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2 years ago

Can someone help me with this page please I have an exam tomorrow, I need to remember the answers unfortunately :)

Mathematics

1 answer:

zimovet [89]2 years ago

8 0

Answer:

1. B. ∠2 and ∠6

2. 50°

3. Option 1, Option 5, and Option 6.

4. 133°

<u>Work for question 4:</u>

180°-47° = 133°

Step-by-step explanation:

Alternate means the angles are on different sides of the transversal (horizontal line in this case). Interior means they are between the parallel lines (lines a and b in this case). (∠2 and ∠6) and (∠3 and ∠7) are the alternate interior angles but only the first is an option.

∠10 = ∠8+∠7 (corresponding angles so they are congruent)

∠10 is 140° and ∠8 is a right angle

140-90 = 50

∠7 = 50°

∠4 = 50° (∠7 and ∠4 are vertical angles so they are congruent)

Sense all angles of a triangle add up to 180 and the ratio of angles is 3:3:6 the we can find the angle with the equation x+x+2x=180

Simplify.

4x=180

Solve by dividing 4 from both sides

x=45

so it is a 45, 45, 90 triangle. (right triangle because the 90 and icoceles because other 2 angles are congruent so option 5 is correct)

m∠J= 45°

m∠K= 45° (Option 1 is correct)

m∠L= 90° (Option 6 is correct)

I honestly don't see how you can solve this without making assumptions so I will make assumptions.

Assuming the whole figure is symmetrical vertically ∠1 is congruent to the same spot on the right side of the shape. This angle would be supplementary to the angle of the angle outside of the shape adjacent on the right making the angle (which is corresponding, therefore congruent to ∠2) 133°.

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Rasek [7]

Answer:

Step-by-step explanation:

just simplify the LHS first.

You can either multiply 1/5 by (x+3) and then solve

multiply both sides by 5 to get rid of 1/5 on LHS

I will multiply by 5

(x+3)= -10x-15 ( 5*1/5(x+3)= -5(2x+3)

now rearrange the equation

x+3=-10x-15

-10x-15-x-3=0

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x= -17/11

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3 years ago

Write a recursive rule and an explicit rule for each arithmetic sequence.

I am Lyosha [343]

Hope this helps!! Lol

6 0

3 years ago

A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. mater

BartSMP [9]

Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x² (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
C = 20(1.651)² + 180/1.651 = $163.54

Answer: $163.54

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3 years ago

To rent a moving truck for the day, it costs $50 plus $3 for every mile driven. Write an algebraic expression for the cost to re

malfutka [58]

Multiply the cost per mile by number of miles “m” and add that amount to the $50:

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3 0

2 years ago

Read 2 more answers

The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o

timurjin [86]

Answer:

a) Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

b) $p_v =2*P(t_{(24)}$

c) If we compare the p value and the significance level given $\alpha=0.05$ 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 for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

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

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

The values obtained are:

$\bar X=85272$ represent the mean annual salary for the sample

$s=11039.23$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =90000$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t 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 salary differs from 90000, the system of hypothesis would be:

Null hypothesis: $\mu = 90000$

Alternative hypothesis: $\mu \neq 90000$

If we analyze the size for the sample is < 30 and we don't know the population deviation so 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:

$t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(24)}$

Part c: Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ 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 for the salary differs from 9000 at 5% of significance.

6 0

3 years ago