Ask question

Ask question

All categories

3 years ago

6

A store allows customers to fill their own bags of candy. Terri decides she only wants jelly beans and chocolate drops. Jelly be

ans sell for $0.90 per pound, and chocolate drops sell for $0.70 per pound. Terri’s bag weighs 5 pounds and it costs $4.10.
a. 2 pounds of jellybeans; 3 pounds of chocolate drops

b. 4 pounds of jellybeans; 1 pound of chocolate drops

c. 1 pound of jellybeans; 4 pounds of chocolate drops

d. 3 pounds of jellybeans; 2 pounds of chocolate drops

1 answer:

NNADVOKAT [17]3 years ago

4 0

Answer:

Option D is correct that she took 3 pounds of jellybeans and 2 pounds of chocolate drops

Step-by-step explanation:

Given :

Terri wants jelly beans and chocolate drops.

Jelly beans sell for $0.90 per pound

Chocolate drops sell for $0.70 per pound.

Terri’s bag weighs 5 pounds

It costs $4.10.

To Find : How much she bought jellybeans and chocolate drops?

Solution :

Let she took x pounds of jellybeans.

Let she took y pounds of chocolate drops.

Since we are given that her bag weighs 5 pounds .

⇒ $x+y=5$ ---(A)

Now cost of 1 pound of jelly beans = $0.90

So, Cost of x pounds of jellybeans. = $0.90 x

Now cost of 1 pound of chocolate drops. =$0.70

So, Cost of y pounds of chocolate drops. = $0.70 y

Since we are given that total cost of her bag of 5 pounds is $4.10

⇒ $0.90 x+0.70 y= 4.10$ ---(B)

Solving A and B by using substitution method

Substitute value of x from (A) in (B)

⇒ $0.90 (5-y)+0.70 y= 4.10$

⇒ $4.5-0.90 y+0.70 y= 4.10$

⇒ $4.5-0.20 y= 4.10$

⇒ $4.5-4.10= 0.20 y$

⇒ $0.4= 0.20 y$

⇒ $\frac{0.4}{0.20} =y$

⇒ $2 =y$

Thus, she took y = 2 pounds of chocolate drops.

Now to calculate x substitute this value of y in (A)

⇒ $x+2=5$

⇒ $x=5-2$

⇒ $x=3$

Thus, she took x = 3 pounds of jellybeans

Hence , Option D is correct that she took 3 pounds of jellybeans and 2 pounds of chocolate drops

You might be interested in

If a, b, and c are positive integers, what

r-ruslan [8.4K]

The greatest common factor is 2ab

To determine this you need to determine what is divide in both 18 and 8. The only number that can divide in both numbers is 2. Which means they have a common factor/number. And then you continue looking at the expression and see what other numbers or letters are common. The only common thing besides the number is a and b since it’s found in both. There is no c in 18ab.
Hope this makes sense

Please mark as a brainliest (crown) above my comment. Would be much appreciated

4 0

3 years ago

Nadia is ordering cheesecake at a restaurant, and the server tells her that she can have up to five toppings: caramel, whipped c

Nesterboy [21]

Answer:

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125

Step-by-step explanation:

There are up to 5 toppings, such that the toppings are:

caramel

whipped cream

butterscotch sauce

strawberries

hot fudge

We want to find the probability that, If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.

First, we need to find the total number of possible combinations.

let's separate them in number of toppings.

0 toppins:

Here is one combination.

1 topping:

here we have one topping and 5 options, so there are 5 different combinations of 1 topping.

2 toppings.

Assuming that each topping can be used only once, for the first topping we have 5 options.

And for the second topping we have 4 options (because one is already used)

The total number of combinations is equal to the product between the number of options for each topping, so here we have:

c = 4*5 = 20 combinations.

But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.

Then the number of different combinations is:

c' = 20/2! = 10

3 toppings.

similarly to the previous case.

for the first topping there are 5 options

for the second there are 4 options

for the third there are 3 options

the total number of different combinations is:

c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10

4 toppings:

We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.

5 toppings:

Similar to the first case, here is only one combination with 5 toppings.

So the total number of different combinations is:

C = 1 + 5 + 10 + 10 + 5 + 1 = 32

There are 32 different combinations.

And we want to find the probability of getting one particular combination (all of them have the same probability)

Then the probability is the quotient between one and the total number of different combinations.

p = 1/32

The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125

8 0

3 years ago

Prime factorization of 39

Black_prince [1.1K]

Lets quickly run through the prime numbers and see what it is not divisible by

39 is not divisible by 2
39 IS divisible by 3

So lets stop right here.

What is 39 divided by 3? 13 !

And 13 is a prime number too!

So that is all we can do.

So prime factorization of 39 is <u>3 x 13</u><u><em /></u>

4 0

3 years ago

Navy PilotsThe US Navy requires that fighter pilots have heights between 62 inches and78 inches.(a) Find the percentage of women

Zigmanuir [339]

The first part of the question is missing and it says;

Use these parameters: Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.

Answer:

A) Percentage of women meeting the height requirement = 72.24%

B) Percentage of men meeting the height requirement = 0.875%

C) Corresponding women's height =67.42 inches while corresponding men's height = 72.19 inches

Step-by-step explanation:

From the question,

For men;

Mean μ = 68.6 in

Standard deviation σ = 2.8 in

For women;

Mean μ = 63.7 in

Standard deviation σ = 2.9 in

Now let's calculate the standardized scores;

The formula is z = (x - μ)/σ

A) For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.7224

So, percentage of women meeting the height requirement is 72.24%.

B) For men;

Z = (62 - 68.6)/2.8 = -2.36

Z = (78 - 68.6)/2.8 = 3.36

Thus, the probability of only men will take the form of;

P(-2.36 < Z < 3.36) = P(Z<3.36) - P(Z > - 2.36)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<3.36) = 0.99961

And P(Z > -2.36) = 0.99086

Thus;

P(Z<3.36) - P(Z > -2.36) 0.99961 - 0.99086 = 0.00875

So, percentage of women meeting the height requirement is 72.24%.

B)For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.00875

So, percentage of women meeting the height requirement is 0.875%

C) Since the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women.

For women;

Let's find the z-value with a right-tail of 10%. From the second table i attached ;

invNorm(0.90) = 1.2816

Thus, the corresponding women's height:: x = (1.2816 x 2.9) + 63.7= 67.42 inches

For men;

We have seen that,

invNorm(0.90) = 1.2816

Thus ;

Thus, the corresponding men's height:: x = (1.2816 x 2.8) + 68.6 = 72.19 inches

7 0

3 years ago

The equation $a^7xy-a^6y-a^5x=a^4(b^4-1)$ is equivalent to the equation $(a^mx-a^n)(a^py-a^2)=a^4b^4$ for some integers $m$, $n$

Ksivusya [100]

Let <span>simplify the equations $a^7xy-a^6y-a^5x=a^4(b^4-1)$ and $(a^mx-a^n)(a^py-a^2)=a^4b^4$ :
</span>
<span>1) $a^7xy-a^6y-a^5x+a^4=a^4b^4$
</span>
<span>and
</span>
<span>2) $a^{m+p}xy-a^{n+p}y-a^{m+2}x+a^{n+2}=a^4b^4$ .
</span>
<span>Equate the coefficients:
</span><span>
</span><span> $xy: m+p=7 \\ y: n+p=6 \\ x: m+2=5 \\ 1: n+2=4$ .</span>
Then $n=2 \\ p=4 \\ m=3$ and mnp=24.
<span />

3 0

3 years ago