Ask question

Ask question

All categories

3 years ago

13

Mr. McKay wrote an algebra test with a total of 15 questions consisting of multiple choice and short response style questions. M

ultiple choice questions, x, were worth 5 points each and short response questions, y, were worth 10 points each. There were 100 total possible points on the test. Write and graph a system of linear equations for this situation to determine the number of each type of question.

1 answer:

tankabanditka [31]3 years ago

5 0

Step-by-step explanation:

x = number of multiple choice questions

y = number of short response questions

x + y = 15

5x + 10y = 100

=>

x + 2y = 20

let's subtract the first from the second equation :

x + 2y = 20

- x + y = 15

--------------------

0 y = 5

x + y = 15

x + 5 = 15

x = 10

to graph you need to consider both equations as linear functions. and you need to transform them into e.g. a slope intercept form : y = ax + b

a is the slope, b is the y- intercept.

x + y = 15

transforms to

y = -x + 15

this line goes e.g. through the points (0, 15) and (1, 14).

and

x + 2y = 20

transforms to

2y = -x + 20

y = -x/2 + 10

this line goes e.g through (0, 10) and (2, 9).

the crossing point of both lines is the solution and should therefore be the point (10, 5) as calculated above.

You might be interested in

Fowle Marketing Research Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean tim

sergejj [24]

Answer:

a) Null hypothesis: $\mu \leq 15$

Alternative hypothesis: $\mu > 15$

b) $t=\frac{17-15}{\frac{4}{\sqrt{35}}}=2.958$

c) $p_v =P(t_{34}>2.958)=0.0028$

d) If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.

Step-by-step explanation:

Data given and notation

The sample mean is given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation is:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=17$ represent the sample mean

$s=4$ represent the sample standard deviation

$n=35$ sample size

$\mu_o =15$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less or equal than 15, the system of hypothesis would be:

Null hypothesis: $\mu \leq 15$

Alternative hypothesis: $\mu > 15$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{17-15}{\frac{4}{\sqrt{35}}}=2.958$

Part c P-value

The degrees of freedom are given by:

$df = n-1= 35-1=34$

Since is a right tailed test the p value would be:

$p_v =P(t_{34}>2.958)=0.0028$

Part d Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 15 at 1% of signficance.

7 0

3 years ago

60 − (7 + 4) × 5 what is the answer

hichkok12 [17]

Answer:

5

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Kyra has a rock collection. When she puts her rocks into 2 equal plies, there are no rocks left over. When she puts her rocks in

Nat2105 [25]

Step-by-step explanation:

According to this description we need a number that can be divided by 2,3 and 4 since the amount of rocks can be described by a natural number. However if a number is divided by 4 it is divided by 2 as well since 2*2=4.

$\frac{x}{4} = \alpha \\ \frac{x}{2} = 2 \alpha$

If α is a natural number then 2*α is a natural number as well as the product of two natural numbers.

Which means that we need a number devided by 3 and 4.

The smallest number that fulfills this demand is 3*4=12.

Also any product of 12 with any natural number can be devided by 3, 4 and 2.

If the exercise asks for the numbers that are divided only by 2,3 and 4 these are:

${3}^{ \alpha } \times 12 \: and \: {4}^{ \alpha } \times 12 \: \\ where \: \alpha \: belongs \: to \: the \: set \: of \: all \: \\ natural \: numbers$

8 0

3 years ago

*PLEASE HELP MEEEEEE* You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board.

yawa3891 [41]

Answer:

19.63%

Step-by-step explanation:

The probability of scoring 8 points is the probability of getting a dart into the green circle.

That probability is equivalent to the area of the circle divided by the total area of the square board.

The area of the circle according to $A=\pi*r^2$ , is $25\pi$ cm squared

The area of the whole square board is one side squared: 20 squared = 400 cm squared

The probability is therefore equal to $25\pi/400 = \pi/16=0.19634=19.63%$ %

8 0

3 years ago

How do I solve this?

vladimir1956 [14]

Answer:

3p³ + 2p² – 3p – 11

Step-by-step explanation:

From the question given above, the following data were obtained:

Side 1 (S₁) = –1(p + 5)

Side 2 (S₂) = 2(p² – 3)

Side 3 (S₃) = 3p³ – 2p

Perimeter (P) =?

The perimeter of the triangle can be obtained as follow

P = S₁ + S₂ + S₃

P = –1(p + 5) + 2(p² – 3) + 3p³ – 2p

Clear bracket

P = –p – 5 + 2p² – 6 + 3p³ – 2p

Rearrange

P = 3p³ + 2p² – 2p – p – 6 – 5

P = 3p³ + 2p² – 3p – 11

Therefore, the perimeter of the triangle is 3p³ + 2p² – 3p – 11

4 0

3 years ago