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3 years ago

S=t+5 4s+2t=110 pls help me

Mathematics

2 answers:

Neko [114]3 years ago

8 0

Answer:

t = 40/3 (exact)

t = 13.3 (decimal)

t = 13 1/3 (mixed number)

Step-by-step explanation:

Simplify 4 (t + 5) + 2 (t + 5).

6t + 30 = 110

Move all terms not containing t to the right side of the equation.

6t = 80

Divide each term by 6 and simplify.

t = 40/3

The result can be shown in multiple forms.

t = 40/3 (exact)

t = 13.3 (decimal)

t = 13 1/3 (mixed number)

maria [59]3 years ago

3 0

Answer:

s=20

Step-by-step explanation:

First, plug in s to the equation.

4(t+5) + 2t =110

Then, distribute. That means multiply 4 to the variable and number inside the parentheses.

4t + 20 +2t = 110

Now, add like terms. The two numbers, 4t and 2t can be combined because they have the same variable.

6t + 20 = 110

Subtract 20 from 110 to isolate the variable.

6t = 90

Now, divide 90 by 6 to further isolate the variable.

t = 15

Now we have to find s. To find s, plug t = 15 into the equation.

s = 15 + 5

Lastly, add the two numbers to find s.

s = 20

Check your work! Plug in t = 15 and s = 20 to the equation.

4(20) + 2(15) = 110

Multiply.

80 + 30 = 110

110 = 110

This means your answers are correct! Hope this helped! :)

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3 years ago

10m/

AlladinOne [14]

Answer:

Answer is D 312m^2

As D= 8m x 11m = A =88x 3 = 264+ 48 = 312

1/2 x 6 x 8 = 24

This makes triangle base of 6m

triangle side =8m

Rectangle side = 8m

and rectangle length = 11m

Step-by-step explanation:

First finding

A= 6 x 11 = 66m^2 (rectangle area) or 10 x 9 = 90sq^2

A = 1/2 x 6 x 11 = 33 (1/2bh) triangle

33+ 33 + 66 +66 + 66 = 264 or 33+ 33+ 90+90+90 =336

As 336 was not in the answer we do not know what 10m/9m represents, we then see this triangle prism is not a normal shape and its length is same as its height

a) is not in usual proportions.

We try again reversing which makes triangle sides 10m+ base 9m

= 1/2 x 10 x 10 = 50m^2 = triangle face area

we cannot continue the reverse as the triangle sides do not match the rectangle height. We therefore have to use the first answer C 264m^2

As 10m, 9m <do not match >6m 11m 8m

However if the given sizes 10m, 9m = bases of two different rectangles we would calculate 2 faces and add them each to one unknown face being one of the other face sizes we found to make 3.

10 x 8 = 80

9 x 8 = 72

To make one of these SA totals for rectangles alone

=80+80+72=232 or 72+72+80 =224

Then add to the 33 m^2 triangles

= 232+ 33+ 33 =297m^2

= 224+33+33 =310m^2

We can now determine that these measurements represent irregular values and are not answers within multiple choice, however d) we can state the triangle is regular prism where triangle sides are regular too creating isosceles triangle 6,8,8,

8m x 11m = A =88x 3 = 264+ 48 = 312

1/2 x 6 x 8 = 24

As we have ruled out rectangle with side 8m x 11m + A (33m^2) of triangle would equal 310m^2 (88+88+88+33+33) =330m

And ruled out rectangle with side 8m x 6m= 48m^2 (48+48+48+33+33 =210sqm)

So therefore if triangles were to equal 1/2 x 6 x 8 = 24

24 x 3= 72sqm

add the rectangle amounts above

= 72 + 88+ 88+ 88 =336^2

try another way and we find D. here below.

answer D= 72+ 80+80+80 = 312m^2 this can makes a correct answer D.

As last rule out is;

72 + 72 +72 (+triangle of 72) =288^2 would be irregular as this is equal to (9 x 8) x 3 and then the 11m is not used. It is also not a listed answer. Therefore; D=312m^2 is correct.

A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

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Answer:

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And the standard error for the mean would be:

$\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14$

b) We want this probability:

$P(\bar X >120)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143$

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

$P( z>2.143) = 1-P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error for the mean would be:

$\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14$

Part b

We want this probability:

$P(\bar X >120)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143$

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

$P( z>2.143) = 1-P(Z$

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