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2 years ago

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Aa if #2 wasn't confusing enough, laura is now trying to come up with a number where three less than 8 times the number is equal

to half of 16 times the number after it was increased by 1

1 answer:

umka21 [38]2 years ago

4 0

Answer: Laura cannot find the number, as explained below.

Explanation:

1) The question is aimed to determine the number that Laura is trying to come up with.

Such question is solved by stating an algebraic equation from the word statement, which is done step by step.

2) Using the name x for the unknown, the expression "three less than 8 times the number" is translated to: 8x - 3

3) The expression "half of 16 times the number after it was increased by 1" is translated to: (1/2) (16x + 1)

4) Finally, since they are equal, you can set the equation:

8x - 3 = (1/2) (16x + 1)

5) And solve for x in this way:

i) Distributive property:

8x - 3 = 8x + 1/2

ii) At this stage you can see that the both 8x terms (on the left and on the right) cancel each other, which leads to the impossibility to determine the value of the unknown:

-3 = 1/2 which is alwasy false, meaning that the equation has no solution.

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A bridge is rated to a capacity of 100 British tons. What is the maximum weight the bridge can support in kilograms? (Round to t

S_A_V [24]

Maximum weight the bridge can support in kilograms is 101696

Step-by-step explanation:

Step 1: Given capacity of bridge = 100 British tons. Find how many kilograms are equivalent to 1 British ton.

1 British ton = 2240 pounds

1 pound = 0.454 kg

⇒ 1 British ton = 2240 × 0.454 kg = 1016.96 kg

Step 2: Find how many kilograms are in 100 British tons.

⇒ 100 × 1016.96 = 101696

3 0

2 years ago

Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0,

lesya692 [45]

Answer:

A line passing through the points (-1,-4),(0,0) and (1,4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

Part 1) A line passing through the points (-4,0) and (0,-2)

This line not represent a direct variation, because the line not passes through the origin.

Part 2) A line passing through the points (-5,4) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 3) A line passing through the points (-4,-6) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)

The line passes through the origin

Find out the value of k

$k=y/x$

For the point (-1,-4)

substitute

$k=-4/-1$

$k=4$

For the point (1,4)

substitute

$k=4/1$

$k=4$

The linear equation is

$y=4x$

This line represent a direct variation

6 0

1 year ago

Read 2 more answers

(10.01 MC) Marko is playing the video game Fort Attack. The purpose of the game is to shoot invading bandits that are trying to

rusak2 [61]

Angle of fire in degrees = 90 + 30 =120 degrees

Angle of fire radians =180 degrees = π

120* π/180=120π /180 OR 4π/6 OR 2π/3

8 0

1 year ago

Read 2 more answers

plz help whats the answer to this question !!! calculate the mass of a gold bar that is 18.00cm long, 9.21cm wide, and 4.45cm hi

erik [133]

We have to find the mass of the gold bar.

We have gold bar in the shape of a rectangular prism.

The length, width, and the height of the gold bar is 18.00 centimeters, 9.21 centimeters, and 4.45 centimeters respectively.

First of all we will find the volume of the gold bar which is given by the volume of rectangular prism:

Volume of the gold bar $= length \times width\times height$

Plugging the values in the equation we get,

Volume of the gold bar $=18.00 \times 9.21 \times 4.45= 737.721cm^3$

Now that we have the volume we can find the mass by using the formula,

$Mass= density \times volume$

The density of the gold is 19.32 grams per cubic centimeter. Plugging in the values of density and volume we get:

$Mass = 19.32\times 737.721=14252.769$ grams

So, the mass of the gold bar is 14252.769 grams

7 0

2 years ago

An annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. If the occupants o

Sunny_sXe [5.5K]

Answer:

Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

Step-by-step explanation:

We are given that an annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. The occupants of half the residences object to being annexed.

Also, a random sample of 10 residents is taken.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 10 residents

r = number of success = at least 3

p = probability of success which in our question is probability that

residents favor the annexation suit, which is calculated as below;

p = $\frac{\text{Number of residents favoring the annexation suit }}{\text{Total number of residents considered } }$ = $\frac{600}{1200}$ = 0.50

<em>LET X = Number of residents favoring the annexation suit</em>

So, it means X ~ $Binom(n=10, p=0.50)$

Now, Probability that in a random sample of 10 at least 3 favor the annexation suit is given by = P(X $\geq$ 3)

P(X $\geq$ 3) = 1 - P(X < 3) = 1 - P(X $\leq$ 2)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

= $1- [\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0} + \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1} +\binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}]$

= $1-[ 1 \times 1 \times 0.50^{10}+10 \times 0.50^{1} \times 0.50^{9}+45 \times 0.50^{2} \times 0.50^{8}]$

= $1-[ 0.50^{10}+10 \times 0.50^{10}+45 \times 0.50^{10}]$

= $1-0.50^{10}[ 1+10 +45 ]$ = $1-0.50^{10} \times 56$

= 0.9453

Therefore, Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

8 0

1 year ago