scale
Answer:
65 and 25
Step-by-step explanation:
90=(5x+10)+(6x-41)
121=11x
11=x
Going back to the angles:
5(11)+10
=55+10
=65 this is the first angle
6(11)-41
=66-41
25 this is the second angle
The probability that Sara wins a raffle is given by the expression n/n+3
Write down an expression, in the form of a combined single fraction, for the probability that Sara does not win.
Answer:
3/(n + 3)
Step-by-step explanation:
The given probability that Sara wins a raffle draw, P = n/(n + 3)
Given that the sum of all probabilities is 1, we get
The probability that Sara does not win, Q = 1 - P
Therefore;
Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)
The probability that Sara does not win, Q = 3/(n + 3)
Ibrahim likes to run a loop around the park near his house that is ⅞ mile long. There is a water fountain ½ way around the loop. Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
Answer:
7/16 mile
Step-by-step explanation:
Distance of the loop = 7/8 mile
Distance of Water fountain = 1/2 of the Distance of the loop
= 1/2 of 7/8
Ibrahim stopped to get a drink of water at the water fountain. How far did Ibrahim run?
= 1/2 of 7/8
= 1/2 * 7/8
= (1 * 7) / (2 * 8)
= 7/16
Ibrahim ran 7/16 mile to drink water at the water fountain around the loop
Subtract the second equation from the first.
Answer:
2y = 8
Step-by-step explanation:
4x+3y = 17
- ( 4x+y = 9)
----------------------
Distribute the minus sign
4x+3y = 17
- 4x -y =- 9
----------------------
0x +2y = 8
Answer:
2y = 8
Step-by-step explanation:
4x+3y=17
-4x-y=9
_______
0+2y=8
2y=8
