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emmainna [20.7K]
1 year ago
6

On a standardized exam, the scores are normally distributed with a mean of 165 and astandard deviation of 40. Find the z-score o

f a person who scored 145 on the exam.
Mathematics
1 answer:
vladimir1956 [14]1 year ago
8 0

The Z-score is calculated by the formula below

\begin{gathered} z-score=\frac{(x-\mu)}{\sigma}_{} \\ \mu=\operatorname{mean} \\ \sigma=s\tan dard\text{ deviation} \\ x=\text{score} \end{gathered}

Step 2: Substitute the given parameters in the formula

\begin{gathered} z-\text{score}=\frac{145-165}{40} \\ Z=-\frac{20}{40} \\ Z=-\frac{1}{2} \\ Z=-0.5 \end{gathered}

Hence, the z-score of a person who scored 145 on the exam is -0.5

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Three forces act on a hook. Determine the magnitude of the resultant of the force.
Novay_Z [31]

Use Hooke's law... (just kidding)

Break down each force vector into horizontal and vertical components.

\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y

\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y

\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y

The resultant force is the sum of these vectors,

\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y

and has magnitude

|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N

The closest answer is D.

5 0
2 years ago
Jana uses 20 cards to play a memory game the cards are either animal cards or fruit cards. The ratio of animal cards to fruit ca
Verdich [7]

Given that,

Total no of cards = 20

The ratio of animal cards to fruit cards is 2:3

No of animal cards = 20

Solution,

Let there are 2x animal cards and 3x fruit cards. ATQ,

2x+3x = 20

5x = 20

x = 4

Animal cards = 2x

= 2(4)

= 8

Fruit cards = 3x

= 3(4)

= 12

It is also mentioned that, of the cards, 1/3 have bananas on them. It means,

B=\dfrac{1}{3}\times 12\\\\=4

Hence, 4 cards have bananas on them.

5 0
2 years ago
eduardo has 4 1/2 yard of rope light. Exactly how many more yard does he need to finish the car's ceiling
Over [174]

Answer:

2 1/6

Step-by-step explanation:

Because the denominators are different, and there are whole numbers involved, then first make the fractions improper.

4 1/2 -> 9/2

6 2/3 -> 20/3

Next, make the denominators the same by multiplying each fraction by the denominator of the other.

9/2 * 3 = 27/6

20/3 * 2 = 40/6

Then you can subtract the numerators because the denominators are the same:

40/6-27/6= 13/6

Then you can convert to a mixed fraction if need be.

3 0
2 years ago
Please Help me! Algebra 1
dem82 [27]

Option a: The number of bacteria at time x is 0.

Option b: An exponential function that represents the population is y=200(1.5)^x

Option c: The population after 10 minutes is 11534(app)

Explanation:

It is given that the coordinates of the graph are (0,200), (1,300) and (2, 450)

Option a: To determine the number of bacteria x when y = 200

From the graph, we can see that the line meets y = 200 when x = 0

Thus, the coordinates are (0,200)

Hence, the number of bacteria at time x is 0 when y = 200.

Option b: Now, we shall determine the exponential function of the population.

The general formula for exponential function is y=a \cdot b^{x}

Where a is the starting point and a=200

b is the common difference.

To determine the common difference, let us divide,

\frac{300}{200} =1.5

Also, \frac{450}{300} =1.5

Hence, the common difference is b=1.5

Thus, substituting the values a=200 and b=1.5 in the formula y=a \cdot b^{x},

we have, y=200(1.5)^x

Hence, An exponential function that represents the population is y=200(1.5)^x

Option c: To determine the population after 10 minutes, let us substitute x=10 in y=200(1.5)^x, since the x represents the population of the bacteria in minutes.

Thus, we have,

\begin{aligned}y &=200(1.5)^{x} \\&=200(1.5)^{10} \\&=200(57.67) \\&=11534\end{aligned}

Hence, the population after 10 minutes is 11534(app)

7 0
3 years ago
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guajiro [1.7K]
I believe that it's answer c.
6 0
3 years ago
Read 2 more answers
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