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2 years ago

11

Jeff has ten packages that he wants to mail. Nun identical packages weigh 2 7/8 pounds each. A tenth package weighs two times as

much of one the nine packages. How many ponds do all packages weigh?

1 answer:

Arturiano [62]2 years ago

7 0

Answer:31.625

2 7/8 8 times 9 =25.875 +(2.875 times 2) =31.625

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A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft, and it weighs 50 lbs. T

Lady_Fox [76]

Answer:

116 units of the first product

380 units of the second product

Step-by-step explanation:

Product 1 has a unit volume of 10 cu ft

Product 2 has a unit volume of 3 cu ft

The truck has 2300 cu ft of space

Product 1 weighs 50 lbs

Product 2 weighs 40 lbs

The truck can carry 21000 lbs

Let X be the units of product 1

Let Y be the units of product 2

The given information can be expressed as:

10X+3Y=2300...(1)

50X+40Y=21000...(2)

Solving the system of equations:

10X+3Y=2300...(1)

10X=2300-3Y

X=(2300-3Y)/10

Substituting X in (2) we have:

50X+40Y=21000

50[(2300-3Y)/10]+40Y=21000

50[(2300/10)-(3Y/10)]+40Y=21000

50[230-(3Y/10)+40Y=21000

11500-(150Y/10)+40Y=21000

11500-15Y+40Y=21000

11500+25Y=21000

25Y=21000-11500

25Y=9500

Y=380

Substituting Y in (1) we have:

10X+3Y=2300...(1)

10X+3(380)=2300

10X+1140=2300

10X=2300-1140

10X=1160

X=116

So 116 units of the first product and 380 units of the second product can be transported in a single shipment with one truck.

8 0

2 years ago

Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. L

lesya692 [45]

Answer: $A(t)=-8t+52$

Step-by-step explanation:

<h3> The missing question is: "What is the Functions formula A(t)=?"</h3><h2 />

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

According to the data given in the exercise, you know that:

- $A(t)$ represents the area to paint the Hiros' romm as a function of time.

- The rate he painted the room was 8 square meters per hour.

- The area left to paint after 3 hours was 28 m².

Therefore, based on this, you can idenfity that:

1. The slope of the line is:

$m=-8$

2. One of the point on the line is:

$(3,28)$

So you must substitute the slope and the coordinates of that point into $y=mx+b$ and then solve for "b" in order to find its value:

$28=-8(3)+b\\\\28+24=b\\\\b=52$

Therefore, you can determine that the function $A(t)$ is:

$A(t)=-8t+52$

4 0

1 year ago

points P and Q lie 240 m apart in line with and on opposite sides of a communications tower. the angles of elevation to the top

Leona [35]

Answer:

The height of the tower is 130.5m

Step-by-step explanation:

In the question, we are given the following values:

The angles of elevation to the top of the tower from P = 50°

The angles of elevation to the top of the tower from Q = 45°

The angles of elevation to the top of the tower from P = 50°

Hence,cot P = 1/ tan(50°)

The angles of elevation to the top of the tower from Q = 45°

Hence, tan 45° = 1

In the question,we are told Points P and Q lie 240 m apart in line with and on opposite sides of a communications tower.

Therefore,

PQ = height of the tower( tan Q + 1/tan P)

240m = height of the tower( tan 45° + 1/ tan 50°)

240m = h(1 + 1/tan 50°)

h = (240 m)/(1 + 1/tan (50°))

h = 130.49863962 meters

Therefore, the height of the tower to the nearest tenth of a meter is 130.5 meters(m)

5 0

2 years ago

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a

STatiana [176]

Answer:

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085

Step-by-step explanation:

The given parameters are;

The coordinates of parallelogram RSTU are;

R(-4, -3), S(-5, 1), T(4, 3), U(5, -1)

The lengths of the sides are (using an online length calculator);

RS = 4.1231

RT = 10

ST = 9.2195

SU = 10.198

TU = 4.1231

UR = 9.2195

Therefore, by definition of a parallelogram, we have;

RS║TU and ST║UR

The slope of RS = (1 - (-3))/(-5 - (-4)) = -4

The slope of ST = (3 - 1)/(4 - (-5)) = 2/9

The equation of the line perpendicular to ST is therefore;

y - 1 = -9/2×(x - (-5))

y = -9x/2 - 43/2

The equation of RS = y - (-3) = 1/4×(x - (-4)) = x/4 + 1

y = x/4 - 2

The point where the two lines meet is therefore;

-9x/2 - 43/2 = x/4 - 2

x = -78/19

y = -115/38

The length of the side of the rectangle = 4.1245

The excess width of the rectangle = 0.1085

The value that can be subtracted from the area of the rectangle to give the area of the parallelogram = 1/2 × 4.1245 × 0.1085.

6 0

1 year ago

Recent homebuyers from a local developer allege that 30% of the houses this developer constructs have some major defect that wil

umka21 [38]

Answer:

3.54% probability of observing at most two defective homes out of a random sample of 20

Step-by-step explanation:

For each house that this developer constructs, there are only two possible outcomes. Either there are some major defect that will require substantial repairs, or there is not. The probability of a house having some major defect that will require substantial repairs is independent of other houses. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

30% of the houses this developer constructs have some major defect that will require substantial repairs.

This means that $p = 0.3$

If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20

This is $P(X \leq 2)$ when n = 20. So

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{20,0}.(0.3)^{0}.(0.7)^{20} = 0.0008$

$P(X = 1) = C_{20,1}.(0.3)^{1}.(0.7)^{19} = 0.0068$

$P(X = 2) = C_{20,2}.(0.3)^{2}.(0.7)^{18} = 0.0278$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0008 + 0.0068 + 0.0278 = 0.0354$

3.54% probability of observing at most two defective homes out of a random sample of 20

5 0

1 year ago