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Harlamova29_29 [7]

3 years ago

10

At what point does the graph of 3x + 4y = 15 intersect the graph of x^2 + y^2 = 9? Express any non-integer coordinate as a commo

n fraction.

2 answers:

mars1129 [50]3 years ago

8 0

Answer

12 and 36 and 13

laiz [17]3 years ago

6 0

If you need an explanation;

let's first isolate x in 3x + 4y = 15 ---

x = (15 - 4y) / 3

now substitute as x in the second equation provided ---

((15 - 4y) / 3)^2) + y^2 = 9,

((15 - 4y) / 3)^2) +( 3y/3)^2 = 9,

((15 - 4y)^2 + (3y/3)^2)/3^2 = 9,

225 - 120y +25y^2/9 = 9,

225 - 120y +25y^2 = 81,

25y^2 - 120y + 144 = 0

we now solve using the quadratic formula ---

$y_{1,\:2}=\frac{-\left(-120\right)\pm \sqrt{\left(-120\right)^2-4\cdot \:25\cdot \:144}}{2\cdot \:25}\\=\frac{-\left(-120\right)\pm \sqrt{0}}{2\cdot \:25}\\=\frac{-\left(-120\right)\pm \sqrt{0}}{2\cdot \:25}\\\\= 12/5$

So then x = (15 - 4*12/5)/3 = 9/5. Our solution = (9/5, 12/5)

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The height, h, in feet of a golf ball above the ground after being hit into the air is given by the equation, h = -16t 2 + 64t,

coldgirl [10]

Answer:

4 seconds

Step-by-step explanation:

When the ball is on the ground h = 0, hence

- 16t² + 64t = 0 ( solve for t )

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equate each factor to zero and solve for t

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3 years ago

Write the time 8:30 then write this time in two other ways using words

guajiro [1.7K]

Half past eight or thirty minutes to nine

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3 years ago

The area of a trapezium is 800 cm2

svlad2 [7]

Answer:

The distance between the parallel sides is 20cm.

Step-by-step explanation:

Area of a trapezoid:

$A=\frac{a+b}{2}\times h$

where a and b are the 2 bases, and h is the height. The value we're trying to find here is the height.

3 of the 4 variables in this equation are already given:

A = 800

a = 48

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5 0

3 years ago

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We are conducting a hypothesis test to determine if fewer than 80% of ST 311 Hybrid students complete all modules before class.

Juli2301 [7.4K]

Answer:

$z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124$

Null hypothesis: $p\geq 0.8$

Alternative hypothesis: $p < 0.8$

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

$p_v =P(Z$

So the p value obtained was a very high value and using the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis: $p\leq 0.8$

Alternative hypothesis: $p > 0.8$

$p_v =P(Z>2.124)=0.013$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation

n=110 represent the random sample taken

X=97 represent the students who completed the modules before class

$\hat p=\frac{97}{110}=0.882$ estimated proportion of students who completed the modules before class

$p_o=0.8$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v{/tex} represent the p value (variable of interest) 2) Concepts and formulas to use We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.8 or 80%: Null hypothesis:[tex]p\geq 0.8$

Alternative hypothesis: $p < 0.8$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.881 -0.8}{\sqrt{\frac{0.8(1-0.8)}{110}}}=2.124$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level assumed $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v =P(Z$

So the p value obtained was a very high value and using the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

Be Careful with the system of hypothesis!

If we conduct the test with the following hypothesis:

Null hypothesis: $p\leq 0.8$

Alternative hypothesis: $p > 0.8$

$p_v =P(Z>2.124)=0.013$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

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Sedbober [7]

The ratio for this question is 5:9.

7 0

3 years ago

Read 2 more answers