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3 years ago

What is the value of x in this equation? 4(x + 6) – 3x = 26

Mathematics

1 answer:

alexdok [17]3 years ago

5 0

Answer:

x = 2

4 (x + 6) - 3x = 26

solve the parenthesis

4x + 24 - 3x = 26

subtract 24 from both sides to get x by itself

4x - 3x = 2

solve

x = 2

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Two friends live 3 miles apart along the same road. If they walk toward each other at rates that differ by half mile per hour an

Slav-nsk [51]

Answer: their speeds are 3.5mph and 4 mph

Step-by-step explanation:

Since both friends live 3 miles apart along the same road, by the time they meet, they would have covered 3 miles.

Let x represent the speed of the slower friend.

If differ by half mile per hour, it means that the speed of the faster friend is (x + 0.5) mph

They meet after 24 minutes(24/60 = 0.4 hours)

Distance = speed × time

Distance covered by the slower friend in 0.4 hours is

x × 0.4 = 0.4x

Distance covered by the faster friend in 0.4 hours is

0.4(x + 0.5) = 0.4x + 0.2

Since the total distance is 3 miles, then

0.4x + 0.4x + 0.2 = 3

0.8x = 3 - 0.2 = 2.8

x = 2.8/0.8

x = 3.5 mph

The speed of the faster friend is

3.5 + 0.5 = 4 mph

8 0

3 years ago

If the lengths of two sides of a triangle are 6 and 7, the length of the third side may be

Ghella [55]

Answer:

The third side may be between 1 and 13 units

Step-by-step explanation:

Let the missing side is x.

According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than the third side.

<u>We have inequalities:</u>

6 + 7 > x ⇒ x < 13
6 + x > 7 ⇒ x > 1
7 + x > 6 ⇒ x > - 1

<u>The common solution is:</u>

1 < x < 13

5 0

3 years ago

the manufacturer of an Airport baggage conveyor recommends a slope of no more than .25. If the baggage conveyor and the figure b

Daniel [21]

In order to solve this problem, it is helpful to draw a diagram (see image below). Since slope is “rise over run” you can make an equation of 4/x = .25 . Then by multiplying each side by x, you can get rid of the fraction. Next, you divide both sides by .25 . You will end up with x=16

4 0

3 years ago

Anna has 196 pepper plants that she wants to plant in a square formation how many pepper plants should she plant in each row

skad [1K]

She should plant 14 plants in each row

Step-by-step explanation:

Given

Total pepper plants = 196

As the plants have to be in square shape, the number of rows and the plants in each row will be equal

Let x be the number of rows

Then

$x^2 = 196\\$

Taking square root on both sides

$\sqrt{x^2} = \sqrt{196}\\x = 14$

Hence,

She should plant 14 plants in each row

Keywords: Square root, Radicals

Learn more about square root at:

#LearnwithBrainly

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3 years ago

A normally distributed population has mean 57,800 and standard deviation 750. Find the probability that a single randomly select

Stels [109]

Answer:

(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411

(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621

Step-by-step explanation:

We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; $\mu$ = 57,800 and $\sigma$ = 750.

Let X = randomly selected element of the population

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)

P(X <= 58,000) = P( $\frac{X-\mu}{\sigma}$ <= $\frac{58000-57800}{750}$ ) = P(Z <= 0.27) = 0.60642

P(X < 57000) = P( $\frac{X-\mu}{\sigma}$ < $\frac{57000-57800}{750}$ ) = P(Z < -1.07) = 1 - P(Z <= 1.07)

= 1 - 0.85769 = 0.14231

Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .

(b) Now, we are given sample of size, n = 100

So, Mean of X, X bar = 57,800 same as before

But standard deviation of X, s = $\frac{\sigma}{\sqrt{n} }$ = $\frac{750}{\sqrt{100} }$ = 75

The z probability is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)

P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)

P(X bar <= 58,000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{58000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z <= 2.67) = 0.99621

P(X < 57000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{57000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z < -10.67) = P(Z > 10.67)

This probability is that much small that it is very close to 0

Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .

7 0

3 years ago