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vlada-n [284]
3 years ago
11

This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of

proportionality?
1/25
1/20
1/15
1/10

Mathematics
2 answers:
alisha [4.7K]3 years ago
8 0
(60,4)(120,8)
slope = (8 - 4) / (120 - 60) = 4/60 = 1/15 <== the constant of proportionality is the slope
Ilya [14]3 years ago
4 0

Answer:

The correct option is 3.

Step-by-step explanation:

Form the given figure it is noticed that the line is passing through the points (60,4) and (120,8).

y\propto x

y=kx

Where, k is the constant of proportionality or slope.

The slope of a line is defined as

k=\frac{y_2-y_1}{x_2-x_1}

k=\frac{8-4}{120-60}

k=\frac{4}{60}

k=\frac{1}{15}

Therefore option 3 is correct.

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Construct a sample (with at least two different values in the set) of 4 measurements whose mean, median, and mode are equal. If
KiRa [710]

Answer:

The first set 4 , 6 , 6 , 8

The second set 2 , 6 , 6 , 10

Step-by-step explanation:

Mean is the average of the values in a set. This can be found by summing all the numbers and dividing by the total number. The median is the middle number when the values are listed in order of increasing size. The mode is the number(s) that appear the most often in the set.

The first set 4 , 6 , 6 , 8

mean = (4 + 6 + 6 + 8 )/4 = 6

median = (6+6)/2 = 6

Mode = 6

The second set 2 , 6 , 6 , 10

mean = (2 + 6 + 6 + 10)/4 = 6

median = (6+6)/2 = 6

Mode = 6

3 0
3 years ago
4. A restaurant charges $9.95 for a large pizza with two toppings, and $1.25 for
bearhunter [10]

Answer:

3 toppings is the answer

Step-by-step explanation:

3 0
3 years ago
The systolic blood pressure (BP) of adults in the USA is nearly normally distributed with a mean of 121 and standard deviation o
Wittaler [7]

Answer:

Around 0.73% of adults in the USA have stage 2 high blood pressure

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 121 and standard deviation of 16.

This means that \mu = 121, \sigma = 16

Around what percentage of adults in the USA have stage 2 high blood pressure

The proportion is 1 subtracted by the p-value of Z when X = 160. So

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

Z = \frac{160 - 121}{16}

Z = 2.44

Z = 2.44 has a p-value of 0.9927.

1 - 0.9927 = 0.0073

0.0073*100% = 0.73%

Around 0.73% of adults in the USA have stage 2 high blood pressure

5 0
3 years ago
The two triangle­shaped gardens are congruent. Find all of the missing side lengths and angle measures. Show any necessary work
pantera1 [17]
The two figures are in the file attached.

Congruency means that all the respcetive sides and angles are equals.

Then, the three angles are :

y = 38°

x = 90°

w = 180° - 90° - 38° = 52


The three sides are:

z= 10yd
v= 7.9yd
u=6.2yd


You have all the measures as a function of yd, but you do not have any information about yd, then it is not possible to find the real lenghts.

All you can tell is that the sides obey Pythagoream theorem:

u^2 + v^2 = z^2   

But that is not enough to find one side, because you do not know any of them.

For example if you apply Pytagorean theorem you cand do"

(7.9yd)^2 + (6.2)^2 = (10yd)^2

but that cannot be solved for yd, because they are factors of all the terms in both sides, which mean that they cancel to obtain:

(7.9)^2 + (6.2)^2 = (10)^2, which is not any new information.

Also you can think about sine theorem, but it does not help, because you also need one side.


Then you only can tell the missing angles, as I have shown, but not the misssing lengths.


Download docx
8 0
3 years ago
Identify the relative maximum value of g(x) for the function shown below g(x)=7/x^2+5
Liula [17]
To find t<span>he relative maximum value of the function we need to find where the function has its first derivative equal to 0.

Its first derivative is -7*(2x)/(x^2+5)^2
</span>7*(2x)/(x^2+5)^2 =0 the numerator needs to be eqaul to 0
2x=0
x=0

g(0) = 7/5

The <span>relative maximum value is at the point (0, 7/5).</span>
8 0
3 years ago
Read 2 more answers
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