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3 years ago

What is the quality of 4x+27x=5

Mathematics

1 answer:

Nadya [2.5K]3 years ago

8 0

Answer:

Step-by-step explanation:

Isolate x on one side of the equation.

4x+27x=31x (Combine like terms, group like terms, & Add.)

31x=5

31x/31=5/31 (Divide by 31 from both sides.)

5/31=0.16

x=5/31=0.16

In conclusion, the correct answer is x=5/31=0.16.

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The weight of laboratory grasshoppers follows a Normal distribution, with a mean of 90 grams and a standard deviation of 2 grams

JulsSmile [24]

Answer:

95.44% of the grasshoppers weigh between 86 grams and 94 grams.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 90 grams and a standard deviation of 2 grams.

This means that $\mu = 90, \sigma = 2$

What percentage of the grasshoppers weigh between 86 grams and 94 grams?

The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 86. So

X = 94

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{94 - 90}{2}$

$Z = 2$

$Z = 2$ has a p-value of 0.9772.

X = 86

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{86 - 90}{2}$

$Z = -2$

$Z = -2$ has a p-value of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544*100% = 95.44%

95.44% of the grasshoppers weigh between 86 grams and 94 grams.

5 0

2 years ago

Ken is thinking of a number. nine more than the product of 4 and the number is 73. Find Kens number.

rewona [7]

I got 16 for this one

5 0

3 years ago

Read 2 more answers

If possible help me in this. I need to find the two odd numbers...

Lelechka [254]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

<h3>Answer: x+2</h3>

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

<h3>Answer: x^2 + (x+2)^2 = 394</h3>

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\$

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

<h3>Answer: Either 13, 15 or -15, -13</h3>

4 0

2 years ago

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ______ units. The poi

nalin [4]

Circle formula
(x-h)^2+(y-k)^2=r^2 where (h,k) is the center
and r=radius

to find the radius
we are given one of the points and the center
distnace from them is the radius
distance formula
D= $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$
points (-3,2) and (1,5)
D= $\sqrt{(1-(-3))^{2}+(5-2)^{2}}$
D= $\sqrt{(4)^{2}+(3)^{2}}$
D= $\sqrt{16+9}$
D= $\sqrt{25}$
D=5

center is -3,2
r=5
input
(x-(-3))^2+(y-2)^2=5^2
(x+3)^2+(y-2)^2=25 is equation
radius =5
input -7 for x and solve for y
(-7+3)^2+(y-2)^2=25
(-4)^2+(y-2)^2=25
16+(y-2)^2=25
minus 16
(y-2)^2=9
sqqrt
y-2=+/-3
add 2
y=2+/-3
y=5 or -1

the point (-7,5) and (7,-1) lie on this circle

radius=5 units
the points (-7,5) and (-7,1) lie on this circle

3 0

3 years ago

Is -2(-3) a positive or negative answer???

Natalija [7]

Answer: positive

Step-by-step explanation: it’s positive because if you multiply two negative numbers they cancel each other out and it makes a positive number

5 0

3 years ago

Read 2 more answers