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miv72 [106K]
2 years ago
8

A recipe requires 13 ounces of sugar and 18 ounces of flour. If only 10 ounces of sugar are used, how much flour, to the nearest

ounce, should be used? (A) 13 (B) 23 (C) 24 (D) 14 (E) 15
Mathematics
2 answers:
FrozenT [24]2 years ago
8 0
The answer is letter B
postnew [5]2 years ago
8 0
We can list the amount of sugar and flour required into ratios then solve the questions by fractions. 

From the given information, the ratio of the amount of sugar to the amount of flour needed in the recipe should be 13:18.
This ratio can also be written as 13/18.

In the question, the ratio should not be changed, just that the amount of each turns different. 

So, let y be the amount of flour needed. 
13/18 = 10/y
Use cross method to solve this,
18 x 10 = 13y
180 = 13y
y = 180/13
y = <span>13.8461538462
the answer should be </span><span>13.8461538462 ounces, 
</span>and round to the nearest ounce, 
the answer should be D, 14.
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The graph of a sinusoidal function has a maximum point at (0,5)(0,5)left parenthesis, 0, comma, 5, right parenthesis and then ha
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Answer:

sinusoidal functions have the standard form of Asin(Bx - C) + D

Where A is the amplitude, 2pi/B gives us our period, C gives us our horizontal shifts in the opposite direction of the sign (because it's inside the parenthesis), and D gives us our vertical shifts in the same direction as the sign of D (positive or negative).

The easiest part is assigning the amplitude which is 3 as stated in the problem. This means that all of the max/mins of the graph will be multiplied by a factor of 3. However, this could be a positive or negative 3 depending on other info in the problem. We'll come back to this in a second.

We know 2pi/B = 8 in our problem. Solving for B gives us B = pi/4.

Now we need to find the corresponding maximum and minimums for a sin/cos function with a period of 8 by taking x values 0, pi/2, pi, 3pi/2, and 2pi (these are all values where normal sin/cos functions are either at their max/min or zero) and then divide each by pi/4. This will give us our new max/mins for a function with period 8. These values are 0, 2, 4, 6, and 8.

Since 2 is a minimum, then we know that there are no horizontal shifts. So C = o

Now we need to figure out if this is a sin or cos graph. A normal cos graph has a value of 0 at x = pi/2 which corresponds x = 2 in our problem. Your problem says that x = 2 will give us a minimum value so this tells us that our function must be a sin graph, not a cos graph. However, a sin graph has a maximum at 2 (which is pi/2 in a normal sin graph) while your problem calls for a minimum. This means that the amplitude we found earlier of 3 must actually be a -3 (I told you we'd get back to this!). The negative sign flips all of the maximums to minimums and vice versa of the sinusoidal graph.

Ok, let's put together what we know so far. A = -3, B = pi/4, and C = 0. So f(x) = -3sin((pi/4)x) + d

......But what about D?

Well, your problem says that one minimum of the graph is (2,1). In a graph without vertical shifts, we would expect the minimum to be at (2,-3). The difference between -3 and 1 is 4. This means in order to get from -3 to 1 we have to shift upwards of 4 units. In other words, D = 4.

Answer: -3sin((pi/4)x) + 4

Step-by-step explanation:

4 0
2 years ago
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Which two equations would be most appropriately solved by using the zero product property? Select each correct answer.
LekaFEV [45]
The zero product property tells us that if the product of two or more factors is zero, then each one of these factors CAN be zero.

For more context let's look at the first equation in the problem that we can apply this to: (x-3)(x+4)=0

Through zero property we know that the factor (x-3) can be equal to zero as well as (x+4). This is because, even if only one of them is zero, the product will immediately be zero.

The zero product property is best applied to factorable quadratic equations in this case.

Another factorable equation would be 2x^{2}+6x=0 since we can factor out 2x and end up with 2x(x+3)=0. Now we'll end up with two factors, 2x and (x+3), which we can apply the zero product property to.

The rest of the options are not factorable thus the zero product property won't apply to them.
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2 years ago
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A father lifts a toddler 1.5 m up in the air. The child gains 187.5 J of energy in her gravitational potential energy store as a
bearhunter [10]

The mass of the toddler is 12.5 kg.

Step-by-step explanation:

The equation for gravitational potential energy is Ep=mgh where;

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Given that ; h= 1.5m, Ep=187.5J , g=10 N/kg then finding m;

Ep=mgh

187.5=m*10*1.5

187.5=15m

187.5/15 =15m/15

12.5 kg=m

Learn More

  • Gravitation potential energy : brainly.com/question/939365

Keyword : Mass, gravitational potential energy

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Circle 1 has center (−4, −7) and a radius of 12 cm. Circle 2 has center (3, 4) and a radius of 15 cm.
CaHeK987 [17]
<h3>Answer with explanation:</h3>

It is given that:

Circle 1 has center (−4, −7) and a radius of 12 cm.

Circle 2 has center (3, 4) and a radius of 15 cm.

Two circles are said to be similar if by some translation and dilation it could be placed over the other to form the same circle.

The circles are similar because the transformation rule ( x,y ) → (x+7,y+11) can be applied to Circle 1 and then dilate it using a scale factor of 5/4

( Since, as the center of circle 1 is (-4,-7)

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(-4+7,-7+11) → (3,4)

( Since, the radius of circle 1 is 12 and that of circle 2 is 15 cm.

so, let the scale factor be k .

that means :

12\times k=15\\\\k=\dfrac{15}{12}\\\\k=\dfrac{5}{4}  )

7 0
2 years ago
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Juli2301 [7.4K]
A = (1/2) * b * h
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A = (1/2) * 10 * 2
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7 0
2 years ago
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