Simplify the expression you wrote in number 1 to find the cost of the security guard and the deejay. *

A factory dumps an average of 2.43 tons of pollutants into a river every week. if the standard deviation is 0.88 tons, what is t

vovikov84 [41]

25.8%
First, determine how many standard deviations from the norm that 3 tons are. So:
(3 - 2.43) / 0.88 = 0.57/0.88 = 0.647727273
So 3 tons would be 0.647727273 deviations from the norm. Now using a standard normal table, lookup the value 0.65 (the table I'm using has z-values to only 2 decimal places, so I rounded the z-value I got from 0.647727273 to 0.65). The value I got is 0.24215. Now this value is the probability of getting a value between the mean and the z-score. What I want is the probability of getting that z-score and anything higher. So subtract the value from 0.5, so 0.5 - 0.24215 = 0.25785 = 25.785%
So the probability that more than 3 tons will be dumped in a week is 25.8%

5 0

3 years ago

Help asap will give brainliest

ArbitrLikvidat [17]

Answer:

• Equation = $2(\frac{7}{4}w + w) = 176$

• length = 56 ft

• width = 32 ft

Step-by-step explanation:

The ratio of the length to width is 7:4.

∴ $\frac{l}{w} = \frac{7}{4}$

⇒ $l = \frac{7}{4} w$ [Equation 1]

We know that the perimeter of the garden is 176 feet.

∴ $2(l + w) = 176$

⇒ $2(\frac{7}{4}w + w) = 176$

⇒ $\frac{7}{4} w + w = 88$ [From Equation 1]

⇒ $\frac{7 w + 4w}{4} = 88$

⇒ $\frac{11w}{4} = 88$

⇒ $11w = 352$

⇒ $w = \bf 32 \space\ ft$

We know from Equation 1 that:

$l = \frac{7}{4} w$

∴ $l = \frac{7}{4} (32)$

⇒ $l = \bf 56 \space\ ft$

7 0

2 years ago

A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?

N76 [4]

If the series is made up of numbers in an arithmetic progression, you have

$\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185$

where $a_1$ is the first term and $d$ is the common difference between terms.

Since the last term in the series is $a_{18}=275$ , you have

$a_{18}=a_1+(18-1)d\implies a_1+17d=275$

Solve the system

$\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}$

and you'll find that the first term is $a_1=190$ (with $d=5$ ).

5 0

3 years ago

HEY CAN ANYONE HELP ME!

nataly862011 [7]

Answer:

Given: In triangle ABC and triangle DBE where DE is parallel to AC.

In ΔABC and ΔDBE

$DE || AC$ [Given]

As we know, a line that cuts across two or more parallel lines. In the given figure, the line AB is a transversal.

Line segment AB is transversal that intersects two parallel lines. [Conclusion from statement 1.]

Corresponding angles theorem: two parallel lines are cut by a transversal, then the corresponding angles are congruent.

then;

$\angle BDE \cong \angle BAC$ and

$\angle BEC \cong \angle BCA$

Reflexive property of equality states that if angles in geometric figures can be congruent to themselves.

by Reflexive property of equality:

$\angle B \cong \angle B$

By AAA (Angle Angle Angle) similarity postulates states that all three pairs of corresponding angles are the same then, the triangles are similar

therefore, by AAA similarity postulates theorem

$\triangle ABC \sim \triangle DBE$

Similar triangles are triangles with equal corresponding angles and proportionate side.

then, we have;

$\frac{BD}{BA}$ [By definition of similar triangles]

therefore, the missing statement and the reasons are

Statement Reason

3. $\angle BDE \cong \angle BAC$ Corresponding angles theorem

and $\angle BEC \cong \angle BCA$

5. $\triangle ABC \sim \triangle DBE$ AAA similarity postulates

6. BD over BA Definition of similar triangle

7 0

3 years ago

Read 2 more answers

N a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find:

kirza4 [7]

First find the length of leg BC by using the Pythagorean theorem BC=132+52=12 ft if we find the midpoint of BC which is 6 ft we find where the angle bisector would touch the BC. From there we construct another triangle ANC where AC is equal to 5 ft and NC is equal to 6 ft where we can again use the Pythagorean theorem to find the length of the hypotenuse which is the angle bisector AN=Angle Bisector=62+52=7.8102 ft.

5 0

3 years ago