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andreev551 [17]
3 years ago
14

Twice the difference of a number and 2 is equal to three times the sum of the number and 3. Find the number. The number is nothi

ng.
Mathematics
1 answer:
trasher [3.6K]3 years ago
3 0

The number is -13.

In order to find this, we first need to make each part of the statement into a mathematical statement.

Twice the difference of a number and 2.

2(x - 2)

Three times the sum of the number and 3

3(x + 3)

Now we can set them equal to each other and solve.

2(x - 2) = 3(x + 3) ----> Distribute

2x - 4 = 3x + 9 ------> Subtract 2x from both sides

-4 = x + 9 -----> Subtract 9 from both sides

-13 = x

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Answer:

true

Step-by-step explanation:

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3 years ago
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at the start of the shift your part counter reads 250 at the end of the shift the part counter reads 1075 how many parts did you
Luden [163]
This can be mathematically expressed to
 250 + X  = 1075
where X represents the parts you produce before the shift ends
Transpose 250 to the other side by subtracting each side by 250
Thus, it goes like this
X = 1075 - 250
X = 825

You produced 825 parts in the middle of the shift.

5 0
3 years ago
√3×sinx+cosx=0 tmf nghiệm
Crazy boy [7]

Answer:

x= -30

Step-by-step explanation:

√3×sinx+cosx=0

√3sinx=-cosx

√3sinx/-cosx=1

-sinx/cosx=1/√3

-tanx=1/√3

(tan(180-30))=1/√3

tan(-30)=1/√3

Therefore, x= -30

7 0
2 years ago
4. Calculate the surface area of this triangular prism.
attashe74 [19]

Answer:

Surface Area of a Triangular Prism Calculator

In the general surface area is defined as the total area the surface of the object occupies. A triangular prism is a polyhedron that  has a triangular base. It has 5 faces and 9 edges. Use our online surface area of a triangular prism calculator to efficiently calculate the total surface area occupied by the triangular based prism. Enter the triangle's sides, base, height, and prism height in the prism calculator to find the SA of the triangular prism.

Step-by-step explanation:

7 0
3 years ago
A research group needs to determine a 90% confidence interval for the mean repair cost for all car insurance small claims. From
lutik1710 [3]

Answer:

a) z = 1.645

b) The should sample at least 293 small claims.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645, which means that the answer of question a is z = 1.645.

Now, find  the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample?

They should sample at least n small claims, in which n is found when

M = 12, \sigma = 124.88. So

M = z*\frac{\sigma}{\sqrt{n}}

12 = 1.645*\frac{124.88}{\sqrt{n}}

12\sqrt{n} = 205.43

\sqrt{n} = \frac{205.43}{12}

\sqrt{n} = 17.12

\sqrt{n}^{2} = (17.12)^{2}

n = 293

The should sample at least 293 small claims.

8 0
3 years ago
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