Question 16 of 46

A fruit company delivers its fruit in two types of boxes large and small a delivery of three large boxes and five box that has a

Savatey [412]

Answer:

The weight of large box is 13.25 kilograms and the weight of small box is 6.25 kilograms.

Step-by-step explanation:

Given:

A fruit company delivers its fruit in two types of boxes large and small a delivery of three large boxes and five small boxes that has a total weight of 71 kilograms and a delivery of six large boxes and two small boxes has a total weight of 92 kilograms.

Now, to find the weight of each type of box.

Let the weight of large box be $x$ .

And let the weight of small box be $y.$

A delivery of three large boxes and five small boxes has a total weight of 71 kilograms:

$3x+5y=71\ \ \ .....(1)$

And, the delivery of six large boxes and two small boxes has a total weight of 92 kilograms:

$6x+2y=92\\\\Subtracting\ both\ sides\ by\ 6x:\\\\2y=92-6x\\\\Dividing\ both\ sides \ by\ 2\ we\ get:\\\\y=46-3x\ \ \ \ ......(2)$

Now, substituting the value of $y$ from equation (2) in equation (1):

$3x+5y=71\\\\3x+5(46-3x)=71\\\\$

$3x+230-15x=71\\\\230-12x=71\\\\$

Subtracting 230 on both sides we get:

$-12x=-159$

Dividing both sides by -12 we get:

$x=13.25.$

The weight of large box = 13.25 kilograms.

Now, substituting the value of $x$ in equation (1) we get:

$3x+5y=71\\\\3(13.25)+5y=71\\\\39.75+5y=71\\\\Subtracting\ both\ sides by\ 39.75\ we\ get:\\\\5y=31.25\\\\Dividing\ both\ sides\ by\ 5\ we\ get:\\\\y=6.25.$

The weight of small box = 6.25 kilograms.

Therefore, the weight of large box is 13.25 kilograms and the weight of small box is 6.25 kilograms.

3 0

3 years ago

Which type of triangle, if any, can be formed with sides measuring 8 inches, 8 inches, and 3

Tju [1.3M]

Answer:

An isosceles triangle

Step-by-step explanation:

An isosceles triangle has two equal sides.

4 0

4 years ago

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product betw

Wewaii [24]

Answer:

The probability of assembling the product between 7 to 9 minutes is 0.50.

Step-by-step explanation:

Let X = assembling time for a product.

Since the random variable is defined for time interval the variable X is continuously distributed.

It is provided that the random variable X is Uniformly distributed with parameters a = 6 minutes and b = 10 minutes.

The probability density function of a continuous Uniform distribution is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a};\ a$

Compute the probability of assembling the product between 7 to 9 minutes as follows:

$P(7$

$=\frac{1}{4}\times \int\limits^{9}_{7}{1}\, dx$

$=\frac{1}{4}\times [x]^{9}_{7}\\$

$=\frac{1}{4}\times (9-7)\\$

$=\frac{1}{2}\\=0.50$

Thus, the probability of assembling the product between 7 to 9 minutes is 0.50.

5 0

4 years ago

Write an inequality using variables x and y whose graph is described by the given information. The points (2,5) and (-3,-5) lie

luda_lava [24]

The inequality using variables x and y which satisfy the points are; y>-3x+3.

<h3>What is inequality?</h3>

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the points (2,5) and (-3,-5) lie on the boundary line.

The system of inequality is given by:

y>-3x+3-

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies the inequality.

a) (6, 5)

when x=6 and y= 5

then we have:

y>-3x+3

6 > -3×5 + 3

6>- 15+3

5 > -12

This means that the point will lie in the solution set.

Also, (-2, -3) when x= -2 and y= -3

then we have:

5 > -3×(-2) + 3

5> 6 + 3

5> 9

Hence, the inequality using variables x and y which satisfy the points are; y>-3x+3.

Learn more about inequality ;

brainly.com/question/14164153

#SPJ1

8 0

2 years ago

I don’t understand this.. will someone please help? Will mark Brainliest along with 20 points.

inn [45]

To say two quantities $a$ and $b$ "vary directly" with one another means that a change in one of the quantities results in a proportional change in the other quantity. For example, if $a=2b$ , then $b$ is proportional to $a$ by a factor of 2, or $a$ is proportional to $b$ by a factor of 1/2. In other words, if you change $b$ by some fixed amount, then $a$ changes by double that amount.

Mathematically this means there is some constant scaling factor $k$ such that $a=kb$ . In question 4, we're told $f(x)$ varies directly with $x^2$ , which means there's some $k$ such that

$f(x)=kx^2$

We're given that $f(x)=40$ when $x=2$ , so

$40=k\cdot2^2\implies40=4k\implies k=10$

Then when $x=5$ , we get

$f(5)=10\cdot5^2=10\cdot25=250$

- - -

For $a,b$ to "vary inversely" with one another means that a change in one quantity results in an "opposite" change in the other. In other words, if $a$ increases, then $b$ decreases, and vice versa.

Mathematically, this is the same as saying there is some fixed number $k$ such that $ab=k$ .

For example, if $k=1$ and we start with $a=1$ , then $b=1$ also. If we change to $a=2$ , then $b=\dfrac12$ ; if $a=10$ , then $b=\dfrac1{10}$ , and so on.