MATHEMATICS COLLEGE

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Answers

Answer 1

Answer:

Answer: 151

Step-by-step

you need to first find the area of each piece of the tent

the 2 rectangular flaps would be 6*8= 48 each

the bottom would be 4*8=32

to find the area of the triangular pieces we need to know the height of each triangle, right now we only know sides. To find the height (the altitude) you draw a line straight down to make a 90 degree angle.

that will also cut your base in half (2 instead of 4) and make 6 your hypotenuse

now use the Pythagorean theorem to find the height of the triangle

$a^(2) +b^(2) =c^(2) \n\na^(2) +2^(2) =6^(2) \na^(2) +4=36\na^(2) =32\na=√(32) = 5.66$

Area of a triangle is

$(1)/(2) bh\n(1)/(2) (4)(5.66)= 11.31$

the area of one triangle is 11.31

so together it is 48+48+32+11.31+11.31= 150.6

round up to 151

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Please help ! Thanks

Answers

Answer: 12x - 24y - 2

Step-by-step explanation:

Answer:

12x-24y-2

Step-by-step explanation:

So, we multiple all the values in the bracket with six to get something like this:

$(6*2x)+(6*-4y)+(6*-(1)/(3) )\n= 12x + (-24y) + (-2)\n= 12x -24y -2$

2. In an industrial training program, students have been averaging about 64 points on a standardized test. The lecture system was replaced by teaching machines with a lab instructor. There was some doubt as to whether the scores would decrease, increase, or stay the same. A sample of n = 60 students using the teaching machines was tested, resulting in a mean of 68 and a standard deviation of 12. Perform a hypothesis test to see if scores would decrease, increase, or stay the same. Use α = 0.05. Be sure to:1. State your hypotheses.
2. Find the value of the Test Statistic.
3. Find the p-value
4. State your decision (Reject or not)
5. State your conclusion.

Answers

Answer:

Case I

Null hypothesis: $\mu = 64$

Alternative hypothesis: $\mu \neq 64$

$t=(68-64)/((12)/(√(60)))=2.582$

$df=n-1=60-1=59$

Since is a two sided test the p value would given by:

$p_v =2*P(t_((59))>2.582)=0.012$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis.

We can say that at 5% of significance the true mean is different from 64.

Case II

Null hypothesis: $\mu \leq 64$

Alternative hypothesis: $\mu > 64$

The statistic not changes but the p value does and we have:

$p_v =P(t_((59))>2.582)=0.006$

And we reject the null hypothesis on this case.

So we can conclude that the true mean is significantly higher than 64 at 5% of singnificance

Step-by-step explanation:

Data given and notation

$\bar X=68$ represent the sample mean

$s=12$ represent the sample standard deviation

$n=60$ sample size

$\mu_o =64$ 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)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the population mean is different from 64 the system of hypothesis are :

Null hypothesis: $\mu = 64$

Alternative hypothesis: $\mu \neq 64$

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:

$t=(\bar X-\mu_o)/((s)/(√(n)))$ (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".

Calculate the statistic

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

$t=(68-64)/((12)/(√(60)))=2.582$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=60-1=59$

Since is a two sided test the p value would given by:

$p_v =2*P(t_((59))>2.582)=0.012$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis.

We can say that at 5% of significance the true mean is different from 64.

Now let's assume that we want to see if the mean is significantly higher than 64

Null hypothesis: $\mu \leq 64$

Alternative hypothesis: $\mu > 64$

The statistic not changes but the p value does and we have:

$p_v =P(t_((59))>2.582)=0.006$

And we reject the null hypothesis on this case.

So we can conclude that the true mean is significantly higher than 64 at 5% of singnificance

What is 62 divided by 17 plus 29

I will mark brainliest

Answers

62/17=3.647059+29= 32.64059 but if you round just say 33!

Answer:

32.647

Step-by-step explanation:

(1) -3x-4y+11z from-9y+6z-3x
(2) 3x⁴-4x³+7x-2 from 9-7x⁴+6x³-2x²-11x

Answers

Answer:

1) 5y + 5z

2) 10x⁴ - 10x³ + 2x² + 18x - 11

Step-by-step explanation:

Given the subtraction of the following polynomial expressions:

(1) -3x - 4y + 11z from -9y + 6z - 3x

In order to make it easier for us to perform the required mathematical operations, we must first rearrange the terms in the subtrahend by alphabetical order.

-3x - 4y + 11z

-3x - 9y + 6z ⇒ This is the subtrahend.

Now, we can finally perform the subtraction on both trinomials:

$\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}} \right.}$

In the subtrahend, the coefficients of x and y are both negative. Thus, performing the subtraction operations on these coefficients transforms their sign into positive.

$\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:\:0x\:+\:5y\:+5z$

The difference is: 5y + 5z.

(2) 3x⁴- 4x³ + 7x - 2 from 9 - 7x⁴ + 6x³- 2x² - 11x

Similar to the how we arranged the given trinomials in Question 1, we must rearrange the given polynomials in descending degree of terms before subtracting like terms.

3x⁴- 4x³ + 7x - 2 ⇒ Already in descending order (degree).

9 - 7x⁴ + 6x³- 2x² - 11x ⇒ -7x⁴ + 6x³- 2x² - 11x + 9

In subtracting polynomials, we can only subtract like terms, which are terms that have the same variables and exponents.

$\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.}$

In the minuend, I added the "0x²" to make it less-confusing for us to perform the subtraction operations.

The same rules apply in terms of coefficients with negative signs in the subtrahend, such as: -7x⁴, - 2x², and - 11x ⇒ their coefficients turn into positive when performing subtraction.

$\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:10x^4-10x^3+2x^2+18x\:-11$

Therefore, the difference is: 10x⁴ - 10x³ + 2x² + 18x - 11.

Which fraction is equivalent to 0.36

Answers

Answer: 9/25, Percentage: 36%

Final answer:

The fraction equivalent to 0.36 is 36/100, which can be further simplified to 9/25.

Explanation:

In the subject of mathematics, to convert a decimal into a fraction, one must understand the place value of the decimal. In your case, the decimal 0.36 is in the hundredths place, which means you can express this decimal as 36 over 100. Therefore, the fraction equivalent to 0.36 is 36/100. To simplify this fraction, we can divide both the numerator (36) and the denominator (100) by the greatest common divisor, which is 4. This gives us a simplified fraction of 9/25.

Learn more about Equivalent Fraction here:

brainly.com/question/23075364

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A deck of cards contains RED cards numbered 1,2,3, BLUE cards numbered 1,2,3,4,5,6, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is GREEN AND has an ODD number? Provide the final answer as a fraction.