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Explanation:
We have 12 oz of 50% chocolate syrup, which means we have 0.50*12 = 6 oz of pure chocolate from this bottle. We add on x more ounces of pure chocolate from the second batch. So we have 6+x ounces of pure chocolate.
This is out of 12+x ounces of mixed syrup (chocolate + other stuff) overall.
The fraction (6+x)/(12+x) represents the proportion of pure chocolate to the mixed syrup batch. Set this equal to 0.75 and solve for x.
(6+x)/(12+x) = 0.75
6+x = 0.75(12+x)
6+x = 0.75(12)+0.75(x)
6+x = 9+0.75x
x-0.75x = 9-6
0.25x = 3
x = 3/0.25
x = 12
So we must add 12 ounces of pure chocolate to the mix
--------------------
We can think of this problem in terms of colored blocks.
Let's say a brown block represents a unit of pure chocolate, while a blue block is something else (say sugar or whatever other ingredients).
Currently we have 6 brown blocks (the 6 oz of pure chocolate) out of 12 blocks overall (6 brown + 6 blue).
If we add on 12 more brown blocks, then we get 6+12 = 18 brown blocks overall out of 12+12 = 24 blocks (brown+blue).
Then notice how 18/24 = 0.75 = 75% to represent the fact that 75% of the blocks are brown. So 75% of the syrup is pure chocolate.
This thought experiment is one way to help verify the answer.
Answer:
12
Step-by-step explanation:
.5 * 12 = 6
(6 + x) /( 12 + x)
[tex]\frac{x+6}{x+12} = .75[/tex]
x + 6 = .75(x+12)
x = 12
what is the the value of ∣9∣
Hey there! I'm happy to help!
This symbol is an absolute value symbol. It means that we are looking for that number's distance from 0. There is no such thing as a negative distance; the distances are all positive, so both ∣9∣ and ∣-9∣ have a value of 9.
Have a wonderful day and keep on learning! :D
given that y/√5 = √20 ×10^-3×10^5x. and lgy- mx = c for x>0 and y>0, find the values of m and c
Answer:
m = 5 and c = -2
Step-by-step explanation:
[tex]let \: y = \sqrt{20} \times {10}^{ - 3} \times {10}^{5x} \\ be \: equation \: 1[/tex]
Now
[tex]y = \sqrt{5} ( \sqrt{20} \times {10}^{ - 3} \times {10}^{5x} ) \\ y = \sqrt{100} \times {10}^{ - 3} \times {10}^{5x} \\ y = 10 \times {10}^{ - 3} \times {10}^{5x} [/tex]
[tex]using \: rules \: of \: indices \: we \: get \\ y = {10}^{1 - 3 + 5x} \\ y = {10}^{ - 2 + 5x} \\ [/tex]
[tex]now \: take \: log \: of \: both \: sides \: and \: use \: laws \: of \: logarithm \\ we \: get \\ [/tex]
[tex] log(y) = log( {10}^{ - 2 + 5x} ) \\ log(y) = ( - 2 + 5x) log(10) \\ log(y) = - 2 + 5x \\ log(y) - 5x = - 2 \\ \\ comparing \: this \: to \: \\ log(y) - mx = c \\ \\ we \: get \: m \: = 5 \: and \: c = - 2[/tex]
Which graph corresponds to the function f(x) = x2 + 4x – 1?
Answer:
1
Step-by-step explanation:
I graphed it to check. x^2+4x-1 has a vertex of (-2,-5).
What is the value of a? Round to the nearest tenth.
Answer:
50 percent?
Step-by-step explanation:
Let's make some smores! Chocolate bars come in packs of 8 and graham crackers come in packs of 12. What is the smallest number of chocolate bars and graham crackers we would need to buy so we don't have any left over?
Answer:
3 chocolate bars and 2 graham crackers
Step-by-step explanation:
8 times 3 equals 24
12 times 2 equals 24
Amanda rented a bike from Ted's Bikes.
It costs $10 for the helmet plus $4.25 per hour.
If Amanda paid about $33.38, how many hours did she rent the bike?
a) Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
≈ 5.51 hours
Equation: 4.25h + 10
The number of hours Amanda rented the bike is 5.5 hours.
The equation used to solve this problem is 33.38 = 10 + 4.25h.
The rent cost for the helmet is $10.
The rent cost for the bike per hour is $4.25.
We need to find the number of hours Amanda rented the bike as she paid $33.38 in total.
We also have to make an equation that would solve this problem.
Consider h = number of hours Amanda rented the bike.
The cost for renting the helmet = $10.
And rent cost for the bike per hour = $4.25.
Amanda's total cost = Helmet rent cost + bike rent cost
Since we do not know the number of hours the bike was rented we will denote bike rent cost = $4.25 x h
We have,
$33.38 = $10 + $4.25 x h
33.38 = 10 + 4.25 x h
33.38 - 10 = 4.25 x h
23.38 = 4.25 x h
h = 23.38 / 4.25
h = 5.5011
Rounding to the nearest tenths we get,
h = 5.5 hours
The number of hours Amanda rented the bike is 5.5 hours.
The equation used to solve this problem is 33.38 = 10 + 4.25h.
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Geometry, please answer question ASAP
9514 1404 393
Answer:
D. 180°
Step-by-step explanation:
The letter S is symmetrical about its center. The letter looks the same when it is rotated 180° about its center.
A square has area x cm^2, and perimeter of x cm . What is the value of x?
Let the perimeter be 100cm
Then value of x = 100/4
x = 25cm
Answered by Gauthmath must click thanks and mark brainliest
Find the common ratio of the geometric sequence: 2/3,−2, 6,…
A. −1/3
B. -3
C. -1
D. 3
Answer:
B. -3
Step-by-step explanation:
Find the common ratio by dividing a term in the sequence by the one before it:
6/-2
= -3
So, the common ratio is -3.
The correct answer is B. -3
Answer:
B
Step-by-step explanation:
The geometric ratio is a3/a2=a2/a1=-2/(2/3)=-3.
Can you help me calculate the angles from this kite in the attachment?
AY =, XZ =,
Answer:
AY=8, XZ=20
Step-by-step explanation:
WY=WA+AY, plug in values: 14=6+AY, subtract 6 from both sides: 8=AY, AY=8cm
ZA=10cm and WY bisects XZ at A, so XA=ZA and XZ = XA+ZA = 2ZA =2*10 = 20 cm
There are 4512 marbles which will be divided equally among 48 students how many marbles will each student get
Answer:
94 marbles
Step-by-step explanation:
4512/48 = 94
A charity gala is held in a hotel ballroom each year. The cost is $150 for the ballroom and an additional $22.50 for each attendee. Write an equation showing how the cost of the gala, y, depends on the number of attendees, x. Do not include dollar signs in the equation. y=
Given:
Fixed cost = $150
Additional cost = $22.50
To find:
The equation that showing the cost of the gala depends on the number of attendees.
Solution:
Let x be the number of attendees and y be the cost of the gala.
Total cost = Fixed cost +Variable cost
We have,
Fixed cost = $150
Variable cost = Additional cost × Number of attendees
= [tex]22.50\times x[/tex]
= [tex]22.50x[/tex]
Total cost of gala is:
[tex]y=150+22.50x[/tex]
Therefore, the required equation is [tex]y=150+22.50x[/tex].
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 4.5 ft long with a diameter of 1.4 ft. Suppose oil is drained at a rate of
1.7 ft per minute. If the tank starts completely full, how many minutes will it take to empty the tank?
Hey there! I'm happy to help!
First, let's find the volume of the cylindrical tank.
To find the volume of a cylinder, take the area of the circle base and multiply it by the height of the cylinder.
To find the area of a circle, you square the radius and multiply it by pi (we will use 3.14).
The diameter is always twice the radius, so we divide by two to find the radius.
1.4/2=0.7
We square this.
0.7²=0.49
And we multiply by 3.14.
0.49×3.14=1.5386
Now that we have the area of the circle, we multiply by the height (length in our case since the cylinder is sideways).
1.5386×4.5=6.9237
Now, we see that we will be losing 1.7 feet every minute. To see how many times 1.7 feet goes into our cylinder, we just divide!
6.9237÷1.7= 4.07276470588
So we see that it will take just over 4 minutes for the tank to empty.
Have a wonderful day and keep on learning! :D
what is the sum of 1+2+.....+50?
Answer:
sum is 1275
Step-by-step explanation:
[tex]sum = \frac{n}{2} [2a + (n - 1)d] \\ \\ sum = \frac{50}{2} [(2 \times 1) + (50 - 1) \times 1] \\ \\ sum = 25(51) \\ sum = 1275[/tex]
Sheldon is baking 2-inch cookies. He has 3 trays that are the same size. On one tray, he makes 5 rows with 4 cookies in each row. He cannot fit any more cookies on the tray. He fills the second tray completely and only part of the third tray. How many cookies could Sheldon have made?
Answer: Sheldon has made 50 cookies
Step-by-step explanation: for the first test because there are 5 rows and 4 cookies on each row you would multiply 4 times 5. That equals 20. The first tray has twenty and all trays are the same size so if the second one is completely full then it also has twenty. The third one is only half way full meaning twenty divided by two equals ten. Ten is the amount of cookies on the third tray. If you add that all together that is 20+20+10=50
The number of cookies made by Sheldon will be equal to 50.
What is an arithmetic operation?
The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
For the first test, you would multiply 4 by 5 because there are 5 rows and 4 cookies on each row. 20 is the result.
Since all trays are the same size and the first tray has twenty, if the second tray is totally filled, it will also have twenty.
Twenty divided by two equals 10 because the third one is only half full.
There are ten cookies on the third tray.
The total is,
20+20+10 = 50.
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Simplify -23.
wjfnwkfnfffkmwnkfm
Answer:
-23 = - 23
Step-by-step explanation:
there you go...hopefully it makes sense :)
Which of the following steps were applied to ABC obtain AA'B'C?
12
8
B
6
A
-6
-2
4
6
10
A. Shifted 4 units left and 3 units down
B. Shifted 4 units left and 2 units down
C. Shifted 3 units left and 3 units down
D. Shifted 3 units left and 2 units down
Will give brainliest pls help!!!
Answer: B
Step-by-step explanation:
The transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, a triangle ABC has undergone a transformation to form A'B'C' we need to identify the steps of transformation
So, considering the point B and B', we see, that, x-coordinate of B is at 5 and that of B' is at 1, that mean there is a shift of 4 units left,
Now, consider the y-coordinate, we see, that B is at 9 and B' is at 7 that gives a downward shifting of 2 units.
Hence, the transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.
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In a triangle, a segment connecting the midpoints of two sides of the triangle is
called:
Answer:
A.) Midsegment
Step-by-step explanation:
Trust me bro
i need help again.lol
Answer:
[tex]13\ units[/tex]
Step-by-step explanation:
One is asked to find the distance between two points on a coordinate plane. The easiest way to do so is to use the distance formula, this formula is the following:
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2[/tex]
Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the points which one needs to find the distance between. In this case, these points are as follows:
[tex]k\ (-3,5)[/tex]
[tex]j\ (-8, -7)[/tex]
Substitute these points into the formula and solve for the distance between these points,
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2[/tex]
[tex]D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2[/tex]
Simplify,
[tex]D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2[/tex]
[tex]D=\sqrt{(-3+8)^2+(5+7)^2[/tex]
[tex]D=\sqrt{(5)^2+(12)^2[/tex]
[tex]D=\sqrt{25+144}[/tex]
[tex]D=\sqrt{169}[/tex]
[tex]D=13[/tex]
Help me please I need it
Answer:
Equation B.
Step-by-step explanation:
Subtract 4 from both sides in the equation 11r+4=55. You will see that it is equivalent to equation B.
helphelphelphelphelphelp
Answer:
see image
Step-by-step explanation:
Find an equation of the line having the given slope and containing the given point. m= 4/5,(1,-8).
The equation of the line is y=‽
Answer:
y=4x/5-44/5
Step-by-step explanation:
First, we know that we can write any linear equation in the form y=ax+b, where a is the slope. This means that y=(4/5)x+b. Now, it has the point (1, -8). Plugging in x=1 and y=-8 gives us -8=(4/5)+b, which means that b=-44/5. Plugging this in gives us y=(4/5)x-44/5. Hope it helped!
Which transformation can NOT be used to prove that ABC is congruent to
DEF?
O A. dilation
B. rotation
C. reflection
ОО
D. translation
Answer
A. dilation
Step-by-step explanation:
if we dilate the diagram it will be enlargedd so cannot be proved as congruent
The transformation that can not be used to prove that ABC is congruent will be dilation. The correct option is A.
What is transformation?Transformation a process by which one figure, expression, or function is converted into another one of similar value. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
When the triangle is rotated its original shape and size will not change it only changes its position then the triangle will remain congruent.
When the triangle is reflected it means that its mirror image is formed then the size and shape will again remain unchanged the triangle will be congruent.
When the triangle is translated then also its size will not change only it changes its position. The triangle will be congruent.
When the triangle is dilated it means that the shape of the triangle is increased or decreased then the triangle will not be congruent when it is dilated.
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using trig find the missing angle
Answer:
sh ma at me Ej as he be as h
Step-by-step explanation:
c my zzz bb
dbdgj dd d
sin(24) = x/16
x = 6.51
After two people answer one of my questions, how do I give brainlyist to one of them?
do what you want ok and choose
Find the missing value.
Hint: Use the number line to find the missing value.
+5 = -2
开
-15
5
0
-5
10
15
-10
Stuck? Review related articles/videos or use a hint.
Answer:
-7
Step-by-step explanation:
x + 5 = -2
I hope this helped! :)Find the values of the unknown angles marked with letters. 50 points!!!!!!!
a ?
b ?
c ?
d ?
Answer:
a = 115°, alternate interior angles are congruentb = 70°, same as abovec = 180° - 115° = 65°, angles forming a straight angle are supplementaryd = 180° - 70° = 110°, same as aboveC:-
[tex]\\ \sf\longmapsto c+115=180[/tex]
[tex]\\ \sf\longmapsto c=180-115[/tex]
[tex]\\ \sf\longmapsto c=65°[/tex]
D:-
[tex]\\ \sf\longmapsto d+70=180[/tex]
[tex]\\ \sf\longmapsto d=180-70[/tex]
[tex]\\ \sf\longmapsto d=110°[/tex]
The temperature in Miami, Florida Is 22 degrees warmer than three times the temperature in Bangor, Maine. The temperature in Miami is 82 degrees. Write an equation to determine the temperature in Bangor.
3x + 82 = 22
3x + 22 = 82
3x - 22 = 82
3x - 82 = 22
Answer:
the answer is c I believe
What is the answer of 603 x 42 , this question is multiply , it’s of my brother who is just in g-4 …… pls help if you know but teach by process
Answer:
25326Step-by-step explanation:
please refer to the picture above
[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
will marks brainlest helppp
Answer:
The value is -10
Step-by-step explanation:
