When cooked, 85% of the kernels in a bag of microwave popcorn popped. There were 120 kernels of popcorn in the bag.How many kernels popped?

A.

102

B.

105

C.

141

D.

205

Answers

Answer 1

Answer: $p\%=(p)/(100)\n\n85\%=(85)/(100)=(85:5)/(100:5)=(17)/(20)\n\n85\%\ of\ 120=(17)/(20)\cdot120=17\cdot6=\boxed{102}\leftarrow answer\ \boxed{\boxed{A}}$

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Based only on the given information, it is guaranteed that AB is perpendicular to CD. True or false

Answers

Answer:

true

Step-by-step explanation:

because CD divided AB into equal halves, so they are of course perpendicular.

Answer:

Step-by-step explanation:

This is definitely true. AC is congruent to BD, and by the Isosceles Triangle Theorem, if this congruency is true, then the angles across from these congruent sides are also congruent. This means that angle ACD is congruent to angle BCD. That makes CD a bisector of angle ACB; it also makes CD a bisector of side AB. The definition of a perpendicular bisector is that the segment splits its angle in half (and it does) and that it splits the side it goes through in half (which it does). This makes CD, in a nutshell, the perpendicular bisector of AB (which also means that CD is perpendicular to AB).

Use multiplication to find three ratios equivalent to 8 : 12

Answers

16:24
24:36
32:48

Multiplied by 2, 3, and 4, respectively

Final answer:

The equivalent ratios to 8:12 are 16:24, 24:36, and 32:48. We can find these by multiplying or dividing every term in the ratio by the same positive number.

Explanation:

To find the equivalent ratios for 8:12, we can multiply both the numbers in the ratio by the same value. Let's do this for three different values:

Multiplying by two will give us 16:24.
Multiplying by three will give us 24:36.
Multiplying by four will give us 32:48.

Therefore, the equivalent ratios to 8:12 (or in reduced form, 2:3) are 16:24 (or 2:3), 24:36 (or 2:3), and 32:48 (or 2:3). The key here is to multiply (or divide) every term in the ratio by the same positive number.

Learn more about Equivalent Ratios here:

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Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y?

Answers

Answer with explanation:

Cost of Peaches per pound = $ 2

If x, is the total number of pound of peaches bought = x

→Total cost of pound of peaches bought = Cost of Peaches per pound × Total number of pound of peaches bought

It is given that,y is the total cost of peaches.

→→y=$ 2 × x

→→y=2 x→→Relationship between value of x and y

Total Cost of peaches=price of 1 pound x number of pounds bought
y=2x

The Nelson family drank of a gallon of orange juice on Saturday morning and of a gallon of orange juice on Sunday morning. How much orange juice did they drink in All

Answers

Answer:

2 gallons of orange juice

Step-by-step explanation:

Solve 2cos^2x+5cosx+2=0

Answers

$2cos^2x+5cosx+2=0\n x\in<-1;1>\n \Delta=b^2-4ac\n \Delta=9\n √(\Delta)=3\n cosx=1\n or\n cosx=-6\n -6\notin<-1;1>\n$

Then using trygonometric table or a graph we read that:
$cosx=1\Leftrightarrow(x)=0$

Period of cosinus function = 2π
So the last answer is $x=0+2k\pi\n$